TSTP Solution File: NUM978_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM978_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:43:56 EDT 2023
% Result : Theorem 5.88s 2.38s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 185
% Syntax : Number of formulae : 327 ( 136 unt; 45 typ; 0 def)
% Number of atoms : 598 ( 188 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2327 ( 54 ~; 9 |; 41 &;1965 @)
% ( 30 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 9 con; 0-4 aty)
% Number of variables : 462 ( 0 ^; 428 !; 2 ?; 462 :)
% ( 32 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_type,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_type,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[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(ring_n68954251visors_type,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_type,type,
ordere216010020id_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(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[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(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_type,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(twoSqu1567020053sum2sq_type,type,
twoSqu1567020053sum2sq: int > $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(m_type,type,
m: int ).
thf(n_type,type,
n: nat ).
thf(t_type,type,
t: int ).
thf(tn_type,type,
tn: nat ).
thf(72,axiom,
! [A: nat] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zero__less__int__conv) ).
thf(333,plain,
! [A: nat] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(68,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(320,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(10,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(158,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__eq__self__zero) ).
thf(308,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
ordere216010020id_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(247,plain,
ordere216010020id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(90,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_34_add__less__mono1) ).
thf(379,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)],[90]) ).
thf(51,axiom,
~ ( twoSqu1567020053sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_nQ1) ).
thf(269,plain,
~ ( twoSqu1567020053sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(97,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(408,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(18,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__Pls) ).
thf(170,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ n ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(142,plain,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_double__add__less__zero__iff__single__add__less__zero) ).
thf(500,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(74,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_46_add__strict__left__mono) ).
thf(340,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)],[74]) ).
thf(8,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I46_J) ).
thf(153,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(88,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_36_trans__less__add1) ).
thf(372,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)],[88]) ).
thf(80,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(357,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(138,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(542,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(9,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(157,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__Bit0__Bit0) ).
thf(189,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(100,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(421,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(38,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mult__Bit0) ).
thf(228,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__imp__add__positive) ).
thf(316,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ? [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
& ( ( plus_plus @ nat @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(261,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pos__add__strict) ).
thf(492,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(106,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Nat_Oadd__0__right) ).
thf(443,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,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_73_nat__add__left__cancel) ).
thf(321,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)],[69]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_of__nat__less__0__iff) ).
thf(353,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_gr__implies__not0) ).
thf(280,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(221,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(44,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rel__simps_I39_J) ).
thf(243,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(64,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(312,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(46,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_15_add__right__cancel) ).
thf(248,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)],[46]) ).
thf(127,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__not__refl) ).
thf(512,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(134,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_45_add__strict__mono) ).
thf(529,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)],[134]) ).
thf(91,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_59_nat__neq__iff) ).
thf(381,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)],[91]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rel__simps_I14_J) ).
thf(366,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(41,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_25_add__left__imp__eq) ).
thf(233,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)],[41]) ).
thf(108,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__nat__add) ).
thf(452,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_double__zero__sym) ).
thf(302,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12,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_24_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(160,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)],[12]) ).
thf(23,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(192,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_eq__number__of) ).
thf(197,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(84,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_20_add__less__cancel__left) ).
thf(361,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)],[84]) ).
thf(131,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__zeroE) ).
thf(522,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(111,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_54_nat__less__cases) ).
thf(461,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)],[111]) ).
thf(56,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_rel__simps_I2_J) ).
thf(285,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(169,plain,
ring_n68954251visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(122,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(499,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(225,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add__gr__0) ).
thf(476,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) )
& ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(133,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_21_add__less__cancel__right) ).
thf(526,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)],[133]) ).
thf(117,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ tn,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tn0) ).
thf(489,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ tn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,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_35_trans__less__add2) ).
thf(328,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)],[70]) ).
thf(112,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_not__less0) ).
thf(471,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_double__eq__0__iff) ).
thf(393,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(128,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(515,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(19,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rel__simps_I38_J) ).
thf(173,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(87,axiom,
ordere216010020id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(371,plain,
ordere216010020id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(124,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__0) ).
thf(503,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(76,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(343,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(83,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(360,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I48_J) ).
thf(205,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ B )
= ( bit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit0 @ B )
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__is__0) ).
thf(412,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(103,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_p0) ).
thf(430,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(14,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(166,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(180,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(149,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(102,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_neq0__conv) ).
thf(423,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(95,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_not__add__less1) ).
thf(402,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
<=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__less__double__add__iff__zero__less__single__add) ).
thf(291,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(28,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(204,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(92,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_43_add__less__imp__less__left) ).
thf(391,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)],[92]) ).
thf(65,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_47_add__strict__right__mono) ).
thf(313,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)],[65]) ).
thf(4,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(144,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,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_14_add__left__cancel) ).
thf(236,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)],[42]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I51_J) ).
thf(181,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ B )
= ( bit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit1 @ B )
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
ordere223160158up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(159,plain,
ordere223160158up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_even__less__0__iff) ).
thf(274,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(52,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_32_less__add__eq__less) ).
thf(271,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)],[52]) ).
thf(126,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__0__right) ).
thf(509,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ring_n68954251visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult__eq__0__iff) ).
thf(434,plain,
! [TA: $tType] :
( ( ring_n68954251visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( zero_zero @ TA ) ) )
=> ( ( times_times @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(120,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_31_add__lessD1) ).
thf(494,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)],[120]) ).
thf(30,axiom,
semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(213,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(115,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add_Ocomm__neutral) ).
thf(483,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__pos__pos) ).
thf(520,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(71,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_of__nat__0) ).
thf(330,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_of__nat__1) ).
thf(399,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(109,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__zero__right) ).
thf(455,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(61,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_less__nat__zero__code) ).
thf(299,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(36,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(226,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(104,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_plus__nat_Oadd__0) ).
thf(431,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(15,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(167,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_of__nat__less__imp__less) ).
thf(490,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(135,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(531,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__not__refl2) ).
thf(548,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(89,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_17_nat__add__left__cancel__less) ).
thf(374,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)],[89]) ).
thf(129,axiom,
~ ( ( ord_less @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
=> ~ ( twoSqu1567020053sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_smaller_I2_J) ).
thf(516,plain,
~ ( ( ord_less @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
=> ~ ( twoSqu1567020053sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(75,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(342,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(79,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_44_add__less__imp__less__right) ).
thf(355,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)],[79]) ).
thf(110,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_gr0I) ).
thf(458,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(24,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(194,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rel__simps_I50_J) ).
thf(145,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(132,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_smaller_I1_J) ).
thf(525,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(7,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_27_add__right__imp__eq) ).
thf(150,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)],[7]) ).
thf(98,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__0__left) ).
thf(409,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__imp__of__nat__less) ).
thf(338,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(82,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(359,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__not__refl3) ).
thf(544,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(107,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( plus_plus @ TA @ B @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add__0__iff) ).
thf(446,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( plus_plus @ TA @ B @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(3,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(143,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(39,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(231,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(137,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(539,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(27,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(203,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,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_26_add__imp__eq) ).
thf(218,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)],[32]) ).
thf(58,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(290,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,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_74_nat__add__right__cancel) ).
thf(346,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)],[77]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_rel__simps_I49_J) ).
thf(214,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(57,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_of__nat__0__less__iff) ).
thf(287,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(66,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(315,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(96,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_58_linorder__neqE__nat) ).
thf(405,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)],[96]) ).
thf(101,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(422,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(16,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(168,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_of__nat__eq__iff) ).
thf(262,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(242,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_rel__simps_I17_J) ).
thf(294,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(358,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Bit0__Pls) ).
thf(195,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(113,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__neg__neg) ).
thf(474,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(136,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__reorient) ).
thf(532,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(125,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__irrefl__nat) ).
thf(506,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(50,axiom,
ord_less @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_t1) ).
thf(268,plain,
ord_less @ int @ ( one_one @ int ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_left__distrib__number__of) ).
thf(163,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_of__nat__less__iff) ).
thf(277,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(116,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mult__zero__left) ).
thf(486,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(139,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(543,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(34,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_right__distrib__number__of) ).
thf(222,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(121,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_not__add__less2) ).
thf(496,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(85,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_33_add__less__mono) ).
thf(364,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)],[85]) ).
thf(40,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(232,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I44_J) ).
thf(254,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(37,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(227,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(552,plain,
$false,
inference(e,[status(thm)],[333,320,158,308,247,379,269,408,170,142,500,340,153,372,357,542,157,189,421,228,316,261,492,443,321,353,280,221,243,312,248,512,529,381,366,233,452,302,160,192,197,361,522,461,285,169,499,225,476,526,489,328,471,393,515,173,371,503,343,360,205,412,430,166,180,149,423,402,291,204,391,313,144,236,181,159,274,271,509,434,494,213,483,520,330,399,455,299,226,431,167,490,531,548,374,516,342,355,458,194,145,525,150,409,338,359,544,446,143,231,539,203,218,290,346,214,287,315,405,422,168,262,242,294,358,195,474,532,506,268,163,277,486,543,222,496,364,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM978_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 17:22:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.00 % [INFO] Parsing done (172ms).
% 1.50/1.01 % [INFO] Running in sequential loop mode.
% 1.85/1.20 % [INFO] eprover registered as external prover.
% 1.85/1.20 % [INFO] cvc4 registered as external prover.
% 1.85/1.20 % [INFO] Scanning for conjecture ...
% 2.16/1.29 % [INFO] Found a conjecture and 139 axioms. Running axiom selection ...
% 2.39/1.35 % [INFO] Axiom selection finished. Selected 139 axioms (removed 0 axioms).
% 2.74/1.46 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.74/1.48 % [INFO] Type checking passed.
% 2.74/1.48 % [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 ...
% 5.88/2.38 % External prover 'e' found a proof!
% 5.88/2.38 % [INFO] Killing All external provers ...
% 5.88/2.38 % Time passed: 1872ms (effective reasoning time: 1369ms)
% 5.88/2.38 % 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)>
% 5.88/2.38 % Axioms used in derivation (139): fact_19_double__zero__sym, fact_18_of__nat__eq__iff, fact_76_mult__zero__left, arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, arity_Int_Oint___Groups_Oordered__comm__monoid__add, fact_37_not__add__less2, arity_Int_Oint___Groups_Oone, fact_95_right__distrib__number__of, fact_30_plus__nat_Oadd__0, fact_33_add__less__mono, fact_24_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Rings_Olinordered__idom, fact_42_add__0__left, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Int_Oring__char__0, fact_43_add__less__imp__less__left, fact_65_less__imp__add__positive, fact_88_rel__simps_I14_J, fact_63_pos__add__strict, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_28_add__eq__self__zero, fact_55_less__not__refl3, fact_17_nat__add__left__cancel__less, fact_72_rel__simps_I48_J, fact_12_of__nat__0, fact_81_rel__simps_I50_J, fact_67_add__0__iff, fact_94_left__distrib__number__of, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_3_less__nat__zero__code, fact_45_add__strict__mono, fact_13_t1, fact_2_neq0__conv, fact_80_rel__simps_I39_J, fact_83_rel__simps_I44_J, fact_4_less__zeroE, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_7_gr__implies__not0, fact_26_add__imp__eq, arity_Int_Oint___Int_Onumber__ring, fact_41_add__0, arity_Int_Oint___Rings_Osemiring__1, fact_35_trans__less__add2, arity_Nat_Onat___Groups_Ocomm__monoid__add, arity_Nat_Onat___Rings_Omult__zero, fact_74_nat__add__right__cancel, fact_89_of__nat__1, fact_50_of__nat__less__imp__less, fact_6_not__less0, fact_47_add__strict__right__mono, fact_20_add__less__cancel__left, fact_16_add__is__0, fact_23_of__nat__add, fact_1_smaller_I1_J, fact_29_Nat_Oadd__0__right, fact_11_of__nat__less__iff, fact_25_add__left__imp__eq, fact_59_nat__neq__iff, fact_73_nat__add__left__cancel, fact_27_add__right__imp__eq, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_10_double__add__less__zero__iff__single__add__less__zero, fact_90_mult__Pls, fact_51_less__imp__of__nat__less, arity_Int_Oint___Rings_Oring__no__zero__divisors, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_75_nQ1, fact_52_add__neg__neg, fact_40_add__0__right, fact_49_of__nat__less__0__iff, arity_Nat_Onat___Rings_Olinordered__semidom, fact_66_zero__less__int__conv, arity_Int_Oint___Rings_Osemiring, fact_8_gr0I, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Int_Oint___Groups_Omonoid__add, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_78_mult__eq__0__iff, fact_62_smaller_I2_J, fact_87_rel__simps_I2_J, fact_53_add__pos__pos, fact_79_rel__simps_I46_J, fact_9_zero__less__double__add__iff__zero__less__single__add, fact_82_rel__simps_I49_J, fact_31_add__lessD1, fact_84_rel__simps_I38_J, fact_71_rel__simps_I51_J, fact_86_rel__simps_I17_J, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_93_p0, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_77_mult__zero__right, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_21_add__less__cancel__right, arity_Nat_Onat___Int_Onumber, arity_Nat_Onat___Nat_Osemiring__char__0, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_60_less__not__refl, fact_92_add__Bit0__Bit0, fact_44_add__less__imp__less__right, arity_Nat_Onat___Groups_Oone, fact_91_mult__Bit0, fact_48_zero__reorient, arity_Int_Oint___Groups_Oab__semigroup__add, fact_38_not__add__less1, fact_39_add_Ocomm__neutral, arity_Nat_Onat___Rings_Osemiring, fact_54_nat__less__cases, fact_32_less__add__eq__less, fact_64_even__less__0__iff, fact_36_trans__less__add1, help_pp_1_1_U, fact_14_add__left__cancel, fact_56_less__not__refl2, arity_Nat_Onat___Groups_Omonoid__add, fact_5_of__nat__0__less__iff, fact_15_add__right__cancel, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Rings_Omult__zero, fact_34_add__less__mono1, fact_58_linorder__neqE__nat, fact_46_add__strict__left__mono, fact_22_add__gr__0, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, fact_0_tn0, arity_Int_Oint___Rings_Olinordered__semidom, fact_61_double__eq__0__iff, fact_85_Bit0__Pls, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_70_eq__number__of, fact_57_less__irrefl__nat
% 5.88/2.38 % No. of inferences in proof: 282
% 5.88/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1872 ms resp. 1369 ms w/o parsing
% 6.29/2.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.29/2.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------