%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL773_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 : n016.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 07:52:50 AM UTC 2026
% Result : Theorem 10.05s 3.92s
% Output : Refutation 10.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 121
% Syntax : Number of formulae : 244 ( 130 unt; 0 typ; 0 def)
% Number of atoms : 565 ( 230 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 2940 ( 74 ~; 15 |; 47 &;2628 @)
% ( 22 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 9 con; 0-5 aty)
% Number of variables : 492 ( 0 ^; 472 !; 20 ?; 492 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $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(sgn_if_decl,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(sgn_sgn_decl,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_decl,type,
bool_size: bool > nat ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(beta_decl,type,
beta: dB > dB > $o ).
thf(abs_decl,type,
abs: dB > dB ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( dB @ fun ) ).
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(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
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(i_decl,type,
i: nat ).
thf(r_decl,type,
r: dB ).
thf(6,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_beta__cases_I2_J) ).
thf(129,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(100,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Var__apps__neq__Abs__apps) ).
thf(497,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(79,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_appR) ).
thf(401,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
i @ var @ ( r @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(346,plain,
i @ var @ ( r @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(9,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(138,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__reorient) ).
thf(347,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)],[64]) ).
thf(91,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_subst__App) ).
thf(468,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(35,axiom,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ subst ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_beta__cases_I3_J) ).
thf(234,plain,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ subst ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(116,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_subst__eq) ).
thf(555,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(36,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_liftn_Osimps_I2_J) ).
thf(247,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(72,axiom,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_int__if__cong) ).
thf(379,plain,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_of__nat__0) ).
thf(511,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)],[105]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_transfer__int__nat__relations_I2_J) ).
thf(408,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_int__int__eq) ).
thf(170,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_sgn0) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_linorder__neqE__nat) ).
thf(538,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)],[110]) ).
thf(46,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(288,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_sgn__0__0) ).
thf(436,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(74,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_IT_OVar) ).
thf(389,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(102,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_int__0) ).
thf(504,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(66,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_dB_Osize_I1_J) ).
thf(357,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_transfer__int__nat__relations_I1_J) ).
thf(157,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_sgn__sgn) ).
thf(189,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(57,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ? [B: nat] :
( ( A
= ( B @ ( int @ semiring_1_of_nat ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__less__imp__eq__int) ).
thf(325,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ? [B: nat] :
( ( A
= ( B @ ( int @ semiring_1_of_nat ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(152,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(47,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_neq0__conv) ).
thf(289,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)],[47]) ).
thf(54,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_subst__Var__IT) ).
thf(316,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(39,axiom,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Abs__App__neq__Var__apps) ).
thf(261,plain,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(89,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
<=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_IT_Osimps) ).
thf(443,plain,
! [A: dB] :
( ( ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) )
=> ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
& ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(106,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_int__eq__0__conv) ).
thf(514,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sgn__less) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(43,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(280,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,axiom,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_size__bool) ).
thf(428,plain,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(40,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Var__apps__eq__Var__apps__conv) ).
thf(265,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lift__IT) ).
thf(206,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(51,axiom,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_char__size) ).
thf(307,plain,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(69,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_apps__eq__tail__conv) ).
thf(366,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(59,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_dB_Osimps_I9_J) ).
thf(334,plain,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(38,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(260,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(118,axiom,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_size__literal__def) ).
thf(561,plain,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(48,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__IT) ).
thf(297,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dB_Osimps_I8_J) ).
thf(424,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(22,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(192,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(41,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__zeroE) ).
thf(275,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_linorder__neqE__linordered__idom) ).
thf(165,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_zless__int) ).
thf(484,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(25,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_gr0I) ).
thf(197,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(114,axiom,
! [A: dB,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( C @ var @ subst ) ) )
= ( C @ var ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_subst__lt) ).
thf(551,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)],[114]) ).
thf(32,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_lift_Osimps_I2_J) ).
thf(224,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(80,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_beta__cases_I1_J) ).
thf(403,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(20,axiom,
int @ sgn_if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(188,plain,
int @ sgn_if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',fact_81_of__nat__eq__iff) ).
thf(141,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)],[10]) ).
thf(92,axiom,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_nat_Osize_I3_J) ).
thf(471,plain,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(124,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(115,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(554,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(23,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Lambda) ).
thf(193,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_sgn__greater) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__not__refl3) ).
thf(547,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(7,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(134,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_80_of__nat__0__less__iff) ).
thf(360,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)],[67]) ).
thf(111,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_dB_Osimps_I4_J) ).
thf(541,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(77,axiom,
r @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(398,plain,
r @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',fact_20_dB_Osimps_I10_J) ).
thf(558,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)],[117]) ).
thf(5,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(128,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(62,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__nat__zero__code) ).
thf(343,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(148,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_83_of__nat__less__iff) ).
thf(375,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)],[71]) ).
thf(45,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_transfer__int__nat__numerals_I1_J) ).
thf(286,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(121,axiom,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_bool_Osize_I2_J) ).
thf(577,plain,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(122,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_subst__lift) ).
thf(579,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_gr__implies__not0) ).
thf(281,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(112,axiom,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_bool_Osize_I1_J) ).
thf(545,plain,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(75,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_substn__subst__0) ).
thf(391,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)],[75]) ).
thf(53,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 @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Orecs_I2_J) ).
thf(313,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 @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( 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)],[53]) ).
thf(81,axiom,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_bool_Osize_I4_J) ).
thf(406,plain,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(55,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_dB_Osimps_I5_J) ).
thf(318,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_of__nat__less__0__iff) ).
thf(208,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(104,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(509,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(87,axiom,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nat_Osize_I1_J) ).
thf(434,plain,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(73,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_appL) ).
thf(387,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__irrefl__nat) ).
thf(494,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nat__neq__iff) ).
thf(213,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)],[31]) ).
thf(14,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_lift__preserves__beta) ).
thf(155,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(58,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dB_Osimps_I6_J) ).
thf(330,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(78,axiom,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_bool_Osize_I3_J) ).
thf(399,plain,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(42,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_subst__preserves__beta) ).
thf(278,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__not__refl2) ).
thf(394,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(135,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zero__less__int__conv) ).
thf(299,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(86,axiom,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_int__less__0__conv) ).
thf(431,plain,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_not__less0) ).
thf(473,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(97,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(490,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(70,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(374,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1,conjecture,
nat @ zero_zero @ ( i @ var @ ( r @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( nat @ zero_zero @ ( i @ var @ ( r @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(123,plain,
~ ( nat @ zero_zero @ ( i @ var @ ( r @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_85_of__nat__less__imp__less) ).
thf(355,plain,
! [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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(108,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_liftn__0) ).
thf(525,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_dB_Osimps_I1_J) ).
thf(414,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)],[83]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_substn__subst__n) ).
thf(310,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)],[52]) ).
thf(4,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(127,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_apps__preserves__beta) ).
thf(338,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Orecs_I1_J) ).
thf(203,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)],[27]) ).
thf(37,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Abs__apps__eq__Abs__apps__conv) ).
thf(250,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,axiom,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_size__char) ).
thf(465,plain,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(34,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_dB_Osize_I4_J) ).
thf(231,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(151,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_abs) ).
thf(168,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_49_nat__less__cases) ).
thf(564,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)],[119]) ).
thf(50,axiom,
! [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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__imp__of__nat__less) ).
thf(305,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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(30,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__not__refl) ).
thf(210,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(103,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_substn_Osimps_I2_J) ).
thf(506,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(24,axiom,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_beta) ).
thf(195,plain,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(120,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(575,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(109,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_dB_Osimps_I2_J) ).
thf(528,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26,axiom,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dB_Orecs_I3_J) ).
thf(200,plain,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dB_Osimps_I3_J) ).
thf(178,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(101,axiom,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_nat__size) ).
thf(501,plain,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(33,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_dB_Osimps_I7_J) ).
thf(227,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(56,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_dB_Osimps_I11_J) ).
thf(322,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( 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)],[56]) ).
thf(98,axiom,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dB_Osimps_I12_J) ).
thf(491,plain,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Beta) ).
thf(364,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(587,plain,
$false,
inference(e,[status(thm)],[129,497,401,346,138,347,468,234,555,247,379,511,408,170,340,538,288,436,389,504,357,157,189,325,152,289,316,261,443,514,480,280,428,265,206,307,366,334,260,561,297,424,192,275,165,484,197,522,551,224,403,188,141,471,124,554,193,476,547,134,360,541,398,558,128,343,148,375,286,577,579,281,545,391,313,406,318,208,509,434,387,494,213,155,330,399,278,394,135,299,431,473,490,374,123,355,525,414,310,127,338,203,250,465,231,151,168,564,305,210,506,195,575,528,200,178,501,227,322,491,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL773_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
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 23:37:14 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.29 % [INFO] Parsing done (297ms).
% 1.89/1.30 % [INFO] Running in sequential loop mode.
% 2.70/1.71 % [INFO] eprover registered as external prover.
% 2.70/1.72 % [INFO] Scanning for conjecture ...
% 2.87/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 120 axioms. Running axiom selection ...
% 3.09/2.01 % [INFO] Axiom selection finished. Selected 120 axioms (removed 0 axioms).
% 3.94/2.21 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.94/2.24 % [INFO] Type checking passed.
% 3.94/2.25 % [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 ...
% 4.52/2.48 % [INFO] [Domain constraints] Detected constraint on bool
% 4.52/2.49 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.77/2.54 % [INFO] [Domain constraints] Detected constraint on bool
% 4.77/2.54 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.77/2.57 % [INFO] [Domain constraints] Detected constraint on bool
% 4.77/2.57 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 10.05/3.91 % External prover 'e' found a proof!
% 10.05/3.91 % [INFO] Killing All external provers ...
% 10.05/3.91 % Time passed: 3377ms (effective reasoning time: 2603ms)
% 10.05/3.91 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.05/3.92 % Axioms used in derivation (120): fact_73_apps__eq__tail__conv, fact_26_dB_Orecs_I1_J, fact_86_of__nat__less__0__iff, fact_96_transfer__int__nat__relations_I1_J, fact_47_sgn__sgn, fact_15_substn__subst__n, fact_30_sgn0, fact_82_of__nat__0, fact_3_dB_Osimps_I1_J, fact_64_appR, fact_37_dB_Osimps_I9_J, fact_52_less__irrefl__nat, arity_Int_Oint___Rings_Olinordered__idom, fact_17_bool_Osize_I4_J, arity_Nat_Onat___Rings_Osemiring__1, fact_46_less__zeroE, fact_39_dB_Osimps_I7_J, fact_22_size__bool, fact_14_bool_Osize_I2_J, fact_83_of__nat__less__iff, fact_45_less__nat__zero__code, fact_27_dB_Orecs_I2_J, help_fTrue_1_1_T, fact_78_beta__cases_I3_J, fact_13_substn_Osimps_I2_J, fact_59_sgn__0__0, fact_10_dB_Osize_I4_J, fact_53_linorder__neqE__nat, fact_60_size__char, fact_8_dB_Osize_I1_J, fact_65_appL, fact_40_subst__lift, fact_0_Var__IT, fact_50_less__not__refl3, help_fTrue_1_1_U, fact_33_dB_Osimps_I3_J, fact_84_less__imp__of__nat__less, fact_70_Abs__apps__eq__Abs__apps__conv, arity_Int_Oint___Rings_Osemiring__1, fact_11_substn__subst__0, help_fFalse_1_1_T, fact_74_ext, fact_85_of__nat__less__imp__less, fact_19_nat_Osize_I3_J, fact_67_abs, fact_49_nat__less__cases, fact_77_apps__preserves__beta, help_If_1_1_T, fact_43_Lambda, fact_48_linorder__neqE__linordered__idom, fact_55_less__not__refl, fact_87_IT_Osimps, fact_79_IT_OVar, fact_54_nat__neq__iff, fact_41_sgn__less, fact_2_subst__App, fact_98_transfer__int__nat__numerals_I1_J, fact_90_int__less__0__conv, fact_29_char__size, fact_76_Abs__App__neq__Var__apps, fact_62_beta, fact_18_bool_Osize_I3_J, fact_56_gr0I, fact_42_sgn__greater, fact_9_zero__reorient, fact_88_zero__less__int__conv, fact_92_int__0, arity_Nat_Onat___Rings_Olinordered__semidom, arity_Nat_Onat___Groups_Ozero, fact_89_int__int__eq, fact_51_less__not__refl2, help_If_3_1_T, help_If_2_1_T, fact_12_bool_Osize_I1_J, fact_23_liftn_Osimps_I2_J, fact_35_dB_Orecs_I3_J, fact_7_dB_Osimps_I5_J, fact_68_subst__preserves__beta, fact_36_dB_Osimps_I8_J, fact_1_subst__Var__IT, fact_16_nat_Osize_I1_J, fact_66_beta__cases_I1_J, conj_1, fact_69_lift__preserves__beta, fact_28_subst__lt, arity_Nat_Onat___Nat_Osemiring__char__0, fact_32_dB_Osimps_I12_J, fact_63_size__literal__def, fact_4_dB_Osimps_I2_J, fact_80_of__nat__0__less__iff, fact_81_of__nat__eq__iff, fact_94_zero__less__imp__eq__int, help_fFalse_1_1_U, fact_58_not__less0, fact_91_int__eq__0__conv, fact_57_gr__implies__not0, fact_20_dB_Osimps_I10_J, fact_61_Beta, arity_Int_Oint___Groups_Osgn__if, fact_34_lift_Osimps_I2_J, fact_44_neq0__conv, fact_93_zless__int, fact_6_dB_Osimps_I4_J, fact_5_subst__eq, help_pp_1_1_U, arity_Int_Oint___Groups_Ozero, fact_75_Var__apps__neq__Abs__apps, conj_0, fact_25_liftn__0, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_97_int__if__cong, fact_95_transfer__int__nat__relations_I2_J, fact_24_nat__size, fact_31_lift__IT, fact_38_dB_Osimps_I6_J, fact_72_beta__cases_I2_J, fact_71_Var__apps__eq__Var__apps__conv, fact_21_dB_Osimps_I11_J
% 10.05/3.92 % No. of inferences in proof: 244
% 10.05/3.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3377 ms resp. 2603 ms w/o parsing
% 10.63/4.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.63/4.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------