%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM977_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:10:34 AM UTC 2026
% Result : Theorem 8.61s 3.53s
% Output : Refutation 9.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 115
% Syntax : Number of formulae : 232 ( 112 unt; 0 typ; 0 def)
% Number of atoms : 492 ( 158 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2352 ( 57 ~; 6 |; 53 &;2043 @)
% ( 31 <=>; 162 =>; 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 : 31 ( 29 usr; 8 con; 0-4 aty)
% Number of variables : 330 ( 0 ^; 330 !; 0 ?; 330 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[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(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[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(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(twoSqu1567020053sum2sq_decl,type,
twoSqu1567020053sum2sq: int > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(m_decl,type,
m: int ).
thf(t_decl,type,
t: int ).
thf(tn_decl,type,
tn: nat ).
thf(69,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zero__less__int__conv) ).
thf(352,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(98,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_p0) ).
thf(476,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(52,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(295,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(96,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__nat__zero__code) ).
thf(470,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(47,axiom,
! [A: int] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_odd__nonzero) ).
thf(276,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)],[47]) ).
thf(109,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_less__zeroE) ).
thf(511,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(75,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(385,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zadd__int) ).
thf(142,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_zero__is__num__zero) ).
thf(340,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [A: int,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zmult__zless__mono2) ).
thf(185,plain,
! [A: int,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_45_left__distrib__number__of) ).
thf(320,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)],[59]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_18_eq__number__of) ).
thf(504,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)],[108]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__simps_I17_J) ).
thf(460,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I49_J) ).
thf(421,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__lessD1) ).
thf(152,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_of__nat__less__iff) ).
thf(289,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__not__refl2) ).
thf(261,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zless__int) ).
thf(179,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(67,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_int__0) ).
thf(348,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',fact_8_add__special_I3_J) ).
thf(480,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)],[100]) ).
thf(4,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(121,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_7_add__special_I2_J) ).
thf(514,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)],[110]) ).
thf(48,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__less0) ).
thf(280,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(30,axiom,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zadd__int__left) ).
thf(221,plain,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__less__mono) ).
thf(293,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_bin__less__0__simps_I1_J) ).
thf(132,plain,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I48_J) ).
thf(411,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)],[84]) ).
thf(87,axiom,
! [A: int] :
( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bin__less__0__simps_I3_J) ).
thf(428,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(42,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(265,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__irrefl__nat) ).
thf(233,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_11_one__add__one__is__two) ).
thf(248,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)],[38]) ).
thf(1,conjecture,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(90,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_int__eq__0__conv) ).
thf(439,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__Bit1__Bit0) ).
thf(201,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)],[26]) ).
thf(71,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mult__Pls) ).
thf(366,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(45,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Nat_Oadd__0__right) ).
thf(270,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(115,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(529,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(79,axiom,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nQ1) ).
thf(392,plain,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_linorder__neqE__nat) ).
thf(297,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(17,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(165,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nat__add__left__cancel__less) ).
thf(329,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(31,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_int__1) ).
thf(224,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_of__nat__1) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__not__refl3) ).
thf(388,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(11,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(141,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,axiom,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_int__less__0__conv) ).
thf(457,plain,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I16_J) ).
thf(173,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__number__of) ).
thf(371,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(8,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__less__mono1) ).
thf(134,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_less__special_I3_J) ).
thf(244,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t1) ).
thf(266,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_rel__simps_I14_J) ).
thf(311,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_of__nat__add) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(116,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(530,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mult__Bit0) ).
thf(425,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)],[86]) ).
thf(18,axiom,
t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_qf1pt) ).
thf(166,plain,
t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I50_J) ).
thf(148,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(53,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(296,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_add__is__0) ).
thf(375,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I51_J) ).
thf(191,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)],[25]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nat__neq__iff) ).
thf(204,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(107,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I4_J) ).
thf(498,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__eq__self__zero) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_gr__implies__not0) ).
thf(335,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(36,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rel__simps_I44_J) ).
thf(236,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( B @ twoSqu1567020053sum2sq )
=> ( ( A @ twoSqu1567020053sum2sq )
=> ( A @ ( B @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_is__mult__sum2sq) ).
thf(350,plain,
! [A: int,B: int] :
( ( B @ twoSqu1567020053sum2sq )
=> ( ( A @ twoSqu1567020053sum2sq )
=> ( A @ ( B @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',fact_53_add__number__of__eq) ).
thf(187,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)],[23]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fact_46_right__distrib__number__of) ).
thf(434,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)],[88]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__gr__0) ).
thf(303,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(99,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_plus__nat_Oadd__0) ).
thf(477,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(77,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( t @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_t__l__p) ).
thf(387,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( t @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(105,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_not__add__less2) ).
thf(494,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(65,axiom,
tn @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tn0) ).
thf(345,plain,
tn @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I10_J) ).
thf(323,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(10,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(140,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_number__of__Pls) ).
thf(483,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__nat__eq__iff) ).
thf(251,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(112,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__Bit0__Bit0) ).
thf(521,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)],[112]) ).
thf(6,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_rel__simps_I2_J) ).
thf(130,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I39_J) ).
thf(394,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(32,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(226,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(44,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_not__add__less1) ).
thf(267,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(19,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I12_J) ).
thf(167,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(97,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_mult__Bit1) ).
thf(473,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)],[97]) ).
thf(103,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(490,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit0__Bit1) ).
thf(342,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(13,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_of__nat__0) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat__less__cases) ).
thf(154,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__C0_C) ).
thf(386,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(106,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(497,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_trans__less__add1) ).
thf(231,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_double__eq__0__iff) ).
thf(450,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)],[92]) ).
thf(113,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I46_J) ).
thf(524,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(29,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__not__refl) ).
thf(218,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__special_I4_J) ).
thf(517,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__add__eq__less) ).
thf(258,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
<=> ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_pos__zmult__eq__1__iff) ).
thf(401,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) )
=> ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) ) )
& ( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(119,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(66,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Bit0__Pls) ).
thf(346,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_50_arith__simps_I32_J) ).
thf(300,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)],[55]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_49_mult__number__of__left) ).
thf(447,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)],[91]) ).
thf(83,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_p) ).
thf(410,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)],[83]) ).
thf(24,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(190,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_52_add__number__of__left) ).
thf(273,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)],[46]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__nat__0__less__iff) ).
thf(136,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(70,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_neq0__conv) ).
thf(358,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_trans__less__add2) ).
thf(437,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(49,axiom,
! [A: int] :
( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bin__less__0__simps_I4_J) ).
thf(283,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(528,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(72,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Pls__def) ).
thf(369,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_less__special_I1_J) ).
thf(227,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_less__special_I2_J) ).
thf(486,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(5,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I38_J) ).
thf(122,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_numeral__1__eq__1) ).
thf(215,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(104,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_gr0I) ).
thf(491,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(534,plain,
$false,
inference(e,[status(thm)],[352,476,295,470,276,511,385,142,340,185,320,504,460,421,152,289,261,179,348,480,121,514,280,221,293,132,411,428,265,233,248,117,439,201,366,270,529,392,297,165,329,224,317,388,141,457,173,371,134,244,266,311,398,530,425,166,148,296,375,191,204,498,466,335,236,350,187,434,303,477,387,494,345,323,140,483,251,521,130,394,226,267,167,473,490,342,145,154,386,497,231,450,524,218,517,258,401,119,346,300,447,410,190,273,136,358,437,283,528,369,227,486,122,215,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM977_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 04:22:09 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.25 % [INFO] Parsing done (289ms).
% 1.53/1.26 % [INFO] Running in sequential loop mode.
% 2.50/1.67 % [INFO] eprover registered as external prover.
% 2.50/1.68 % [INFO] Scanning for conjecture ...
% 2.93/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 3.15/1.94 % [INFO] Axiom selection finished. Selected 114 axioms (removed 1 axioms).
% 3.51/2.12 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.76/2.14 % [INFO] Type checking passed.
% 3.76/2.14 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.61/3.52 % External prover 'e' found a proof!
% 8.61/3.53 % [INFO] Killing All external provers ...
% 8.61/3.53 % Time passed: 2993ms (effective reasoning time: 2255ms)
% 8.61/3.53 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.61/3.53 % Axioms used in derivation (114): fact_74_add__lessD1, fact_59_add__Bit1__Bit0, help_pp_1_1_U, fact_90_int__1, fact_27_rel__simps_I50_J, fact_36_rel__simps_I17_J, fact_20_rel__simps_I51_J, fact_35_neq0__conv, fact_49_mult__number__of__left, fact_16_of__nat__0__less__iff, arity_Int_Oint___Rings_Olinordered__idom, fact_55_rel__simps_I16_J, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Int_Oring__char__0, fact_62_not__add__less1, fact_19_add__is__0, fact_7_add__special_I2_J, fact_56_of__nat__less__iff, fact_96_int__less__0__conv, fact_17_tn0, fact_81_not__less0, fact_14_mult__Bit1, fact_52_add__number__of__left, fact_37_rel__simps_I2_J, fact_93_int__eq__0__conv, fact_11_one__add__one__is__two, fact_65_linorder__neqE__nat, fact_58_rel__simps_I4_J, fact_61_less__not__refl, fact_4_is__mult__sum2sq, fact_3_p, fact_71_add__less__mono1, fact_78_plus__nat_Oadd__0, fact_24_double__eq__0__iff, fact_39_of__nat__add, arity_Int_Oint___Int_Onumber__ring, fact_73_less__add__eq__less, fact_82_Pls__def, fact_66_less__irrefl__nat, fact_94_int__0, fact_84_zadd__int__left, arity_Int_Oint___Rings_Osemiring__1, fact_76_add__eq__self__zero, fact_92_zmult__zless__mono2, fact_67_less__not__refl2, fact_31_Bit0__Pls, fact_60_add__Bit0__Bit1, fact_8_add__special_I3_J, fact_18_eq__number__of, fact_95_odd__nonzero, fact_23_of__nat__eq__iff, fact_22_nat__add__left__cancel__less, fact_10_less__special_I4_J, fact_15_numeral__1__eq__1, fact_29_rel__simps_I44_J, fact_64_nat__neq__iff, fact_79_gr0I, fact_89_bin__less__0__simps_I3_J, fact_42_mult__Bit0, fact_1_nQ1, fact_43_add__Bit0__Bit0, fact_72_add__less__mono, fact_28_rel__simps_I49_J, fact_80_gr__implies__not0, arity_Nat_Onat___Rings_Olinordered__semidom, fact_85_zadd__int, fact_12_less__special_I1_J, fact_88_bin__less__0__simps_I1_J, fact_38_rel__simps_I14_J, fact_34_less__nat__zero__code, arity_Int_Oint___Rings_Osemiring, fact_69_trans__less__add1, fact_54_rel__simps_I12_J, fact_6_t__l__p, fact_53_add__number__of__eq, fact_70_trans__less__add2, fact_47_number__of__Pls, fact_2__C0_C, fact_91_zero__is__num__zero, fact_41_mult__Pls, fact_40_of__nat__1, fact_45_left__distrib__number__of, fact_63_not__add__less2, fact_87_bin__less__0__simps_I4_J, fact_26_rel__simps_I39_J, fact_51_of__nat__0, fact_77_Nat_Oadd__0__right, fact_48_less__number__of, fact_13_less__special_I3_J, arity_Nat_Onat___Int_Onumber, fact_46_right__distrib__number__of, fact_0_t1, fact_57_rel__simps_I10_J, arity_Nat_Onat___Nat_Osemiring__char__0, fact_50_arith__simps_I32_J, fact_5_qf1pt, fact_9_less__special_I2_J, fact_86_zless__int, fact_83_zero__less__int__conv, arity_Nat_Onat___Rings_Osemiring, fact_21_rel__simps_I48_J, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_97_pos__zmult__eq__1__iff, arity_Int_Oint___Int_Onumber, fact_68_less__not__refl3, fact_44_p0, arity_Int_Oint___Nat_Osemiring__char__0, fact_32_add__gr__0, arity_Int_Oint___Rings_Olinordered__semidom, help_pp_2_1_U, fact_75_nat__less__cases, fact_25_rel__simps_I46_J, fact_33_less__zeroE, fact_30_rel__simps_I38_J
% 8.61/3.53 % No. of inferences in proof: 232
% 8.61/3.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2993 ms resp. 2255 ms w/o parsing
% 9.05/3.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.38/3.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------