%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM932_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 : n006.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 08:10:29 AM UTC 2026
% Result : Theorem 9.38s 3.82s
% Output : Refutation 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 115
% Syntax : Number of formulae : 232 ( 110 unt; 0 typ; 0 def)
% Number of atoms : 473 ( 182 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2216 ( 21 ~; 0 |; 50 &;1954 @)
% ( 32 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 3 con; 0-3 aty)
% Number of variables : 328 ( 0 ^; 328 !; 0 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[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(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > 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(zprime_decl,type,
zprime: int > $o ).
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(m_decl,type,
m: int ).
thf(91,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_67_mult__numeral__1) ).
thf(404,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)],[91]) ).
thf(47,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_15_eq__number__of) ).
thf(249,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)],[47]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mult__2__right) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(55,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(276,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(67,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_42_le__special_I1_J) ).
thf(308,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)],[67]) ).
thf(5,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(120,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult__2) ).
thf(269,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(15,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_int__distrib_I2_J) ).
thf(142,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_left__distrib__number__of) ).
thf(153,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(125,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(79,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_83_number__of1) ).
thf(357,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)],[79]) ).
thf(59,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Bit1__def) ).
thf(284,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(18,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I19_J) ).
thf(152,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_semiring__numeral__1__eq__1) ).
thf(216,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(121,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,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_44_number__of__reorient) ).
thf(221,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)],[40]) ).
thf(103,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I39_J) ).
thf(453,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(89,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_35_le__number__of) ).
thf(396,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)],[89]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_number__of__Bit1) ).
thf(411,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(44,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Bit0__Pls) ).
thf(243,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(96,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_50_less__eq__int__code_I16_J) ).
thf(428,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)],[96]) ).
thf(51,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(265,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(68,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_11_add__Bit1__Bit0) ).
thf(312,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)],[68]) ).
thf(42,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(233,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)],[42]) ).
thf(1,conjecture,
int @ one_one @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ one_one @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ( int @ one_one @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(84,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I27_J) ).
thf(381,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)],[84]) ).
thf(39,axiom,
int @ zero_zero @ ( m @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096m_A_060_061_A0_096) ).
thf(220,plain,
int @ zero_zero @ ( m @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(74,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_84_le__nat__number__of) ).
thf(334,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)],[74]) ).
thf(22,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__is__num__zero) ).
thf(160,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_semiring__numeral__0__eq__0) ).
thf(297,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_le__special_I4_J) ).
thf(407,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_add__special_I2_J) ).
thf(137,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,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_55_less__eq__number__of__int__code) ).
thf(165,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)],[24]) ).
thf(31,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_int__distrib_I1_J) ).
thf(197,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(80,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(361,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_add__special_I3_J) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zero__le__double__add__iff__zero__le__single__add) ).
thf(229,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__right__cancel) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(20,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__is__id) ).
thf(156,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__left__cancel) ).
thf(188,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_right__distrib__number__of) ).
thf(256,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(9,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(124,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I50_J) ).
thf(212,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(88,axiom,
! [A: int] :
( ( A @ zprime )
=> ( ( A
!= ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) ) )
=> ( ( A
!= ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) ) )
=> ( A @ ( pls @ bit1 @ bit0 @ bit1 @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_prime__g__5) ).
thf(393,plain,
! [A: int] :
( ( A @ zprime )
=> ( ( A
!= ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) ) )
=> ( ( A
!= ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) ) )
=> ( A @ ( pls @ bit1 @ bit0 @ bit1 @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,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_28_rel__simps_I31_J) ).
thf(457,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)],[104]) ).
thf(12,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I38_J) ).
thf(129,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I51_J) ).
thf(371,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)],[83]) ).
thf(52,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_49_number__of__Bit0) ).
thf(266,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)],[52]) ).
thf(116,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_64_less__eq__int__code_I14_J) ).
thf(508,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)],[116]) ).
thf(3,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(118,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nat__mult__2__right) ).
thf(281,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,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_31_add__Bit0__Bit0) ).
thf(259,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)],[49]) ).
thf(87,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat__1__add__1) ).
thf(391,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(99,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_nat__numeral__1__eq__1) ).
thf(445,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I48_J) ).
thf(498,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)],[115]) ).
thf(106,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Bit0__def) ).
thf(466,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(43,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_18_double__eq__0__iff) ).
thf(236,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)],[43]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_double__zero__sym) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(77,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_41_le__special_I3_J) ).
thf(350,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)],[77]) ).
thf(21,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(159,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__Pls__right) ).
thf(172,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(219,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(245,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_rel__simps_I21_J) ).
thf(318,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)],[70]) ).
thf(97,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_30_mult__Bit0) ).
thf(434,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)],[97]) ).
thf(65,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_mult__Pls) ).
thf(303,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(81,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_51_less__eq__int__code_I13_J) ).
thf(362,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)],[81]) ).
thf(102,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Pls__def) ).
thf(451,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__Pls) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(113,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_38_add__number__of__left) ).
thf(494,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)],[113]) ).
thf(14,axiom,
~ ( m @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096_126_A1_A_060_061_Am_096) ).
thf(140,plain,
~ ( m @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,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_63_number__of__add) ).
thf(278,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)],[57]) ).
thf(66,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_one__is__num__one) ).
thf(306,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_one__add__one__is__two) ).
thf(162,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_numeral__1__eq__1) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(16,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(145,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__le__cancel__right) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(8,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(123,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(94,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_92_eq__number__of__0) ).
thf(414,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)],[94]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_double__add__le__zero__iff__single__add__le__zero) ).
thf(327,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_mult__Bit1) ).
thf(331,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(105,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_36_mult__number__of__left) ).
thf(463,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)],[105]) ).
thf(108,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_91_eq__0__number__of) ).
thf(470,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)],[108]) ).
thf(27,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_rel__simps_I22_J) ).
thf(175,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)],[27]) ).
thf(114,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(497,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(101,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(450,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__le__cancel__left) ).
thf(203,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(82,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_56_times__numeral__code_I5_J) ).
thf(368,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)],[82]) ).
thf(86,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zprime__2) ).
thf(390,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(25,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(171,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_double__number__of__Bit0) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat__number__of__Pls) ).
thf(207,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(109,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_62_number__of__mult) ).
thf(478,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)],[109]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I49_J) ).
thf(272,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(76,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I46_J) ).
thf(346,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(60,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_37_arith__simps_I32_J) ).
thf(287,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)],[60]) ).
thf(61,axiom,
! [A: int] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_odd__nonzero) ).
thf(290,plain,
! [A: int] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(4,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(119,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,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_10_add__Bit0__Bit1) ).
thf(300,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)],[64]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_semiring__mult__2) ).
thf(447,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(69,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_68_mult__numeral__1__right) ).
thf(315,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)],[69]) ).
thf(50,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__Pls) ).
thf(262,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,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_14_rel__simps_I32_J) ).
thf(146,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)],[17]) ).
thf(95,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_26_rel__simps_I34_J) ).
thf(422,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)],[95]) ).
thf(30,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_semiring__norm_I113_J) ).
thf(195,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(98,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I44_J) ).
thf(437,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_le__special_I2_J) ).
thf(400,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(62,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_61_add__numeral__0__right) ).
thf(294,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)],[62]) ).
thf(11,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_60_add__numeral__0) ).
thf(126,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)],[11]) ).
thf(32,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_39_add__number__of__eq) ).
thf(200,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)],[32]) ).
thf(56,axiom,
int @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(277,plain,
int @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(122,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(107,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_p) ).
thf(469,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_semiring__one__add__one__is__two) ).
thf(354,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring__mult__2__right) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(568,plain,
$false,
inference(e,[status(thm)],[404,249,481,276,308,120,269,142,153,125,357,284,152,216,121,221,453,396,411,243,428,265,312,233,117,381,220,334,160,297,407,137,165,197,361,324,229,484,156,188,256,124,212,393,457,129,371,266,508,118,281,259,391,445,498,466,236,181,350,159,172,219,245,318,434,303,362,451,387,494,140,278,306,162,209,145,342,123,414,327,331,463,470,175,497,450,203,368,390,171,246,207,478,272,346,287,290,119,300,447,315,262,146,422,195,437,400,294,126,200,277,122,469,354,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM932_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 04:21:10 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 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
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.24 % [INFO] Parsing done (248ms).
% 1.45/1.25 % [INFO] Running in sequential loop mode.
% 2.38/1.64 % [INFO] eprover registered as external prover.
% 2.38/1.65 % [INFO] Scanning for conjecture ...
% 2.55/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 2.75/1.89 % [INFO] Axiom selection finished. Selected 114 axioms (removed 2 axioms).
% 3.35/2.04 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.35/2.05 % [INFO] Type checking passed.
% 3.35/2.06 % [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 ...
% 9.38/3.82 % External prover 'e' found a proof!
% 9.38/3.82 % [INFO] Killing All external provers ...
% 9.38/3.82 % Time passed: 3267ms (effective reasoning time: 2561ms)
% 9.38/3.82 % 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)>
% 9.38/3.82 % Axioms used in derivation (114): fact_22_rel__simps_I49_J, fact_26_rel__simps_I34_J, arity_Int_Oint___Groups_Oone, fact_5_le__special_I2_J, fact_51_less__eq__int__code_I13_J, fact_75_mult__2__right, fact_48_odd__nonzero, fact_73_mult__2, arity_Int_Oint___Rings_Olinordered__idom, fact_0__096m_A_060_061_A0_096, fact_13_rel__simps_I27_J, arity_Int_Oint___Int_Oring__char__0, fact_14_rel__simps_I32_J, fact_31_add__Bit0__Bit0, fact_63_number__of__add, fact_6_le__special_I4_J, fact_69_semiring__numeral__1__eq__1, fact_89_add__le__cancel__left, fact_2_p, fact_19_rel__simps_I46_J, arity_Nat_Onat___Int_Onumber__semiring, fact_27_rel__simps_I19_J, fact_67_mult__numeral__1, fact_85_add__left__cancel, fact_3_add__special_I2_J, fact_92_eq__number__of__0, fact_23_rel__simps_I44_J, fact_71_double__number__of__Bit0, fact_33_right__distrib__number__of, fact_28_rel__simps_I31_J, fact_1__096_126_A1_A_060_061_Am_096, fact_82_zprime__2, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_38_add__number__of__left, arity_Int_Oint___Int_Onumber__semiring, fact_65_Bit1__def, fact_78_double__add__le__zero__iff__single__add__le__zero, arity_Int_Oint___Int_Onumber__ring, fact_59_plus__numeral__code_I9_J, fact_66_number__of__Bit1, fact_57_int__distrib_I1_J, fact_62_number__of__mult, fact_9_numeral__1__eq__1, fact_52_add__Pls__right, fact_36_mult__number__of__left, fact_91_eq__0__number__of, fact_50_less__eq__int__code_I16_J, fact_54_Bit0__def, fact_41_le__special_I3_J, fact_70_one__is__num__one, fact_76_semiring__one__add__one__is__two, fact_88_add__le__cancel__right, fact_60_add__numeral__0, fact_68_mult__numeral__1__right, fact_35_le__number__of, fact_93_nat__numeral__1__eq__1, fact_7_one__add__one__is__two, fact_8_mult__Bit1, fact_77_nat__1__add__1, fact_17_rel__simps_I48_J, fact_74_semiring__mult__2__right, fact_42_le__special_I1_J, arity_Int_Oint___Rings_Osemiring, fact_44_number__of__reorient, fact_61_add__numeral__0__right, fact_56_times__numeral__code_I5_J, fact_18_double__eq__0__iff, arity_Nat_Onat___Groups_Ozero, fact_21_rel__simps_I50_J, fact_53_add__Pls, fact_4_add__special_I3_J, fact_49_number__of__Bit0, fact_94_semiring__norm_I113_J, fact_11_add__Bit1__Bit0, fact_72_semiring__mult__2, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_29_mult__Pls, fact_86_add__right__cancel, arity_Nat_Onat___Int_Onumber, fact_84_le__nat__number__of, fact_34_number__of__Pls, fact_37_arith__simps_I32_J, fact_58_int__distrib_I2_J, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_30_mult__Bit0, fact_95_nat__mult__2__right, fact_24_rel__simps_I38_J, arity_Nat_Onat___Groups_Oone, fact_32_left__distrib__number__of, fact_47_zero__is__num__zero, fact_25_Bit0__Pls, fact_40_rel__simps_I22_J, fact_39_add__number__of__eq, fact_83_number__of1, arity_Nat_Onat___Rings_Osemiring, fact_64_less__eq__int__code_I14_J, fact_46_semiring__numeral__0__eq__0, fact_81_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_90_nat__number__of__Pls, fact_43_Pls__def, fact_55_less__eq__number__of__int__code, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_45_number__of__is__id, fact_80_prime__g__5, arity_Int_Oint___Groups_Ozero, fact_20_rel__simps_I39_J, fact_12_rel__simps_I21_J, fact_87_double__zero__sym, fact_79_zero__le__double__add__iff__zero__le__single__add, fact_16_rel__simps_I51_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_15_eq__number__of, fact_10_add__Bit0__Bit1
% 9.38/3.82 % No. of inferences in proof: 232
% 9.38/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3267 ms resp. 2561 ms w/o parsing
% 9.85/3.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.85/3.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------