%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM942_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 : n005.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 20.08s 5.56s
% Output : Refutation 20.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 110
% Syntax : Number of formulae : 257 ( 113 unt; 0 typ; 0 def)
% Number of atoms : 509 ( 366 equ; 0 cnn)
% Maximal formula atoms : 18 ( 1 avg)
% Number of connectives : 2513 ( 68 ~; 46 |; 52 &;2193 @)
% ( 14 <=>; 140 =>; 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 : 20 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 471 ( 0 ^; 470 !; 1 ?; 471 :)
% 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(m_decl,type,
m: int ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_58_mult__2) ).
thf(329,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)],[64]) ).
thf(11,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(129,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,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_49_number__of__Bit1) ).
thf(187,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)],[30]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(263,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)],[44]) ).
thf(40,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_55_zmult__eq__1__iff) ).
thf(237,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)],[40]) ).
thf(238,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: 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 ) ) ) ) ) ),
inference(miniscope,[status(thm)],[237]) ).
thf(239,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( ( C @ ( D @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( C
!= ( min @ ( int @ number_number_of ) ) )
| ( D
!= ( min @ ( int @ number_number_of ) ) ) )
& ( ( ( C @ ( D @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( C
!= ( int @ one_one ) )
| ( D
!= ( int @ one_one ) ) )
& ( ( A
= ( min @ ( int @ number_number_of ) ) )
| ( A
= ( int @ one_one ) )
| ( ( A @ ( B @ ( int @ times_times ) ) )
!= ( int @ one_one ) ) )
& ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( A
= ( int @ one_one ) )
| ( ( A @ ( B @ ( int @ times_times ) ) )
!= ( int @ one_one ) ) )
& ( ( A
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) )
| ( ( A @ ( B @ ( int @ times_times ) ) )
!= ( int @ one_one ) ) )
& ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) )
| ( ( A @ ( B @ ( int @ times_times ) ) )
!= ( int @ one_one ) ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(244,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( A
!= ( int @ one_one ) )
| ( B
!= ( int @ one_one ) ) ),
inference(cnfConj,[status(thm)],[239]) ).
thf(248,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( A
!= ( int @ one_one ) )
| ( B
!= ( int @ one_one ) ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(249,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) ) )
= ( int @ one_one ) ),
inference(simp,[status(thm)],[248]) ).
thf(101,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__Pls) ).
thf(468,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(26,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(170,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(115,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(217,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)],[36]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(308,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)],[58]) ).
thf(243,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( A
!= ( min @ ( int @ number_number_of ) ) )
| ( B
!= ( min @ ( int @ number_number_of ) ) ) ),
inference(cnfConj,[status(thm)],[239]) ).
thf(246,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
| ( A
!= ( min @ ( int @ number_number_of ) ) )
| ( B
!= ( min @ ( int @ number_number_of ) ) ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(247,plain,
( ( min @ ( int @ number_number_of ) @ ( min @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( int @ one_one ) ),
inference(simp,[status(thm)],[246]) ).
thf(46,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_42_int__distrib_I2_J) ).
thf(269,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)],[46]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(384,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)],[82]) ).
thf(16,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(142,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_semiring__norm_I110_J) ).
thf(500,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_nat__add__right__cancel) ).
thf(404,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(320,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)],[61]) ).
thf(42,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_11_arith__simps_I32_J) ).
thf(257,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)],[42]) ).
thf(29,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_54_pos__zmult__eq__1__iff__lemma) ).
thf(184,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)],[29]) ).
thf(77,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(372,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(357,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)],[72]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(284,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)],[51]) ).
thf(20,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(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)],[20]) ).
thf(108,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Bit1__Min) ).
thf(492,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(79,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Bit0__Pls) ).
thf(376,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(105,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(485,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(8,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_47_number__of__add) ).
thf(119,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)],[8]) ).
thf(120,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( TA @ number_ring )
| ( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(86,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_5_mult__Bit1) ).
thf(397,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)],[86]) ).
thf(12,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__Pls__right) ).
thf(130,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(131,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(cnf,[status(esa)],[130]) ).
thf(132,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(lifteq,[status(thm)],[131]) ).
thf(13,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Bit0__def) ).
thf(133,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(116,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I44_J) ).
thf(312,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(98,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I51_J) ).
thf(452,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)],[98]) ).
thf(6,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(117,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(439,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)],[96]) ).
thf(81,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(381,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)],[81]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(220,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)],[37]) ).
thf(75,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_10_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)],[75]) ).
thf(56,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_13_eq__number__of) ).
thf(297,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)],[56]) ).
thf(92,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nat__mult__2__right) ).
thf(424,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)],[92]) ).
thf(48,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I40_J) ).
thf(275,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(24,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_62_nat__1__add__1) ).
thf(165,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)],[24]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(260,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)],[43]) ).
thf(69,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_one__is__num__one) ).
thf(349,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(25,axiom,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_eq__number__of__Pls__Min) ).
thf(167,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(168,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(polarity_switch,[status(thm)],[167]) ).
thf(169,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(90,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(420,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)],[90]) ).
thf(102,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_50_mult__numeral__1) ).
thf(471,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)],[102]) ).
thf(107,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__Pls) ).
thf(489,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(266,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)],[45]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_59_semiring__mult__2__right) ).
thf(360,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)],[73]) ).
thf(59,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_p) ).
thf(311,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)],[59]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_numeral__1__eq__1) ).
thf(126,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(127,plain,
! [TA: $tType] :
( ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[126]) ).
thf(128,plain,
! [TA: $tType] :
( ~ ( TA @ number_ring )
| ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(67,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_8_add__Bit1__Bit0) ).
thf(343,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(89,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I38_J) ).
thf(412,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(94,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I43_J) ).
thf(430,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(149,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)],[19]) ).
thf(91,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(423,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(54,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_12_mult__number__of__left) ).
thf(291,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)],[54]) ).
thf(7,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(118,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(281,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)],[50]) ).
thf(66,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I47_J) ).
thf(335,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(181,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)],[28]) ).
thf(350,plain,
( ( pls @ bit1 @ ( int @ number_number_of ) )
= ( int @ one_one ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(22,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_34_right__distrib__number__of) ).
thf(159,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)],[22]) ).
thf(104,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_35_number__of__reorient) ).
thf(477,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)],[104]) ).
thf(83,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(387,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)],[83]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(494,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)],[109]) ).
thf(62,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I37_J) ).
thf(323,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(34,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nat__numeral__1__eq__1) ).
thf(213,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I39_J) ).
thf(155,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_56_double__number__of__Bit0) ).
thf(462,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)],[99]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(278,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)],[49]) ).
thf(38,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I46_J) ).
thf(223,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_nat__mult__2) ).
thf(394,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)],[85]) ).
thf(134,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(95,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zprime__2) ).
thf(438,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(162,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)],[23]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
<=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_nat__1__eq__mult__iff) ).
thf(200,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)],[32]) ).
thf(201,plain,
( ! [A: nat,B: nat] :
( ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) )
=> ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) ) )
& ! [A: nat,B: nat] :
( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ) ),
inference(miniscope,[status(thm)],[200]) ).
thf(202,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( ( nat @ one_one )
= ( C @ ( D @ ( nat @ times_times ) ) ) )
| ( C
!= ( nat @ one_one ) )
| ( D
!= ( nat @ one_one ) ) )
& ( ( A
= ( nat @ one_one ) )
| ( ( nat @ one_one )
!= ( A @ ( B @ ( nat @ times_times ) ) ) ) )
& ( ( B
= ( nat @ one_one ) )
| ( ( nat @ one_one )
!= ( A @ ( B @ ( nat @ times_times ) ) ) ) ) ),
inference(cnf,[status(esa)],[201]) ).
thf(205,plain,
! [B: nat,A: nat] :
( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
| ( A
!= ( nat @ one_one ) )
| ( B
!= ( nat @ one_one ) ) ),
inference(cnfConj,[status(thm)],[202]) ).
thf(208,plain,
! [B: nat,A: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) )
| ( A
!= ( nat @ one_one ) )
| ( B
!= ( nat @ one_one ) ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(209,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ times_times ) ) )
= ( nat @ one_one ) ),
inference(simp,[status(thm)],[208]) ).
thf(1,conjecture,
( ( 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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( 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(neg_conjecture,[status(cth)],[1]) ).
thf(112,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)],[2]) ).
thf(336,plain,
( ! [A: int] :
( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ! [A: int] :
( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(miniscope,[status(thm)],[335]) ).
thf(337,plain,
! [B: int,A: int] :
( ( ( ( B @ bit1 )
= min )
| ( B != min ) )
& ( ( A = min )
| ( ( A @ bit1 )
!= min ) ) ),
inference(cnf,[status(esa)],[336]) ).
thf(339,plain,
! [A: int] :
( ( ( A @ bit1 )
= min )
| ( A != min ) ),
inference(cnfConj,[status(thm)],[337]) ).
thf(341,plain,
! [A: int] :
( ( ( A @ bit1 )
= min )
| ( A != min ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(342,plain,
( ( min @ bit1 )
= min ),
inference(simp,[status(thm)],[341]) ).
thf(17,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_46_number__of__mult) ).
thf(143,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)],[17]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(497,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)],[110]) ).
thf(100,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_25_add__Bit0__Bit0) ).
thf(465,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)],[100]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(363,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)],[74]) ).
thf(57,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I42_J) ).
thf(304,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(84,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I45_J) ).
thf(390,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(114,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I48_J) ).
thf(171,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)],[27]) ).
thf(15,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(139,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(156,plain,
~ ? [A: int] :
( pls
= ( A @ bit1 ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(157,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(cnf,[status(esa)],[156]) ).
thf(158,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(lifteq,[status(thm)],[157]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_4_Legendre__1mod4) ).
thf(351,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)],[70]) ).
thf(47,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_number__of__is__id) ).
thf(272,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(346,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)],[68]) ).
thf(53,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(290,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_60_mult__2__right) ).
thf(378,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)],[80]) ).
thf(214,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(52,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_41_int__distrib_I1_J) ).
thf(287,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)],[52]) ).
thf(18,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_7_add__Bit0__Bit1) ).
thf(146,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)],[18]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',fact_89_crossproduct__eq) ).
thf(190,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)],[31]) ).
thf(78,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_51_mult__numeral__1__right) ).
thf(373,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)],[78]) ).
thf(33,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(210,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)],[33]) ).
thf(63,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_24_mult__Bit0) ).
thf(326,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)],[63]) ).
thf(103,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_40_times__numeral__code_I5_J) ).
thf(474,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)],[103]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I49_J) ).
thf(400,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(55,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_33_left__distrib__number__of) ).
thf(294,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)],[55]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',fact_57_semiring__mult__2) ).
thf(136,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)],[14]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(332,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)],[65]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(427,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)],[93]) ).
thf(276,plain,
min != pls,
inference(polarity_switch,[status(thm)],[275]) ).
thf(277,plain,
pls != min,
inference(lifteq,[status(thm)],[276]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_86_crossproduct__noteq) ).
thf(442,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(76,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(369,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)],[76]) ).
thf(106,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_9_add__number__of__eq) ).
thf(486,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)],[106]) ).
thf(9,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I50_J) ).
thf(122,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(71,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_61_semiring__one__add__one__is__two) ).
thf(354,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)],[71]) ).
thf(35,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Numeral1__eq1__nat) ).
thf(215,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_semiring__numeral__1__eq__1) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) )
<=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nat__mult__eq__1__iff) ).
thf(227,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) )
=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2028,plain,
$false,
inference(e,[status(thm)],[329,129,187,263,249,468,170,115,217,308,247,269,384,142,500,404,320,257,184,372,357,284,152,492,376,485,121,397,132,133,116,312,452,117,439,381,220,366,297,424,275,165,260,349,169,420,471,489,266,360,311,128,343,237,412,430,149,423,291,118,281,335,181,350,159,477,387,494,323,213,155,462,130,278,223,394,135,438,167,162,209,112,342,143,497,465,363,304,390,114,171,139,158,351,272,346,290,119,378,214,287,146,190,373,210,326,474,400,294,126,136,332,427,200,277,442,369,486,122,354,215,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM942_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 04:22:02 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 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
% 0.86/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.21 % [INFO] Parsing done (257ms).
% 1.52/1.22 % [INFO] Running in sequential loop mode.
% 2.43/1.61 % [INFO] eprover registered as external prover.
% 2.43/1.62 % [INFO] Scanning for conjecture ...
% 2.59/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 111 axioms. Running axiom selection ...
% 2.78/1.86 % [INFO] Axiom selection finished. Selected 109 axioms (removed 2 axioms).
% 3.06/2.03 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.39/2.04 % [INFO] Type checking passed.
% 3.39/2.04 % [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 ...
% 20.08/5.55 % External prover 'e' found a proof!
% 20.08/5.55 % [INFO] Killing All external provers ...
% 20.08/5.55 % Time passed: 5044ms (effective reasoning time: 4325ms)
% 20.08/5.55 % 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)>
% 20.08/5.56 % Axioms used in derivation (109): fact_45_add__numeral__0__right, fact_39_Bit0__def, fact_6_numeral__1__eq__1, fact_21_rel__simps_I38_J, fact_28_Bit1__Min, fact_30_rel__simps_I40_J, fact_20_rel__simps_I44_J, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_58_mult__2, fact_31_rel__simps_I45_J, fact_57_semiring__mult__2, arity_Int_Oint___Int_Oring__char__0, fact_86_crossproduct__noteq, fact_25_add__Bit0__Bit0, fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_36_number__of__is__id, fact_95_nat__mult__eq__1__iff, fact_22_Bit0__Pls, arity_Nat_Onat___Int_Onumber__semiring, fact_19_rel__simps_I49_J, fact_44_add__numeral__0, fact_65_semiring__norm_I110_J, fact_33_left__distrib__number__of, fact_5_mult__Bit1, fact_12_mult__number__of__left, fact_60_mult__2__right, arity_Int_Oint___Int_Onumber__semiring, fact_49_number__of__Bit1, fact_1_add__special_I2_J, arity_Int_Oint___Int_Onumber__ring, fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_7_add__Bit0__Bit1, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_16_rel__simps_I46_J, fact_61_semiring__one__add__one__is__two, fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_0_p, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_89_crossproduct__eq, fact_52_semiring__numeral__1__eq__1, fact_53_one__is__num__one, fact_14_rel__simps_I51_J, fact_68_nat__mult__2__right, fact_55_zmult__eq__1__iff, fact_92_Numeral1__eq1__nat, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_23_mult__Pls, fact_37_add__Pls__right, fact_41_int__distrib_I1_J, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_29_rel__simps_I37_J, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_50_mult__numeral__1, fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int_Oint___Rings_Osemiring, fact_40_times__numeral__code_I5_J, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_66_eq__number__of__Pls__Min, fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_94_nat__1__eq__mult__iff, fact_17_rel__simps_I39_J, fact_35_number__of__reorient, fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_26_rel__simps_I47_J, fact_9_add__number__of__eq, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_8_add__Bit1__Bit0, fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_59_semiring__mult__2__right, fact_48_Bit1__def, fact_2_add__special_I3_J, fact_18_rel__simps_I50_J, arity_Nat_Onat___Int_Onumber, fact_11_arith__simps_I32_J, fact_54_pos__zmult__eq__1__iff__lemma, fact_24_mult__Bit0, fact_46_number__of__mult, fact_62_nat__1__add__1, fact_34_right__distrib__number__of, fact_27_rel__simps_I43_J, arity_Nat_Onat___Rings_Osemiring, fact_63_zprime__2, fact_42_int__distrib_I2_J, fact_10_add__number__of__left, fact_47_number__of__add, fact_51_mult__numeral__1__right, fact_13_eq__number__of, arity_Int_Oint___Int_Onumber, fact_4_Legendre__1mod4, fact_38_add__Pls, fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_3_one__add__one__is__two, fact_32_rel__simps_I42_J, fact_43_plus__numeral__code_I9_J, fact_15_rel__simps_I48_J, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_67_nat__mult__2, fact_64_nat__numeral__1__eq__1, fact_96_nat__add__right__cancel, fact_56_double__number__of__Bit0
% 20.08/5.56 % No. of inferences in proof: 257
% 20.08/5.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5044 ms resp. 4325 ms w/o parsing
% 20.51/5.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.51/5.68 % [INFO] Killing All external provers ...
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