TSTP Solution File: NUM948_5 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM948_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 : Tue May 7 08:02:27 EDT 2024
% Result : Theorem 5.87s 2.62s
% Output : Refutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 133
% Syntax : Number of formulae : 243 ( 76 unt; 25 typ; 0 def)
% Number of atoms : 536 ( 136 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 2606 ( 22 ~; 3 |; 93 &;2266 @)
% ( 48 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 367 ( 0 ^ 350 !; 2 ?; 367 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
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(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(zcong_type,type,
zcong: int > int > int > $o ).
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_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(m_type,type,
m: int ).
thf(s1_type,type,
s1: int ).
thf(thesis_type,type,
thesis: $o ).
thf(75,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I17_J) ).
thf(384,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J) ).
thf(152,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,axiom,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(503,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(82,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_95_number__of__Bit1) ).
thf(409,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)],[82]) ).
thf(59,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_zle__add1__eq__le) ).
thf(314,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(93,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_92_odd__nonzero) ).
thf(450,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)],[93]) ).
thf(95,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_mult__Pls) ).
thf(459,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rel__simps_I16_J) ).
thf(276,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(57,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_76_plus__numeral__code_I9_J) ).
thf(308,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)],[57]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__int__code_I15_J) ).
thf(379,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(19,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_72_less__eq__number__of__int__code) ).
thf(174,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)],[19]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_le__number__of__eq__not__less) ).
thf(417,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) )
& ( ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(89,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_52_add__Bit1__Bit0) ).
thf(436,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)],[89]) ).
thf(43,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_rel__simps_I4_J) ).
thf(257,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,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_65_less__eq__int__code_I16_J) ).
thf(389,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)],[76]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(110,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,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_43_add__number__of__eq) ).
thf(196,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)],[25]) ).
thf(15,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I21_J) ).
thf(157,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)],[15]) ).
thf(105,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(492,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(20,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_34_add__Bit0__Bit0) ).
thf(179,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)],[20]) ).
thf(73,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_40_mult__number__of__left) ).
thf(376,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)],[73]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I49_J) ).
thf(253,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I15_J) ).
thf(238,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(67,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Bit0__def) ).
thf(348,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(78,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(397,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)],[78]) ).
thf(53,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_74_int__distrib_I1_J) ).
thf(293,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)],[53]) ).
thf(38,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Bit1__def) ).
thf(243,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(40,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_42_add__number__of__left) ).
thf(248,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)],[40]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I14_J) ).
thf(439,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(46,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pls__def) ).
thf(270,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(31,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_numeral__1__eq__1) ).
thf(220,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,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_97_mult__numeral__1__right) ).
thf(334,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)],[64]) ).
thf(23,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_39_le__number__of) ).
thf(192,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)],[23]) ).
thf(48,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I19_J) ).
thf(275,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(17,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(165,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)],[17]) ).
thf(34,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_96_mult__numeral__1) ).
thf(229,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)],[34]) ).
thf(70,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_81_add__numeral__0__right) ).
thf(361,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)],[70]) ).
thf(106,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_10_le__special_I1_J) ).
thf(493,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)],[106]) ).
thf(80,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_number__of__is__id) ).
thf(403,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(69,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_49_rel__simps_I32_J) ).
thf(356,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)],[69]) ).
thf(11,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I38_J) ).
thf(141,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(85,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_35_left__distrib__number__of) ).
thf(420,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)],[85]) ).
thf(108,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I39_J) ).
thf(499,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(104,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_11_le__special_I3_J) ).
thf(489,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)],[104]) ).
thf(29,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_73_times__numeral__code_I5_J) ).
thf(212,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)],[29]) ).
thf(61,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I2_J) ).
thf(328,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(99,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_even__less__0__iff) ).
thf(471,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__special_I2_J) ).
thf(124,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I50_J) ).
thf(225,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,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_60_number__of__reorient) ).
thf(128,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)],[9]) ).
thf(58,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_82_number__of__mult) ).
thf(311,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)],[58]) ).
thf(83,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I29_J) ).
thf(412,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(12,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(148,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)],[12]) ).
thf(54,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I46_J) ).
thf(296,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(91,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(444,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(86,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_33_mult__Bit0) ).
thf(423,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)],[86]) ).
thf(51,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I22_J) ).
thf(286,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)],[51]) ).
thf(52,axiom,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_zmult__zless__mono2) ).
thf(291,plain,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ A @ C ) @ ( times_times @ int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(118,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__int__code_I13_J) ).
thf(281,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_semiring__numeral__0__eq__0) ).
thf(204,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(92,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_bin__less__0__simps_I4_J) ).
thf(445,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(98,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bin__less__0__simps_I3_J) ).
thf(466,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I33_J) ).
thf(187,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(81,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(406,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)],[81]) ).
thf(101,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(477,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(41,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zero__is__num__zero) ).
thf(251,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(62,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(330,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(96,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(462,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)],[96]) ).
thf(66,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_53_add__Bit0__Bit1) ).
thf(345,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)],[66]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
<=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__int__def) ).
thf(367,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ A )
=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) )
=> ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(32,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bin__less__0__simps_I1_J) ).
thf(223,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(77,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_75_int__distrib_I2_J) ).
thf(394,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)],[77]) ).
thf(10,axiom,
? [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ! [B: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ B @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ B @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1_A_061_As_093_A_Imod_A4_A_K_Am_A_L_A1_J_096) ).
thf(135,plain,
? [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ A @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ! [B: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ B @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
& ( zcong @ s1 @ B @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,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_36_right__distrib__number__of) ).
thf(267,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)],[45]) ).
thf(87,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I44_J) ).
thf(426,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(16,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_41_arith__simps_I32_J) ).
thf(162,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)],[16]) ).
thf(4,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(112,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)],[4]) ).
thf(26,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I5_J) ).
thf(199,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__number__of__int__code) ).
thf(182,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(63,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_83_number__of__add) ).
thf(331,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)],[63]) ).
thf(97,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(463,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)],[97]) ).
thf(8,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(127,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_zless__add1__eq) ).
thf(319,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
=> ( ( ord_less @ int @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ int @ B @ A )
| ( B = A ) )
=> ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(68,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_66_less__eq__int__code_I13_J) ).
thf(351,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)],[68]) ).
thf(18,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_less__special_I3_J) ).
thf(171,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rel__simps_I12_J) ).
thf(119,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_add__Pls) ).
thf(433,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(28,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_31_rel__simps_I31_J) ).
thf(207,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)],[28]) ).
thf(102,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(478,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)],[102]) ).
thf(47,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_9_one__add__one__is__two) ).
thf(272,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)],[47]) ).
thf(36,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_number__of__Pls) ).
thf(235,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Bit0__Pls) ).
thf(246,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(13,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(151,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_rel__simps_I27_J) ).
thf(300,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)],[55]) ).
thf(44,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_rel__simps_I10_J) ).
thf(262,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(56,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__Pls__right) ).
thf(305,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(24,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_p0) ).
thf(195,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(100,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_less__special_I4_J) ).
thf(474,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(79,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_80_add__numeral__0) ).
thf(400,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)],[79]) ).
thf(3,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(111,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(103,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_less__special_I1_J) ).
thf(486,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(65,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(337,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)],[65]) ).
thf(30,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_29_rel__simps_I34_J) ).
thf(215,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)],[30]) ).
thf(71,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_59_mult__Bit1) ).
thf(364,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)],[71]) ).
thf(35,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_94_number__of__Bit0) ).
thf(232,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)],[35]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__number__of) ).
thf(496,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(94,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_88_less__eq__int__code_I14_J) ).
thf(454,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)],[94]) ).
thf(506,plain,
$false,
inference(e,[status(thm)],[384,152,503,409,314,450,459,276,308,379,174,417,436,257,389,110,196,157,492,179,376,253,238,348,397,293,243,248,439,270,220,334,192,275,165,229,361,493,403,356,141,420,499,489,212,328,471,124,225,128,311,412,148,296,444,423,286,291,118,281,204,445,466,187,406,477,251,330,462,345,367,223,394,135,267,426,162,112,199,182,331,463,127,319,351,171,119,433,207,478,272,235,246,151,300,262,305,195,474,400,111,486,337,215,364,232,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM948_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 12:28:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.06 % [INFO] Parsing done (183ms).
% 1.50/1.07 % [INFO] Running in sequential loop mode.
% 2.17/1.34 % [INFO] eprover registered as external prover.
% 2.17/1.35 % [INFO] cvc4 registered as external prover.
% 2.17/1.35 % [INFO] Scanning for conjecture ...
% 2.39/1.45 % [INFO] Found a conjecture and 110 axioms. Running axiom selection ...
% 2.62/1.53 % [INFO] Axiom selection finished. Selected 107 axioms (removed 3 axioms).
% 2.97/1.65 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.97/1.66 % [INFO] Type checking passed.
% 2.97/1.66 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.87/2.62 % External prover 'e' found a proof!
% 5.87/2.62 % [INFO] Killing All external provers ...
% 5.87/2.62 % Time passed: 2086ms (effective reasoning time: 1544ms)
% 5.87/2.62 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.87/2.62 % Axioms used in derivation (107): fact_6_le__special_I4_J, fact_33_mult__Bit0, fact_38_less__number__of, fact_36_right__distrib__number__of, fact_31_rel__simps_I31_J, fact_78_le__number__of__eq__not__less, fact_41_arith__simps_I32_J, fact_5_le__special_I2_J, fact_27_rel__simps_I2_J, fact_1_p0, fact_48_rel__simps_I22_J, arity_Int_Oint___Int_Oring__char__0, fact_72_less__eq__number__of__int__code, arity_Int_Oint___Rings_Olinordered__idom, fact_2_p, fact_19_rel__simps_I46_J, fact_7_less__special_I2_J, fact_42_add__number__of__left, fact_80_add__numeral__0, fact_59_mult__Bit1, fact_74_int__distrib_I1_J, fact_3_add__special_I2_J, fact_53_add__Bit0__Bit1, fact_23_rel__simps_I44_J, fact_10_le__special_I1_J, fact_34_add__Bit0__Bit0, fact_75_int__distrib_I2_J, arity_Int_Oint___Int_Onumber__semiring, fact_64_less__int__code_I13_J, arity_Int_Oint___Int_Onumber__ring, fact_43_add__number__of__eq, fact_44_rel__simps_I12_J, fact_35_left__distrib__number__of, fact_51_rel__simps_I21_J, fact_92_odd__nonzero, fact_94_number__of__Bit0, fact_40_mult__number__of__left, fact_56_rel__simps_I5_J, fact_76_plus__numeral__code_I9_J, fact_66_less__eq__int__code_I13_J, fact_14_zle__add1__eq__le, fact_71_less__number__of__int__code, fact_61_number__of__is__id, fact_69_add__Pls, fact_8_less__special_I4_J, fact_39_le__number__of, fact_9_one__add__one__is__two, fact_85_less__int__code_I15_J, fact_79_semiring__numeral__0__eq__0, fact_22_rel__simps_I49_J, fact_30_rel__simps_I19_J, fact_63_less__int__code_I16_J, arity_Int_Oint___Orderings_Olinorder, fact_11_le__special_I3_J, fact_17_rel__simps_I48_J, fact_49_rel__simps_I32_J, fact_86_bin__less__0__simps_I1_J, fact_87_bin__less__0__simps_I3_J, fact_46_rel__simps_I10_J, fact_12_less__special_I1_J, fact_83_number__of__add, fact_32_mult__Pls, fact_28_rel__simps_I14_J, fact_91_Bit1__def, arity_Int_Oint___Rings_Osemiring, fact_73_times__numeral__code_I5_J, fact_18_double__eq__0__iff, fact_21_rel__simps_I50_J, fact_45_rel__simps_I16_J, fact_4_add__special_I3_J, fact_52_add__Bit1__Bit0, fact_88_less__eq__int__code_I14_J, fact_29_rel__simps_I34_J, fact_70_Bit0__def, fact_62_Pls__def, fact_13_less__special_I3_J, fact_54_numeral__1__eq__1, fact_67_less__int__def, fact_96_mult__numeral__1, fact_24_rel__simps_I38_J, fact_25_Bit0__Pls, fact_95_number__of__Bit1, fact_90_zmult__zless__mono2, fact_81_add__numeral__0__right, fact_68_add__Pls__right, fact_89_zero__is__num__zero, fact_77_even__less__0__iff, fact_58_rel__simps_I15_J, fact_65_less__eq__int__code_I16_J, fact_37_number__of__Pls, fact_55_rel__simps_I29_J, fact_93_zless__add1__eq, fact_47_rel__simps_I4_J, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_60_number__of__reorient, fact_84_bin__less__0__simps_I4_J, fact_97_mult__numeral__1__right, fact_82_number__of__mult, conj_0, fact_26_rel__simps_I17_J, fact_20_rel__simps_I39_J, fact_16_rel__simps_I51_J, fact_50_rel__simps_I27_J, fact_57_rel__simps_I33_J, fact_15_eq__number__of, fact_0__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1_A_061_As_093_A_Imod_A4_A_K_Am_A_L_A1_J_096
% 5.87/2.62 % No. of inferences in proof: 218
% 5.87/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2086 ms resp. 1544 ms w/o parsing
% 6.46/2.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.46/2.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------