%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV633_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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:06 AM UTC 2026
% Result : Theorem 9.61s 5.19s
% Output : Refutation 10.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 149
% Syntax : Number of formulae : 300 ( 152 unt; 0 typ; 0 def)
% Number of atoms : 505 ( 248 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 2836 ( 19 ~; 6 |; 21 &;2620 @)
% ( 10 <=>; 160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 7 con; 0-4 aty)
% Number of variables : 544 ( 0 ^; 544 !; 0 ?; 544 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(uminus_decl,type,
uminus:
!>[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(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_decl,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(ii_decl,type,
ii: complex ).
thf(fFT_Mirabelle_root_decl,type,
fFT_Mirabelle_root: nat > complex ).
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(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(i_decl,type,
i: nat ).
thf(j_decl,type,
j: nat ).
thf(m_decl,type,
m: nat ).
thf(14,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(173,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(93,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_54_left__distrib__number__of) ).
thf(365,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)],[93]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(333,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(352,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(170,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(142,axiom,
nat @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(523,plain,
nat @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(120,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).
thf(449,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)],[120]) ).
thf(96,axiom,
! [A: int] :
( ( A @ bit0 @ ( int @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_minus__Bit0) ).
thf(379,plain,
! [A: int] :
( ( A @ bit0 @ ( int @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(57,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_12_eq__number__of) ).
thf(269,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)],[57]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_compl__eq__compl__iff) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TB @ ( TA @ fun ),B: TA] :
( ( B @ ( A @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_fun__Compl__def) ).
thf(217,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TB @ ( TA @ fun ),B: TA] :
( ( B @ ( A @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(58,axiom,
complex @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) ).
thf(276,plain,
complex @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_power__Suc2) ).
thf(440,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(138,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_51_add__Bit0__Bit1) ).
thf(511,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)],[138]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(384,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(149,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__Pls__right) ).
thf(550,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(126,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(472,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ext) ).
thf(153,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
real @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ouminus) ).
thf(174,plain,
real @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
int @ idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oidom) ).
thf(185,plain,
int @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(68,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(301,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_mult__left__idem) ).
thf(389,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(196,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_rel__simps_I49_J) ).
thf(421,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(62,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(284,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(75,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Bit0__Pls) ).
thf(316,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(118,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_mult__Pls) ).
thf(443,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(77,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ plus_plus ) ) )
= ( A @ suc @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add__2__eq__Suc_H) ).
thf(321,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ plus_plus ) ) )
= ( A @ suc @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(37,axiom,
int @ ring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(211,plain,
int @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(50,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_rel__simps_I46_J) ).
thf(238,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(139,axiom,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_power__Suc) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(131,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_18_arith__simps_I32_J) ).
thf(492,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)],[131]) ).
thf(9,axiom,
real @ idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
thf(164,plain,
real @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(60,axiom,
complex @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(280,plain,
complex @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(43,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(221,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(105,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
thf(396,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_70_int__distrib_I1_J) ).
thf(428,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)],[113]) ).
thf(56,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rel__simps_I50_J) ).
thf(265,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(144,axiom,
complex @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring) ).
thf(527,plain,
complex @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(33,axiom,
bool @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ouminus) ).
thf(201,plain,
bool @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(220,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_67_times__numeral__code_I5_J) ).
thf(302,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)],[69]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ suc @ ( B @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(349,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ suc @ ( B @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_uminus__apply) ).
thf(160,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_power__add) ).
thf(392,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(192,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,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)],[10]) ).
thf(124,axiom,
( ( pls @ ( int @ uminus_uminus ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_minus__Pls) ).
thf(467,plain,
( ( pls @ ( int @ uminus_uminus ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(229,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_96_mult__2__right) ).
thf(252,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)],[52]) ).
thf(91,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(361,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_minus__number__of__mult) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(63,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(285,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Oboolean__algebra) ).
thf(156,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(188,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(101,axiom,
complex @ ring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1) ).
thf(388,plain,
complex @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(12,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(169,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(499,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(45,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(225,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(130,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_48_add__number__of__eq) ).
thf(489,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)],[130]) ).
thf(148,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(547,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(38,axiom,
real @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(212,plain,
real @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',fact_62_number__of__add) ).
thf(508,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)],[137]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_times_Oidem) ).
thf(298,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(112,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_53_right__distrib__number__of) ).
thf(425,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)],[112]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(166,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
int @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ouminus) ).
thf(176,plain,
int @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_number__of__reorient) ).
thf(286,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_power3__eq__cube) ).
thf(281,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_power__mult__distrib) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(191,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_29_number__of__mult) ).
thf(402,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)],[107]) ).
thf(97,axiom,
complex @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(382,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ suc @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_power__odd__eq) ).
thf(313,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ suc @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(20,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(181,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
real @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(159,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(187,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_mult__numeral__1__right) ).
thf(362,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)],[92]) ).
thf(76,axiom,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zpower__zpower) ).
thf(318,plain,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
! [A: nat] :
( ( A @ suc @ suc @ suc )
= ( A @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Suc3__eq__add__3) ).
thf(434,plain,
! [A: nat] :
( ( A @ suc @ suc @ suc )
= ( A @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(100,axiom,
complex @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(387,plain,
complex @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(39,axiom,
real @ ring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1) ).
thf(213,plain,
real @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(128,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(483,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(141,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(520,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(80,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_17_mult__number__of__left) ).
thf(330,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)],[80]) ).
thf(122,axiom,
( ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ fFT_Mirabelle_root )
= ii ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_root4) ).
thf(462,plain,
( ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ fFT_Mirabelle_root )
= ii ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(106,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ suc @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__2__eq__Suc) ).
thf(399,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ suc @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(71,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(306,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(46,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_15_mult__Bit0) ).
thf(226,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)],[46]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_mult__numeral__1) ).
thf(505,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)],[136]) ).
thf(114,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_49_add__number__of__left) ).
thf(431,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)],[114]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_crossproduct__eq) ).
thf(473,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(53,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rel__simps_I39_J) ).
thf(255,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(35,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(209,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_66_int__distrib_I2_J) ).
thf(355,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)],[89]) ).
thf(150,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_power__even__eq) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(66,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_four__x__squared) ).
thf(295,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( real @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ suc @ ( B @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(327,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ suc @ ( B @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(310,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(31,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(199,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(135,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_power2__eq__square__number__of) ).
thf(502,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(147,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_power2__eq__square) ).
thf(544,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(18,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(177,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
real @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(182,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(82,axiom,
complex @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(336,plain,
complex @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(16,axiom,
real @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(175,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(446,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(143,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_power__mult) ).
thf(524,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(132,axiom,
complex @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ouminus) ).
thf(495,plain,
complex @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(94,axiom,
complex @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(368,plain,
complex @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_power2__sum) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(5,axiom,
bool @ boolean_algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Oboolean__algebra) ).
thf(158,plain,
bool @ boolean_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
real @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(186,plain,
real @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_power2__minus) ).
thf(418,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49,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_46_add__Bit0__Bit0) ).
thf(235,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(98,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(383,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(346,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(146,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rel__simps_I44_J) ).
thf(536,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(214,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,conjecture,
( ( j @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( i @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
= ( j @ ( i @ ( nat @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( j @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( i @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
!= ( j @ ( i @ ( nat @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(151,plain,
( ( j @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( i @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
!= ( j @ ( i @ ( nat @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( m @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_mult__idem) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I51_J) ).
thf(405,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)],[108]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ uminus )
=> ( TA @ ( TB @ fun ) @ uminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ouminus) ).
thf(183,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ uminus )
=> ( TA @ ( TB @ fun ) @ uminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(305,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(36,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(210,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
<=> ( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_power2__eq__iff) ).
thf(242,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ! [A: TA,B: TA] :
( ( ( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
| ( B = A ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
=> ( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(65,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(294,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__numeral__0) ).
thf(358,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)],[90]) ).
thf(29,axiom,
real @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(195,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(116,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_52_add__Bit1__Bit0) ).
thf(437,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)],[116]) ).
thf(109,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_57_mult__Bit1) ).
thf(415,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)],[109]) ).
thf(104,axiom,
complex @ idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
thf(395,plain,
complex @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_number__of__minus) ).
thf(464,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(145,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rel__simps_I38_J) ).
thf(528,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ power_power ) ) )
= ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_ring__1__class_Opower__minus__even) ).
thf(459,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ power_power ) ) )
= ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_double__compl) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__numeral__0__right) ).
thf(277,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)],[59]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_crossproduct__noteq) ).
thf(369,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(8,axiom,
real @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(163,plain,
real @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(200,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
thf(486,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_arith__simps_I30_J) ).
thf(337,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(469,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: TA] :
( ( A @ suc @ ( B @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(222,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(48,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__Pls) ).
thf(232,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(556,plain,
$false,
inference(e,[status(thm)],[173,365,333,352,170,523,449,379,269,202,217,276,440,511,384,550,472,340,153,174,185,301,389,196,421,284,316,443,321,211,238,514,492,164,280,221,396,428,265,527,307,201,220,302,349,160,392,192,165,467,229,252,361,324,285,156,188,388,169,499,225,489,547,212,343,508,298,425,166,176,286,281,259,191,402,382,313,181,159,187,362,318,434,387,213,483,520,330,462,399,306,226,505,431,473,255,209,355,553,295,327,310,199,502,544,177,182,336,175,446,524,495,368,517,158,186,418,235,383,346,536,214,151,262,405,183,305,210,242,294,358,195,437,415,395,464,528,459,178,277,369,163,200,486,337,469,222,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV633_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
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 14:45:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.84/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.35 % [INFO] Parsing done (404ms).
% 1.60/1.38 % [INFO] Running in sequential loop mode.
% 2.63/1.91 % [INFO] eprover registered as external prover.
% 2.63/1.92 % [INFO] Scanning for conjecture ...
% 2.98/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 150 axioms. Running axiom selection ...
% 3.29/2.32 % [INFO] Axiom selection finished. Selected 148 axioms (removed 2 axioms).
% 3.87/2.61 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.87/2.64 % [INFO] Type checking passed.
% 3.87/2.65 % [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 ...
% 9.61/5.19 % External prover 'e' found a proof!
% 9.61/5.19 % [INFO] Killing All external provers ...
% 9.61/5.19 % Time passed: 4716ms (effective reasoning time: 3801ms)
% 9.61/5.19 % 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)>
% 9.61/5.19 % Axioms used in derivation (148): fact_61_number__of__minus, fact_59_add__2__eq__Suc, arity_Int_Oint___Groups_Ouminus, fact_44_minus__Pls, arity_Nat_Onat___Groups_Omonoid__mult, fact_31_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, arity_Int_Oint___Int_Oring__char__0, fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_84_power__Suc2, fact_70_int__distrib_I1_J, fact_45_minus__Bit0, arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_66_int__distrib_I2_J, fact_56_power__Suc, arity_Complex_Ocomplex___Power_Opower, fact_16_rel__simps_I48_J, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_62_number__of__add, fact_73_uminus__apply, arity_Nat_Onat___Int_Onumber__semiring, fact_47_compl__eq__compl__iff, arity_RealDef_Oreal___Int_Onumber__semiring, arity_Nat_Onat___Power_Opower, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, fact_17_mult__number__of__left, arity_Complex_Ocomplex___Rings_Oidom, arity_Complex_Ocomplex___Int_Oring__char__0, arity_HOL_Obool___Lattices_Oboolean__algebra, fact_86_Suc3__eq__add__3, fact_94_mult__idem, fact_88_add__numeral__0, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, arity_Complex_Ocomplex___Groups_Ouminus, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Onumber__ring, fact_58_add__2__eq__Suc_H, fact_32_mult__numeral__1, fact_35_four__x__squared, fact_5_Bit0__Pls, arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_40_power__mult, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef_Oreal___Groups_Ouminus, fact_34_power3__eq__cube, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_55_minus__number__of__mult, arity_Int_Oint___Rings_Oring__1, fact_36_root4, fact_60_power2__minus, fact_75_fun__Compl__def, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_39_power__odd__eq, arity_Complex_Ocomplex___Rings_Osemiring, fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_46_add__Bit0__Bit0, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_77_crossproduct__noteq, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Int_Oint___Groups_Omonoid__mult, arity_RealDef_Oreal___Int_Onumber__ring, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_83_Bit0__def, fact_49_add__number__of__left, fact_7_rel__simps_I44_J, fact_33_mult__numeral__1__right, fact_67_times__numeral__code_I5_J, fact_18_arith__simps_I32_J, fact_43_power__mult__distrib, arity_fun___Groups_Ouminus, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_53_right__distrib__number__of, fact_74_double__compl, fact_42_power2__sum, fact_48_add__number__of__eq, fact_82_add__Pls__right, arity_RealDef_Oreal___Rings_Oidom, arity_RealDef_Oreal___Rings_Oring__1, fact_95_power2__eq__iff, fact_51_add__Bit0__Bit1, fact_30_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_6_rel__simps_I38_J, arity_Int_Oint___Rings_Osemiring, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_14_mult__Pls, fact_19_zpower__zpower, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_4_power2__eq__square, fact_72_ext, fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_9_rel__simps_I50_J, arity_RealDef_Oreal___Int_Oring__char__0, fact_37_mult__left__idem, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_52_add__Bit1__Bit0, fact_3_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, arity_RealDef_Oreal___Rings_Osemiring, fact_13_rel__simps_I51_J, fact_29_number__of__mult, arity_fun___Lattices_Oboolean__algebra, arity_Int_Oint___Rings_Oidom, arity_Complex_Ocomplex___Int_Onumber__ring, arity_Int_Oint___Power_Opower, fact_96_mult__2__right, fact_12_eq__number__of, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_28_number__of__reorient, fact_10_rel__simps_I39_J, fact_8_rel__simps_I49_J, fact_87_add__numeral__0__right, arity_Nat_Onat___Int_Onumber, fact_41_ring__1__class_Opower__minus__even, fact_2_power__even__eq, fact_50_arith__simps_I30_J, fact_80_crossproduct__eq, fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_54_left__distrib__number__of, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_11_rel__simps_I46_J, arity_Complex_Ocomplex___Groups_Omonoid__mult, arity_Nat_Onat___Rings_Osemiring, arity_RealDef_Oreal___Power_Opower, fact_57_mult__Bit1, fact_81_add__Pls, fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, arity_HOL_Obool___Groups_Ouminus, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, arity_Complex_Ocomplex___Int_Onumber__semiring, fact_1_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, arity_RealDef_Oreal___Int_Onumber, fact_93_times_Oidem, fact_0_power2__eq__square__number__of, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Complex_Ocomplex___Int_Onumber, arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult, arity_Int_Oint___Int_Onumber, arity_Complex_Ocomplex___Rings_Oring__1, fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_15_mult__Bit0, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_63_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_85_power__add, fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J
% 9.61/5.19 % No. of inferences in proof: 300
% 9.61/5.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4716 ms resp. 3801 ms w/o parsing
% 10.16/5.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.16/5.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------