%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM994_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 : n001.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 08:10:36 AM UTC 2026
% Result : Theorem 7.74s 3.69s
% Output : Refutation 8.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 127
% Syntax : Number of formulae : 256 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 670 ( 176 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2661 ( 21 ~; 28 |; 77 &;2226 @)
% ( 36 <=>; 273 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 6 con; 0-3 aty)
% Number of variables : 398 ( 0 ^; 398 !; 0 ?; 398 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[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(ordered_ring_decl,type,
ordered_ring:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_ring_decl,type,
linordered_ring:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(ordered_ring_abs_decl,type,
ordered_ring_abs:
!>[TA: $tType] : $o ).
thf(ordered_semiring_decl,type,
ordered_semiring:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ordere1490568538miring_decl,type,
ordere1490568538miring:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(ordere453448008miring_decl,type,
ordere453448008miring:
!>[TA: $tType] : $o ).
thf(ordere142940540dd_abs_decl,type,
ordere142940540dd_abs:
!>[TA: $tType] : $o ).
thf(abs_abs_decl,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[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_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(v_decl,type,
v: int ).
thf(w_decl,type,
w: int ).
thf(94,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(476,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_arith__simps_I32_J) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(41,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_le0) ).
thf(249,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mult__right__mono__neg) ).
thf(518,plain,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(120,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(555,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(67,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I50_J) ).
thf(352,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ ordered_ring_abs )
=> ! [A: TA,B: TA] :
( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
| ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_abs__eq__mult) ).
thf(365,plain,
! [TA: $tType] :
( ( TA @ ordered_ring_abs )
=> ! [A: TA,B: TA] :
( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
| ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(10,axiom,
nat @ ordered_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).
thf(138,plain,
nat @ ordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,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_1_le__special_I3_J) ).
thf(217,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)],[34]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ abs_abs ) @ ( TA @ ord_less_eq ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_abs__le__zero__iff) ).
thf(449,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ abs_abs ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ abs_abs ) @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(114,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_40_less__eq__number__of__int__code) ).
thf(533,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)],[114]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_mult__numeral__1__right) ).
thf(550,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(13,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(142,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_semiring__norm_I112_J) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(18,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(153,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,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_4_rel__simps_I32_J) ).
thf(174,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)],[24]) ).
thf(59,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__norm_I113_J) ).
thf(320,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mult__Bit0) ).
thf(389,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_number__of__is__id) ).
thf(184,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ ordere1490568538miring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__mult__left__mono) ).
thf(504,plain,
! [TA: $tType] :
( ( TA @ ordere1490568538miring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(128,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(587,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zero__le__mult__iff) ).
thf(344,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I48_J) ).
thf(189,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)],[29]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zero__reorient) ).
thf(421,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(93,axiom,
int @ ordere453448008miring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).
thf(475,plain,
int @ ordere453448008miring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA] : ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zero__le__square) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA] : ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(98,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_37_less__eq__int__code_I16_J) ).
thf(485,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)],[98]) ).
thf(38,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_53_eq__number__of__0) ).
thf(238,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)],[38]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_no__zero__divisors) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_le__0__eq) ).
thf(221,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(52,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 @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_semiring__mult__number__of) ).
thf(293,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 @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
nat @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(132,plain,
nat @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
nat @ ordere453448008miring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
thf(133,plain,
nat @ ordere453448008miring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA] :
( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_split__mult__pos__le) ).
thf(411,plain,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA] :
( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(45,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_rel__simps_I21_J) ).
thf(265,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)],[45]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mult__is__0) ).
thf(206,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
thf(307,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(40,axiom,
int @ ordere142940540dd_abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
thf(248,plain,
int @ ordere142940540dd_abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(108,axiom,
int @ linordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(512,plain,
int @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( A @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_number__of1) ).
thf(160,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( A @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
int @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(392,plain,
int @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(84,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(429,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__left__mono) ).
thf(275,plain,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(9,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(137,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(113,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
<=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_conj__le__cong) ).
thf(522,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) )
& ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mult__zero__left) ).
thf(493,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(88,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_mult__0__right) ).
thf(456,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mult__le__0__iff) ).
thf(229,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(97,axiom,
pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(484,plain,
pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( ( A @ ( TA @ abs_abs ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_abs__eq__0) ).
thf(578,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ abs_abs ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ abs_abs ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_mult__number__of__left) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(20,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I39_J) ).
thf(156,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(68,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_46_less__eq__int__code_I14_J) ).
thf(356,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)],[68]) ).
thf(12,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(141,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ times_times ) ) @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__left__mono__neg) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ times_times ) ) @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1,conjecture,
( ( w @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( v @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( w @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( v @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(129,plain,
~ ( ( w @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( v @ ( int @ abs_abs ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(134,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
int @ ordered_ring_abs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring__abs) ).
thf(237,plain,
int @ ordered_ring_abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(205,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
int @ linord581940658strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(508,plain,
int @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ( ( TA @ zero_zero @ ( TA @ abs_abs ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_abs__zero) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ( ( TA @ zero_zero @ ( TA @ abs_abs ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mult__right__mono) ).
thf(558,plain,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(23,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).
thf(166,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_abs__mult__self) ).
thf(279,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__mult) ).
thf(375,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_split__mult__neg__le) ).
thf(513,plain,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(85,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I38_J) ).
thf(430,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(25,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(180,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I51_J) ).
thf(296,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)],[53]) ).
thf(73,axiom,
int @ ordered_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__semiring) ).
thf(382,plain,
int @ ordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(125,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_rel__simps_I22_J) ).
thf(572,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)],[125]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_abs__mult__pos) ).
thf(498,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(64,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_12_eq__number__of) ).
thf(335,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)],[64]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_abs__idempotent) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,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_8_le__number__of) ).
thf(540,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)],[116]) ).
thf(28,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__is__num__zero) ).
thf(187,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_abs__mult) ).
thf(362,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(107,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_mult__0) ).
thf(509,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] : ( A @ ( TA @ abs_abs ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_abs__ge__zero) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] : ( A @ ( TA @ abs_abs ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(95,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_27_rel__simps_I31_J) ).
thf(477,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)],[95]) ).
thf(61,axiom,
! [A: int,B: int] :
( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
<=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_le__nat__number__of) ).
thf(323,plain,
! [A: int,B: int] :
( ( ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(96,axiom,
int @ ordere1490568538miring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__comm__semiring) ).
thf(483,plain,
int @ ordere1490568538miring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__nonneg__nonpos) ).
thf(520,plain,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(42,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_32_number__of__reorient) ).
thf(251,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)],[42]) ).
thf(90,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_54_eq__0__number__of) ).
thf(462,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)],[90]) ).
thf(54,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(306,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(135,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
<=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_imp__le__cong) ).
thf(438,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) ) )
& ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(65,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__eq__nat_Osimps_I1_J) ).
thf(342,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(119,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Pls__def) ).
thf(553,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mult__cancel2) ).
thf(282,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mult__numeral__1) ).
thf(150,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,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_0_le__special_I1_J) ).
thf(199,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)],[30]) ).
thf(62,axiom,
int @ ring_n68954251visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(331,plain,
int @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult__mono) ).
thf(585,plain,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(91,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Bit0__Pls) ).
thf(470,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(117,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_25_rel__simps_I34_J) ).
thf(544,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)],[117]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( D @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mult__mono_H) ).
thf(154,plain,
! [TA: $tType] :
( ( TA @ ordered_semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( D @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(57,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mult__Pls) ).
thf(314,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(124,axiom,
int @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(571,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_divisors__zero) ).
thf(143,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(121,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(556,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ times_times ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(115,axiom,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_number__of2) ).
thf(539,plain,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult__nonneg__nonpos2) ).
thf(203,plain,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(110,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I19_J) ).
thf(517,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mult__eq__0__iff) ).
thf(401,plain,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(139,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ abs_abs ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_abs__of__nonneg) ).
thf(418,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ abs_abs ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(378,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__nonpos__nonneg) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(74,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_rel__simps_I27_J) ).
thf(383,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)],[74]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mult__zero__right) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(15,axiom,
int @ ordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring) ).
thf(146,plain,
int @ ordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mult__nonpos__nonpos) ).
thf(273,plain,
! [TA: $tType] :
( ( TA @ ordered_ring )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(8,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(136,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(105,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__number__of__Pls) ).
thf(506,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(415,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(78,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_38_less__eq__int__code_I13_J) ).
thf(395,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)],[78]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_number__of__Pls) ).
thf(332,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_semiring__numeral__0__eq__0) ).
thf(459,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(3,axiom,
nat @ ordere1490568538miring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).
thf(131,plain,
nat @ ordere1490568538miring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] : ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_abs__ge__self) ).
thf(277,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA] : ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_times__numeral__code_I5_J) ).
thf(501,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(60,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(322,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
<=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__cancel1) ).
thf(560,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mult__nonneg__nonneg) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ ordere453448008miring )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ abs_abs ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_abs__le__D1) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ ordere142940540dd_abs )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ abs_abs ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(592,plain,
$false,
inference(e,[status(thm)],[476,259,249,518,555,352,365,138,217,449,533,550,142,472,153,174,320,389,184,504,587,344,189,421,475,164,485,238,147,221,293,132,133,411,265,206,307,248,512,160,392,429,275,137,522,493,456,229,484,578,317,156,356,141,393,129,134,237,205,508,311,558,166,279,375,513,430,180,296,382,572,498,335,181,540,187,362,509,271,477,323,483,520,251,462,306,135,438,342,553,282,150,199,331,585,470,544,154,314,571,143,556,539,203,517,401,139,418,378,246,383,262,146,273,136,506,415,395,332,459,131,277,501,322,560,491,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM994_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
% 0.15/0.40 % Computer : n001.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 04:30:42 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.29 % [INFO] Parsing done (291ms).
% 1.84/1.30 % [INFO] Running in sequential loop mode.
% 2.54/1.69 % [INFO] eprover registered as external prover.
% 2.54/1.70 % [INFO] Scanning for conjecture ...
% 2.92/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 126 axioms. Running axiom selection ...
% 3.10/1.96 % [INFO] Axiom selection finished. Selected 126 axioms (removed 0 axioms).
% 3.66/2.15 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.66/2.17 % [INFO] Type checking passed.
% 3.66/2.17 % [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 ...
% 7.74/3.68 % External prover 'e' found a proof!
% 7.74/3.68 % [INFO] Killing All external provers ...
% 7.74/3.68 % Time passed: 3133ms (effective reasoning time: 2375ms)
% 7.74/3.69 % 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)>
% 7.74/3.69 % Axioms used in derivation (126): fact_10_number__of__Pls, fact_61_nat__number__of__Pls, fact_0_le__special_I1_J, fact_56_abs__mult__self, fact_65_abs__mult, arity_Int_Oint___Rings_Oordered__semiring, fact_41_times__numeral__code_I5_J, fact_42_semiring__numeral__0__eq__0, arity_Nat_Onat___Groups_Oab__semigroup__mult, fact_68_zero__le__square, fact_16_abs__eq__0, arity_Int_Oint___Rings_Olinordered__ring__strict, arity_Nat_Onat___Rings_Oordered__semiring, fact_5_rel__simps_I22_J, fact_35_abs__ge__self, arity_Int_Oint___Rings_Oordered__cancel__semiring, arity_Int_Oint___Rings_Olinordered__idom, fact_66_conj__le__cong, fact_15_abs__idempotent, fact_4_rel__simps_I32_J, fact_91_le__0__eq, arity_Int_Oint___Int_Oring__char__0, arity_Int_Oint___Rings_Olinordered__ring, fact_54_eq__0__number__of, fact_34_abs__le__D1, fact_39_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_72_mult__nonneg__nonpos, fact_96_mult__0, fact_32_number__of__reorient, fact_48_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, arity_Nat_Onat___Int_Onumber__semiring, fact_46_less__eq__int__code_I14_J, arity_Int_Oint___Rings_Oordered__ring, arity_Nat_Onat___Rings_Oordered__comm__semiring, fact_93_mult__cancel1, fact_52_le__nat__number__of, fact_60_mult__zero__left, fact_82_mult__mono, fact_11_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_86_abs__mult__pos, arity_Int_Oint___Rings_Ono__zero__divisors, fact_81_mult__mono_H, fact_88_number__of2, arity_Int_Oint___Groups_Oordered__ab__group__add__abs, fact_17_abs__zero, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Onumber__ring, fact_1_le__special_I3_J, fact_30_zero__reorient, fact_70_mult__le__0__iff, arity_Nat_Onat___Rings_Omult__zero, fact_6_arith__simps_I32_J, fact_95_mult__0__right, fact_26_rel__simps_I19_J, fact_80_mult__left__mono__neg, fact_64_divisors__zero, fact_89_le0, fact_2_rel__simps_I21_J, fact_50_mult__numeral__1__right, fact_22_rel__simps_I44_J, fact_37_less__eq__int__code_I16_J, fact_90_less__eq__nat_Osimps_I1_J, fact_28_mult__Pls, fact_3_rel__simps_I27_J, fact_58_mult__eq__0__iff, fact_73_mult__nonneg__nonpos2, fact_87_abs__eq__mult, arity_Int_Oint___Rings_Oring__no__zero__divisors, fact_7_mult__number__of__left, fact_29_mult__Bit0, fact_67_imp__le__cong, fact_27_rel__simps_I31_J, fact_24_Bit0__Pls, arity_Nat_Onat___Rings_Oordered__cancel__semiring, fact_51_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, arity_Nat_Onat___Groups_Ozero, fact_76_mult__right__mono, fact_69_zero__le__mult__iff, fact_75_mult__nonpos__nonpos, fact_19_rel__simps_I39_J, fact_44_abs__ge__zero, fact_13_rel__simps_I51_J, fact_12_eq__number__of, arity_Int_Oint___Rings_Oordered__comm__semiring, fact_23_rel__simps_I38_J, fact_21_rel__simps_I49_J, fact_78_comm__mult__left__mono, arity_Int_Oint___Rings_Oordered__ring__abs, fact_77_mult__left__mono, arity_Nat_Onat___Int_Onumber, fact_79_mult__right__mono__neg, fact_14_rel__simps_I48_J, fact_74_mult__nonpos__nonneg, fact_9_abs__le__zero__iff, fact_36_Pls__def, fact_53_eq__number__of__0, fact_43_abs__of__nonneg, fact_83_split__mult__pos__le, fact_31_ab__semigroup__mult__class_Omult__ac_I1_J, fact_47_zero__is__num__zero, fact_57_semiring__mult__number__of, fact_84_split__mult__neg__le, fact_94_mult__is__0, help_pp_1_1_U, fact_20_rel__simps_I50_J, fact_25_rel__simps_I34_J, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_45_number__of__mult, fact_33_number__of__is__id, fact_63_no__zero__divisors, fact_92_mult__cancel2, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, fact_49_mult__numeral__1, fact_85_semiring__norm_I112_J, help_pp_2_1_U, fact_38_less__eq__int__code_I13_J, fact_71_mult__nonneg__nonneg, fact_8_le__number__of, fact_59_mult__zero__right, fact_18_rel__simps_I46_J, fact_62_semiring__norm_I113_J, fact_55_number__of1, fact_40_less__eq__number__of__int__code
% 7.74/3.69 % No. of inferences in proof: 256
% 7.74/3.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3133 ms resp. 2375 ms w/o parsing
% 8.63/3.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.63/3.83 % [INFO] Killing All external provers ...
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