TSTP Solution File: NUM933_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM933_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:43:50 EDT 2023
% Result : Theorem 51.45s 19.98s
% Output : Refutation 51.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 159
% Syntax : Number of formulae : 303 ( 134 unt; 32 typ; 0 def)
% Number of atoms : 530 ( 196 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 2367 ( 40 ~; 6 |; 37 &;2070 @)
% ( 25 <=>; 189 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 447 ( 0 ^; 422 !; 5 ?; 447 :)
% ( 20 !>; 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(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(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[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(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[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(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[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(zprime_type,type,
zprime: int > $o ).
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(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(twoSqu1567020053sum2sq_type,type,
twoSqu1567020053sum2sq: int > $o ).
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(85,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(421,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_one__is__num__one) ).
thf(356,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(38,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_arith__simps_I32_J) ).
thf(259,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(56,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__numeral__0__right) ).
thf(327,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(114,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(479,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(62,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mult__numeral__1) ).
thf(347,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(58,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_number__of__add) ).
thf(333,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(103,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(468,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(116,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(481,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(94,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__le__imp__le__right) ).
thf(449,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,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_31_left__distrib__number__of) ).
thf(247,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)],[34]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_le__special_I2_J) ).
thf(142,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(107,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(472,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(45,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_less__eq__int__code_I16_J) ).
thf(288,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(48,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__Pls) ).
thf(301,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(90,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_one__reorient) ).
thf(436,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)],[90]) ).
thf(76,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_semiring__add__number__of) ).
thf(389,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(61,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit1 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_number__of__Bit1) ).
thf(344,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit1 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
thf(157,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(110,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(475,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(127,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(492,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I51_J) ).
thf(179,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)],[19]) ).
thf(91,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__right__mono) ).
thf(443,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_plus__numeral__code_I9_J) ).
thf(321,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(72,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_nat__1__add__1) ).
thf(376,plain,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(120,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(485,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(31,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mult__Pls) ).
thf(238,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_semiring__numeral__1__eq__1) ).
thf(353,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(115,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(480,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(25,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).
thf(211,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_le__number__of) ).
thf(253,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
<=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__le__cancel__left) ).
thf(397,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) )
& ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(46,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_less__eq__int__code_I13_J) ).
thf(293,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(96,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__1__left) ).
thf(453,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(4,axiom,
zprime @ ( 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_1_p) ).
thf(132,plain,
zprime @ ( 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)],[4]) ).
thf(5,axiom,
ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0964_A_K_Am_A_L_A1_A_060_061_A1_096) ).
thf(133,plain,
ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__number__of__eq) ).
thf(265,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_times__numeral__code_I5_J) ).
thf(312,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I50_J) ).
thf(203,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(204,plain,
~ ? [A: int,B: int] :
( ( bit1 @ B )
= ( bit0 @ A ) ),
inference(miniscope,[status(thm)],[203]) ).
thf(205,plain,
! [B: int,A: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(cnf,[status(esa)],[204]) ).
thf(206,plain,
! [B: int,A: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(50,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__eq__number__of__int__code) ).
thf(307,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(30,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I31_J) ).
thf(233,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zprime__2) ).
thf(381,plain,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__Bit1__Bit0) ).
thf(160,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(77,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring__mult__number__of) ).
thf(392,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(86,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_83_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(424,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)],[86]) ).
thf(102,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(467,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(119,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(484,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(67,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_semiring__mult__2) ).
thf(361,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(493,plain,
~ ( pp @ fFalse ),
inference(polarity_switch,[status(thm)],[492]) ).
thf(97,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mult__1) ).
thf(456,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(55,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__numeral__0) ).
thf(324,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(44,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_number__of__is__id) ).
thf(285,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(123,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(488,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(27,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Bit0__Pls) ).
thf(225,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(111,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(476,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(124,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(489,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(106,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(471,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(37,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__number__of__left) ).
thf(256,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,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_15_eq__number__of) ).
thf(173,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)],[18]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(129,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: int,B: int] :
( ( twoSqu1567020053sum2sq @ B )
=> ( ( twoSqu1567020053sum2sq @ A )
=> ( twoSqu1567020053sum2sq @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_is__mult__sum2sq) ).
thf(134,plain,
! [A: int,B: int] :
( ( twoSqu1567020053sum2sq @ B )
=> ( ( twoSqu1567020053sum2sq @ A )
=> ( twoSqu1567020053sum2sq @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,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_30_add__Bit0__Bit0) ).
thf(244,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)],[33]) ).
thf(47,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__Pls__right) ).
thf(298,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
<=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__le__cancel__right) ).
thf(412,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) )
& ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(88,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_85_add__imp__eq) ).
thf(430,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)],[88]) ).
thf(11,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(148,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__left__mono) ).
thf(445,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
<=> ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_le__nat__number__of) ).
thf(382,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
=> ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) ) )
& ( ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) )
=> ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(101,axiom,
ordere779506340up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(466,plain,
ordere779506340up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(63,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mult__numeral__1__right) ).
thf(350,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I48_J) ).
thf(187,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)],[20]) ).
thf(81,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_78_add__right__cancel) ).
thf(406,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)],[81]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__le__imp__le__left) ).
thf(451,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(53,axiom,
! [A: int,B: int,C: int] :
( ( times_times @ int @ C @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ int @ ( times_times @ int @ C @ B ) @ ( times_times @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_int__distrib_I2_J) ).
thf(318,plain,
! [A: int,B: int,C: int] :
( ( times_times @ int @ C @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ int @ ( times_times @ int @ C @ B ) @ ( times_times @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(112,axiom,
semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(477,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(128,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(494,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(69,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_semiring__mult__2__right) ).
thf(367,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(118,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(483,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(21,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(195,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(196,plain,
~ ? [A: int] :
( ( bit1 @ A )
= pls ),
inference(miniscope,[status(thm)],[195]) ).
thf(197,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(cnf,[status(esa)],[196]) ).
thf(198,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(lifteq,[status(thm)],[197]) ).
thf(57,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_number__of__mult) ).
thf(330,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(99,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_mult_Ocomm__neutral) ).
thf(462,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(3,axiom,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096_126_A1_A_060_061_Am_096) ).
thf(130,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_number__of__reorient) ).
thf(278,plain,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( ( number_number_of @ TA @ B )
= A )
=> ( A
= ( number_number_of @ TA @ B ) ) )
& ( ( A
= ( number_number_of @ TA @ B ) )
=> ( ( number_number_of @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(135,plain,
! [B: int,A: int] :
( ~ ( twoSqu1567020053sum2sq @ B )
| ~ ( twoSqu1567020053sum2sq @ A )
| ( twoSqu1567020053sum2sq @ ( times_times @ int @ B @ A ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(32,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_29_mult__Bit0) ).
thf(241,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)],[32]) ).
thf(108,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(473,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(125,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(490,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(122,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(487,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_le__special_I4_J) ).
thf(145,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I39_J) ).
thf(199,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__2__right) ).
thf(370,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(105,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(470,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(59,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__eq__int__code_I14_J) ).
thf(336,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(13,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
thf(154,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(143,plain,
! [TA: $tType,A: int] :
( ~ ( number_ring @ TA )
| ~ ( linordered_idom @ TA )
| ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
| ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) ),
inference(cnf,[status(esa)],[142]) ).
thf(26,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I38_J) ).
thf(218,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,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_32_right__distrib__number__of) ).
thf(250,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)],[35]) ).
thf(100,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(465,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(117,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(482,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(49,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Bit0__def) ).
thf(304,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(8,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__special_I3_J) ).
thf(139,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
! [A: nat] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_nat__mult__2) ).
thf(418,plain,
! [A: nat] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(73,axiom,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prime__g__5) ).
thf(378,plain,
! [A: int] :
( ( zprime @ A )
=> ( ( A
!= ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
!= ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(89,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_86_add__right__imp__eq) ).
thf(433,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)],[89]) ).
thf(24,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
thf(207,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(113,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(478,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(12,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mult__Bit1) ).
thf(151,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ D @ C )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__mono) ).
thf(447,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ D @ C )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(52,axiom,
! [A: int,B: int,C: int] :
( ( times_times @ int @ ( plus_plus @ int @ C @ B ) @ A )
= ( plus_plus @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_int__distrib_I1_J) ).
thf(315,plain,
! [A: int,B: int,C: int] :
( ( times_times @ int @ ( plus_plus @ int @ C @ B ) @ A )
= ( plus_plus @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_rel__simps_I32_J) ).
thf(273,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(71,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_semiring__one__add__one__is__two) ).
thf(373,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(17,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I27_J) ).
thf(168,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(39,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__number__of__left) ).
thf(262,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(208,plain,
~ ? [A: int,B: int] :
( ( bit0 @ B )
= ( bit1 @ A ) ),
inference(miniscope,[status(thm)],[207]) ).
thf(209,plain,
! [B: int,A: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(cnf,[status(esa)],[208]) ).
thf(210,plain,
! [B: int,A: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(7,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_add__special_I2_J) ).
thf(136,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(60,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Bit1__def) ).
thf(341,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(41,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I22_J) ).
thf(268,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(66,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( times_times @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_double__number__of__Bit0) ).
thf(358,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( times_times @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(109,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(474,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,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_77_add__left__cancel) ).
thf(400,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)],[80]) ).
thf(83,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_nat__mult__2__right) ).
thf(415,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(78,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_nat__numeral__1__eq__1) ).
thf(395,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(87,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_84_add__left__imp__eq) ).
thf(427,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)],[87]) ).
thf(98,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_mult__1__right) ).
thf(459,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(131,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ m ),
inference(polarity_switch,[status(thm)],[130]) ).
thf(16,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I21_J) ).
thf(163,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I34_J) ).
thf(227,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(121,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(486,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(104,axiom,
ab_semigroup_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(469,plain,
ab_semigroup_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(126,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(491,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(495,plain,
( ( ord_less_eq @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ ( one_one @ int ) )
!= ( ord_less_eq @ int @ ( one_one @ int ) @ m ) ),
inference(paramod_ordered,[status(thm)],[133,131]) ).
thf(496,plain,
( ( ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) )
!= ( one_one @ int ) )
| ( m
!= ( one_one @ int ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(68,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mult__2) ).
thf(364,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(29,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I19_J) ).
thf(232,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(63914,plain,
$false,
inference(cvc4,[status(thm)],[421,356,259,327,479,347,333,468,481,449,247,142,472,288,301,436,389,344,157,475,492,179,443,321,376,485,238,353,480,211,253,397,293,453,132,133,265,312,206,307,233,381,160,392,424,467,484,361,493,456,324,285,488,225,476,489,471,256,173,129,134,244,298,412,430,148,445,382,466,350,187,406,451,318,477,494,367,483,198,330,462,130,278,135,241,473,490,487,145,199,370,470,336,154,143,218,250,465,482,203,304,139,418,378,433,207,478,151,447,315,273,373,168,262,210,136,341,268,358,195,474,400,415,395,427,459,131,163,227,486,469,491,496,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM933_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 17:05:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.01 % [INFO] Parsing done (161ms).
% 1.44/1.02 % [INFO] Running in sequential loop mode.
% 1.79/1.22 % [INFO] eprover registered as external prover.
% 1.79/1.22 % [INFO] cvc4 registered as external prover.
% 1.79/1.22 % [INFO] Scanning for conjecture ...
% 2.11/1.30 % [INFO] Found a conjecture and 126 axioms. Running axiom selection ...
% 2.11/1.32 % [INFO] Axiom selection finished. Selected 126 axioms (removed 0 axioms).
% 2.60/1.44 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.70/1.46 % [INFO] Type checking passed.
% 2.70/1.46 % [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 ...
% 51.45/19.97 % External prover 'cvc4' found a proof!
% 51.45/19.98 % [INFO] Killing All external provers ...
% 51.45/19.98 % Time passed: 19451ms (effective reasoning time: 18953ms)
% 51.45/19.98 % 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)>
% 51.45/19.98 % Axioms used in derivation (126): fact_73_semiring__add__number__of, fact_33_le__number__of, fact_70_prime__g__5, fact_85_add__imp__eq, arity_Nat_Onat___Groups_Omonoid__mult, fact_50_int__distrib_I2_J, fact_61_semiring__numeral__1__eq__1, fact_11_add__Bit0__Bit1, arity_Int_Oint___Groups_Oone, arity_Nat_Onat___Groups_Oab__semigroup__mult, fact_83_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Rings_Olinordered__idom, fact_65_mult__2, arity_Int_Oint___Int_Oring__char__0, fact_1_p, fact_43_less__eq__int__code_I13_J, arity_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_31_left__distrib__number__of, fact_9_mult__Bit1, fact_79_add__le__cancel__right, fact_5_add__special_I3_J, fact_81_nat__mult__2, fact_48_times__numeral__code_I5_J, fact_67_mult__2__right, fact_96_mult_Ocomm__neutral, arity_Nat_Onat___Int_Onumber__semiring, fact_64_semiring__mult__2, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_14_rel__simps_I27_J, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Int_Onumber__ring, fact_80_nat__mult__2__right, fact_44_add__Pls__right, fact_26_rel__simps_I19_J, fact_54_number__of__mult, fact_66_semiring__mult__2__right, fact_91_add__le__imp__le__right, fact_12_add__Bit1__Bit0, fact_71_zprime__2, fact_76_add__le__cancel__left, fact_22_rel__simps_I44_J, fact_28_mult__Pls, fact_39_rel__simps_I32_J, fact_55_number__of__add, fact_45_add__Pls, fact_2__0964_A_K_Am_A_L_A1_A_060_061_A1_096, fact_94_mult__1, fact_88_add__right__mono, fact_3_is__mult__sum2sq, arity_Int_Oint___Groups_Omonoid__mult, fact_6_le__special_I2_J, fact_4_add__special_I2_J, fact_37_add__number__of__eq, fact_46_Bit0__def, fact_95_mult__1__right, fact_29_mult__Bit0, fact_52_add__numeral__0, fact_63_double__number__of__Bit0, fact_17_rel__simps_I48_J, fact_86_add__right__imp__eq, fact_58_number__of__Bit1, fact_68_semiring__one__add__one__is__two, fact_90_add__mono, fact_7_le__special_I4_J, arity_Int_Oint___Rings_Osemiring, fact_30_add__Bit0__Bit0, fact_27_rel__simps_I31_J, fact_24_Bit0__Pls, fact_60_mult__numeral__1__right, fact_56_less__eq__int__code_I14_J, fact_49_int__distrib_I1_J, fact_93_mult__1__left, fact_36_add__number__of__left, fact_19_rel__simps_I39_J, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_75_nat__numeral__1__eq__1, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_34_mult__number__of__left, fact_62_one__is__num__one, fact_69_nat__1__add__1, fact_41_number__of__is__id, fact_53_add__numeral__0__right, fact_8_one__add__one__is__two, fact_72_le__nat__number__of, fact_32_right__distrib__number__of, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_23_rel__simps_I38_J, fact_21_rel__simps_I49_J, arity_Nat_Onat___Int_Onumber, fact_0__096_126_A1_A_060_061_Am_096, fact_13_rel__simps_I21_J, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_84_add__left__imp__eq, arity_Nat_Onat___Groups_Oone, fact_78_add__right__cancel, fact_51_plus__numeral__code_I9_J, fact_74_semiring__mult__number__of, arity_Int_Oint___Groups_Oab__semigroup__add, fact_38_rel__simps_I22_J, arity_Nat_Onat___Rings_Osemiring, fact_42_less__eq__int__code_I16_J, fact_59_mult__numeral__1, help_pp_1_1_U, fact_20_rel__simps_I50_J, fact_25_rel__simps_I34_J, fact_77_add__left__cancel, fact_10_numeral__1__eq__1, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_57_Bit1__def, fact_35_arith__simps_I32_J, arity_Int_Oint___Int_Onumber, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, help_pp_2_1_U, fact_47_less__eq__number__of__int__code, fact_16_rel__simps_I51_J, fact_89_add__left__mono, fact_18_rel__simps_I46_J, fact_82_ab__semigroup__mult__class_Omult__ac_I1_J, fact_92_add__le__imp__le__left, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_40_number__of__reorient, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_15_eq__number__of, fact_87_one__reorient
% 51.45/19.98 % No. of inferences in proof: 271
% 51.45/19.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19451 ms resp. 18953 ms w/o parsing
% 51.61/20.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.61/20.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------