%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN017_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:18:32 AM UTC 2026
% Result : Theorem 8.62s 3.64s
% Output : Refutation 9.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 137
% Syntax : Number of formulae : 276 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 642 ( 167 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2883 ( 42 ~; 3 |; 99 &;2475 @)
% ( 55 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 330 ( 0 ^; 330 !; 0 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(n_decl,type,
n: nat ).
thf(v_decl,type,
v: int ).
thf(w_decl,type,
w: int ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_even__less__0__iff) ).
thf(628,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_number__of__reorient) ).
thf(329,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(83,axiom,
( v
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
thf(408,plain,
( v
!= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_power__eq__0__iff__number__of) ).
thf(217,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(138,axiom,
nat @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(655,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(30,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(202,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(105,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I38_J) ).
thf(523,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(117,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Pls__def) ).
thf(582,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__int__code_I16_J) ).
thf(550,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(5,axiom,
real @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(142,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
real @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(153,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__less__power2) ).
thf(174,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(87,axiom,
! [A: int] :
( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_eq__number__of__0) ).
thf(417,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(60,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rel__simps_I21_J) ).
thf(320,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(135,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(651,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(45,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zero__is__num__zero) ).
thf(257,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I31_J) ).
thf(570,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(75,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__simps_I29_J) ).
thf(372,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I49_J) ).
thf(587,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__number__of) ).
thf(344,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(92,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I50_J) ).
thf(460,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(20,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(157,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(131,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__Bit0__Bit0) ).
thf(638,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(86,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(416,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(152,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__number__of__eq) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(53,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I4_J) ).
thf(289,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_power2__less__0) ).
thf(591,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(34,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__eq__int__code_I16_J) ).
thf(211,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(40,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(238,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__number__of__left) ).
thf(348,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10,axiom,
real @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(147,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_power2__less__imp__less) ).
thf(411,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit0 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_number__of__Bit0) ).
thf(248,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit0 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sum__power2__ge__zero) ).
thf(270,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring__norm_I112_J) ).
thf(561,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(82,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_n0) ).
thf(407,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_J) ).
thf(275,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(59,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__Pls) ).
thf(317,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(19,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(156,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(81,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I39_J) ).
thf(403,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(121,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_nat__number__of__Pls) ).
thf(593,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(4,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(141,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(126,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I17_J) ).
thf(610,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(63,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(328,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__eq__0__iff) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_less__special_I3_J) ).
thf(339,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__int__code_I13_J) ).
thf(476,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(133,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__eq__int__code_I13_J) ).
thf(642,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(27,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(193,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I16_J) ).
thf(537,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(78,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(393,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(74,axiom,
int @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(371,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(102,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_rel__simps_I27_J) ).
thf(503,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zero__le__power2) ).
thf(605,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(67,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(343,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_eq__number__of) ).
thf(360,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_power2__eq__imp__eq) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(112,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
thf(558,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(128,axiom,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ zero_zero ) )
<=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_realpow__two__sum__zero__iff) ).
thf(618,plain,
! [A: real,B: real] :
( ( ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ zero_zero ) )
=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(88,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I22_J) ).
thf(425,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I51_J) ).
thf(513,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(11,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(148,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
real @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(149,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(123,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__number__of) ).
thf(601,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(584,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(80,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(402,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__numeral__0__right) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_semiring__numeral__0__eq__0) ).
thf(413,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(132,axiom,
int @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(641,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(7,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(144,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__Bit1__Bit0) ).
thf(498,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__int__code_I15_J) ).
thf(181,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__eq__number__of__int__code) ).
thf(187,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,axiom,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0960_A_060_Av_A_094_A2_096) ).
thf(274,plain,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(103,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I46_J) ).
thf(509,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(127,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Bit0__Pls) ).
thf(616,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I33_J) ).
thf(387,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(72,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I19_J) ).
thf(367,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3,axiom,
real @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(140,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I32_J) ).
thf(251,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(155,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__number__of__eq__not__less) ).
thf(198,plain,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__nat__number__of) ).
thf(278,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(79,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I44_J) ).
thf(394,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(36,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(226,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I48_J) ).
thf(431,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(137,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I2_J) ).
thf(653,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I14_J) ).
thf(162,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(106,axiom,
! [A: int] :
( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__0__number__of) ).
thf(531,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(134,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Bit0__def) ).
thf(648,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(33,axiom,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096v_A_094_A2_A_L_Aw_A_094_A2_A_061_A0_096) ).
thf(209,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_le__special_I3_J) ).
thf(194,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
real @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(145,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_sum__power2__eq__zero__iff) ).
thf(295,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(13,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(150,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(62,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(327,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__nat__number__of) ).
thf(441,plain,
! [A: int,B: int] :
( ( ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(101,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(502,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(109,axiom,
! [A: int] :
( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_bin__less__0__simps_I3_J) ).
thf(544,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__int__code_I14_J) ).
thf(470,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(116,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I34_J) ).
thf(576,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(17,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(154,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int,B: int] :
( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_semiring__add__number__of) ).
thf(314,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int,B: int] :
( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(122,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rel__simps_I12_J) ).
thf(595,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(6,axiom,
real @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(143,plain,
real @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__eq__power2) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__int__def) ).
thf(450,plain,
! [A: int,B: int] :
( ( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(111,axiom,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bin__less__0__simps_I1_J) ).
thf(556,plain,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__add) ).
thf(495,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(73,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__Pls__right) ).
thf(368,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(96,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I5_J) ).
thf(482,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_less__special_I1_J) ).
thf(203,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(304,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(130,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__number__of__int__code) ).
thf(632,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1,conjecture,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(139,plain,
~ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le__special_I1_J) ).
thf(158,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(136,axiom,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0960_A_060_061_Aw_A_094_A2_096) ).
thf(652,plain,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
thf(351,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__power2__le__zero__iff) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_power2__le__imp__le) ).
thf(207,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(49,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_semiring__norm_I113_J) ).
thf(272,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14,axiom,
real @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(151,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(146,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I10_J) ).
thf(168,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(47,axiom,
! [A: int] :
( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_eq__0__number__of) ).
thf(262,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) ) )
& ( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(114,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__eq__int__code_I14_J) ).
thf(564,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
! [A: int] :
( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_bin__less__0__simps_I4_J) ).
thf(305,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
int @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(326,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__numeral__0) ).
thf(239,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__eq__int__code_I15_J) ).
thf(242,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I15_J) ).
thf(464,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(100,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(501,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_number__of__Pls) ).
thf(607,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(37,axiom,
nat @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(227,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__sum__power2__lt__zero) ).
thf(337,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(108,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(543,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(656,plain,
$false,
inference(e,[status(thm)],[628,329,408,217,655,202,523,582,550,142,153,174,417,320,651,257,570,372,587,344,460,157,638,416,152,228,289,591,211,238,348,147,411,248,270,561,407,275,317,156,403,593,141,610,328,488,339,476,642,193,537,393,371,503,605,343,360,311,558,618,425,513,148,149,601,584,402,259,413,641,144,498,181,187,274,509,616,387,367,140,251,155,198,278,394,226,431,653,162,531,648,209,194,145,295,150,327,441,502,544,470,576,154,314,595,143,231,450,556,495,368,482,203,304,632,139,158,652,351,378,207,272,151,146,168,262,564,305,326,239,242,464,501,607,227,337,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN017_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n020.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 04:27:04 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.28 % [INFO] Parsing done (273ms).
% 1.34/1.30 % [INFO] Running in sequential loop mode.
% 2.42/1.69 % [INFO] eprover registered as external prover.
% 2.61/1.70 % [INFO] Scanning for conjecture ...
% 2.79/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 138 axioms. Running axiom selection ...
% 2.97/1.96 % [INFO] Axiom selection finished. Selected 136 axioms (removed 2 axioms).
% 3.35/2.11 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.35/2.13 % [INFO] Type checking passed.
% 3.63/2.13 % [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 ...
% 8.62/3.63 % External prover 'e' found a proof!
% 8.62/3.64 % [INFO] Killing All external provers ...
% 8.62/3.64 % Time passed: 3071ms (effective reasoning time: 2334ms)
% 8.62/3.64 % 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)>
% 8.62/3.64 % Axioms used in derivation (136): fact_61_semiring__norm_I113_J, fact_39_add__number__of__left, fact_6_zero__eq__power2, fact_79_semiring__norm_I112_J, fact_54_add__nat__number__of, fact_11_add__Bit0__Bit1, fact_13_rel__simps_I4_J, fact_35_add__Bit0__Bit0, fact_46_less__0__number__of, arity_Int_Oint___Rings_Olinordered__idom, fact_43_rel__simps_I32_J, arity_Nat_Onat___Rings_Osemiring__1, fact_93_number__of__Bit0, arity_Int_Oint___Int_Oring__char__0, fact_69_less__int__code_I14_J, fact_86_bin__less__0__simps_I3_J, fact_27_Bit0__Pls, fact_63_less__eq__int__code_I13_J, fact_31_rel__simps_I34_J, fact_36_number__of__Pls, fact_68_less__eq__int__code_I15_J, fact_38_le__number__of, fact_62_less__eq__int__code_I16_J, fact_80_add__numeral__0, fact_45_rel__simps_I21_J, arity_RealDef_Oreal___Int_Onumber__semiring, fact_34_rel__simps_I31_J, arity_Nat_Onat___Int_Onumber__semiring, fact_22_rel__simps_I39_J, arity_Nat_Onat___Power_Opower, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_66_le__number__of__eq__not__less, fact_32_nat__number__of__Pls, fact_65_number__of__reorient, fact_15_rel__simps_I16_J, fact_74_add__Pls, fact_1__0960_A_060_Av_A_094_A2_096, fact_64_less__int__def, fact_2__0960_A_060_061_Aw_A_094_A2_096, fact_78_semiring__numeral__0__eq__0, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Onumber__ring, fact_42_rel__simps_I22_J, fact_95_sum__power2__eq__zero__iff, arity_HOL_Obool___Orderings_Olinorder, fact_59_plus__numeral__code_I9_J, fact_16_n0, arity_Int_Oint___Rings_Osemiring__1, arity_Nat_Onat___Rings_Omult__zero, fact_33_rel__simps_I19_J, fact_28_rel__simps_I17_J, fact_90_power2__less__imp__less, fact_57_less__eq__number__of__int__code, fact_40_add__number__of__eq, fact_12_add__Bit1__Bit0, fact_47_less__nat__number__of, arity_Nat_Onat___Orderings_Olinorder, fact_75_Bit0__def, fact_24_rel__simps_I49_J, arity_RealDef_Oreal___Rings_Osemiring__1, fact_18_rel__simps_I51_J, fact_3__096v_A_094_A2_A_L_Aw_A_094_A2_A_061_A0_096, fact_96_realpow__two__sum__zero__iff, arity_RealDef_Oreal___Int_Onumber__ring, fact_29_rel__simps_I2_J, fact_21_rel__simps_I46_J, fact_94_power2__less__0, fact_92_sum__power2__ge__zero, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_70_Pls__def, arity_Int_Oint___Orderings_Olinorder, fact_23_rel__simps_I50_J, arity_Nat_Onat___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_73_add__Pls__right, fact_72_less__int__code_I13_J, fact_10_sum__power2__gt__zero__iff, fact_60_zero__is__num__zero, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Int_Oring__char__0, fact_88_power2__le__imp__le, fact_76_semiring__add__number__of, fact_51_rel__simps_I5_J, fact_53_rel__simps_I15_J, fact_85_bin__less__0__simps_I1_J, fact_0__096v_A_126_061_A0_096, fact_52_rel__simps_I33_J, arity_RealDef_Oreal___Rings_Ono__zero__divisors, fact_49_eq__0__number__of, arity_Int_Oint___Power_Opower, fact_91_sum__power2__le__zero__iff, fact_25_rel__simps_I44_J, fact_67_less__eq__int__code_I14_J, fact_58_less__number__of__int__code, arity_RealDef_Oreal___Orderings_Olinorder, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, fact_56_le__special_I1_J, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_37_less__number__of, fact_44_rel__simps_I27_J, fact_82_number__of__add, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_7_less__special_I1_J, fact_5_zero__power2, fact_20_double__eq__0__iff, arity_Int_Oint___Rings_Ozero__neq__one, fact_9_not__sum__power2__lt__zero, fact_4_zero__less__power2, fact_8_less__special_I3_J, fact_83_less__int__code_I15_J, fact_26_rel__simps_I38_J, fact_97_power__eq__0__iff__number__of, fact_14_rel__simps_I10_J, fact_71_less__int__code_I16_J, fact_77_even__less__0__iff, fact_50_rel__simps_I29_J, fact_81_add__numeral__0__right, arity_RealDef_Oreal___Power_Opower, fact_17_eq__number__of, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Int_Onumber, fact_87_power2__eq__imp__eq, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_19_rel__simps_I48_J, fact_84_bin__less__0__simps_I4_J, fact_55_le__special_I3_J, arity_Int_Oint___Rings_Omult__zero, fact_89_zero__le__power2, fact_30_rel__simps_I14_J, arity_Int_Oint___Rings_Olinordered__semidom, fact_48_eq__number__of__0, arity_Nat_Onat___Rings_Ozero__neq__one, fact_41_rel__simps_I12_J
% 8.62/3.64 % No. of inferences in proof: 276
% 8.62/3.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3071 ms resp. 2334 ms w/o parsing
% 9.21/3.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.21/3.77 % [INFO] Killing All external provers ...
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