%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW497_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:41 AM UTC 2026
% Result : Theorem 10.80s 3.47s
% Output : Refutation 11.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 176
% Syntax : Number of formulae : 354 ( 230 unt; 0 typ; 0 def)
% Number of atoms : 585 ( 310 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2251 ( 17 ~; 0 |; 52 &;2007 @)
% ( 23 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 6 con; 0-4 aty)
% Number of variables : 400 ( 0 ^; 400 !; 0 ?; 400 :)
% 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(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[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(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(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(real_n2089651433ebra_1_decl,type,
real_n2089651433ebra_1:
!>[TA: $tType] : $o ).
thf(real_n1866405975lgebra_decl,type,
real_n1866405975lgebra:
!>[TA: $tType] : $o ).
thf(complex1_decl,type,
complex1: real > real > complex ).
thf(complex_case_decl,type,
complex_case:
!>[TA: $tType] : ( ( TA @ ( real @ fun ) @ ( real @ fun ) ) > complex > TA ) ).
thf(complex_rec_decl,type,
complex_rec:
!>[TA: $tType] : ( ( TA @ ( real @ fun ) @ ( real @ fun ) ) > complex > TA ) ).
thf(fundam1563812824_csqrt_decl,type,
fundam1563812824_csqrt: complex > complex ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(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(sqrt_decl,type,
sqrt: real > real ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(norm_norm_decl,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(x_decl,type,
x: real ).
thf(y_decl,type,
y: real ).
thf(z_decl,type,
z: complex ).
thf(141,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_number__of__Pls) ).
thf(550,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(172,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).
thf(645,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)],[172]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__special_I3_J) ).
thf(365,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(115,axiom,
real @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(479,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(113,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Bit1__def) ).
thf(468,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(40,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(234,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(117,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(481,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,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_77_left__distrib__number__of) ).
thf(333,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)],[70]) ).
thf(46,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(249,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(130,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_94_power__mult__distrib) ).
thf(523,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)],[130]) ).
thf(36,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( C @ ( D @ complex1 ) )
= ( A @ ( B @ complex1 ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_complex_Oinject) ).
thf(217,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ complex1 ) )
= ( A @ ( B @ complex1 ) ) ) )
& ( ( ( C @ ( D @ complex1 ) )
= ( A @ ( B @ complex1 ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(173,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_number__of__is__id) ).
thf(655,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(21,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(202,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
~ ! [A: real,B: real] :
( z
!= ( B @ ( A @ complex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(185,plain,
~ ! [A: real,B: real] :
( z
!= ( B @ ( A @ complex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(98,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A @ ( B @ complex1 ) @ ( C @ ( D @ complex1 ) @ ( complex @ plus_plus ) ) )
= ( A @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( D @ ( real @ plus_plus ) ) @ complex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_complex__add) ).
thf(417,plain,
! [A: real,B: real,C: real,D: real] :
( ( A @ ( B @ complex1 ) @ ( C @ ( D @ complex1 ) @ ( complex @ plus_plus ) ) )
= ( A @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( D @ ( real @ plus_plus ) ) @ complex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(104,axiom,
real @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(436,plain,
real @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(7,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(184,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(155,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_20_add__number__of__left) ).
thf(587,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)],[155]) ).
thf(15,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(196,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(159,axiom,
real @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(606,plain,
real @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(97,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(416,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(35,axiom,
int @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(216,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult_Ocomm__neutral) ).
thf(492,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(108,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rel__simps_I38_J) ).
thf(443,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(321,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(120,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ times_times ) ) @ sqrt )
= ( A @ sqrt @ ( B @ sqrt @ ( real @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_real__sqrt__mult) ).
thf(485,plain,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ times_times ) ) @ sqrt )
= ( A @ sqrt @ ( B @ sqrt @ ( real @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(44,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(238,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_norm__mult) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(116,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(480,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(30,axiom,
complex @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(211,plain,
complex @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(48,axiom,
real @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(253,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(92,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(397,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(58,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(293,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(132,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_one__is__num__one) ).
thf(527,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(25,axiom,
int @ linord581940658strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(206,plain,
int @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(233,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(106,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_85_power2__eq__square__number__of) ).
thf(439,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)],[106]) ).
thf(139,axiom,
real @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(546,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(20,axiom,
complex @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(201,plain,
complex @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(381,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_nat__add__left__cancel) ).
thf(270,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(133,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_84_zero__power2) ).
thf(529,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)],[133]) ).
thf(62,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(302,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,axiom,
! [A: int,B: real,C: real] :
( ( ( B @ ( C @ complex1 ) )
= ( A @ ( complex @ number_number_of ) ) )
<=> ( ( B
= ( real @ zero_zero ) )
& ( C
= ( A @ ( real @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Complex__eq__number__of) ).
thf(349,plain,
! [A: int,B: real,C: real] :
( ( ( ( B
= ( real @ zero_zero ) )
& ( C
= ( A @ ( real @ number_number_of ) ) ) )
=> ( ( B @ ( C @ complex1 ) )
= ( A @ ( complex @ number_number_of ) ) ) )
& ( ( ( B @ ( C @ complex1 ) )
= ( A @ ( complex @ number_number_of ) ) )
=> ( ( B
= ( real @ zero_zero ) )
& ( C
= ( A @ ( real @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(146,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_add__right__cancel) ).
thf(561,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(60,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nat__1__add__1) ).
thf(297,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(101,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_14_eq__number__of) ).
thf(424,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)],[101]) ).
thf(11,axiom,
complex @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(192,plain,
complex @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(119,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(484,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(16,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(197,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(167,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_norm__eq__zero) ).
thf(625,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) )
& ( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(153,axiom,
! [A: real,B: real,C: real,D: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( D @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( real @ times_times ) ) @ sqrt @ ( real @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( D @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( real @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_real__sqrt__sum__squares__mult__squared__eq) ).
thf(583,plain,
! [A: real,B: real,C: real,D: real] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( D @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( real @ times_times ) ) @ sqrt @ ( real @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( D @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ ( real @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(163,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(615,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(99,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_78_right__distrib__number__of) ).
thf(420,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)],[99]) ).
thf(114,axiom,
! [A: real] :
( ( ( A @ sqrt )
= ( real @ one_one ) )
<=> ( A
= ( real @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_real__sqrt__eq__1__iff) ).
thf(471,plain,
! [A: real] :
( ( ( A
= ( real @ one_one ) )
=> ( ( A @ sqrt )
= ( real @ one_one ) ) )
& ( ( ( A @ sqrt )
= ( real @ one_one ) )
=> ( A
= ( real @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__imp__eq) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(12,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(193,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(177,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_one__power2) ).
thf(669,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(131,axiom,
real @ linord581940658strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
thf(526,plain,
real @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(156,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(590,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)],[156]) ).
thf(140,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_95_power__commutes) ).
thf(547,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)],[140]) ).
thf(31,axiom,
complex @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(212,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__add__commute) ).
thf(622,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(148,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__right__imp__eq) ).
thf(569,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_semiring__numeral__1__eq__1) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
complex @ real_normed_vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(205,plain,
complex @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_one__reorient) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(154,axiom,
real @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(586,plain,
real @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(176,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_double__zero__sym) ).
thf(662,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(72,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_23_add__Bit1__Bit0) ).
thf(343,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)],[72]) ).
thf(43,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(237,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(165,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rel__simps_I50_J) ).
thf(618,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_numeral__1__eq__1) ).
thf(264,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
complex @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring) ).
thf(180,plain,
complex @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(100,axiom,
real @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(423,plain,
real @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(191,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(151,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_21_add__number__of__eq) ).
thf(577,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)],[151]) ).
thf(23,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(204,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__left__imp__eq) ).
thf(413,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(170,axiom,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex1 ) @ ( C @ ( TA @ complex_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_complex_Osimps_I2_J) ).
thf(641,plain,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex1 ) @ ( C @ ( TA @ complex_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(87,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(382,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(149,axiom,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ norm_norm ) )
= ( real @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_norm__one) ).
thf(572,plain,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ norm_norm ) )
= ( real @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(42,axiom,
complex @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(236,plain,
complex @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(4,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(181,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(137,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_72_mult__number__of__left) ).
thf(540,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)],[137]) ).
thf(94,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I39_J) ).
thf(406,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(84,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(377,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_number__of__mult) ).
thf(451,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__special_I2_J) ).
thf(318,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(27,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(208,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(164,axiom,
( ( real @ one_one @ sqrt )
= ( real @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_real__sqrt__one) ).
thf(616,plain,
( ( real @ one_one @ sqrt )
= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult__1__left) ).
thf(303,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(90,axiom,
! [A: complex] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ fundam1563812824_csqrt @ ( complex @ power_power ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_csqrt) ).
thf(387,plain,
! [A: complex] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ fundam1563812824_csqrt @ ( complex @ power_power ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(135,axiom,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ sqrt )
= B )
=> ( A
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_real__sqrt__sum__squares__eq__cancel) ).
thf(535,plain,
! [A: real,B: real] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ sqrt )
= B )
=> ( A
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(161,axiom,
! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ sqrt )
= ( A @ ( B @ sqrt @ ( real @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_real__sqrt__power) ).
thf(609,plain,
! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ sqrt )
= ( A @ ( B @ sqrt @ ( real @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(32,axiom,
complex @ real_n1866405975lgebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) ).
thf(213,plain,
complex @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult__1) ).
thf(520,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(17,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(198,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_power__one) ).
thf(330,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(54,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(278,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(111,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_73_power__eq__0__iff) ).
thf(455,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)],[111]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_sum__squares__eq__zero__iff) ).
thf(306,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(61,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_36_add__numeral__0__right) ).
thf(299,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)],[61]) ).
thf(52,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_19_add__Bit0__Bit0) ).
thf(267,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)],[52]) ).
thf(102,axiom,
( z
= ( y @ ( x @ complex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_z) ).
thf(431,plain,
( z
= ( y @ ( x @ complex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(174,axiom,
nat @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(658,plain,
nat @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(83,axiom,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex1 ) @ ( C @ ( TA @ complex_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_complex_Orecs) ).
thf(374,plain,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex1 ) @ ( C @ ( TA @ complex_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(28,axiom,
complex @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(209,plain,
complex @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(142,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__Pls) ).
thf(553,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(13,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(194,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(144,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [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_49_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(557,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [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)],[144]) ).
thf(152,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_semiring__norm_I110_J) ).
thf(580,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(169,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(640,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(55,axiom,
real @ real_n1866405975lgebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) ).
thf(282,plain,
real @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(18,axiom,
complex @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(199,plain,
complex @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(182,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_rel__simps_I49_J) ).
thf(370,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(75,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(359,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(71,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_83_zero__eq__power2) ).
thf(336,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)],[71]) ).
thf(157,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_35_add__numeral__0) ).
thf(600,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)],[157]) ).
thf(89,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(386,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(162,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_number__of__Bit1) ).
thf(612,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(136,axiom,
real @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(539,plain,
real @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(124,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(495,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(80,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(368,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,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_71_arith__simps_I32_J) ).
thf(250,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)],[47]) ).
thf(112,axiom,
! [A: real,B: real] :
( ( A @ ( B @ complex1 ) @ ( complex @ norm_norm ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ sqrt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_complex__norm) ).
thf(465,plain,
! [A: real,B: real] :
( ( A @ ( B @ complex1 ) @ ( complex @ norm_norm ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) @ sqrt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(37,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(231,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(77,axiom,
real @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(363,plain,
real @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(143,axiom,
real @ real_n2089651433ebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) ).
thf(556,plain,
real @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(118,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Numeral1__eq1__nat) ).
thf(482,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(22,axiom,
complex @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(203,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat__add__left__commute) ).
thf(517,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(390,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(168,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rel__simps_I44_J) ).
thf(632,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(147,axiom,
real @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(568,plain,
real @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(41,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(235,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(103,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__Pls__right) ).
thf(433,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(26,axiom,
complex @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(207,plain,
complex @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_nat__add__assoc) ).
thf(383,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(73,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_34_number__of__add) ).
thf(346,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)],[73]) ).
thf(33,axiom,
complex @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__add) ).
thf(214,plain,
complex @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_one__add__one__is__two) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(85,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Bit0__def) ).
thf(378,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_power__one__right) ).
thf(315,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ norm_norm ) )
= ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_norm__power) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ norm_norm ) )
= ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(50,axiom,
( ( real @ zero_zero @ sqrt )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_real__sqrt__zero) ).
thf(262,plain,
( ( real @ zero_zero @ sqrt )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
complex @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) ).
thf(190,plain,
complex @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(183,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(158,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mult__1__right) ).
thf(603,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(29,axiom,
complex @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add) ).
thf(210,plain,
complex @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [A: real,B: real] :
( ( ( B @ sqrt )
= ( A @ sqrt ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_real__sqrt__eq__iff) ).
thf(239,plain,
! [A: real,B: real] :
( ( ( B = A )
=> ( ( B @ sqrt )
= ( A @ sqrt ) ) )
& ( ( ( B @ sqrt )
= ( A @ sqrt ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,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_24_add__Bit0__Bit1) ).
thf(294,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)],[59]) ).
thf(126,axiom,
! [A: real] :
( ( ( A @ sqrt )
= ( real @ zero_zero ) )
<=> ( A
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_real__sqrt__eq__0__iff) ).
thf(506,plain,
! [A: real] :
( ( ( A
= ( real @ zero_zero ) )
=> ( ( A @ sqrt )
= ( real @ zero_zero ) ) )
& ( ( ( A @ sqrt )
= ( real @ zero_zero ) )
=> ( A
= ( real @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(14,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(195,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(105,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Bit0__Pls) ).
thf(437,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(134,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_plus__numeral__code_I9_J) ).
thf(532,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add__left__cancel) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(150,axiom,
( ( z @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(575,plain,
( ( z @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(171,axiom,
real @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(644,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(19,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(200,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
= ( real @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
!= ( real @ one_one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(178,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( real @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( real @ power_power ) ) @ ( real @ plus_plus ) ) )
!= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,axiom,
real @ real_normed_vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(442,plain,
real @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(81,axiom,
real @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(369,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(160,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nat__numeral__1__eq__1) ).
thf(607,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(49,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_33_number__of__reorient) ).
thf(254,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)],[49]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nat__add__right__cancel) ).
thf(322,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(175,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_norm__zero) ).
thf(659,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(138,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_semiring__one__add__one__is__two) ).
thf(543,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(34,axiom,
complex @ real_n2089651433ebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) ).
thf(215,plain,
complex @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(145,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(560,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(122,axiom,
real @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(491,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(78,axiom,
real @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(364,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(38,axiom,
complex @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) ).
thf(232,plain,
complex @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(125,axiom,
! [A: real,B: real] :
( ( ( A @ ( B @ complex1 ) )
= ( complex @ one_one ) )
<=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Complex__eq__1) ).
thf(496,plain,
! [A: real,B: real] :
( ( ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ one_one ) ) )
=> ( ( A @ ( B @ complex1 ) )
= ( complex @ one_one ) ) )
& ( ( ( A @ ( B @ complex1 ) )
= ( complex @ one_one ) )
=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(110,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(454,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(703,plain,
$false,
inference(e,[status(thm)],[550,645,365,479,468,234,481,333,249,523,217,655,202,185,417,436,184,587,196,606,416,216,492,443,321,485,238,514,480,211,253,397,293,527,206,233,439,546,201,381,270,529,302,349,561,297,424,192,484,197,625,583,615,420,471,488,193,669,526,590,547,212,622,569,360,205,398,586,662,343,237,618,264,180,423,191,577,204,413,641,382,572,236,181,540,406,377,451,318,208,616,303,387,535,609,213,520,198,330,278,455,306,299,267,431,658,374,209,553,194,557,580,640,282,199,182,370,359,336,600,386,612,539,495,368,250,465,231,363,556,482,203,517,390,632,568,235,433,207,383,346,214,290,378,315,410,262,190,183,603,210,239,294,506,195,437,532,283,575,644,200,178,442,369,607,254,322,659,543,215,560,491,364,232,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW497_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % 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
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 16:07:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.59/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.87 % [INFO] Parsing done (175ms).
% 0.99/0.88 % [INFO] Running in sequential loop mode.
% 1.84/1.08 % [INFO] eprover registered as external prover.
% 1.84/1.08 % [INFO] Scanning for conjecture ...
% 2.12/1.17 % [INFO] Found a conjecture (or negated_conjecture) and 177 axioms. Running axiom selection ...
% 2.28/1.26 % [INFO] Axiom selection finished. Selected 175 axioms (removed 2 axioms).
% 2.90/1.43 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.90/1.45 % [INFO] Type checking passed.
% 2.90/1.45 % [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 ...
% 10.80/3.46 % External prover 'e' found a proof!
% 10.80/3.46 % [INFO] Killing All external provers ...
% 10.80/3.47 % Time passed: 2987ms (effective reasoning time: 2585ms)
% 10.80/3.47 % 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)>
% 10.80/3.47 % Axioms used in derivation (175): fact_6_numeral__1__eq__1, arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra, fact_60_nat__add__left__commute, arity_Nat_Onat___Groups_Omonoid__mult, fact_10_rel__simps_I44_J, fact_30_Bit0__def, arity_Int_Oint___Rings_Olinordered__ring__strict, fact_80_norm__zero, arity_Int_Oint___Groups_Oone, fact_70_double__eq__0__iff, arity_Complex_Ocomplex___Groups_Oab__semigroup__add, arity_Nat_Onat___Rings_Osemiring__1, fact_17__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_RealDef_Oreal___Rings_Olinordered__ring__strict, arity_Int_Oint___Int_Oring__char__0, fact_86_real__sqrt__mult, fact_95_power__commutes, fact_20_add__number__of__left, arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra, fact_5_add__special_I3_J, fact_92_mult__1, arity_Complex_Ocomplex___Power_Opower, fact_66_real__sqrt__sum__squares__mult__squared__eq, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_61_nat__add__commute, arity_RealDef_Oreal___Groups_Ozero, fact_16_rel__simps_I48_J, fact_82_Complex__eq__1, arity_Nat_Onat___Int_Onumber__semiring, arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add, fact_55_complex__norm, fact_19_add__Bit0__Bit0, arity_RealDef_Oreal___Int_Onumber__semiring, fact_8_Bit0__Pls, fact_69_double__zero__sym, arity_Nat_Onat___Power_Opower, fact_25_nat__1__add__1, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, fact_1_z, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, arity_Complex_Ocomplex___Int_Oring__char__0, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_21_add__number__of__eq, fact_87_number__of__mult, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Int_Onumber__semiring, fact_28_add__Pls__right, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_46_add__right__cancel, arity_Int_Oint___Int_Onumber__ring, arity_Int_Oint___Rings_Osemiring__1, fact_63_real__sqrt__eq__1__iff, arity_Nat_Onat___Rings_Omult__zero, fact_68_real__sqrt__sum__squares__eq__cancel, fact_83_zero__eq__power2, fact_67_complex_Orecs, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_7_semiring__one__add__one__is__two, fact_48_number__of__is__id, fact_77_left__distrib__number__of, fact_51_add__imp__eq, fact_65_real__sqrt__power, fact_88_norm__mult, fact_76_Complex__eq__number__of, fact_54_power__one__right, fact_39_semiring__norm_I110_J, fact_78_right__distrib__number__of, fact_14_eq__number__of, arity_RealDef_Oreal___Rings_Osemiring__1, fact_79_number__of__Pls, fact_12_rel__simps_I50_J, fact_37_number__of__Bit1, fact_81_norm__eq__zero, arity_Complex_Ocomplex___Rings_Osemiring, fact_85_power2__eq__square__number__of, arity_RealDef_Oreal___Int_Onumber__ring, fact_4_add__special_I2_J, fact_27_plus__numeral__code_I9_J, arity_Int_Oint___Groups_Omonoid__mult, fact_52_add__right__imp__eq, fact_36_add__numeral__0__right, fact_89_sum__squares__eq__zero__iff, fact_42_power__one, fact_94_power__mult__distrib, arity_Complex_Ocomplex___Rings_Omult__zero, fact_64_real__sqrt__eq__iff, fact_49_ab__semigroup__add__class_Oadd__ac_I1_J, fact_74_real__sqrt__zero, arity_Int_Oint___Rings_Osemiring, fact_72_mult__number__of__left, fact_11_rel__simps_I49_J, fact_71_arith__simps_I32_J, fact_24_add__Bit0__Bit1, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1, fact_62_real__sqrt__one, arity_Nat_Onat___Groups_Ozero, fact_56_nat__add__left__cancel, fact_91_mult__1__right, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_RealDef_Oreal___Int_Oring__char__0, fact_53_one__reorient, arity_RealDef_Oreal___Rings_Omult__zero, fact_93_mult__1__left, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_29_add__Pls, arity_RealDef_Oreal___Rings_Osemiring, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, arity_Complex_Ocomplex___Int_Onumber__ring, fact_38_semiring__numeral__1__eq__1, arity_Int_Oint___Power_Opower, fact_47_add__left__cancel, arity_Int_Oint___Groups_Ocancel__semigroup__add, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, arity_Complex_Ocomplex___Rings_Osemiring__1, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_57_nat__add__right__cancel, arity_RealDef_Oreal___Groups_Oone, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_73_power__eq__0__iff, fact_13_rel__simps_I39_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_32_Numeral1__eq1__nat, fact_40_norm__one, arity_Complex_Ocomplex___Groups_Oone, arity_RealDef_Oreal___Groups_Omonoid__mult, arity_Nat_Onat___Groups_Oone, fact_31_one__is__num__one, fact_84_zero__power2, fact_90_mult_Ocomm__neutral, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_41_complex__add, arity_Int_Oint___Groups_Oab__semigroup__add, fact_35_add__numeral__0, arity_Nat_Onat___Rings_Osemiring, fact_59_nat__add__assoc, arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add, arity_RealDef_Oreal___Power_Opower, fact_33_number__of__reorient, fact_50_add__left__imp__eq, fact_26_Bit1__def, arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1, fact_23_add__Bit1__Bit0, arity_Complex_Ocomplex___Int_Onumber__semiring, fact_75_real__sqrt__eq__0__iff, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_58_complex_Osimps_I2_J, arity_Complex_Ocomplex___Int_Onumber, arity_RealDef_Oreal___Int_Onumber, fact_22_nat__numeral__1__eq__1, fact_45_complex_Oinject, arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_0_assms, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, fact_3_one__add__one__is__two, fact_44_norm__power, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_34_number__of__add, fact_15_rel__simps_I51_J, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_18_rel__simps_I46_J, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_2_one__power2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_9_rel__simps_I38_J, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_43_csqrt
% 10.80/3.47 % No. of inferences in proof: 354
% 10.80/3.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2987 ms resp. 2585 ms w/o parsing
% 11.71/3.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.71/3.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------