%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL793_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:56 AM UTC 2026
% Result : Theorem 8.26s 4.68s
% Output : Refutation 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 117
% Syntax : Number of formulae : 236 ( 124 unt; 0 typ; 0 def)
% Number of atoms : 490 ( 196 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2175 ( 48 ~; 10 |; 30 &;1895 @)
% ( 20 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 7 con; 0-5 aty)
% Number of variables : 476 ( 0 ^; 474 !; 2 ?; 476 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_decl,type,
bool_size: bool > nat ).
thf(it_decl,type,
it: dB > $o ).
thf(app_decl,type,
app: dB > dB > dB ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_rec_decl,type,
dB_rec:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( TA @ fun ) @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB > nat > dB ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB > dB > nat > dB ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(nat_size_decl,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(char_size_decl,type,
char_size: char > nat ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t_decl,type,
t: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__strict__right__mono) ).
thf(125,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(108,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_subst__lift) ).
thf(479,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(38,axiom,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nat_Osize_I1_J) ).
thf(234,plain,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(73,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(352,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__strict__mono) ).
thf(120,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(117,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_substn_Osimps_I2_J) ).
thf(511,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(32,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(217,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__0__left) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__is__0) ).
thf(500,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(105,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(472,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(25,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_not__add__less1) ).
thf(189,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_double__add__less__zero__iff__single__add__less__zero) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_lift__IT) ).
thf(448,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__less__imp__less__right) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_dB_Osimps_I4_J) ).
thf(376,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(118,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( TA @ fun ) @ ( dB @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_dB_Orecs_I2_J) ).
thf(514,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( TA @ fun ) @ ( dB @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(74,axiom,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( C @ var ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_liftn_Osimps_I1_J) ).
thf(353,plain,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( C @ var ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_dB_Osimps_I10_J) ).
thf(221,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(100,axiom,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_size__char) ).
thf(453,plain,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__imp__eq) ).
thf(133,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_of__nat__less__iff) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(46,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat_Oadd__0__right) ).
thf(265,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(31,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_nat__less__cases) ).
thf(206,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(81,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__add__left__cancel__less) ).
thf(380,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(95,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ~ ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ? [D: nat] :
( ~ ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( C @ ( D @ ( nat @ ord_less ) ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_infinite__descent0) ).
thf(439,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ~ ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ? [D: nat] :
( ~ ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( C @ ( D @ ( nat @ ord_less ) ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(77,axiom,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bool_Osize_I2_J) ).
thf(366,plain,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(57,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_neq0__conv) ).
thf(302,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_nat__add__assoc) ).
thf(192,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_trans__less__add1) ).
thf(260,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(72,axiom,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_char__size) ).
thf(349,plain,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(75,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_dB_Osize_I1_J) ).
thf(361,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(93,axiom,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat_Osize_I3_J) ).
thf(435,plain,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(101,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_subst__Var__IT) ).
thf(456,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(64,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_subst__App) ).
thf(324,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_of__nat__0) ).
thf(224,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__add__commute) ).
thf(403,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__less__cancel__right) ).
thf(169,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,axiom,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_bool_Osize_I4_J) ).
thf(420,plain,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(114,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(499,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(5,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(124,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(107,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__not__refl) ).
thf(476,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_gr__implies__not0) ).
thf(371,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_linorder__neqE__nat) ).
thf(237,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(42,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_dB_Osimps_I2_J) ).
thf(244,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) ) )
& ( ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(56,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ app ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_dB_Osimps_I5_J) ).
thf(298,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ app ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(90,axiom,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_size__literal__def) ).
thf(425,plain,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(17,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(166,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__left__imp__eq) ).
thf(161,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_double__zero__sym) ).
thf(279,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(96,axiom,
ua @ it,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(444,plain,
ua @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(20,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(176,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
nat @ zero_zero @ ( u @ lift ) @ it,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096IT_A_Ilift_Au_A0_J_096) ).
thf(286,plain,
nat @ zero_zero @ ( u @ lift ) @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(54,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_not__less0) ).
thf(291,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_dB_Osimps_I11_J) ).
thf(445,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__less__mono) ).
thf(313,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_of__nat__eq__iff) ).
thf(144,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(103,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_gr0I) ).
thf(466,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(68,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(335,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(39,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(236,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__less__imp__less__left) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_dB_Osimps_I1_J) ).
thf(406,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_less__not__refl3) ).
thf(230,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(61,axiom,
u @ it,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(318,plain,
u @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(48,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(271,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__gr__0) ).
thf(387,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(112,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ app ) @ it ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_app__Var__IT) ).
thf(494,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ app ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_nat__add__left__cancel) ).
thf(483,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__eq__self__zero) ).
thf(240,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__less__mono1) ).
thf(198,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_add__lessD1) ).
thf(330,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(106,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ app ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_liftn_Osimps_I2_J) ).
thf(473,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ app ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_nat__add__right__cancel) ).
thf(458,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)],[102]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_less__add__eq__less) ).
thf(327,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(58,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__zeroE) ).
thf(310,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add__less__cancel__left) ).
thf(127,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_nat__neq__iff) ).
thf(338,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(69,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(336,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(82,axiom,
t @ it,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(386,plain,
t @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(11,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(143,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__add__left__commute) ).
thf(450,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(33,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_dB_Orecs_I1_J) ).
thf(218,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(78,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_substn__subst__0) ).
thf(368,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(109,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(482,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(30,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_substn__subst__n) ).
thf(203,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(62,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_liftn__0) ).
thf(319,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_trans__less__add2) ).
thf(258,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(158,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_less__nat__zero__code) ).
thf(186,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ app ) @ it,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ app ) @ it ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ app ) @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(116,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(510,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zero__less__double__add__iff__zero__less__single__add) ).
thf(272,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_of__nat__0__less__iff) ).
thf(287,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_add__right__cancel) ).
thf(151,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_of__nat__add) ).
thf(315,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__0) ).
thf(432,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(45,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__irrefl__nat) ).
thf(262,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ app ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ app ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_lift_Osimps_I2_J) ).
thf(183,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ app ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add_Ocomm__neutral) ).
thf(422,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(47,axiom,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_size__bool) ).
thf(268,plain,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(27,axiom,
! [A: dB,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( C @ var @ subst ) ) )
= ( C @ var ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_subst__lt) ).
thf(195,plain,
! [A: dB,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( C @ var @ subst ) ) )
= ( C @ var ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(94,axiom,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_bool_Osize_I3_J) ).
thf(437,plain,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__not__refl2) ).
thf(294,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__left__cancel) ).
thf(136,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_zero__reorient) ).
thf(395,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(67,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_plus__nat_Oadd__0) ).
thf(332,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(131,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dB_Osize_I4_J) ).
thf(200,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add__right__imp__eq) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_not__add__less2) ).
thf(227,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(63,axiom,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_bool_Osize_I1_J) ).
thf(322,plain,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(104,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_subst__eq) ).
thf(469,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(111,axiom,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__size) ).
thf(491,plain,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__0__right) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(76,axiom,
! [A: nat] : ( A @ var @ it ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Var__IT) ).
thf(364,plain,
! [A: nat] : ( A @ var @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(70,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(337,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__strict__left__mono) ).
thf(122,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(526,plain,
$false,
inference(e,[status(thm)],[125,479,234,352,120,511,217,276,500,472,189,416,448,164,376,514,353,221,453,133,428,265,206,380,439,366,302,192,260,349,361,435,456,324,224,403,169,420,499,124,476,173,371,237,244,298,425,166,161,279,444,176,286,291,445,313,144,466,335,236,181,406,230,318,271,387,494,483,240,198,330,473,458,327,310,127,338,336,386,143,450,218,368,482,203,319,258,158,186,119,510,272,287,151,315,432,262,183,422,268,195,437,294,136,395,332,131,200,178,227,322,469,491,496,364,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL793_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
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Fri Sep 25 23:36:54 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 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
% 0.83/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.50 % [INFO] Parsing done (392ms).
% 1.71/1.52 % [INFO] Running in sequential loop mode.
% 2.55/2.07 % [INFO] eprover registered as external prover.
% 2.55/2.07 % [INFO] Scanning for conjecture ...
% 2.77/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 2.92/2.40 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 3.46/2.62 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.46/2.64 % [INFO] Type checking passed.
% 3.46/2.65 % [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 ...
% 4.25/3.08 % [INFO] [Domain constraints] Detected constraint on bool
% 4.25/3.08 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.25/3.11 % [INFO] [Domain constraints] Detected constraint on bool
% 4.25/3.11 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 8.26/4.67 % External prover 'e' found a proof!
% 8.26/4.67 % [INFO] Killing All external provers ...
% 8.26/4.67 % Time passed: 4060ms (effective reasoning time: 3138ms)
% 8.26/4.67 % 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)>
% 8.26/4.68 % Axioms used in derivation (116): fact_37_liftn__0, fact_39_less__nat__zero__code, fact_84_nat__add__left__commute, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_88_add__left__imp__eq, fact_78_less__add__eq__less, fact_35_subst__lt, fact_6_app__Var__IT, fact_12_dB_Osize_I1_J, fact_16_bool_Osize_I1_J, fact_58_nat__add__right__cancel, fact_56_add__right__cancel, fact_34_dB_Orecs_I2_J, fact_90_add__0__left, fact_72_not__add__less1, arity_Nat_Onat___Rings_Osemiring__1, fact_46_less__irrefl__nat, fact_55_infinite__descent0, fact_22_bool_Osize_I4_J, fact_70_add__gr__0, fact_92_add__0__right, fact_28_substn_Osimps_I2_J, fact_3__096IT_A_Ilift_Au_A0_J_096, help_fTrue_1_1_T, fact_89_ab__semigroup__add__class_Oadd__ac_I1_J, fact_26_dB_Osimps_I10_J, fact_82_plus__nat_Oadd__0, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_2_uIT, fact_5_Var__IT, fact_29_nat__size, help_fTrue_1_1_U, fact_8_dB_Osimps_I1_J, fact_0__096IT_At_096, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_73_not__add__less2, fact_18_subst__App, fact_11_dB_Osimps_I5_J, fact_98_add__less__imp__less__left, help_fFalse_1_1_T, fact_95_add__strict__left__mono, fact_60_of__nat__eq__iff, fact_24_nat_Osize_I3_J, fact_61_double__zero__sym, fact_9_dB_Osimps_I2_J, fact_44_less__not__refl3, fact_77_add__less__mono, fact_23_bool_Osize_I3_J, fact_96_add__strict__mono, fact_27_dB_Osimps_I11_J, fact_47_linorder__neqE__nat, fact_59_nat__add__left__cancel, fact_63_add__less__cancel__right, fact_25_substn__subst__0, fact_51_gr__implies__not0, fact_50_gr0I, fact_74_trans__less__add1, fact_65_nat__add__left__cancel__less, fact_54_liftn_Osimps_I1_J, fact_48_nat__neq__iff, fact_49_less__not__refl, fact_21_nat_Osize_I1_J, fact_85_nat__add__commute, fact_68_of__nat__0, fact_76_add__less__mono1, fact_1_Var_I3_J, fact_62_add__less__cancel__left, arity_Nat_Onat___Rings_Olinordered__semidom, fact_86_add__right__imp__eq, fact_81_Nat_Oadd__0__right, arity_Nat_Onat___Groups_Ozero, fact_43_nat__less__cases, fact_38_neq0__conv, fact_19_subst__eq, fact_93_add_Ocomm__neutral, fact_83_nat__add__assoc, fact_79_add__lessD1, fact_36_char__size, fact_41_size__char, fact_75_trans__less__add2, fact_32_liftn_Osimps_I2_J, fact_17_bool_Osize_I2_J, fact_64_add__is__0, fact_67_zero__less__double__add__iff__zero__less__single__add, fact_53_of__nat__0__less__iff, arity_Nat_Onat___Nat_Osemiring__char__0, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_45_less__not__refl2, fact_52_size__literal__def, fact_14_dB_Osize_I4_J, fact_4_lift__IT, fact_91_add__0, fact_57_add__left__cancel, fact_69_of__nat__less__iff, fact_7_lift_Osimps_I2_J, fact_10_dB_Osimps_I4_J, help_fFalse_1_1_U, fact_20_subst__lift, fact_33_dB_Orecs_I1_J, help_pp_1_1_U, fact_30_size__bool, fact_42_not__less0, fact_94_add__strict__right__mono, fact_71_of__nat__add, arity_Nat_Onat___Groups_Omonoid__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_66_double__add__less__zero__iff__single__add__less__zero, fact_13_zero__reorient, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_15_subst__Var__IT, fact_31_substn__subst__n, help_pp_2_1_U, fact_80_add__eq__self__zero, fact_40_less__zeroE, fact_87_add__imp__eq, fact_97_add__less__imp__less__right
% 8.26/4.68 % No. of inferences in proof: 236
% 8.26/4.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4060 ms resp. 3138 ms w/o parsing
% 8.80/4.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.80/4.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------