TSTP Solution File: LCL755_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL755_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 : Fri May 19 11:31:27 EDT 2023
% Result : Theorem 6.30s 2.46s
% Output : Refutation 6.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 150
% Syntax : Number of formulae : 265 ( 96 unt; 37 typ; 0 def)
% Number of atoms : 506 ( 180 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2631 ( 60 ~; 6 |; 22 &;2307 @)
% ( 18 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 7 con; 0-5 aty)
% Number of variables : 592 ( 0 ^; 566 !; 5 ?; 592 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_type,type,
it: dB > $o ).
thf(abs_type,type,
abs: dB > dB ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_rec_type,type,
dB_rec:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) > ( fun @ dB @ ( fun @ TA @ TA ) ) > dB > TA ) ).
thf(lift_type,type,
lift: dB > nat > dB ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(suc_type,type,
suc: nat > nat ).
thf(nat_case_type,type,
nat_case:
!>[TA: $tType] : ( TA > ( fun @ nat @ TA ) > nat > TA ) ).
thf(nat_rec_type,type,
nat_rec:
!>[TA: $tType] : ( TA > ( fun @ nat @ ( fun @ TA @ TA ) ) > nat > TA ) ).
thf(semiri532925092at_aux_type,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( fun @ TA @ TA ) > nat > TA > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(pp_type,type,
pp: bool > $o ).
thf(ia_type,type,
ia: nat ).
thf(ja_type,type,
ja: nat ).
thf(ra_type,type,
ra: dB ).
thf(31,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__strict__mono) ).
thf(184,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ ( suc @ A ) )
<=> ( ( ord_less @ nat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__Suc__eq) ).
thf(361,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( ( ord_less @ nat @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( B = A ) )
=> ( ord_less @ nat @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(48,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__left__cancel) ).
thf(244,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(10,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(138,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(107,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__eq__plus1__left) ).
thf(468,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus @ nat @ ( one_one @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(77,axiom,
! [A: dB,B: dB,C: dB,D: nat,E: nat] :
( ( ord_less @ nat @ E @ ( plus_plus @ nat @ D @ ( one_one @ nat ) ) )
=> ( ( subst @ ( subst @ C @ ( lift @ B @ E ) @ ( suc @ D ) ) @ ( subst @ A @ B @ D ) @ E )
= ( subst @ ( subst @ C @ A @ E ) @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_subst__subst) ).
thf(352,plain,
! [A: dB,B: dB,C: dB,D: nat,E: nat] :
( ( ord_less @ nat @ E @ ( plus_plus @ nat @ D @ ( one_one @ nat ) ) )
=> ( ( subst @ ( subst @ C @ ( lift @ B @ E ) @ ( suc @ D ) ) @ ( subst @ A @ B @ D ) @ E )
= ( subst @ ( subst @ C @ A @ E ) @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1,conjecture,
it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(115,plain,
~ ( it @ ( abs @ ( subst @ ra @ ( var @ ( suc @ ia ) ) @ ( suc @ ja ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_less__not__refl2) ).
thf(217,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(64,axiom,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lift__IT) ).
thf(308,plain,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_dB_Osimps_I1_J) ).
thf(269,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(12,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__right__imp__eq) ).
thf(142,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ( A
!= ( suc @ B ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ B @ C )
=> ( A
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_lessE) ).
thf(340,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ( A
!= ( suc @ B ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ B @ C )
=> ( A
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(89,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_dB_Osimps_I3_J) ).
thf(404,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(92,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dB_Orecs_I3_J) ).
thf(417,plain,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ A )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ B @ C )
=> ( A
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Suc__lessE) ).
thf(301,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ A )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ B @ C )
=> ( A
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(97,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ B @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__add__Suc1) ).
thf(436,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ B @ ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(70,axiom,
! [A: fun @ nat @ bool,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( pp @ ( aa @ nat @ bool @ A @ D ) ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( pp @ ( aa @ nat @ bool @ A @ ( suc @ D ) ) )
=> ( pp @ ( aa @ nat @ bool @ A @ D ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_strict__inc__induct) ).
thf(325,plain,
! [A: fun @ nat @ bool,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( pp @ ( aa @ nat @ bool @ A @ D ) ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( pp @ ( aa @ nat @ bool @ A @ ( suc @ D ) ) )
=> ( pp @ ( aa @ nat @ bool @ A @ D ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_termination__basic__simps_I1_J) ).
thf(152,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__Suc) ).
thf(289,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( ( liftn @ A @ ( var @ C ) @ B )
= ( var @ C ) ) )
& ( ~ ( ord_less @ nat @ C @ B )
=> ( ( liftn @ A @ ( var @ C ) @ B )
= ( var @ ( plus_plus @ nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_liftn_Osimps_I1_J) ).
thf(448,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( ( liftn @ A @ ( var @ C ) @ B )
= ( var @ C ) ) )
& ( ~ ( ord_less @ nat @ C @ B )
=> ( ( liftn @ A @ ( var @ C ) @ B )
= ( var @ ( plus_plus @ nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(67,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_subst__eq) ).
thf(316,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Suc__less__eq) ).
thf(475,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(22,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(164,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
<=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__less__cancel__left) ).
thf(121,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) )
& ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ A )
=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Suc__lessD) ).
thf(348,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ A )
=> ( ord_less @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ? [C: nat] :
( A
= ( suc @ ( plus_plus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__imp__Suc__add) ).
thf(480,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ? [C: nat] :
( A
= ( suc @ ( plus_plus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__add__commute) ).
thf(147,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
<=> ? [C: nat] :
( A
= ( suc @ ( plus_plus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__iff__Suc__add) ).
thf(397,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
=> ? [C: nat] :
( A
= ( suc @ ( plus_plus @ nat @ B @ C ) ) ) )
& ( ? [C: nat] :
( A
= ( suc @ ( plus_plus @ nat @ B @ C ) ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(56,axiom,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_liftn__lift) ).
thf(280,plain,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(45,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_nat__less__cases) ).
thf(221,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__not__refl3) ).
thf(132,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__less__imp__less__right) ).
thf(116,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(206,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
=> ( ( lift @ ( var @ B ) @ A )
= ( var @ B ) ) )
& ( ~ ( ord_less @ nat @ B @ A )
=> ( ( lift @ ( var @ B ) @ A )
= ( var @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_lift_Osimps_I1_J) ).
thf(292,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ B @ A )
=> ( ( lift @ ( var @ B ) @ A )
= ( var @ B ) ) )
& ( ~ ( ord_less @ nat @ B @ A )
=> ( ( lift @ ( var @ B ) @ A )
= ( var @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(84,axiom,
! [A: dB] :
( ( it @ A )
=> ( it @ ( abs @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Lambda) ).
thf(380,plain,
! [A: dB] :
( ( it @ A )
=> ( it @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_nat__add__assoc) ).
thf(201,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(94,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_lift__Suc__mono__less__iff) ).
thf(424,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ( ord_less @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(23,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(165,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
=> ( ord_less @ nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__lessD1) ).
thf(188,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
=> ( ord_less @ nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__strict__left__mono) ).
thf(169,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(93,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Suc__n__not__n) ).
thf(420,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(108,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ B @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__add__Suc2) ).
thf(471,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ B @ ( suc @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(6,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__right__cancel) ).
thf(124,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
order @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(193,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(103,axiom,
it @ ra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(457,plain,
it @ ra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
<=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__less__cancel__right) ).
thf(173,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) )
& ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ B @ A )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__antisym) ).
thf(412,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ B @ A )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_trans__less__add1) ).
thf(166,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(21,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_less__not__refl) ).
thf(161,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(82,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ ( abs @ C ) @ B @ A )
= ( abs @ ( substn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_substn_Osimps_I3_J) ).
thf(375,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ ( abs @ C ) @ B @ A )
= ( abs @ ( substn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat__add__right__cancel) ).
thf(176,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(58,axiom,
! [A: nat,B: dB] :
( ( lift @ ( abs @ B ) @ A )
= ( abs @ ( lift @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_lift_Osimps_I3_J) ).
thf(286,plain,
! [A: nat,B: dB] :
( ( lift @ ( abs @ B ) @ A )
= ( abs @ ( lift @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(4,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__left__imp__eq) ).
thf(118,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ A ) @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add__less__mono1) ).
thf(204,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ A ) @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_linorder__neqE__linordered__idom) ).
thf(259,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(100,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I10_J) ).
thf(445,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Suc__inject) ).
thf(382,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(66,axiom,
! [A: dB,B: dB,C: nat,D: nat] :
( ( ord_less @ nat @ D @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) )
=> ( ( lift @ ( subst @ B @ A @ C ) @ D )
= ( subst @ ( lift @ B @ D ) @ ( lift @ A @ D ) @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lift__subst__lt) ).
thf(313,plain,
! [A: dB,B: dB,C: nat,D: nat] :
( ( ord_less @ nat @ D @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) )
=> ( ( lift @ ( subst @ B @ A @ C ) @ D )
= ( subst @ ( lift @ B @ D ) @ ( lift @ A @ D ) @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(71,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__eq__plus1) ).
thf(335,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(76,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lift__Suc__mono__less) ).
thf(350,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__less__imp__less__left) ).
thf(159,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA,B: nat,C: fun @ TA @ TA] :
( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
= ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__nat__aux_Osimps_I2_J) ).
thf(345,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA,B: nat,C: fun @ TA @ TA] :
( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
= ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(112,axiom,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subst__lift) ).
thf(483,plain,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ( plus_plus @ nat @ B @ C )
= ( plus_plus @ nat @ D @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__add__eq__less) ).
thf(155,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ( plus_plus @ nat @ B @ C )
= ( plus_plus @ nat @ D @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(198,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(105,axiom,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) )
=> ( ( lift @ ( lift @ A @ C ) @ ( suc @ B ) )
= ( lift @ ( lift @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_lift__lift) ).
thf(462,plain,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ ( one_one @ nat ) ) )
=> ( ( lift @ ( lift @ A @ C ) @ ( suc @ B ) )
= ( lift @ ( lift @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(130,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Suc__mono) ).
thf(455,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(87,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_dB_Osimps_I12_J) ).
thf(394,plain,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(61,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_lessI) ).
thf(299,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(98,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_dB_Osimps_I6_J) ).
thf(438,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_linorder__neqE__nat) ).
thf(241,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) )
=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Suc__less__SucD) ).
thf(473,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ B ) @ ( suc @ A ) )
=> ( ord_less @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(114,axiom,
! [A: nat,B: dB,C: nat] :
( ( liftn @ C @ ( abs @ B ) @ A )
= ( abs @ ( liftn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_liftn_Osimps_I3_J) ).
thf(490,plain,
! [A: nat,B: dB,C: nat] :
( ( liftn @ C @ ( abs @ B ) @ A )
= ( abs @ ( liftn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(50,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__irrefl__nat) ).
thf(255,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(78,axiom,
! [TA: $tType,A: nat,B: fun @ nat @ TA,C: TA] :
( ( nat_case @ TA @ C @ B @ ( suc @ A ) )
= ( aa @ nat @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_nat__case__Suc) ).
thf(355,plain,
! [TA: $tType,A: nat,B: fun @ nat @ TA,C: TA] :
( ( nat_case @ TA @ C @ B @ ( suc @ A ) )
= ( aa @ nat @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(104,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_dB_Osimps_I7_J) ).
thf(458,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(36,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(194,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__add__one) ).
thf(145,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_termination__basic__simps_I2_J) ).
thf(150,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(65,axiom,
! [A: nat,B: dB,C: dB] :
( ( subst @ ( abs @ C ) @ B @ A )
= ( abs @ ( subst @ C @ ( lift @ B @ ( zero_zero @ nat ) ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_subst__Abs) ).
thf(310,plain,
! [A: nat,B: dB,C: dB] :
( ( subst @ ( abs @ C ) @ B @ A )
= ( abs @ ( subst @ C @ ( lift @ B @ ( zero_zero @ nat ) ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ B @ A )
<=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_not__less__eq) ).
thf(370,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) )
& ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ~ ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__trans__Suc) ).
thf(338,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(17,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(154,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat_Oinject) ).
thf(386,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_nat__add__left__cancel__less) ).
thf(250,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(106,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Orecs_I1_J) ).
thf(465,plain,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_nat__neq__iff) ).
thf(231,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(68,axiom,
! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA] :
( ( nat_rec @ TA @ C @ B @ ( suc @ A ) )
= ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( nat_rec @ TA @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_nat__rec__Suc) ).
thf(319,plain,
! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA] :
( ( nat_rec @ TA @ C @ B @ ( suc @ A ) )
= ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( nat_rec @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(51,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(258,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(19,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(158,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(32,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(186,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ D @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__less__mono) ).
thf(171,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ D @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not__add__less1) ).
thf(139,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(83,axiom,
! [A: nat,B: nat] : ( it @ ( subst @ ra @ ( var @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(378,plain,
! [A: nat,B: nat] : ( it @ ( subst @ ra @ ( var @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__SucE) ).
thf(433,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(42,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_not__add__less2) ).
thf(207,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__imp__eq) ).
thf(190,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(30,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(183,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(168,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_one__reorient) ).
thf(262,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(63,axiom,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( subst @ ( var @ C ) @ A @ B )
= ( var @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_subst__lt) ).
thf(305,plain,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( subst @ ( var @ C ) @ A @ B )
= ( var @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__add__left__cancel) ).
thf(210,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_trans__less__add2) ).
thf(136,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(79,axiom,
! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA,D: fun @ nat @ TA] :
( ! [E: nat] :
( ( aa @ nat @ TA @ D @ E )
= ( nat_rec @ TA @ C @ B @ E ) )
=> ( ( aa @ nat @ TA @ D @ ( suc @ A ) )
= ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( aa @ nat @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_def__nat__rec__Suc) ).
thf(358,plain,
! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA,D: fun @ nat @ TA] :
( ! [E: nat] :
( ( aa @ nat @ TA @ D @ E )
= ( nat_rec @ TA @ C @ B @ E ) )
=> ( ( aa @ nat @ TA @ D @ ( suc @ A ) )
= ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( aa @ nat @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nat__add__left__commute) ).
thf(195,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__Suc__right) ).
thf(283,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__SucI) ).
thf(415,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ B @ A )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_not__less__less__Suc__eq) ).
thf(427,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ B @ A )
=> ( ( ( ord_less @ nat @ B @ ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ord_less @ nat @ B @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__Suc__shift) ).
thf(277,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ( ( suc @ B )
!= A )
=> ( ord_less @ nat @ ( suc @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__lessI) ).
thf(442,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ( ( suc @ B )
!= A )
=> ( ord_less @ nat @ ( suc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(69,axiom,
! [A: dB,B: dB,C: nat,D: nat] :
( ( ord_less @ nat @ D @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) )
=> ( ( lift @ ( subst @ B @ A @ D ) @ C )
= ( subst @ ( lift @ B @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) ) @ ( lift @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_lift__subst) ).
thf(322,plain,
! [A: dB,B: dB,C: nat,D: nat] :
( ( ord_less @ nat @ D @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) )
=> ( ( lift @ ( subst @ B @ A @ D ) @ C )
= ( subst @ ( lift @ B @ ( plus_plus @ nat @ C @ ( one_one @ nat ) ) ) @ ( lift @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(113,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_n__not__Suc__n) ).
thf(486,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(493,plain,
$false,
inference(e,[status(thm)],[184,361,244,138,468,352,115,217,308,269,142,340,404,417,301,436,325,152,289,448,316,475,164,121,348,480,147,397,280,221,132,116,206,292,380,201,424,165,188,169,420,471,124,193,457,173,412,166,161,375,176,286,118,204,259,445,382,313,335,350,159,345,483,155,198,462,130,455,394,299,438,241,473,490,255,355,458,194,145,150,310,370,338,154,386,250,465,231,319,258,158,186,171,139,378,433,207,190,183,168,262,305,210,136,358,195,283,415,427,277,442,322,486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL755_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:58:03 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.01 % [INFO] Parsing done (171ms).
% 1.47/1.02 % [INFO] Running in sequential loop mode.
% 1.84/1.21 % [INFO] eprover registered as external prover.
% 1.84/1.21 % [INFO] cvc4 registered as external prover.
% 1.84/1.22 % [INFO] Scanning for conjecture ...
% 2.12/1.30 % [INFO] Found a conjecture and 112 axioms. Running axiom selection ...
% 2.34/1.36 % [INFO] Axiom selection finished. Selected 112 axioms (removed 0 axioms).
% 2.71/1.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.71/1.50 % [INFO] Type checking passed.
% 2.71/1.50 % [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 ...
% 6.30/2.45 % External prover 'e' found a proof!
% 6.30/2.45 % [INFO] Killing All external provers ...
% 6.30/2.45 % Time passed: 1939ms (effective reasoning time: 1432ms)
% 6.30/2.45 % 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)>
% 6.30/2.46 % Axioms used in derivation (112): arity_Nat_Onat___Rings_Osemiring__1, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_30_less__not__refl3, fact_79_add__strict__mono, fact_51_add__Suc__right, fact_48_nat__add__right__cancel, fact_33_not__less__less__Suc__eq, fact_75_add__left__imp__eq, arity_HOL_Obool___Orderings_Oorder, fact_50_add__Suc, fact_85_lift_Osimps_I1_J, fact_59_add__less__mono, fact_15_dB_Osimps_I12_J, fact_20_nat__rec__Suc, fact_17_dB_Orecs_I1_J, fact_87_liftn_Osimps_I3_J, fact_72_add__right__cancel, fact_47_strict__inc__induct, fact_0_Lambda, fact_44_lessE, fact_26_nat__neq__iff, fact_45_Suc__lessE, fact_66_less__add__Suc2, fact_42_lift__Suc__mono__less, fact_35_less__SucI, fact_91_lift__lift, fact_93_lift__subst__lt, fact_71_add__left__cancel, fact_9_Suc__inject, fact_54_nat__add__left__commute, fact_18_nat__case__Suc, fact_49_nat__add__left__cancel, fact_86_lift_Osimps_I3_J, fact_74_add__imp__eq, fact_39_Suc__lessD, fact_76_ab__semigroup__add__class_Oadd__ac_I1_J, fact_55_nat__add__commute, fact_38_less__SucE, fact_89_Suc__eq__plus1__left, fact_13_of__nat__aux_Osimps_I2_J, fact_81_add__less__imp__less__left, fact_7_n__not__Suc__n, fact_6_dB_Osimps_I6_J, fact_88_Suc__eq__plus1, fact_73_add__right__imp__eq, fact_94_less__add__one, fact_67_less__add__Suc1, fact_58_less__add__eq__less, fact_69_add__less__cancel__right, fact_80_add__less__imp__less__right, fact_41_lift__Suc__mono__less__iff, fact_52_nat__add__left__cancel__less, fact_70_less__imp__Suc__add, fact_11_subst__lift, fact_25_less__not__refl, fact_90_one__reorient, arity_Nat_Onat___Rings_Olinordered__semidom, fact_56_add__Suc__shift, fact_24_Suc__mono, fact_34_less__antisym, fact_22_not__less__eq, fact_31_nat__less__cases, fact_32_less__Suc__eq, fact_36_Suc__lessI, fact_64_not__add__less1, fact_40_Suc__less__SucD, fact_62_trans__less__add1, fact_37_less__trans__Suc, fact_97_subst__Abs, fact_5_dB_Osimps_I7_J, fact_21_lessI, fact_14_dB_Osimps_I10_J, fact_43_def__nat__rec__Suc, fact_46_liftn_Osimps_I1_J, fact_63_not__add__less2, fact_68_add__less__cancel__left, fact_96_linorder__neqE__linordered__idom, fact_82_termination__basic__simps_I1_J, fact_3_nat_Oinject, conj_1, fact_12_liftn__lift, fact_92_lift__subst, fact_23_Suc__less__eq, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, arity_Nat_Onat___Groups_Oone, fact_8_Suc__n__not__n, fact_16_dB_Orecs_I3_J, fact_10_lift__IT, fact_60_add__less__mono1, arity_Nat_Onat___Orderings_Oorder, fact_84_subst__subst, fact_65_less__iff__Suc__add, fact_77_add__strict__right__mono, help_pp_1_1_U, fact_27_linorder__neqE__nat, fact_28_less__irrefl__nat, fact_95_substn_Osimps_I3_J, fact_2_dB_Osimps_I1_J, fact_4_subst__eq, fact_19_subst__lt, fact_83_termination__basic__simps_I2_J, fact_57_add__lessD1, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_61_trans__less__add2, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, conj_0, help_pp_2_1_U, fact_1_dB_Osimps_I3_J, fact_29_less__not__refl2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_53_nat__add__assoc, fact_78_add__strict__left__mono
% 6.30/2.46 % No. of inferences in proof: 228
% 6.30/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1939 ms resp. 1432 ms w/o parsing
% 6.59/2.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.59/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------