%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM951_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:31 AM UTC 2026
% Result : Theorem 7.80s 3.60s
% Output : Refutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 122
% Syntax : Number of formulae : 246 ( 138 unt; 0 typ; 0 def)
% Number of atoms : 411 ( 258 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2082 ( 20 ~; 7 |; 29 &;1897 @)
% ( 11 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 386 ( 0 ^; 386 !; 0 ?; 386 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[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(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
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(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(min_decl,type,
min: int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(s_decl,type,
s: int ).
thf(7,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_right__distrib__number__of) ).
thf(138,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)],[7]) ).
thf(75,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(347,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(70,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(333,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mult__Bit0) ).
thf(234,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)],[42]) ).
thf(114,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(481,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mult__1__right) ).
thf(379,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(101,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(440,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(31,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I37_J) ).
thf(202,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__numeral__0__right) ).
thf(385,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)],[86]) ).
thf(122,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Bit0__def) ).
thf(500,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I40_J) ).
thf(340,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(185,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_add__special_I2_J) ).
thf(320,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)],[64]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
<=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zmult__eq__1__iff) ).
thf(257,plain,
! [A: int,B: int] :
( ( ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) )
=> ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) ) )
& ( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_95_add__imp__eq) ).
thf(196,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)],[29]) ).
thf(15,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(157,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(189,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_power__add) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: nat,C: TA] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_power__m1__even) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(112,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_diff__bin__simps_I10_J) ).
thf(475,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(83,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__Pls__right) ).
thf(376,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_semiring__numeral__1__eq__1) ).
thf(485,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_number__of__add) ).
thf(238,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)],[44]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_93_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(348,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)],[76]) ).
thf(119,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I46_J) ).
thf(492,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(18,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I43_J) ).
thf(164,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__Pls) ).
thf(147,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__1) ).
thf(280,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)],[54]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_80_power__commutes) ).
thf(132,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)],[5]) ).
thf(57,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_int__distrib_I2_J) ).
thf(292,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(106,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Bit1__def) ).
thf(452,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_number__of__mult) ).
thf(248,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)],[46]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_82_power__mult) ).
thf(334,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)],[71]) ).
thf(96,axiom,
! [A: int] :
( ( A @ bit0 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_diff__bin__simps_I5_J) ).
thf(424,plain,
! [A: int] :
( ( A @ bit0 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__number__of__left) ).
thf(275,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)],[51]) ).
thf(111,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I38_J) ).
thf(467,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_number__of__Bit1) ).
thf(461,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)],[109]) ).
thf(38,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(224,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_arith__simps_I32_J) ).
thf(317,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)],[63]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__Bit1__Bit0) ).
thf(388,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)],[87]) ).
thf(8,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_nat__numeral__1__eq__1) ).
thf(141,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(121,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(499,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__numeral__0) ).
thf(328,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)],[68]) ).
thf(117,axiom,
nat @ comm_monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(488,plain,
nat @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(28,axiom,
! [A: nat] :
( ( ( A @ ( min @ ( int @ number_number_of ) @ ( int @ power_power ) ) )
= ( min @ ( int @ number_number_of ) ) )
| ( ( A @ ( min @ ( int @ number_number_of ) @ ( int @ power_power ) ) )
= ( int @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_neg__one__power) ).
thf(193,plain,
! [A: nat] :
( ( ( A @ ( min @ ( int @ number_number_of ) @ ( int @ power_power ) ) )
= ( min @ ( int @ number_number_of ) ) )
| ( ( A @ ( min @ ( int @ number_number_of ) @ ( int @ power_power ) ) )
= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_left__diff__distrib__number__of) ).
thf(489,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(35,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(212,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1,conjecture,
( ( min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) )
= ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) )
!= ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(124,plain,
( ( min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) )
!= ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_0_one__power2) ).
thf(225,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)],[39]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_power__one) ).
thf(129,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)],[4]) ).
thf(81,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_nat__1__add__1) ).
thf(371,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)],[81]) ).
thf(123,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(503,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(32,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( 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 @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_right__diff__distrib__number__of) ).
thf(205,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( 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 @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(61,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ minus_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__bin__simps_I1_J) ).
thf(311,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ minus_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I50_J) ).
thf(343,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(43,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(237,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(93,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_diff__bin__simps_I6_J) ).
thf(412,plain,
! [A: int] :
( ( A @ bit1 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult__numeral__1__right) ).
thf(161,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)],[17]) ).
thf(53,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(279,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(103,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I42_J) ).
thf(444,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(22,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Bit0__Pls) ).
thf(180,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I44_J) ).
thf(296,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(95,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(423,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(90,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_int__distrib_I3_J) ).
thf(402,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(88,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_pos__zmult__eq__1__iff__lemma) ).
thf(391,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_plus__numeral__code_I9_J) ).
thf(382,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)],[85]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_semiring__norm_I110_J) ).
thf(144,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add__Bit0__Bit0) ).
thf(172,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)],[19]) ).
thf(50,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(274,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(105,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(451,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(99,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_int__distrib_I1_J) ).
thf(434,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(33,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(208,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_numeral__1__eq__1) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(36,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(213,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(47,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_diff__bin__simps_I7_J) ).
thf(251,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(52,axiom,
int @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(278,plain,
int @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(107,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_quartic__square__square) ).
thf(455,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(89,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I47_J) ).
thf(394,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(6,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
thf(135,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)],[6]) ).
thf(98,axiom,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_eq__number__of__Pls__Min) ).
thf(431,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__right__cancel) ).
thf(241,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)],[45]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__number__of__diff1) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(108,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__Bit1) ).
thf(458,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(58,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(295,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
nat @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(150,plain,
nat @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(327,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult__1__left) ).
thf(409,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__numeral__1) ).
thf(199,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)],[30]) ).
thf(69,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Numeral1__eq1__nat) ).
thf(331,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_left__distrib__number__of) ).
thf(441,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)],[102]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_79_power__mult__distrib) ).
thf(177,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)],[21]) ).
thf(23,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_diff__bin__simps_I9_J) ).
thf(182,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_semiring__one__add__one__is__two) ).
thf(154,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)],[14]) ).
thf(20,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_one__is__num__one) ).
thf(175,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_63_power2__eq__square__number__of) ).
thf(314,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)],[62]) ).
thf(9,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(143,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_number__of__is__id) ).
thf(231,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_power2__diff) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__number__of__eq) ).
thf(368,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)],[80]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_eq__number__of) ).
thf(304,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)],[60]) ).
thf(25,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__Pls) ).
thf(186,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__add__one__is__two) ).
thf(158,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)],[16]) ).
thf(77,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_diff__bin__simps_I3_J) ).
thf(351,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(56,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Bit1__Min) ).
thf(290,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mult_Ocomm__neutral) ).
thf(478,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)],[113]) ).
thf(37,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I48_J) ).
thf(214,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)],[37]) ).
thf(13,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_diff__bin__simps_I4_J) ).
thf(151,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I49_J) ).
thf(405,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_88_zpower__zpower) ).
thf(190,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)],[27]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__left__imp__eq) ).
thf(373,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)],[82]) ).
thf(66,axiom,
int @ ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(326,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [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/sandbox2/benchmark/theBenchmark.p',fact_81_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(126,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [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)],[3]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_add__special_I3_J) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_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)],[55]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_number__of__reorient) ).
thf(415,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)],[94]) ).
thf(110,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_int__distrib_I4_J) ).
thf(464,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(97,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I45_J) ).
thf(427,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_number__of__diff) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_times__numeral__code_I5_J) ).
thf(337,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)],[72]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I51_J) ).
thf(354,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)],[78]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__number__of__left) ).
thf(496,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)],[120]) ).
thf(79,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I39_J) ).
thf(364,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(511,plain,
$false,
inference(e,[status(thm)],[138,347,333,234,481,379,440,202,385,500,340,185,320,257,196,157,189,228,448,475,376,485,238,348,492,164,147,280,132,292,452,248,334,424,275,467,461,224,317,388,141,499,328,488,193,489,212,124,225,129,371,503,205,311,343,237,412,161,279,444,180,296,423,402,391,382,144,172,274,451,434,208,323,213,251,278,455,394,135,431,241,209,458,295,150,327,409,199,331,441,177,182,154,175,314,143,231,482,368,304,186,158,351,290,478,214,151,405,190,373,326,126,437,283,415,464,427,254,337,354,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM951_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 04:22:49 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.31 % [INFO] Parsing done (280ms).
% 1.81/1.32 % [INFO] Running in sequential loop mode.
% 2.55/1.71 % [INFO] eprover registered as external prover.
% 2.55/1.71 % [INFO] Scanning for conjecture ...
% 2.75/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 2.93/1.98 % [INFO] Axiom selection finished. Selected 121 axioms (removed 2 axioms).
% 3.52/2.15 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.52/2.16 % [INFO] Type checking passed.
% 3.52/2.17 % [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 ...
% 7.40/3.59 % External prover 'e' found a proof!
% 7.40/3.59 % [INFO] Killing All external provers ...
% 7.40/3.59 % Time passed: 3005ms (effective reasoning time: 2268ms)
% 7.40/3.60 % 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)>
% 7.80/3.60 % Axioms used in derivation (121): fact_79_power__mult__distrib, fact_93_ab__semigroup__add__class_Oadd__ac_I1_J, fact_9_diff__bin__simps_I9_J, fact_8_diff__bin__simps_I3_J, arity_Nat_Onat___Groups_Omonoid__mult, fact_87_int__distrib_I3_J, fact_65_mult__Bit0, fact_11_add__Bit0__Bit1, arity_Int_Oint___Groups_Oone, arity_Nat_Onat___Groups_Oab__semigroup__mult, fact_54_one__is__num__one, arity_Nat_Onat___Rings_Osemiring__1, fact_76_mult__1__right, arity_Int_Oint___Int_Oring__char__0, fact_78_mult__1__left, fact_59_add__right__cancel, fact_64_mult__Pls, fact_77_mult__1, fact_60_add__left__cancel, arity_Nat_Onat___Int_Onumber__semiring, fact_81_ab__semigroup__mult__class_Omult__ac_I1_J, fact_21_Bit0__Pls, fact_23_diff__bin__simps_I7_J, fact_16_rel__simps_I39_J, fact_50_number__of__Bit1, fact_40_add__Pls, fact_44_add__numeral__0, fact_32_add__number__of__eq, fact_35_nat__1__add__1, fact_0_one__power2, arity_Int_Oint___Rings_Oring, fact_69_left__distrib__number__of, fact_86_int__distrib_I4_J, fact_51_semiring__numeral__1__eq__1, fact_45_add__numeral__0__right, fact_27_rel__simps_I37_J, arity_Int_Oint___Int_Onumber__semiring, fact_82_power__mult, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_1_add__special_I2_J, arity_Int_Oint___Int_Onumber__ring, fact_56_quartic__square__square, arity_Int_Oint___Rings_Osemiring__1, fact_4_diff__bin__simps_I5_J, fact_46_number__of__add, fact_15_rel__simps_I46_J, fact_10_diff__bin__simps_I10_J, fact_61_power__m1__even, fact_17_rel__simps_I50_J, fact_47_number__of__diff, fact_94_add__left__imp__eq, fact_80_power__commutes, fact_89_mult__numeral__1__right, fact_49_eq__number__of__Pls__Min, fact_67_mult__number__of__left, fact_19_rel__simps_I44_J, fact_28_rel__simps_I40_J, fact_68_right__distrib__number__of, arity_Int_Oint___Groups_Omonoid__mult, fact_66_arith__simps_I32_J, fact_24_rel__simps_I47_J, fact_88_zpower__zpower, fact_36_Numeral1__eq1__nat, fact_6_diff__bin__simps_I4_J, fact_7_numeral__1__eq__1, arity_Int_Oint___Rings_Osemiring, fact_58_neg__one__power, fact_55_semiring__one__add__one__is__two, fact_57_power__one, fact_52_semiring__norm_I110_J, fact_25_rel__simps_I43_J, fact_22_add__Bit0__Bit0, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_13_rel__simps_I51_J, fact_31_add__number__of__left, fact_29_rel__simps_I45_J, fact_73_number__of__mult, fact_84_int__distrib_I2_J, fact_12_eq__number__of, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_72_mult__Bit1, fact_37_number__of__reorient, fact_85_int__distrib_I1_J, fact_48_Bit1__def, fact_2_add__special_I3_J, arity_Nat_Onat___Int_Onumber, fact_14_rel__simps_I48_J, fact_91_zmult__eq__1__iff, arity_Nat_Onat___Groups_Oone, fact_71_left__diff__distrib__number__of, arity_Int_Oint___Groups_Oab__semigroup__add, fact_18_rel__simps_I49_J, fact_62_power2__diff, fact_74_power__add, fact_30_rel__simps_I42_J, arity_Nat_Onat___Rings_Osemiring, fact_34_add__Bit1__Bit0, fact_33_nat__numeral__1__eq__1, fact_26_Bit1__Min, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_39_add__Pls__right, fact_95_add__imp__eq, fact_5_diff__bin__simps_I6_J, arity_Int_Oint___Int_Onumber, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_42_diff__bin__simps_I1_J, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_3_one__add__one__is__two, fact_43_plus__numeral__code_I9_J, fact_83_times__numeral__code_I5_J, fact_38_number__of__is__id, fact_63_power2__eq__square__number__of, fact_53_add__number__of__diff1, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_70_right__diff__distrib__number__of, fact_20_rel__simps_I38_J, fact_92_pos__zmult__eq__1__iff__lemma, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_41_Bit0__def, fact_90_mult__numeral__1, fact_75_mult_Ocomm__neutral
% 7.80/3.60 % No. of inferences in proof: 246
% 7.80/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3005 ms resp. 2268 ms w/o parsing
% 8.13/3.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.13/3.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------