TSTP Solution File: DAT137^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:48:06 EDT 2024
% Result : Theorem 41.39s 10.91s
% Output : Refutation 42.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 355
% Syntax : Number of formulae : 667 ( 248 unt; 64 typ; 0 def)
% Number of atoms : 1352 ( 598 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 6917 ( 205 ~; 29 |; 44 &;6055 @)
% ( 0 <=>; 584 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 8 con; 0-4 aty)
% Number of variables : 1650 ( 28 ^1520 !; 50 ?;1650 :)
% ( 52 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(numeral_type,type,
numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_1_type,type,
ring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_type,type,
semigroup_add:
!>[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(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1656338222tinuum_type,type,
condit1656338222tinuum:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu493225792length_type,type,
coindu493225792length:
!>[TA: $tType] : ( nat > ( coindu1593790203_llist @ TA ) > extended_enat ) ).
thf(coindu1542816657of_aux_type,type,
coindu1542816657of_aux:
!>[TA: $tType] : ( ( list @ TA ) > ( coindu1593790203_llist @ TA ) > ( list @ TA ) ) ).
thf(coindu1121789889_LCons_type,type,
coindu1121789889_LCons:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1598213697e_LNil_type,type,
coindu1598213697e_LNil:
!>[TA: $tType] : ( coindu1593790203_llist @ TA ) ).
thf(coindu1079202755ist_of_type,type,
coindu1079202755ist_of:
!>[TA: $tType] : ( ( list @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu567634248member_type,type,
coindu567634248member:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(count_list_type,type,
count_list:
!>[TA: $tType] : ( ( list @ TA ) > TA > nat ) ).
thf(gen_length_type,type,
gen_length:
!>[TA: $tType] : ( nat > ( list @ TA ) > nat ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( ( list @ TA ) > TA > $o ) ).
thf(nth_type,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(ord_lexordp_eq_type,type,
ord_lexordp_eq:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(upt_type,type,
upt: nat > nat > ( list @ nat ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(nat_triangle_type,type,
nat_triangle: nat > nat ).
thf(bitM_type,type,
bitM: num > num ).
thf(inc_type,type,
inc: num > num ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_dbl_dec_type,type,
neg_numeral_dbl_dec:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_sub_type,type,
neg_numeral_sub:
!>[TA: $tType] : ( num > num > TA ) ).
thf(bit0_type,type,
bit0: num > num ).
thf(one2_type,type,
one2: num ).
thf(numeral_numeral_type,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(ring_1_iszero_type,type,
ring_1_iszero:
!>[TA: $tType] : ( TA > $o ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(prefixes_type,type,
prefixes:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(ma_type,type,
ma: nat ).
thf(na_type,type,
na: nat ).
thf(222,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_lessI) ).
thf(892,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(195,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_remdups__adj_Ocases) ).
thf(809,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(133,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add__strict__right__mono) ).
thf(629,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(263,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add_Oinverse__distrib__swap) ).
thf(1031,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(71,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_numeral__One) ).
thf(468,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(75,axiom,
order @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_17) ).
thf(479,plain,
order @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',fact_53_measure__induct__rule) ).
thf(1105,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)],[276]) ).
thf(183,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_neq__Nil__conv) ).
thf(777,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat,D: list @ nat] :
( ( ( upt @ A @ B )
= ( cons @ nat @ C @ D ) )
= ( ( ord_less @ nat @ A @ B )
& ( A = C )
& ( ( upt @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ B )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_upt__eq__Cons__conv) ).
thf(555,plain,
! [A: nat,B: nat,C: nat,D: list @ nat] :
( ( ( upt @ A @ B )
= ( cons @ nat @ C @ D ) )
= ( ( ord_less @ nat @ A @ B )
& ( A = C )
& ( ( upt @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_less__add__eq__less) ).
thf(977,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(177,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_lexordp__eq_OCons) ).
thf(762,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_lexordp__eq__simps_I2_J) ).
thf(379,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(216,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__less__mono1) ).
thf(878,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(266,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add__neg__numeral__special_I9_J) ).
thf(1041,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(214,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add__strict__mono) ).
thf(873,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_less__minus__iff) ).
thf(449,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_llist_Oinject) ).
thf(384,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(85,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_neg__numeral__less__one) ).
thf(500,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(237,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_list_Oinducts) ).
thf(945,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__less__cancel__right) ).
thf(538,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add__Suc__shift) ).
thf(670,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( plus_plus @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(225,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) )
= ( neg_numeral_sub @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_add__neg__numeral__simps_I2_J) ).
thf(898,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) )
= ( neg_numeral_sub @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__antisym) ).
thf(1001,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(185,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_semiring__norm_I166_J) ).
thf(782,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(205,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( one_one @ TA ) )
= ( neg_numeral_sub @ TA @ one2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_add__neg__numeral__special_I2_J) ).
thf(841,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( one_one @ TA ) )
= ( neg_numeral_sub @ TA @ one2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_add__mono__thms__linordered__field_I1_J) ).
thf(973,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__less__cancel__left) ).
thf(565,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(139,axiom,
numeral @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).
thf(651,plain,
numeral @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(201,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(829,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(49,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_member__rec_I2_J) ).
thf(404,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
( ( inc @ one2 )
= ( bit0 @ one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inc_Osimps_I1_J) ).
thf(389,plain,
( ( inc @ one2 )
= ( bit0 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(164,axiom,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(719,plain,
cancel_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(186,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_nat__add__left__cancel__less) ).
thf(785,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(34,axiom,
ord @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_5) ).
thf(372,plain,
ord @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_trans__less__add2) ).
thf(702,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(23,axiom,
! [A: num] : ( ord_less @ num @ one2 @ ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_semiring__norm_I76_J) ).
thf(344,plain,
! [A: num] : ( ord_less @ num @ one2 @ ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(234,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_infinite__descent) ).
thf(934,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)],[234]) ).
thf(273,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: list @ TA] : ( B != C ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_lexordp__eq_Ocases) ).
thf(1059,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: list @ TA] : ( B != C ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(104,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__iff__Suc__add) ).
thf(542,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__not__refl2) ).
thf(587,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(204,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_semiring__normalization__rules_I22_J) ).
thf(838,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(213,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_list_Odistinct_I1_J) ).
thf(870,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(125,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( neg_numeral_sub @ TA @ one2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_add__neg__numeral__special_I1_J) ).
thf(606,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( neg_numeral_sub @ TA @ one2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_map__tailrec__rev_Oinduct) ).
thf(770,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(217,axiom,
semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(881,plain,
semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(136,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__trans__Suc) ).
thf(638,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(208,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Suc__lessI) ).
thf(853,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(120,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( suc @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__2__eq__Suc_H) ).
thf(591,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= ( suc @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_llist_Odistinct_I1_J) ).
thf(321,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_numeral__neq__neg__numeral) ).
thf(376,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_add__less__imp__less__left) ).
thf(623,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_one__neq__neg__one) ).
thf(514,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(194,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1598213697e_LNil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_llist__of__eq__LNil__conv) ).
thf(806,plain,
! [TA: $tType,A: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1598213697e_LNil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( one_one @ TA ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_neg__one__eq__numeral__iff) ).
thf(353,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( one_one @ TA ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_one__neq__neg__numeral) ).
thf(480,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(246,axiom,
! [A: num] :
( ( plus_plus @ num @ one2 @ A )
= ( plus_plus @ num @ A @ one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_add__One__commute) ).
thf(981,plain,
! [A: num] :
( ( plus_plus @ num @ one2 @ A )
= ( plus_plus @ num @ A @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(135,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_longest__common__prefix_Oinduct) ).
thf(634,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__Suc) ).
thf(734,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1,conjecture,
( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
= ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
!= ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(293,plain,
( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
!= ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(182,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ? [D: list @ TA] :
( ( A
= ( cons @ TA @ B @ D ) )
& ( C
= ( coindu1079202755ist_of @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_llist__of__eq__LCons__conv) ).
thf(774,plain,
! [TA: $tType,A: list @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ? [D: list @ TA] :
( ( A
= ( cons @ TA @ B @ D ) )
& ( C
= ( coindu1079202755ist_of @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_neg__numeral__less__numeral) ).
thf(396,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(252,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( upt @ A @ B )
= ( cons @ nat @ A @ ( upt @ ( suc @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_upt__conv__Cons) ).
thf(998,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( upt @ A @ B )
= ( cons @ nat @ A @ ( upt @ ( suc @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(10,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit0 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_sub__num__simps_I2_J) ).
thf(312,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ one2 @ ( bit0 @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(64,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_dbl__dec__simps_I3_J) ).
thf(452,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(236,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__neg__numeral__special_I5_J) ).
thf(942,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(99,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_semiring__normalization__rules_I25_J) ).
thf(529,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(231,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( neg_numeral_sub @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__neg__numeral__simps_I1_J) ).
thf(925,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( neg_numeral_sub @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(268,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_add__minus__cancel) ).
thf(1047,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(191,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_infinite__descent__measure) ).
thf(798,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)],[191]) ).
thf(272,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
~ ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_lexordp__eq__simps_I3_J) ).
thf(1057,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA] :
~ ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(294,plain,
( ( coindu1079202755ist_of @ nat @ ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) ) )
!= ( coindu1079202755ist_of @ nat @ ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(1163,plain,
( ( cons @ nat @ ma @ ( upt @ ( suc @ ma ) @ ( plus_plus @ nat @ na @ ( suc @ ma ) ) ) )
!= ( upt @ ma @ ( plus_plus @ nat @ ( suc @ na ) @ ma ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(230,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_remdups__adj_Oinduct) ).
thf(910,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(200,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__not__refl3) ).
thf(825,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(259,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__lessD1) ).
thf(1021,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_minus__less__iff) ).
thf(300,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(301,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
| ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) )
| ~ ( ordered_ab_group_add @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(25,axiom,
numeral @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_19) ).
thf(349,plain,
numeral @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(122,axiom,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_triangle__Suc) ).
thf(598,plain,
! [A: nat] :
( ( nat_triangle @ ( suc @ A ) )
= ( plus_plus @ nat @ ( nat_triangle @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_numeral__eq__iff) ).
thf(297,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_numeral__eq__one__iff) ).
thf(424,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_linordered__field__no__ub) ).
thf(429,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(187,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add__mono__thms__linordered__field_I2_J) ).
thf(788,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Suc__inject) ).
thf(815,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lift__Suc__mono__less) ).
thf(729,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(239,axiom,
! [A: list @ nat] :
( ( A
!= ( nil @ nat ) )
=> ~ ! [B: nat,C: list @ nat] :
( A
!= ( cons @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__encode_Ocases) ).
thf(957,plain,
! [A: list @ nat] :
( ( A
!= ( nil @ nat ) )
=> ~ ! [B: nat,C: list @ nat] :
( A
!= ( cons @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(223,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_add_Oassoc) ).
thf(894,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(174,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1542816657of_aux @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1542816657of_aux @ TA @ ( cons @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_list__of__aux__code_I2_J) ).
thf(746,plain,
! [TA: $tType,A: list @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1542816657of_aux @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1542816657of_aux @ TA @ ( cons @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(274,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__irrefl__nat) ).
thf(1091,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(70,axiom,
semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_15) ).
thf(467,plain,
semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(78,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_lexordp__eq__simps_I1_J) ).
thf(484,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add__mono__thms__linordered__semiring_I4_J) ).
thf(625,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(58,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_one__reorient) ).
thf(435,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)],[58]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_less__minus__one__simps_I4_J) ).
thf(328,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(329,plain,
! [TA: $tType] :
( ~ ( linordered_idom @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(cnf,[status(esa)],[328]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( ord_less @ num @ one2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_one__less__numeral__iff) ).
thf(461,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( ord_less @ num @ one2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(151,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lift__Suc__mono__less__iff) ).
thf(682,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(283,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1128,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(161,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( inc @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_numeral__inc) ).
thf(710,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( inc @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(15,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_dbl__dec__simps_I5_J) ).
thf(324,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl_dec @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(118,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_prefixes_Oinduct) ).
thf(578,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(156,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_nat__1__add__1) ).
thf(697,plain,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(286,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__right__cancel) ).
thf(1143,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(317,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(128,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_linordered__field__class_Osign__simps_I26_J) ).
thf(615,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(278,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1079202755ist_of @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_llist__of__inject) ).
thf(1111,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( coindu1079202755ist_of @ TA @ A )
= ( coindu1079202755ist_of @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(255,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_less__add__one) ).
thf(1006,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_not__numeral__less__neg__numeral) ).
thf(356,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat_Oinject) ).
thf(884,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(292,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_minus__add__distrib) ).
thf(1160,plain,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(262,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_one__plus__numeral) ).
thf(1028,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(489,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_less__minus__one__simps_I2_J) ).
thf(471,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Suc__lessD) ).
thf(901,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(74,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_sub__num__simps_I6_J) ).
thf(476,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( neg_numeral_dbl @ TA @ ( neg_numeral_sub @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__less__mono) ).
thf(679,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_trans__less__add1) ).
thf(970,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(251,axiom,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(997,plain,
ordere236663937imp_le @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(269,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__less__SucD) ).
thf(1050,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(247,axiom,
! [A: num] :
( ( numeral_numeral @ nat @ ( bit0 @ A ) )
= ( suc @ ( numeral_numeral @ nat @ ( bitM @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_eval__nat__numeral_I2_J) ).
thf(984,plain,
! [A: num] :
( ( numeral_numeral @ nat @ ( bit0 @ A ) )
= ( suc @ ( numeral_numeral @ nat @ ( bitM @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(44,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_num_Oinject_I1_J) ).
thf(393,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(279,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_numeral__plus__one) ).
thf(1114,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(22,axiom,
! [A: num] :
~ ( ord_less @ num @ A @ one2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_semiring__norm_I75_J) ).
thf(341,plain,
! [A: num] :
~ ( ord_less @ num @ A @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(342,plain,
~ ? [A: num] : ( ord_less @ num @ A @ one2 ),
inference(miniscope,[status(thm)],[341]) ).
thf(343,plain,
! [A: num] :
~ ( ord_less @ num @ A @ one2 ),
inference(cnf,[status(esa)],[342]) ).
thf(188,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_sublists_Osimps_I1_J) ).
thf(792,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__numeral__extra_I4_J) ).
thf(508,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)],[89]) ).
thf(103,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_2) ).
thf(541,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(271,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: nat] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( suc @ C ) )
= ( nth @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_nth__Cons__Suc) ).
thf(1054,plain,
! [TA: $tType,A: TA,B: list @ TA,C: nat] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( suc @ C ) )
= ( nth @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(46,axiom,
linorder @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_3) ).
thf(398,plain,
linorder @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_less__Suc__induct) ).
thf(558,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(261,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__strict__left__mono) ).
thf(1026,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(181,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(773,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(144,axiom,
( ( plus_plus @ num @ one2 @ one2 )
= ( bit0 @ one2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_semiring__norm_I2_J) ).
thf(662,plain,
( ( plus_plus @ num @ one2 @ one2 )
= ( bit0 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(228,axiom,
ordere223160158up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(906,plain,
ordere223160158up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(52,axiom,
! [A: num > $o,B: num] :
( ( A @ one2 )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( inc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_num__induct) ).
thf(412,plain,
! [A: num > $o,B: num] :
( ( A @ one2 )
=> ( ! [C: num] :
( ( A @ C )
=> ( A @ ( inc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(129,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add__neg__numeral__special_I6_J) ).
thf(618,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( inc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(209,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_semiring__normalization__rules_I24_J) ).
thf(856,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(4,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(296,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_103_linorder__neqE__linordered__idom) ).
thf(444,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)],[61]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nat__neq__iff) ).
thf(601,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)],[123]) ).
thf(91,axiom,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11) ).
thf(513,plain,
ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(287,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add_Oleft__commute) ).
thf(1146,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(290,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_transpose_Ocases) ).
thf(1154,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(198,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_is__num__normalize_I1_J) ).
thf(819,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(155,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
= ( suc @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add__2__eq__Suc) ).
thf(694,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ A )
= ( suc @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(282,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_numeral__Bit0) ).
thf(1125,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(173,axiom,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_fold__atLeastAtMost__nat_Oinduct) ).
thf(743,plain,
! [TA: $tType,A: ( nat > TA > TA ) > nat > nat > TA > $o,B: nat > TA > TA,C: nat,D: nat,E: TA] :
( ! [F: nat > TA > TA,G: nat,H: nat,I: TA] :
( ( ~ ( ord_less @ nat @ H @ G )
=> ( A @ F @ ( plus_plus @ nat @ G @ ( one_one @ nat ) ) @ H @ ( F @ G @ I ) ) )
=> ( A @ F @ G @ H @ I ) )
=> ( A @ B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_add__Suc__right) ).
thf(875,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ( nth @ nat @ ( upt @ A @ C ) @ B )
= ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_nth__upt) ).
thf(545,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ( nth @ nat @ ( upt @ A @ C ) @ B )
= ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(137,axiom,
! [A: num,B: nat] :
( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ A ) @ B ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Suc__nat__number__of__add) ).
thf(641,plain,
! [A: num,B: nat] :
( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ A ) @ B ) )
= ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_neg__one__less__numeral) ).
thf(391,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(38,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_7) ).
thf(382,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( neg_numeral_sub @ TA @ A @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__neg__numeral__special_I3_J) ).
thf(572,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( neg_numeral_sub @ TA @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(69,axiom,
one @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oone_20) ).
thf(466,plain,
one @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(20,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_neq__LNil__conv) ).
thf(335,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(193,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_add__less__imp__less__right) ).
thf(804,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(350,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(162,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_dbl__def) ).
thf(713,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__numeral__less__neg__one) ).
thf(498,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less @ num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_numeral__less__iff) ).
thf(406,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__imp__Suc__add) ).
thf(1117,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(257,axiom,
! [A: nat,B: nat,C: list @ nat,D: nat] :
( ( ( cons @ nat @ A @ ( cons @ nat @ B @ C ) )
= ( upt @ A @ D ) )
= ( ( cons @ nat @ B @ C )
= ( upt @ ( suc @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_upt__conv__Cons__Cons) ).
thf(1011,plain,
! [A: nat,B: nat,C: list @ nat,D: nat] :
( ( ( cons @ nat @ A @ ( cons @ nat @ B @ C ) )
= ( upt @ A @ D ) )
= ( ( cons @ nat @ B @ C )
= ( upt @ ( suc @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_nat__add__right__cancel) ).
thf(990,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(31,axiom,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_enat__less__induct) ).
thf(362,plain,
! [A: extended_enat > $o,B: extended_enat] :
( ! [C: extended_enat] :
( ! [D: extended_enat] :
( ( ord_less @ extended_enat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(171,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_semiring__normalization__rules_I21_J) ).
thf(737,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_neg__numeral__neq__numeral) ).
thf(303,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(178,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__not__refl) ).
thf(764,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(124,axiom,
( suc
= ( ^ [A: nat] : ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Suc__eq__plus1) ).
thf(604,plain,
( suc
= ( ^ [A: nat] : ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(509,plain,
! [TA: $tType] :
( ~ ( linordered_semidom @ TA @ ( type2 @ TA ) )
| ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(cnf,[status(esa)],[508]) ).
thf(57,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_num_Odistinct_I1_J) ).
thf(431,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(432,plain,
~ ? [A: num] :
( one2
= ( bit0 @ A ) ),
inference(miniscope,[status(thm)],[431]) ).
thf(433,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(cnf,[status(esa)],[432]) ).
thf(434,plain,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
inference(lifteq,[status(thm)],[433]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Suc__mono) ).
thf(890,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(41,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_lexordp__eq__refl) ).
thf(387,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(82,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_8) ).
thf(494,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__SucE) ).
thf(631,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(101,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_product__lists_Osimps_I1_J) ).
thf(535,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(126,axiom,
! [TA: $tType] :
( ( coindu1598213697e_LNil @ TA )
= ( coindu1079202755ist_of @ TA @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155__092_060open_062LNil_A_061_Allist__of_A_091_093_092_060close_062) ).
thf(609,plain,
! [TA: $tType] :
( ( coindu1598213697e_LNil @ TA )
= ( coindu1079202755ist_of @ TA @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(121,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_list_OdiscI) ).
thf(594,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_list_Oinject) ).
thf(726,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__SucI) ).
thf(621,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(77,axiom,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_10) ).
thf(483,plain,
strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(94,axiom,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12) ).
thf(520,plain,
ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(18,axiom,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_lmember__code_I1_J) ).
thf(330,plain,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less @ num @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_neg__numeral__less__iff) ).
thf(367,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less @ num @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(109,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( neg_numeral_sub @ TA @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_semiring__norm_I167_J) ).
thf(552,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( neg_numeral_sub @ TA @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(288,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_numeral__plus__numeral) ).
thf(1149,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(241,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_splice_Oinduct) ).
thf(964,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_not__numeral__less__one) ).
thf(399,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(267,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_not__less__eq) ).
thf(1044,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(184,axiom,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Suc__1) ).
thf(780,plain,
( ( suc @ ( one_one @ nat ) )
= ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(65,axiom,
! [A: num,B: num] :
( ( ord_less @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less @ num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_semiring__norm_I78_J) ).
thf(455,plain,
! [A: num,B: num] :
( ( ord_less @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_lexordp__eq__antisym) ).
thf(306,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(298,plain,
! [TA: $tType,B: num,A: num] :
( ~ ( semiring_char_0 @ TA @ ( type2 @ TA ) )
| ( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(cnf,[status(esa)],[297]) ).
thf(299,plain,
! [TA: $tType,B: num,A: num] :
( ( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) )
| ~ ( semiring_char_0 @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(141,axiom,
! [A: num,B: num] :
( ( plus_plus @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_semiring__norm_I6_J) ).
thf(653,plain,
! [A: num,B: num] :
( ( plus_plus @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(152,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add_Ocommute) ).
thf(685,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A != one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_neg__numeral__less__neg__one__iff) ).
thf(521,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A != one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(87,axiom,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_13) ).
thf(505,plain,
comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_neg__numeral__eq__iff) ).
thf(438,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_numeral__neq__neg__one) ).
thf(473,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Suc__lessE) ).
thf(1034,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(189,axiom,
strict2144017051up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(795,plain,
strict2144017051up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(107,axiom,
ordere779506340up_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(548,plain,
ordere779506340up_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Suc__less__eq) ).
thf(812,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(175,axiom,
! [A: ( list @ nat ) > $o,B: list @ nat] :
( ( A @ ( nil @ nat ) )
=> ( ! [C: nat,D: list @ nat] :
( ( A @ D )
=> ( A @ ( cons @ nat @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_list__encode_Oinduct) ).
thf(749,plain,
! [A: ( list @ nat ) > $o,B: list @ nat] :
( ( A @ ( nil @ nat ) )
=> ( ! [C: nat,D: list @ nat] :
( ( A @ D )
=> ( A @ ( cons @ nat @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(515,plain,
! [TA: $tType] :
( ~ ( ring_char_0 @ TA @ ( type2 @ TA ) )
| ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(cnf,[status(esa)],[514]) ).
thf(516,plain,
! [TA: $tType] :
( ( ( uminus_uminus @ TA @ ( one_one @ TA ) )
!= ( one_one @ TA ) )
| ~ ( ring_char_0 @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[515]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__Suc__eq) ).
thf(939,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(458,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_neg__less__iff__less) ).
thf(525,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(3,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_9) ).
thf(295,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(159,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__add__Suc1) ).
thf(705,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(160,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_semiring__normalization__rules_I20_J) ).
thf(707,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ D ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(220,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__left__imp__eq) ).
thf(887,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(16,axiom,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_14) ).
thf(327,plain,
semigroup_add @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(238,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__right__imp__eq) ).
thf(954,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(51,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equation__minus__iff) ).
thf(409,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(250,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_n__not__Suc__n) ).
thf(993,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(148,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__numeral__left) ).
thf(673,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(331,plain,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(cnf,[status(esa)],[330]) ).
thf(60,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_llist_Oexhaust) ).
thf(441,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(86,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_neg__equal__iff__equal) ).
thf(502,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_lmember__code_I2_J) ).
thf(338,plain,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(117,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_numerals_I1_J) ).
thf(576,plain,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(30,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_dbl__simps_I1_J) ).
thf(359,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(265,axiom,
! [A: num,B: num] :
( ( plus_plus @ num @ A @ ( inc @ B ) )
= ( inc @ ( plus_plus @ num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__inc) ).
thf(1038,plain,
! [A: num,B: num] :
( ( plus_plus @ num @ A @ ( inc @ B ) )
= ( inc @ ( plus_plus @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(33,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ex__gt__or__lt) ).
thf(370,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ 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)],[33]) ).
thf(105,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(544,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(229,axiom,
! [A: num] :
( ( plus_plus @ num @ one2 @ ( bitM @ A ) )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_one__plus__BitM) ).
thf(907,plain,
! [A: num] :
( ( plus_plus @ num @ one2 @ ( bitM @ A ) )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(270,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp_eq @ TA @ C @ D )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_lexordp__eq_OCons__eq) ).
thf(1052,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp_eq @ TA @ C @ D )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(211,axiom,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( ring_1_iszero @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_eq__numeral__iff__iszero_I8_J) ).
thf(864,plain,
! [TA: $tType] :
( ( ring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( ring_1_iszero @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(256,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp_eq @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_lexordp__eq__simps_I4_J) ).
thf(1008,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp_eq @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(114,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(571,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_linordered__field__class_Osign__simps_I27_J) ).
thf(612,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(210,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_nat__less__induct) ).
thf(859,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)],[210]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_nat__add__left__cancel) ).
thf(656,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( plus_plus @ nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(260,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_add_Oright__cancel) ).
thf(1023,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(275,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_strict__inc__induct) ).
thf(1094,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(285,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_list__induct2_H) ).
thf(1140,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Suc__less__eq2) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(291,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_not__add__less2) ).
thf(1157,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(96,axiom,
order @ num @ ( type2 @ num ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_4) ).
thf(524,plain,
order @ num @ ( type2 @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(83,axiom,
! [TA: $tType,A: nat] :
( ( gen_length @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_gen__length__code_I1_J) ).
thf(495,plain,
! [TA: $tType,A: nat] :
( ( gen_length @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(176,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_add_Oleft__cancel) ).
thf(759,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( ( A = B )
=> ( ( count_list @ TA @ ( cons @ TA @ A @ C ) @ B )
= ( plus_plus @ nat @ ( count_list @ TA @ C @ B ) @ ( one_one @ nat ) ) ) )
& ( ( A != B )
=> ( ( count_list @ TA @ ( cons @ TA @ A @ C ) @ B )
= ( count_list @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_count__list_Osimps_I2_J) ).
thf(844,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( ( A = B )
=> ( ( count_list @ TA @ ( cons @ TA @ A @ C ) @ B )
= ( plus_plus @ nat @ ( count_list @ TA @ C @ B ) @ ( one_one @ nat ) ) ) )
& ( ( A != B )
=> ( ( count_list @ TA @ ( cons @ TA @ A @ C ) @ B )
= ( count_list @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(277,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_not__less__less__Suc__eq) ).
thf(1108,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(153,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_is__num__normalize_I8_J) ).
thf(688,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ A @ B ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_48_measure__induct) ).
thf(903,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)],[227]) ).
thf(157,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_one__add__one) ).
thf(699,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(240,axiom,
! [A: num] :
( ( plus_plus @ num @ A @ one2 )
= ( inc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_add__One) ).
thf(961,plain,
! [A: num] :
( ( plus_plus @ num @ A @ one2 )
= ( inc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(93,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_dbl__simps_I4_J) ).
thf(517,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_not__one__less__neg__numeral) ).
thf(319,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(140,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(652,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(48,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_uminus__numeral__One) ).
thf(401,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ one2 ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_not__Cons__self2) ).
thf(731,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(113,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( plus_plus @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_minus__add__cancel) ).
thf(568,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( plus_plus @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(90,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_one__eq__numeral__iff) ).
thf(510,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_linorder__neqE__nat) ).
thf(667,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)],[146]) ).
thf(39,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_6) ).
thf(383,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(202,axiom,
! [A: num] :
( ( plus_plus @ num @ ( bitM @ A ) @ one2 )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_BitM__plus__one) ).
thf(832,plain,
! [A: num] :
( ( plus_plus @ num @ ( bitM @ A ) @ one2 )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(24,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_sub__num__simps_I4_J) ).
thf(346,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_sub @ TA @ ( bit0 @ A ) @ one2 )
= ( numeral_numeral @ TA @ ( bitM @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(108,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_gen__length__code_I2_J) ).
thf(549,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(163,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_semiring__normalization__rules_I23_J) ).
thf(716,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ C )
=> ( ord_lexordp_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_lexordp__eq__trans) ).
thf(447,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ C )
=> ( ord_lexordp_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(315,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(242,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_not__add__less1) ).
thf(967,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(203,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( coindu1121789889_LCons @ TA @ A @ ( coindu1079202755ist_of @ TA @ B ) )
= ( coindu1079202755ist_of @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062_092_060And_062xs_Ax_O_ALCons_Ax_A_Illist__of_Axs_J_A_061_Allist__of_A_Ix_A_D_Axs_J_092_060close_062) ).
thf(835,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( coindu1121789889_LCons @ TA @ A @ ( coindu1079202755ist_of @ TA @ B ) )
= ( coindu1079202755ist_of @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(405,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
inference(cnf,[status(esa)],[404]) ).
thf(53,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_not__neg__one__less__neg__numeral) ).
thf(422,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(212,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__left__cancel) ).
thf(867,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(35,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_dbl__simps_I3_J) ).
thf(373,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(304,plain,
! [TA: $tType,B: num,A: num] :
( ~ ( ring_char_0 @ TA @ ( type2 @ TA ) )
| ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
inference(cnf,[status(esa)],[303]) ).
thf(305,plain,
! [TA: $tType,B: num,A: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) )
| ~ ( ring_char_0 @ TA @ ( type2 @ TA ) ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_linordered__field__no__lb) ).
thf(506,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(29,axiom,
linorder @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_16) ).
thf(358,plain,
linorder @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(145,axiom,
! [TA: $tType,A: nat,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu493225792length @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu493225792length @ TA @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_gen__llength__code_I2_J) ).
thf(664,plain,
! [TA: $tType,A: nat,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu493225792length @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu493225792length @ TA @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(100,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_one__plus__numeral__commute) ).
thf(532,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(165,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_add__neg__numeral__simps_I3_J) ).
thf(720,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( uminus_uminus @ TA @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(190,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__add__Suc2) ).
thf(796,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ A @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(232,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( ( A = C )
| ( member @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_member__rec_I1_J) ).
thf(928,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( ( A = C )
| ( member @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(192,axiom,
! [A: num,B: num] :
( ( ord_less @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_enat__ord__number_I2_J) ).
thf(801,plain,
! [A: num,B: num] :
( ( ord_less @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(224,axiom,
semiring_char_0 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).
thf(897,plain,
semiring_char_0 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(179,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_semiring__norm_I168_J) ).
thf(767,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) @ C ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(172,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_linordered__field__class_Osign__simps_I28_J) ).
thf(740,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(248,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_prefixes_Ocases) ).
thf(987,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(68,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
| ( ord_lexordp_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_lexordp__eq__linear) ).
thf(464,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
| ( ord_lexordp_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(116,axiom,
ab_semigroup_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(575,plain,
ab_semigroup_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(98,axiom,
ord @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_18) ).
thf(528,plain,
ord @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(138,axiom,
! [A: num,B: num] :
( ( ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
=> ( ( upt @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( cons @ nat @ ( numeral_numeral @ nat @ A ) @ ( upt @ ( suc @ ( numeral_numeral @ nat @ A ) ) @ ( numeral_numeral @ nat @ B ) ) ) ) )
& ( ~ ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
=> ( ( upt @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( nil @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_upt__rec__numeral) ).
thf(644,plain,
! [A: num,B: num] :
( ( ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
=> ( ( upt @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( cons @ nat @ ( numeral_numeral @ nat @ A ) @ ( upt @ ( suc @ ( numeral_numeral @ nat @ A ) ) @ ( numeral_numeral @ nat @ B ) ) ) ) )
& ( ~ ( ord_less @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
=> ( ( upt @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) )
= ( nil @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(166,axiom,
! [TA: $tType] :
( ( prefixes @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_prefixes_Osimps_I1_J) ).
thf(723,plain,
! [TA: $tType] :
( ( prefixes @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B = C ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_lexordp__eq_Osimps) ).
thf(822,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B = C ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(207,axiom,
! [A: num] :
( ( suc @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Suc__numeral) ).
thf(850,plain,
! [A: num] :
( ( suc @ ( numeral_numeral @ nat @ A ) )
= ( numeral_numeral @ nat @ ( plus_plus @ num @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(254,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__mono__thms__linordered__field_I5_J) ).
thf(1004,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(154,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_list_Oexhaust) ).
thf(691,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(281,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_lessE) ).
thf(1120,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(19,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_dbl__simps_I5_J) ).
thf(332,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(284,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ! [D: list @ TA] : ( C @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp_eq @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_lexordp__eq_Oinducts) ).
thf(1129,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ! [D: list @ TA] : ( C @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp_eq @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(289,axiom,
( upt
= ( ^ [A: nat,B: nat] : ( if @ ( list @ nat ) @ ( ord_less @ nat @ A @ B ) @ ( cons @ nat @ A @ ( upt @ ( suc @ A ) @ B ) ) @ ( nil @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_upt__rec) ).
thf(1152,plain,
( upt
= ( ^ [A: nat,B: nat] : ( if @ ( list @ nat ) @ ( ord_less @ nat @ A @ B ) @ ( cons @ nat @ A @ ( upt @ ( suc @ A ) @ B ) ) @ ( nil @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(55,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_lexordp__eq_ONil) ).
thf(427,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(79,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_minus__equation__iff) ).
thf(486,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(149,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( numeral_numeral @ TA @ A ) )
= ( neg_numeral_sub @ TA @ A @ one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__neg__numeral__special_I4_J) ).
thf(676,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( numeral_numeral @ TA @ A ) )
= ( neg_numeral_sub @ TA @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(81,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add_Oinverse__inverse) ).
thf(491,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(218,axiom,
( suc
= ( plus_plus @ nat @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Suc__eq__plus1__left) ).
thf(882,plain,
( suc
= ( plus_plus @ nat @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(258,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_list__nonempty__induct) ).
thf(1014,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_numeral__eq__neg__one__iff) ).
thf(309,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: num] :
( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_old_Onat_Oinject) ).
thf(659,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1185,plain,
$false,
inference(e,[status(thm)],[892,809,629,1031,468,479,1105,777,555,977,762,379,878,1041,873,449,384,500,945,538,670,898,1001,782,841,973,565,651,829,404,389,719,785,372,702,344,934,1059,542,587,838,870,606,770,881,638,853,591,321,376,623,514,806,353,480,981,634,734,293,774,396,998,312,452,942,529,925,1047,798,1057,1163,910,825,1021,302,349,598,297,424,429,788,815,729,957,894,746,1091,467,484,625,435,329,461,682,1128,710,324,578,697,1143,317,615,1111,1006,356,884,1160,1028,489,328,471,901,476,679,970,997,1050,984,393,1114,343,792,508,541,1054,398,558,1026,773,662,906,412,618,856,296,444,601,513,1146,1154,819,694,1125,743,875,545,641,391,382,572,466,335,804,350,713,498,406,1117,1011,990,362,737,303,764,604,509,434,890,387,494,631,535,609,594,726,621,483,520,330,367,552,1149,964,399,1044,780,455,306,299,431,653,685,521,505,438,473,1034,795,548,812,749,516,939,458,525,295,705,707,887,327,954,409,993,673,331,441,502,338,576,359,1038,370,544,907,1052,864,1008,571,612,859,656,1023,1094,1140,931,1157,524,495,759,844,1108,688,903,699,961,517,319,652,401,731,568,510,667,383,832,346,549,716,300,447,315,967,835,405,422,867,373,305,341,506,358,664,532,720,796,928,294,801,897,767,740,987,464,575,528,644,723,822,850,1004,691,1120,332,1129,1152,427,486,676,491,882,1014,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : DAT137^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 23:32:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.04/1.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.32/1.45 % [INFO] Parsing done (408ms).
% 2.32/1.46 % [INFO] Running in sequential loop mode.
% 3.62/1.88 % [INFO] eprover registered as external prover.
% 3.62/1.88 % [INFO] cvc4 registered as external prover.
% 3.62/1.89 % [INFO] Scanning for conjecture ...
% 4.10/2.07 % [INFO] Found a conjecture (or negated_conjecture) and 290 axioms. Running axiom selection ...
% 4.72/2.25 % [INFO] Axiom selection finished. Selected 290 axioms (removed 0 axioms).
% 5.82/2.58 % [INFO] Problem is higher-order (TPTP THF).
% 6.06/2.61 % [INFO] Type checking passed.
% 6.06/2.61 % [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 ...
% 41.39/10.90 % External prover 'e' found a proof!
% 41.39/10.90 % [INFO] Killing All external provers ...
% 41.39/10.91 % Time passed: 10405ms (effective reasoning time: 9437ms)
% 41.39/10.91 % 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)>
% 41.39/10.91 % Axioms used in derivation (290): fact_134_Suc__eq__plus1, fact_155__092_060open_062LNil_A_061_Allist__of_A_091_093_092_060close_062, fact_173_semiring__norm_I75_J, fact_17_add_Oleft__commute, fact_24_n__not__Suc__n, tcon_Extended__Nat_Oenat___Num_Onumeral_19, fact_213_less__minus__iff, fact_98_nth__upt, fact_159_neq__LNil__conv, fact_156_enat__less__induct, fact_48_measure__induct, tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_15, fact_23_ab__semigroup__add__class_Oadd__ac_I1_J, fact_51_infinite__descent, fact_224_not__numeral__less__neg__one, fact_91_less__add__Suc2, fact_195_minus__add__cancel, fact_202_neg__numeral__less__iff, fact_198_dbl__simps_I1_J, fact_9_add__Suc, fact_32_semiring__normalization__rules_I21_J, fact_77_Suc__less__SucD, fact_15_add__right__imp__eq, fact_199_neg__one__eq__numeral__iff, fact_29_upt__conv__Cons, fact_126_neq__Nil__conv, fact_62_add__strict__mono, tcon_Nat_Onat___Orderings_Olinorder, fact_223_neg__one__less__numeral, fact_112_lexordp__eq__trans, fact_161_llist__of__eq__LNil__conv, fact_220_dbl__def, fact_68_Suc__lessD, fact_238_semiring__norm_I167_J, fact_221_uminus__numeral__One, fact_241_add__neg__numeral__special_I1_J, fact_232_add__One, fact_94_linordered__field__class_Osign__simps_I28_J, fact_28_gen__length__code_I2_J, fact_147_one__plus__numeral__commute, tcon_Num_Onum___Orderings_Olinorder_3, fact_152_prefixes_Oinduct, fact_37_linordered__field__class_Osign__simps_I26_J, fact_13_llist__of__eq__LCons__conv, fact_22_add__mono__thms__linordered__semiring_I4_J, fact_118_lexordp__eq_Osimps, fact_163_one__less__numeral__iff, fact_184_num_Odistinct_I1_J, fact_144_add__numeral__left, fact_225_not__one__less__neg__numeral, fact_174_prefixes_Osimps_I1_J, fact_231_inc_Osimps_I1_J, fact_80_strict__inc__induct, fact_65_add__less__imp__less__left, fact_43_nat__add__left__cancel__less, fact_40_lessI, fact_55_linordered__field__no__ub, fact_45_less__not__refl, tcon_fun___Orderings_Oord, fact_216_minus__equation__iff, fact_63_add__strict__left__mono, tcon_HOL_Obool___Groups_Ouminus_9, fact_154_product__lists_Osimps_I1_J, fact_7_list_Oinject, fact_26_nat__add__right__cancel, fact_12_llist_Oinject, fact_75_Suc__less__eq2, fact_8_add__Suc__shift, fact_31_semiring__normalization__rules_I20_J, fact_1_add__Suc__right, fact_229_num__induct, fact_90_less__add__Suc1, fact_237_semiring__norm_I166_J, fact_233_numeral__inc, fact_58_lift__Suc__mono__less, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_96_upt__eq__Cons__conv, fact_105_lexordp__eq__simps_I2_J, fact_142_numeral__eq__iff, fact_119_lexordp__eq_Ocases, fact_71_less__SucE, fact_176_num_Oinject_I1_J, fact_4_old_Onat_Oinject, fact_186_nat__1__add__1, fact_111_lexordp__eq__linear, fact_240_add__neg__numeral__simps_I2_J, fact_226_not__neg__one__less__neg__numeral, fact_196_add__minus__cancel, fact_131_less__add__one, tcon_Num_Onum___Orderings_Oord_5, fact_136_lexordp__eq_OCons__eq, fact_82_add__lessD1, fact_205_not__numeral__less__neg__numeral, tcon_Nat_Onat___Groups_Oone, fact_133_Suc__eq__plus1__left, fact_137_fold__atLeastAtMost__nat_Oinduct, fact_228_add__neg__numeral__special_I6_J, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_13, fact_113_lexordp__eq__refl, fact_178_semiring__norm_I78_J, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_92_less__iff__Suc__add, tcon_HOL_Obool___Orderings_Olinorder_6, fact_200_numeral__eq__neg__one__iff, fact_180_semiring__norm_I76_J, fact_243_sub__num__simps_I2_J, fact_67_lessE, tcon_Extended__Nat_Oenat___Orderings_Oorder_17, fact_115_one__reorient, tcon_Nat_Onat___Orderings_Oord_2, fact_93_less__imp__Suc__add, fact_206_neg__numeral__less__numeral, tcon_Extended__Nat_Oenat___Orderings_Olinorder_16, fact_104_lexordp__eq__simps_I1_J, fact_110_lexordp__eq__antisym, fact_88_trans__less__add2, fact_76_less__antisym, fact_69_Suc__lessE, fact_197_add__neg__numeral__simps_I3_J, fact_34_semiring__normalization__rules_I23_J, help_If_1_1_T, fact_181_one__add__one, fact_78_less__trans__Suc, fact_83_add__less__mono, fact_242_add__neg__numeral__special_I2_J, fact_95_linordered__field__class_Osign__simps_I27_J, tcon_HOL_Obool___Orderings_Oord_8, fact_52_linorder__neqE__nat, fact_187_dbl__simps_I3_J, fact_188_add__neg__numeral__special_I9_J, fact_149_triangle__Suc, fact_73_less__Suc__eq, fact_210_one__neq__neg__numeral, fact_169_add__One__commute, fact_20_add_Oleft__cancel, fact_36_semiring__normalization__rules_I25_J, fact_38_add__less__cancel__left, fact_128_list_Oexhaust, fact_170_numeral__One, fact_97_upt__rec, fact_81_not__less__less__Suc__eq, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_61_add__mono__thms__linordered__field_I1_J, fact_100_is__num__normalize_I1_J, fact_106_nth__Cons__Suc, fact_116_member__rec_I2_J, fact_204_dbl__simps_I4_J, fact_166_numeral__eq__one__iff, tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_12, fact_101_member__rec_I1_J, fact_165_one__eq__numeral__iff, fact_53_measure__induct__rule, fact_164_one__plus__numeral, fact_250_dbl__dec__simps_I3_J, fact_212_numeral__neq__neg__numeral, fact_127_list_Oinducts, fact_122_remdups__adj_Oinduct, fact_185_numeral__Bit0, fact_30_lmember__code_I2_J, fact_153_enat__ord__number_I2_J, fact_11_nat__add__left__cancel, fact_141_upt__rec__numeral, fact_124_splice_Oinduct, fact_79_less__Suc__induct, fact_86_add__less__mono1, fact_146_not__numeral__less__one, fact_193_neg__numeral__eq__iff, fact_18_add_Ocommute, fact_150_longest__common__prefix_Oinduct, fact_236_sub__num__simps_I6_J, fact_157_llist_Odistinct_I1_J, fact_57_lift__Suc__mono__less__iff, fact_108_less__numeral__extra_I4_J, fact_189_dbl__simps_I5_J, fact_14_not__Cons__self2, fact_190_neg__equal__iff__equal, fact_130_list_Odistinct_I1_J, fact_103_linorder__neqE__linordered__idom, fact_192_neg__less__iff__less, fact_84_not__add__less1, fact_247_BitM__plus__one, fact_182_add__2__eq__Suc, help_If_3_1_T, fact_194_minus__add__distrib, fact_203_neg__numeral__less__neg__one__iff, fact_85_not__add__less2, fact_219_add_Oinverse__distrib__swap, help_If_2_1_T, tcon_HOL_Obool___Orderings_Oorder_7, fact_16_add__left__imp__eq, fact_64_add__strict__right__mono, fact_39_add__less__cancel__right, tcon_Num_Onum___Orderings_Oorder_4, fact_74_not__less__eq, tcon_Extended__Nat_Oenat___Groups_Oone_20, tcon_Nat_Onat___Num_Onumeral, fact_56_linordered__field__no__lb, fact_21_add_Oassoc, fact_60_add__mono__thms__linordered__field_I2_J, fact_72_less__SucI, fact_234_add__neg__numeral__special_I4_J, fact_177_semiring__norm_I6_J, fact_3_nat_Oinject, fact_138_list__encode_Oinduct, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_171_numerals_I1_J, fact_201_semiring__norm_I168_J, fact_179_semiring__norm_I2_J, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_5_add__left__cancel, tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_10, tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_14, fact_107_lexordp__eq__simps_I3_J, fact_143_numeral__less__iff, fact_125_list__induct2_H, fact_41_Suc__mono, fact_207_less__minus__one__simps_I4_J, fact_140_gen__llength__code_I2_J, tcon_Extended__Nat_Oenat___Orderings_Oord_18, fact_145_numeral__plus__numeral, fact_245_eval__nat__numeral_I2_J, fact_191_add_Oinverse__inverse, fact_33_semiring__normalization__rules_I22_J, fact_217_equation__minus__iff, fact_47_less__not__refl3, fact_6_add__right__cancel, fact_172_Suc__nat__number__of__add, fact_209_numeral__neq__neg__one, fact_27_list__of__aux__code_I2_J, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, tcon_fun___Orderings_Oorder, fact_239_add__neg__numeral__simps_I1_J, fact_49_less__irrefl__nat, fact_2_upt__conv__Cons__Cons, tcon_Nat_Onat___Groups_Osemigroup__add, fact_167_Suc__numeral, tcon_Nat_Onat___Orderings_Oorder_1, fact_109_transpose_Ocases, fact_87_trans__less__add1, fact_44_nat__neq__iff, fact_230_add__inc, fact_25_Suc__inject, fact_160_lmember__code_I1_J, fact_162_count__list_Osimps_I2_J, fact_10__092_060open_062_092_060And_062xs_Ax_O_ALCons_Ax_A_Illist__of_Axs_J_A_061_Allist__of_A_Ix_A_D_Axs_J_092_060close_062, fact_139_list__encode_Ocases, tcon_fun___Groups_Ouminus, fact_235_add__neg__numeral__special_I3_J, fact_215_one__neq__neg__one, fact_246_one__plus__BitM, fact_183_add__2__eq__Suc_H, fact_244_sub__num__simps_I4_J, fact_168_numeral__plus__one, fact_42_Suc__less__eq, fact_70_Suc__lessI, fact_19_add_Oright__cancel, fact_114_lexordp__eq_ONil, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_102_ex__gt__or__lt, fact_249_eq__numeral__iff__iszero_I8_J, fact_227_add__neg__numeral__special_I5_J, fact_135_lexordp__eq_OCons, fact_129_list_OdiscI, fact_50_nat__less__induct, fact_158_llist_Oexhaust, fact_132_gen__length__code_I1_J, fact_248_dbl__dec__simps_I5_J, tcon_Nat_Onat___Nat_Osemiring__char__0, fact_117_lexordp__eq_Oinducts, fact_175_Suc__1, fact_46_less__not__refl2, fact_35_semiring__normalization__rules_I24_J, fact_214_minus__less__iff, fact_66_add__less__imp__less__right, fact_218_is__num__normalize_I8_J, fact_99_lexordp__eq__simps_I4_J, fact_208_less__minus__one__simps_I2_J, fact_151_prefixes_Ocases, tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_11, fact_222_neg__numeral__less__one, fact_54_infinite__descent__measure, fact_123_remdups__adj_Ocases, fact_0_llist__of__inject, fact_120_map__tailrec__rev_Oinduct, fact_148_sublists_Osimps_I1_J, fact_89_less__add__eq__less, fact_211_neg__numeral__neq__numeral, fact_59_add__mono__thms__linordered__field_I5_J, fact_121_list__nonempty__induct
% 41.39/10.91 % No. of inferences in proof: 603
% 41.39/10.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10405 ms resp. 9437 ms w/o parsing
% 42.32/11.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.32/11.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------