%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW482_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 : n003.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 09:10:39 AM UTC 2026
% Result : Theorem 9.77s 3.93s
% Output : Refutation 10.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 144
% Syntax : Number of formulae : 290 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 587 ( 317 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2632 ( 46 ~; 5 |; 71 &;2289 @)
% ( 19 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 5 con; 0-4 aty)
% Number of variables : 446 ( 0 ^; 446 !; 0 ?; 446 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(division_ring_decl,type,
division_ring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(field_inverse_zero_decl,type,
field_inverse_zero:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(divisi14063676e_zero_decl,type,
divisi14063676e_zero:
!>[TA: $tType] : $o ).
thf(linord1117847801e_zero_decl,type,
linord1117847801e_zero:
!>[TA: $tType] : $o ).
thf(inverse_divide_decl,type,
inverse_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(abs_abs_decl,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(iszero_decl,type,
iszero:
!>[TA: $tType] : ( TA > $o ) ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(root_decl,type,
root: nat > ( real @ ( real @ fun ) ) ).
thf(sqrt_decl,type,
sqrt: real @ ( real @ fun ) ).
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(y_decl,type,
y: real ).
thf(67,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_19_four__x__squared) ).
thf(333,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)],[67]) ).
thf(37,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(234,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(124,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( real @ abs_abs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_real__sqrt__abs) ).
thf(555,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( real @ abs_abs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ~ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_not__iszero__Numeral1) ).
thf(352,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ~ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(104,axiom,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field ) )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_divide__Numeral1) ).
thf(449,plain,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field ) )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(26,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_90_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(202,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)],[26]) ).
thf(122,axiom,
! [A: real] :
( ( A @ ( A @ ( real @ times_times ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( real @ abs_abs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_real__sqrt__abs2) ).
thf(550,plain,
! [A: real] :
( ( A @ ( A @ ( real @ times_times ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( real @ abs_abs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_power2__abs) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(72,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(340,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(6,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(153,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
int @ ring_n68954251visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(174,plain,
int @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(185,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(94,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_number__of__is__id) ).
thf(417,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( pls @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_iszero__Numeral0) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( pls @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pls__def) ).
thf(257,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(64,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(320,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(128,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zero__is__num__zero) ).
thf(565,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(145,axiom,
! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_real__sqrt__power) ).
thf(619,plain,
! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(196,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(108,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nat__number__of__Pls) ).
thf(460,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(126,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_97_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(559,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)],[126]) ).
thf(21,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(189,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
( y
!= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_y0) ).
thf(421,plain,
( y
!= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(93,axiom,
real @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(416,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(152,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,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_87_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(216,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)],[32]) ).
thf(112,axiom,
real @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(475,plain,
real @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(11,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(164,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_divide__zero) ).
thf(179,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( A @ ( B @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_power__abs) ).
thf(591,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( A @ ( B @ ( TA @ abs_abs ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(65,axiom,
( sqrt
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ root ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_sqrt__def) ).
thf(321,plain,
( sqrt
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ root ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_field__power__not__zero) ).
thf(253,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(39,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(238,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mult__eq__0__iff) ).
thf(221,plain,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(293,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(106,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rel__simps_I46_J) ).
thf(453,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_rel__simps_I49_J) ).
thf(396,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(90,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(411,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rel__simps_I51_J) ).
thf(243,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)],[42]) ).
thf(28,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_85_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(206,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)],[28]) ).
thf(105,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(452,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(101,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_50_power__mult) ).
thf(439,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)],[101]) ).
thf(50,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(270,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(34,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(220,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(136,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_60_power3__eq__cube) ).
thf(598,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)],[136]) ).
thf(97,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_82_times__numeral__code_I5_J) ).
thf(424,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)],[97]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nonzero__power__divide) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iszero__0) ).
thf(165,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(118,axiom,
! [A: real] :
( ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( real @ inverse_divide ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( A @ ( real @ inverse_divide ) ) @ ( real @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_sq4) ).
thf(522,plain,
! [A: real] :
( ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( real @ inverse_divide ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( A @ ( real @ inverse_divide ) ) @ ( real @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_semiring__numeral__0__eq__0) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_number__of__Pls) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(142,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_33_mult__number__of__left) ).
thf(610,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)],[142]) ).
thf(95,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(420,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(44,axiom,
real @ division_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring) ).
thf(256,plain,
real @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(71,axiom,
real @ divisi14063676e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) ).
thf(339,plain,
real @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mult__zero__right) ).
thf(193,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(113,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: int,B: TA,C: TA] :
( ( C
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ inverse_divide ) ) ) )
<=> ( ( ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( C
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_eq__divide__eq__number__of1) ).
thf(476,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: int,B: TA,C: TA] :
( ( ( ( ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( C
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) )
= B ) ) )
=> ( C
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ inverse_divide ) ) ) ) )
& ( ( C
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ inverse_divide ) ) ) )
=> ( ( ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( C
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(121,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_46_number__of__mult) ).
thf(547,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)],[121]) ).
thf(30,axiom,
int @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(212,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(85,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_66_power2__eq__square) ).
thf(393,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)],[85]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_semiring__norm_I112_J) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(83,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ times_times ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_real__sqrt__mult) ).
thf(371,plain,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ times_times ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(139,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_73_ext) ).
thf(605,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)],[139]) ).
thf(27,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(205,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(125,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(558,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(91,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(412,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(99,axiom,
! [A: real,B: real] :
( ( ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_real__sqrt__eq__iff) ).
thf(430,plain,
! [A: real,B: real] :
( ( ( B = A )
=> ( ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) ) )
& ( ( ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(3,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(148,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,axiom,
! [A: real,B: real] :
( ( B @ ( B @ ( real @ times_times ) ) @ ( A @ ( B @ ( real @ times_times ) ) @ ( real @ inverse_divide ) ) )
= ( B @ ( A @ ( real @ inverse_divide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_real__divide__square__eq) ).
thf(264,plain,
! [A: real,B: real] :
( ( B @ ( B @ ( real @ times_times ) ) @ ( A @ ( B @ ( real @ times_times ) ) @ ( real @ inverse_divide ) ) )
= ( B @ ( A @ ( real @ inverse_divide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_no__zero__divisors) ).
thf(161,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,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_88_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(149,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)],[4]) ).
thf(137,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_32_arith__simps_I32_J) ).
thf(601,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)],[137]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_power__commutes) ).
thf(562,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_abs__divide) ).
thf(176,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ abs_abs ) )
= ( A @ ( TA @ abs_abs ) @ ( B @ ( TA @ abs_abs ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(130,axiom,
! [A: real] :
( ( ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) )
<=> ( A
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_real__sqrt__eq__0__iff) ).
thf(577,plain,
! [A: real] :
( ( ( A
= ( real @ zero_zero ) )
=> ( ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) ) )
& ( ( ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) )
=> ( A
= ( real @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(46,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_83_zpower__zpower) ).
thf(259,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)],[46]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zero__power2) ).
thf(413,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(115,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_rel__simps_I39_J) ).
thf(498,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(75,axiom,
( ( real @ zero_zero @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_real__sqrt__zero) ).
thf(350,plain,
( ( real @ zero_zero @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(138,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(604,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(33,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(219,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(129,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rel__simps_I48_J) ).
thf(567,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)],[129]) ).
thf(62,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(318,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int] :
~ ( A @ bit1 @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_iszero__number__of__Bit1) ).
thf(271,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int] :
~ ( A @ bit1 @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(144,axiom,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_divide__Numeral0) ).
thf(616,plain,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(59,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_mult__Pls) ).
thf(303,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(81,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(367,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(141,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(609,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_power__eq__0__iff) ).
thf(323,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(134,axiom,
real @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(594,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mult__zero__left) ).
thf(213,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,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_61_mult__numeral__1__right) ).
thf(240,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)],[41]) ).
thf(8,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_89_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(155,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)],[8]) ).
thf(109,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_62_mult__numeral__1) ).
thf(462,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)],[109]) ).
thf(117,axiom,
real @ field_inverse_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield__inverse__zero) ).
thf(521,plain,
real @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(140,axiom,
nat @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(608,plain,
nat @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ bit0 @ ( TA @ number_number_of ) @ ( TA @ iszero ) )
<=> ( A @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_iszero__number__of__Bit0) ).
thf(306,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ iszero ) )
=> ( A @ bit0 @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) )
& ( ( A @ bit0 @ ( TA @ number_number_of ) @ ( TA @ iszero ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ iszero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,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_49_power__mult__distrib) ).
thf(267,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)],[49]) ).
thf(100,axiom,
real @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(438,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ iszero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_iszero__def) ).
thf(167,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( A @ ( TA @ iszero ) ) )
& ( ( A @ ( TA @ iszero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: TA,C: int] :
( ( ( C @ ( TA @ number_number_of ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) ) )
<=> ( ( ( A
= ( TA @ zero_zero ) )
=> ( ( C @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_eq__divide__eq__number__of) ).
thf(374,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: TA,C: int] :
( ( ( ( ( A
= ( TA @ zero_zero ) )
=> ( ( C @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= B ) ) )
=> ( ( C @ ( TA @ number_number_of ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) ) ) )
& ( ( ( C @ ( TA @ number_number_of ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) ) )
=> ( ( ( A
= ( TA @ zero_zero ) )
=> ( ( C @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(29,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_84_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(209,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)],[29]) ).
thf(74,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rel__simps_I38_J) ).
thf(342,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(78,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(355,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(123,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Bit0__Pls) ).
thf(553,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(119,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_92_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(525,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)],[119]) ).
thf(53,axiom,
! [A: nat] :
( ( real @ zero_zero @ ( A @ root @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_real__root__zero) ).
thf(282,plain,
! [A: nat] :
( ( real @ zero_zero @ ( A @ root @ ( real @ ( real @ aa ) ) ) )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(61,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_rel__simps_I44_J) ).
thf(310,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(25,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_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(199,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)],[25]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_times__divide__eq__right) ).
thf(182,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field ) )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divide__numeral__1) ).
thf(585,plain,
! [TA: $tType] :
( ( ( TA @ number_ring )
& ( TA @ field ) )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(116,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: int,C: TA] :
( ( ( B @ ( TA @ number_number_of ) @ ( C @ ( TA @ inverse_divide ) ) )
= A )
<=> ( ( ( ( B @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_divide__eq__eq__number__of1) ).
thf(502,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: int,C: TA] :
( ( ( ( ( ( B @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) ) ) ) )
=> ( ( B @ ( TA @ number_number_of ) @ ( C @ ( TA @ inverse_divide ) ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) @ ( C @ ( TA @ inverse_divide ) ) )
= A )
=> ( ( ( ( B @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(70,axiom,
real @ field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield) ).
thf(338,plain,
real @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(80,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_15_number__of__reorient) ).
thf(359,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)],[80]) ).
thf(68,axiom,
real @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(336,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(143,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_71_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(613,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)],[143]) ).
thf(7,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(154,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(175,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,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_28_mult__Bit0) ).
thf(446,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)],[103]) ).
thf(135,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ inverse_divide ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ inverse_divide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_real__sqrt__divide) ).
thf(595,plain,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ inverse_divide ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( A @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( B @ ( sqrt @ ( real @ ( real @ aa ) ) ) @ ( real @ inverse_divide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(114,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_70_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(495,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)],[114]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_abs__power2) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ abs_abs ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(110,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_11_eq__number__of) ).
thf(465,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)],[110]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_power__divide) ).
thf(588,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(63,axiom,
real @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(319,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_abs__mult__self) ).
thf(158,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ abs_abs ) @ ( A @ ( TA @ abs_abs ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_divide__zero__left) ).
thf(186,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(56,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_67_power__even__eq) ).
thf(290,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)],[56]) ).
thf(38,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_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(235,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)],[38]) ).
thf(89,axiom,
real @ linord1117847801e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) ).
thf(410,plain,
real @ linord1117847801e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(47,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_semiring__norm_I113_J) ).
thf(262,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
( ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
!= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(146,plain,
( ( pls @ bit1 @ bit0 @ bit0 @ ( real @ number_number_of ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) )
!= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ power_power ) ) @ ( sqrt @ ( real @ ( real @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_divisors__zero) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(52,axiom,
! [A: real,B: real,C: real] :
( ( C
= ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( B @ ( real @ inverse_divide ) ) ) )
<=> ( ( C @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( A @ ( B @ ( real @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_eq__divide__2__times__iff) ).
thf(273,plain,
! [A: real,B: real,C: real] :
( ( ( ( C @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( A @ ( B @ ( real @ inverse_divide ) ) ) )
=> ( C
= ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( B @ ( real @ inverse_divide ) ) ) ) )
& ( ( C
= ( A @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) @ ( B @ ( real @ inverse_divide ) ) ) )
=> ( ( C @ ( pls @ bit1 @ bit0 @ ( real @ number_number_of ) @ ( real @ times_times ) ) )
= ( A @ ( B @ ( real @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,axiom,
real @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(239,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(58,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_power__eq__0__iff__number__of) ).
thf(294,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(73,axiom,
real @ ring_n68954251visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(341,plain,
real @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zero__eq__power2) ).
thf(400,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,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_21_power2__eq__square__number__of) ).
thf(427,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)],[98]) ).
thf(120,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: int,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ inverse_divide ) ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( B
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_divide__eq__eq__number__of) ).
thf(528,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ field_inverse_zero ) )
=> ! [A: int,B: TA,C: TA] :
( ( ( ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( B
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ) )
=> ( ( B @ ( C @ ( TA @ inverse_divide ) ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( C @ ( TA @ inverse_divide ) ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( ( ( B
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) )
& ( ( B
!= ( TA @ zero_zero ) )
=> ( C
= ( B @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(102,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_rel__simps_I50_J) ).
thf(442,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(69,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(337,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(77,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(354,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(643,plain,
$false,
inference(e,[status(thm)],[333,234,555,352,449,202,550,472,340,153,174,185,417,288,257,320,565,619,196,460,559,189,421,416,152,216,475,164,179,591,321,253,238,221,293,453,396,411,243,206,452,439,270,220,598,424,407,165,522,285,356,610,420,256,339,193,476,547,212,393,457,371,605,205,558,412,430,148,264,161,149,601,562,176,577,259,413,498,350,604,219,567,318,271,616,303,367,609,323,594,213,240,155,462,521,608,306,267,438,167,374,209,342,355,553,525,282,310,199,182,585,502,338,359,336,613,154,175,446,595,495,368,465,231,588,319,158,186,290,235,410,262,146,190,273,239,294,341,400,427,528,442,337,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW482_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.13/0.41 % Computer : n003.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 16:10:25 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.29 % [INFO] Parsing done (304ms).
% 1.88/1.31 % [INFO] Running in sequential loop mode.
% 2.38/1.70 % [INFO] eprover registered as external prover.
% 2.59/1.70 % [INFO] Scanning for conjecture ...
% 2.77/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 145 axioms. Running axiom selection ...
% 2.96/2.00 % [INFO] Axiom selection finished. Selected 143 axioms (removed 2 axioms).
% 3.61/2.18 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.78/2.20 % [INFO] Type checking passed.
% 3.78/2.21 % [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 ...
% 9.77/3.92 % External prover 'e' found a proof!
% 9.77/3.93 % [INFO] Killing All external provers ...
% 9.77/3.93 % Time passed: 3375ms (effective reasoning time: 2614ms)
% 9.77/3.93 % 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)>
% 9.77/3.93 % Axioms used in derivation (143): arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_53_eq__divide__eq__number__of, arity_Nat_Onat___Groups_Omonoid__mult, fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_5_rel__simps_I39_J, fact_56_semiring__norm_I112_J, fact_32_arith__simps_I32_J, arity_Int_Oint___Rings_Olinordered__idom, fact_52_divide__eq__eq__number__of, arity_Nat_Onat___Rings_Osemiring__1, fact_17_real__sqrt__abs, arity_Int_Oint___Int_Oring__char__0, fact_63_divide__Numeral0, fact_58_semiring__norm_I113_J, fact_43_iszero__0, fact_15_number__of__reorient, fact_81_number__of__is__id, fact_14_divide__numeral__1, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_67_power__even__eq, fact_83_zpower__zpower, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Nat_Onat___Int_Onumber__semiring, fact_29_real__sqrt__zero, arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero, arity_RealDef_Oreal___Int_Onumber__semiring, fact_55_Pls__def, fact_7_sq4, fact_78_divide__zero__left, arity_Nat_Onat___Power_Opower, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, fact_39_divide__eq__eq__number__of1, arity_RealDef_Oreal___Fields_Ofield__inverse__zero, fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_72_abs__divide, fact_76_mult__zero__right, fact_0_Bit0__Pls, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Onumber__ring, arity_Int_Oint___Rings_Osemiring__1, fact_13_divide__Numeral1, fact_77_mult__eq__0__iff, arity_Nat_Onat___Rings_Omult__zero, fact_62_mult__numeral__1, fact_1_rel__simps_I38_J, fact_57_nonzero__power__divide, fact_21_power2__eq__square__number__of, fact_49_power__mult__distrib, fact_64_iszero__number__of__Bit1, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_69_eq__divide__2__times__iff, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_41_abs__power2, fact_2_rel__simps_I44_J, fact_33_mult__number__of__left, fact_45_iszero__def, arity_RealDef_Oreal___Rings_Osemiring__1, arity_RealDef_Oreal___Fields_Odivision__ring, fact_61_mult__numeral__1__right, fact_44_zero__is__num__zero, fact_79_divide__zero, fact_73_ext, fact_6_rel__simps_I46_J, arity_RealDef_Oreal___Int_Onumber__ring, fact_96_divisors__zero, arity_Int_Oint___Groups_Omonoid__mult, arity_RealDef_Oreal___Fields_Ofield, fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_27_mult__Pls, arity_Int_Oint___Rings_Oring__no__zero__divisors, fact_35_nat__number__of__Pls, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_18_power__divide, fact_28_mult__Bit0, fact_30_real__sqrt__eq__0__iff, fact_19_four__x__squared, fact_25_zero__power2, fact_74_abs__mult__self, fact_65_iszero__Numeral0, fact_8_real__sqrt__eq__iff, fact_59_semiring__numeral__0__eq__0, fact_11_eq__number__of, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_42_power2__abs, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Int_Oring__char__0, fact_80_times__divide__eq__right, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_Int_Oint___Power_Opower, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_66_power2__eq__square, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_48_power__commutes, fact_40_eq__divide__eq__number__of1, arity_RealDef_Oreal___Rings_Ozero__neq__one, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_4_rel__simps_I50_J, fact_68_power__eq__0__iff__number__of, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_31_real__root__zero, fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_3_rel__simps_I49_J, fact_10_rel__simps_I51_J, fact_9_rel__simps_I48_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_16_real__sqrt__power, fact_23_sqrt__def, fact_22_iszero__number__of__Bit0, fact_46_number__of__mult, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_34_power__eq__0__iff, fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_51_field__power__not__zero, fact_47_power__abs, arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero, fact_60_power3__eq__cube, arity_RealDef_Oreal___Power_Opower, fact_38_real__sqrt__abs2, fact_37_number__of__Pls, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_36_real__divide__square__eq, fact_12_real__sqrt__divide, fact_50_power__mult, fact_54_real__sqrt__mult, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, arity_RealDef_Oreal___Int_Onumber, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Rings_Omult__zero, fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_75_mult__zero__left, fact_20_not__iszero__Numeral1, fact_82_times__numeral__code_I5_J, fact_26_y0, fact_24_zero__eq__power2, fact_95_no__zero__divisors
% 9.77/3.93 % No. of inferences in proof: 290
% 9.77/3.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3375 ms resp. 2614 ms w/o parsing
% 10.28/4.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.28/4.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------