TSTP Solution File: NUM932_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM932_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 17.63s 4.14s
% Output : Refutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 257 ( 110 unt; 25 typ; 0 def)
% Number of atoms : 473 ( 182 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2216 ( 21 ~; 0 |; 50 &;1954 @)
% ( 32 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-3 aty)
% Number of variables : 345 ( 0 ^; 328 !; 0 ?; 345 :)
% ( 17 !>; 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(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_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(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : 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(m_type,type,
m: int ).
thf(79,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ A ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ A ) ) )
& ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_number__of1) ).
thf(340,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ A ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ A ) ) )
& ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(6,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(121,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_odd__nonzero) ).
thf(279,plain,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_double__zero__sym) ).
thf(177,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)],[28]) ).
thf(85,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_number__of__Pls) ).
thf(365,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(83,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I51_J) ).
thf(352,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)],[83]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_37_arith__simps_I32_J) ).
thf(276,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)],[60]) ).
thf(5,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(120,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(108,axiom,
! [A: int] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_eq__0__number__of) ).
thf(440,plain,
! [A: int] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(35,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_numeral__1__eq__1) ).
thf(202,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_84_le__nat__number__of) ).
thf(320,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)],[74]) ).
thf(106,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Bit0__def) ).
thf(436,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(94,axiom,
! [A: int] :
( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_eq__number__of__0) ).
thf(389,plain,
! [A: int] :
( ( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(157,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(125,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(81,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__eq__int__code_I13_J) ).
thf(344,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)],[81]) ).
thf(30,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_semiring__norm_I113_J) ).
thf(189,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(101,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(421,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(99,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__numeral__1__eq__1) ).
thf(416,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_add__Bit0__Bit1) ).
thf(289,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)],[64]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I49_J) ).
thf(261,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(41,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
<=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zero__le__double__add__iff__zero__le__single__add) ).
thf(221,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',fact_86_add__right__cancel) ).
thf(453,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)],[111]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I34_J) ).
thf(396,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)],[95]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I31_J) ).
thf(428,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)],[104]) ).
thf(55,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(265,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(65,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_mult__Pls) ).
thf(292,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(44,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Bit0__Pls) ).
thf(233,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__Bit0__Bit0) ).
thf(248,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)],[49]) ).
thf(107,axiom,
zprime @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p) ).
thf(439,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)],[107]) ).
thf(58,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_nat__mult__2__right) ).
thf(270,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)],[58]) ).
thf(91,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mult__numeral__1) ).
thf(380,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)],[91]) ).
thf(1,conjecture,
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/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( 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(neg_conjecture,[status(cth)],[1]) ).
thf(117,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)],[2]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less_eq @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_le__special_I3_J) ).
thf(334,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_56_times__numeral__code_I5_J) ).
thf(349,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)],[82]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',fact_7_one__add__one__is__two) ).
thf(160,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)],[23]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le__special_I1_J) ).
thf(297,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(103,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I39_J) ).
thf(424,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_89_add__le__cancel__left) ).
thf(197,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)],[33]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_J) ).
thf(224,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)],[42]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_mult__Bit1) ).
thf(317,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)],[73]) ).
thf(26,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__Pls__right) ).
thf(169,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_58_int__distrib_I2_J) ).
thf(141,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)],[15]) ).
thf(9,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(124,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(212,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I38_J) ).
thf(129,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fact_80_prime__g__5) ).
thf(371,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)],[88]) ).
thf(80,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(343,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(56,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(266,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(84,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I27_J) ).
thf(360,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)],[84]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I50_J) ).
thf(205,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_4_add__special_I3_J) ).
thf(311,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)],[71]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_57_int__distrib_I1_J) ).
thf(191,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)],[31]) ).
thf(63,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_semiring__numeral__0__eq__0) ).
thf(286,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(3,axiom,
number @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(118,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(144,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_rel__simps_I48_J) ).
thf(466,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)],[115]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_71_double__number__of__Bit0) ).
thf(236,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)],[46]) ).
thf(97,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mult__Bit0) ).
thf(406,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)],[97]) ).
thf(27,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_rel__simps_I22_J) ).
thf(172,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)],[27]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_5_le__special_I2_J) ).
thf(377,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)],[90]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_33_right__distrib__number__of) ).
thf(245,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)],[48]) ).
thf(69,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mult__numeral__1__right) ).
thf(303,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)],[69]) ).
thf(39,axiom,
ord_less_eq @ int @ m @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096m_A_060_061_A0_096) ).
thf(213,plain,
ord_less_eq @ int @ m @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(50,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__Pls) ).
thf(251,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(76,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I46_J) ).
thf(330,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_38_add__number__of__left) ).
thf(462,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)],[113]) ).
thf(70,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rel__simps_I21_J) ).
thf(306,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)],[70]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_63_number__of__add) ).
thf(267,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)],[57]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_35_le__number__of) ).
thf(374,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)],[89]) ).
thf(52,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_number__of__Bit0) ).
thf(255,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_semiring__numeral__1__eq__1) ).
thf(209,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(123,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_39_add__number__of__eq) ).
thf(194,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)],[32]) ).
thf(17,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_rel__simps_I32_J) ).
thf(145,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)],[17]) ).
thf(66,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_one__is__num__one) ).
thf(295,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(18,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I19_J) ).
thf(150,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_88_add__le__cancel__right) ).
thf(327,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)],[75]) ).
thf(98,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I44_J) ).
thf(409,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(20,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_number__of__is__id) ).
thf(154,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_66_number__of__Bit1) ).
thf(386,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)],[93]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_double__add__le__zero__iff__single__add__le__zero) ).
thf(314,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(114,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(465,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_75_mult__2__right) ).
thf(450,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)],[110]) ).
thf(86,axiom,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zprime__2) ).
thf(368,plain,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_73_mult__2) ).
thf(258,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)],[53]) ).
thf(22,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zero__is__num__zero) ).
thf(158,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(96,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__eq__int__code_I16_J) ).
thf(401,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)],[96]) ).
thf(14,axiom,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_126_A1_A_060_061_Am_096) ).
thf(139,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',fact_72_semiring__mult__2) ).
thf(418,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)],[100]) ).
thf(4,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(119,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(235,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_36_mult__number__of__left) ).
thf(433,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)],[105]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_6_le__special_I4_J) ).
thf(383,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)],[92]) ).
thf(40,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_number__of__reorient) ).
thf(214,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)],[40]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_32_left__distrib__number__of) ).
thf(151,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)],[19]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__Bit1__Bit0) ).
thf(300,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)],[68]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_62_number__of__mult) ).
thf(447,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)],[109]) ).
thf(25,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(168,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_85_add__left__cancel) ).
thf(183,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)],[29]) ).
thf(102,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Pls__def) ).
thf(422,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(59,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Bit1__def) ).
thf(273,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',fact_15_eq__number__of) ).
thf(239,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)],[47]) ).
thf(116,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__eq__int__code_I14_J) ).
thf(474,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)],[116]) ).
thf(62,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__numeral__0__right) ).
thf(283,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)],[62]) ).
thf(11,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__numeral__0) ).
thf(126,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)],[11]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',fact_3_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)],[13]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_74_semiring__mult__2__right) ).
thf(459,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)],[112]) ).
thf(87,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__1__add__1) ).
thf(369,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)],[87]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_55_less__eq__number__of__int__code) ).
thf(163,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)],[24]) ).
thf(34,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__number__of__Pls) ).
thf(200,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(51,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(254,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_double__eq__0__iff) ).
thf(227,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)],[43]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_76_semiring__one__add__one__is__two) ).
thf(337,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)],[78]) ).
thf(7,axiom,
semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(122,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2128,plain,
$false,
inference(e,[status(thm)],[340,121,279,177,365,352,276,120,440,202,320,436,389,157,125,344,189,421,416,289,261,221,453,396,428,265,292,233,248,439,270,380,117,334,349,160,297,424,197,224,317,169,141,124,212,129,371,343,266,360,205,311,191,286,118,144,466,236,406,172,377,245,303,213,251,330,462,306,267,374,255,209,123,194,145,295,150,327,409,154,386,314,465,450,368,258,158,401,139,418,119,235,433,383,214,151,300,447,168,183,422,273,239,474,283,126,136,459,369,163,200,254,227,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM932_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 18 16:29:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.92/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.06 % [INFO] Parsing done (174ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.90/1.26 % [INFO] eprover registered as external prover.
% 1.90/1.27 % [INFO] cvc4 registered as external prover.
% 1.90/1.27 % [INFO] Scanning for conjecture ...
% 2.27/1.36 % [INFO] Found a conjecture and 116 axioms. Running axiom selection ...
% 2.49/1.43 % [INFO] Axiom selection finished. Selected 114 axioms (removed 2 axioms).
% 2.87/1.53 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.87/1.54 % [INFO] Type checking passed.
% 2.87/1.54 % [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 ...
% 17.63/4.13 % External prover 'e' found a proof!
% 17.63/4.13 % [INFO] Killing All external provers ...
% 17.63/4.13 % Time passed: 3617ms (effective reasoning time: 3066ms)
% 17.63/4.13 % 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)>
% 17.63/4.14 % Axioms used in derivation (114): fact_22_rel__simps_I49_J, fact_26_rel__simps_I34_J, arity_Int_Oint___Groups_Oone, fact_5_le__special_I2_J, fact_51_less__eq__int__code_I13_J, fact_75_mult__2__right, fact_48_odd__nonzero, fact_73_mult__2, arity_Int_Oint___Rings_Olinordered__idom, fact_0__096m_A_060_061_A0_096, fact_13_rel__simps_I27_J, arity_Int_Oint___Int_Oring__char__0, fact_14_rel__simps_I32_J, fact_31_add__Bit0__Bit0, fact_63_number__of__add, fact_6_le__special_I4_J, fact_69_semiring__numeral__1__eq__1, fact_89_add__le__cancel__left, fact_2_p, fact_19_rel__simps_I46_J, arity_Nat_Onat___Int_Onumber__semiring, fact_27_rel__simps_I19_J, fact_67_mult__numeral__1, fact_85_add__left__cancel, fact_3_add__special_I2_J, fact_92_eq__number__of__0, fact_23_rel__simps_I44_J, fact_71_double__number__of__Bit0, fact_33_right__distrib__number__of, fact_28_rel__simps_I31_J, fact_1__096_126_A1_A_060_061_Am_096, fact_82_zprime__2, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_38_add__number__of__left, arity_Int_Oint___Int_Onumber__semiring, fact_65_Bit1__def, fact_78_double__add__le__zero__iff__single__add__le__zero, arity_Int_Oint___Int_Onumber__ring, fact_59_plus__numeral__code_I9_J, fact_66_number__of__Bit1, fact_57_int__distrib_I1_J, fact_62_number__of__mult, fact_9_numeral__1__eq__1, fact_52_add__Pls__right, fact_36_mult__number__of__left, fact_91_eq__0__number__of, fact_50_less__eq__int__code_I16_J, fact_54_Bit0__def, fact_41_le__special_I3_J, fact_70_one__is__num__one, fact_76_semiring__one__add__one__is__two, fact_88_add__le__cancel__right, fact_60_add__numeral__0, fact_68_mult__numeral__1__right, fact_35_le__number__of, fact_93_nat__numeral__1__eq__1, fact_7_one__add__one__is__two, fact_8_mult__Bit1, fact_77_nat__1__add__1, fact_17_rel__simps_I48_J, fact_74_semiring__mult__2__right, fact_42_le__special_I1_J, arity_Int_Oint___Rings_Osemiring, fact_44_number__of__reorient, fact_61_add__numeral__0__right, fact_56_times__numeral__code_I5_J, fact_18_double__eq__0__iff, arity_Nat_Onat___Groups_Ozero, fact_21_rel__simps_I50_J, fact_53_add__Pls, fact_4_add__special_I3_J, fact_49_number__of__Bit0, fact_94_semiring__norm_I113_J, fact_11_add__Bit1__Bit0, fact_72_semiring__mult__2, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_29_mult__Pls, fact_86_add__right__cancel, arity_Nat_Onat___Int_Onumber, fact_84_le__nat__number__of, fact_34_number__of__Pls, fact_37_arith__simps_I32_J, fact_58_int__distrib_I2_J, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_30_mult__Bit0, fact_95_nat__mult__2__right, fact_24_rel__simps_I38_J, arity_Nat_Onat___Groups_Oone, fact_32_left__distrib__number__of, fact_47_zero__is__num__zero, fact_25_Bit0__Pls, fact_40_rel__simps_I22_J, fact_39_add__number__of__eq, fact_83_number__of1, arity_Nat_Onat___Rings_Osemiring, fact_64_less__eq__int__code_I14_J, fact_46_semiring__numeral__0__eq__0, fact_81_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_90_nat__number__of__Pls, fact_43_Pls__def, fact_55_less__eq__number__of__int__code, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_45_number__of__is__id, fact_80_prime__g__5, arity_Int_Oint___Groups_Ozero, fact_20_rel__simps_I39_J, fact_12_rel__simps_I21_J, fact_87_double__zero__sym, fact_79_zero__le__double__add__iff__zero__le__single__add, fact_16_rel__simps_I51_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_15_eq__number__of, fact_10_add__Bit0__Bit1
% 17.63/4.14 % No. of inferences in proof: 232
% 17.63/4.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3617 ms resp. 3066 ms w/o parsing
% 17.70/4.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.70/4.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------