%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM944_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 : n010.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 08:10:30 AM UTC 2026
% Result : Theorem 8.40s 3.43s
% Output : Refutation 8.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 110
% Syntax : Number of formulae : 222 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 404 ( 260 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2243 ( 33 ~; 8 |; 30 &;2028 @)
% ( 12 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 412 ( 0 ^; 412 !; 0 ?; 412 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zprime_decl,type,
zprime: int > $o ).
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(legendre_decl,type,
legendre: int > int > int ).
thf(quadRes_decl,type,
quadRes: int > int > $o ).
thf(m_decl,type,
m: int ).
thf(40,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_15_eq__number__of) ).
thf(234,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)],[40]) ).
thf(82,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_number__of__is__id) ).
thf(384,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(74,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_12_arith__simps_I32_J) ).
thf(360,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)],[74]) ).
thf(104,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p) ).
thf(466,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(314,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(5,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(115,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(53,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_35_left__distrib__number__of) ).
thf(276,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)],[53]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(404,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(301,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(66,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_nat__numeral__1__eq__1) ).
thf(320,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(46,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Bit1__def) ).
thf(257,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_semiring__mult__2__right) ).
thf(372,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(73,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_9_add__Bit1__Bit0) ).
thf(357,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)],[73]) ).
thf(18,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_5_one__add__one__is__two) ).
thf(152,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)],[18]) ).
thf(38,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Bit0__def) ).
thf(228,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(98,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_48_number__of__mult) ).
thf(448,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)],[98]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(261,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(216,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__Pls) ).
thf(179,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(110,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Bit0__Pls) ).
thf(485,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(121,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32,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_10_add__number__of__eq) ).
thf(211,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)],[32]) ).
thf(45,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rel__simps_I42_J) ).
thf(253,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(86,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_14_right__distrib__number__of) ).
thf(396,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)],[86]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(411,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
<=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat__1__eq__mult__iff) ).
thf(428,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) )
=> ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) ) )
& ( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(6,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(116,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_int__distrib_I1_J) ).
thf(243,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)],[42]) ).
thf(7,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(117,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_times__numeral__code_I5_J) ).
thf(270,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)],[51]) ).
thf(81,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mult__Bit0) ).
thf(381,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)],[81]) ).
thf(76,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_11_add__number__of__left) ).
thf(366,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)],[76]) ).
thf(47,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(260,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_double__number__of__Bit0) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(105,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_4_add__special_I3_J) ).
thf(467,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)],[105]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_crossproduct__eq) ).
thf(197,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(102,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Bit1__Min) ).
thf(461,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_semiring__norm_I110_J) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_numeral__1__eq__1) ).
thf(317,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(22,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(169,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(141,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,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_13_mult__number__of__left) ).
thf(339,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)],[68]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_mult__Bit1) ).
thf(124,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)],[10]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',fact_56_pos__zmult__eq__1__iff__lemma) ).
thf(225,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)],[37]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(298,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(95,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_46_add__numeral__0) ).
thf(425,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)],[95]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_semiring__mult__2) ).
thf(166,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(148,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(264,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(279,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__2__right) ).
thf(375,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(25,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_nat__mult__2__right) ).
thf(176,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nat__mult__2) ).
thf(291,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(8,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I40_J) ).
thf(118,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(172,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(113,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mult__numeral__1) ).
thf(219,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)],[35]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
thf(451,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(70,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(345,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(19,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).
thf(155,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(130,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(87,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_one__is__num__one) ).
thf(399,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(100,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_44_plus__numeral__code_I9_J) ).
thf(455,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)],[100]) ).
thf(50,axiom,
! [A: int] :
( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime )
=> ( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Legendre__1mod4) ).
thf(267,plain,
! [A: int] :
( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime )
=> ( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_crossproduct__noteq) ).
thf(438,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(41,axiom,
( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(241,plain,
( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(107,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(473,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(111,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_64_nat__1__add__1) ).
thf(487,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)],[111]) ).
thf(1,conjecture,
min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(112,plain,
~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_semiring__numeral__1__eq__1) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mult__numeral__1__right) ).
thf(458,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)],[101]) ).
thf(29,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_63_semiring__one__add__one__is__two) ).
thf(194,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)],[29]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_mult__2) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,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_47_add__numeral__0__right) ).
thf(295,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)],[60]) ).
thf(55,axiom,
( ~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) )
=> ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
!= ( int @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_126_061_A1_096) ).
thf(282,plain,
( ~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) )
=> ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
!= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(93,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I47_J) ).
thf(414,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(27,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I39_J) ).
thf(182,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(103,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_int__distrib_I2_J) ).
thf(463,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)],[103]) ).
thf(11,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_51_number__of__Bit1) ).
thf(127,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)],[11]) ).
thf(106,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_3_add__special_I2_J) ).
thf(470,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)],[106]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(363,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(44,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_27_add__Bit0__Bit0) ).
thf(250,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)],[44]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I51_J) ).
thf(304,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)],[63]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(390,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(28,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_36_number__of__reorient) ).
thf(186,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)],[28]) ).
thf(4,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(114,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(401,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(80,axiom,
pls != min,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rel__simps_I37_J) ).
thf(378,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(43,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I45_J) ).
thf(246,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I50_J) ).
thf(207,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rel__simps_I43_J) ).
thf(346,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(33,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Numeral1__eq1__nat) ).
thf(214,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(151,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(410,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(94,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_49_number__of__add) ).
thf(422,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)],[94]) ).
thf(52,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_mult__Pls) ).
thf(273,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zprime__2) ).
thf(294,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(108,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I38_J) ).
thf(474,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_rel__simps_I48_J) ).
thf(131,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)],[13]) ).
thf(20,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__Pls__right) ).
thf(163,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(369,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',fact_57_zmult__eq__1__iff) ).
thf(322,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)],[67]) ).
thf(72,axiom,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_eq__number__of__Pls__Min) ).
thf(354,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,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_8_add__Bit0__Bit1) ).
thf(222,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)],[36]) ).
thf(529,plain,
$false,
inference(e,[status(thm)],[234,384,360,466,314,115,276,404,288,301,320,257,372,357,152,228,448,261,216,179,485,121,211,253,396,411,428,116,243,117,270,381,366,260,407,467,197,461,285,317,169,141,339,124,225,393,173,298,425,166,148,264,279,375,176,291,118,172,113,219,451,387,345,155,130,399,455,267,438,241,473,487,112,342,458,194,145,295,282,414,182,463,127,470,363,482,250,231,304,390,186,114,401,378,246,207,346,214,151,410,422,273,294,474,131,163,369,322,354,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM944_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n010.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 04:22:46 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.86/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.32 % [INFO] Parsing done (307ms).
% 1.79/1.33 % [INFO] Running in sequential loop mode.
% 2.68/1.74 % [INFO] eprover registered as external prover.
% 2.68/1.74 % [INFO] Scanning for conjecture ...
% 2.88/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 111 axioms. Running axiom selection ...
% 3.11/2.00 % [INFO] Axiom selection finished. Selected 109 axioms (removed 2 axioms).
% 3.75/2.19 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.92/2.21 % [INFO] Type checking passed.
% 3.92/2.21 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.40/3.42 % External prover 'e' found a proof!
% 8.40/3.42 % [INFO] Killing All external provers ...
% 8.40/3.42 % Time passed: 2858ms (effective reasoning time: 2081ms)
% 8.40/3.42 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.40/3.43 % Axioms used in derivation (109): arity_Int_Oint___Int_Oring__char__0, fact_3_add__special_I2_J, fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_1__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_126_061_A1_096, fact_41_times__numeral__code_I5_J, fact_25_mult__Pls, fact_47_add__numeral__0__right, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_51_number__of__Bit1, fact_54_semiring__numeral__1__eq__1, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_12_arith__simps_I32_J, fact_64_nat__1__add__1, fact_2_p, arity_Nat_Onat___Int_Onumber__semiring, fact_36_number__of__reorient, fact_40_Bit0__def, fact_52_mult__numeral__1, fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_43_int__distrib_I2_J, fact_30_Bit1__Min, fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_6_mult__Bit1, fact_48_number__of__mult, arity_Int_Oint___Int_Onumber__semiring, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_26_mult__Bit0, arity_Int_Oint___Int_Onumber__ring, fact_49_number__of__add, fact_35_left__distrib__number__of, fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_50_Bit1__def, fact_53_mult__numeral__1__right, fact_37_number__of__is__id, fact_61_semiring__mult__2__right, fact_59_semiring__mult__2, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_65_zprime__2, fact_68_eq__number__of__Pls__Min, fact_14_right__distrib__number__of, fact_22_rel__simps_I44_J, fact_46_add__numeral__0, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_38_add__Pls__right, fact_70_nat__mult__2__right, fact_67_semiring__norm_I110_J, fact_5_one__add__one__is__two, fact_58_double__number__of__Bit0, fact_44_plus__numeral__code_I9_J, fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_8_add__Bit0__Bit1, fact_17_rel__simps_I48_J, fact_90_crossproduct__eq, fact_7_numeral__1__eq__1, fact_13_mult__number__of__left, arity_Int_Oint___Rings_Osemiring, fact_24_Bit0__Pls, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_87_crossproduct__noteq, fact_11_add__number__of__left, fact_29_rel__simps_I43_J, fact_28_rel__simps_I47_J, fact_57_zmult__eq__1__iff, fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_19_rel__simps_I39_J, fact_4_add__special_I3_J, fact_45_Legendre__1mod4, fact_60_mult__2, fact_63_semiring__one__add__one__is__two, fact_69_nat__mult__2, fact_9_add__Bit1__Bit0, fact_34_rel__simps_I42_J, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_56_pos__zmult__eq__1__iff__lemma, fact_23_rel__simps_I38_J, fact_21_rel__simps_I49_J, fact_33_rel__simps_I45_J, arity_Nat_Onat___Int_Onumber, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_96_nat__1__eq__mult__iff, fact_42_int__distrib_I1_J, fact_0__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_62_mult__2__right, fact_32_rel__simps_I40_J, fact_55_one__is__num__one, arity_Nat_Onat___Rings_Osemiring, fact_93_Numeral1__eq1__nat, fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_20_rel__simps_I50_J, fact_39_add__Pls, fact_66_nat__numeral__1__eq__1, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, arity_Int_Oint___Int_Onumber, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_31_rel__simps_I37_J, fact_27_add__Bit0__Bit0, fact_16_rel__simps_I51_J, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_18_rel__simps_I46_J, fact_10_add__number__of__eq, fact_15_eq__number__of
% 8.40/3.43 % No. of inferences in proof: 222
% 8.40/3.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2858 ms resp. 2081 ms w/o parsing
% 8.88/3.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.88/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------