TSTP Solution File: LCL773_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL773_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:35 EDT 2023
% Result : Theorem 6.57s 2.63s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 162
% Syntax : Number of formulae : 285 ( 130 unt; 41 typ; 0 def)
% Number of atoms : 565 ( 230 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 2978 ( 74 ~; 15 |; 47 &;2666 @)
% ( 22 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 9 con; 0-5 aty)
% Number of variables : 511 ( 0 ^; 472 !; 20 ?; 511 :)
% ( 19 !>; 0 ?*; 0 @-; 0 @+)
% 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_type,type,
zero:
!>[TA: $tType] : $o ).
thf(sgn_if_type,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(sgn_sgn_type,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_type,type,
bool_size: bool > nat ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(beta_type,type,
beta: dB > dB > $o ).
thf(abs_type,type,
abs: dB > dB ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_rec_type,type,
dB_rec:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) > ( fun @ dB @ ( fun @ TA @ TA ) ) > dB > TA ) ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(lift_type,type,
lift: dB > nat > dB ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(listsp_type,type,
listsp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(nat_size_type,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(char_size_type,type,
char_size: char > nat ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(pp_type,type,
pp: bool > $o ).
thf(i_type,type,
i: nat ).
thf(r_type,type,
r: dB ).
thf(35,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_beta__cases_I3_J) ).
thf(227,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(63,axiom,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ r ) @ ( var @ i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(333,plain,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ r ) @ ( var @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(99,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__irrefl__nat) ).
thf(468,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(114,axiom,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( subst @ ( var @ C ) @ A @ B )
= ( var @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_subst__lt) ).
thf(523,plain,
! [A: dB,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ( subst @ ( var @ C ) @ A @ B )
= ( var @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(29,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_of__nat__less__0__iff) ).
thf(202,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_lift_Osimps_I2_J) ).
thf(217,plain,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(45,axiom,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_transfer__int__nat__numerals_I1_J) ).
thf(276,plain,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(80,axiom,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_beta__cases_I1_J) ).
thf(385,plain,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(118,axiom,
! [A: literal] :
( ( size_size @ literal @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_size__literal__def) ).
thf(533,plain,
! [A: literal] :
( ( size_size @ literal @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(122,axiom,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_subst__lift) ).
thf(550,plain,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(14,axiom,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_lift__preserves__beta) ).
thf(153,plain,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_dB_Osimps_I3_J) ).
thf(174,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [A: nat] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zero__less__int__conv) ).
thf(288,plain,
! [A: nat] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(53,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_dB_Orecs_I2_J) ).
thf(301,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,axiom,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_beta) ).
thf(189,plain,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(89,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
<=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_IT_Osimps) ).
thf(421,plain,
! [A: dB] :
( ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) )
& ( ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( foldl @ dB @ dB @ app @ C @ A ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_apps__preserves__beta) ).
thf(325,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( foldl @ dB @ dB @ app @ C @ A ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
( ( size_size @ nat @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nat_Osize_I3_J) ).
thf(448,plain,
( ( size_size @ nat @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(101,axiom,
! [A: nat] :
( ( size_size @ nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat__size) ).
thf(475,plain,
! [A: nat] :
( ( size_size @ nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(59,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_dB_Osimps_I9_J) ).
thf(321,plain,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__not__refl2) ).
thf(376,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_of__nat__0) ).
thf(485,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(103,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_substn_Osimps_I2_J) ).
thf(480,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__imp__of__nat__less) ).
thf(293,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
<=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_sgn__greater) ).
thf(453,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(7,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(133,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__zeroE) ).
thf(265,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(116,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_subst__eq) ).
thf(527,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(77,axiom,
pp @ ( aa @ dB @ bool @ it @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(380,plain,
pp @ ( aa @ dB @ bool @ it @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(43,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(270,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(120,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(546,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(78,axiom,
( ( size_size @ bool @ fTrue )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_bool_Osize_I3_J) ).
thf(381,plain,
( ( size_size @ bool @ fTrue )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(33,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_dB_Osimps_I7_J) ).
thf(220,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(64,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_zero__reorient) ).
thf(334,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(68,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Beta) ).
thf(349,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(85,axiom,
! [A: bool] :
( ( size_size @ bool @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_size__bool) ).
thf(407,plain,
! [A: bool] :
( ( size_size @ bool @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(9,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(137,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_abs) ).
thf(165,plain,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(39,axiom,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Abs__App__neq__Var__apps) ).
thf(252,plain,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(27,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_dB_Orecs_I1_J) ).
thf(197,plain,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_sgn__less) ).
thf(456,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(34,axiom,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_dB_Osize_I4_J) ).
thf(224,plain,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__not__refl3) ).
thf(519,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(58,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dB_Osimps_I6_J) ).
thf(317,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(84,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dB_Osimps_I8_J) ).
thf(403,plain,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(81,axiom,
( ( size_size @ bool @ fFalse )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bool_Osize_I4_J) ).
thf(388,plain,
( ( size_size @ bool @ fFalse )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(106,axiom,
! [A: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_int__eq__0__conv) ).
thf(488,plain,
! [A: nat] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(124,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(115,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(526,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(100,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Var__apps__neq__Abs__apps) ).
thf(471,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(40,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Var__apps__eq__Var__apps__conv) ).
thf(256,plain,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_beta__cases_I2_J) ).
thf(129,plain,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_IT_OVar) ).
thf(371,plain,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(134,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(117,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_dB_Osimps_I10_J) ).
thf(530,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(5,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(128,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_dB_Osize_I1_J) ).
thf(343,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(52,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_substn__subst__n) ).
thf(298,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(111,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_dB_Osimps_I4_J) ).
thf(513,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(47,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_neq0__conv) ).
thf(279,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(12,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(149,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_gr0I) ).
thf(191,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(48,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT) ).
thf(286,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(30,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__not__refl) ).
thf(204,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(87,axiom,
( ( nat_size @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nat_Osize_I1_J) ).
thf(413,plain,
( ( nat_size @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(91,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_subst__App) ).
thf(445,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(57,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__less__imp__eq__int) ).
thf(313,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(108,axiom,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_liftn__0) ).
thf(498,plain,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(23,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Lambda) ).
thf(187,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(72,axiom,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_int__if__cong) ).
thf(362,plain,
! [A: nat,B: nat,C: bool] :
( ( ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) )
& ( ~ ( pp @ C )
=> ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ ( if @ nat @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_gr__implies__not0) ).
thf(271,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_of__nat__eq__iff) ).
thf(140,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(104,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(483,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(38,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(251,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_transfer__int__nat__relations_I1_J) ).
thf(155,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__nat__zero__code) ).
thf(330,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(46,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(278,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(55,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_dB_Osimps_I5_J) ).
thf(306,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_int__int__eq) ).
thf(167,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_linorder__neqE__linordered__idom) ).
thf(162,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(121,axiom,
( ( bool_size @ fFalse )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bool_Osize_I2_J) ).
thf(548,plain,
( ( bool_size @ fFalse )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1,conjecture,
pp @ ( aa @ dB @ bool @ it @ ( subst @ r @ ( var @ i ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ dB @ bool @ it @ ( subst @ r @ ( var @ i ) @ ( zero_zero @ nat ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(123,plain,
~ ( pp @ ( aa @ dB @ bool @ it @ ( subst @ r @ ( var @ i ) @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_dB_Orecs_I3_J) ).
thf(194,plain,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
! [A: char] :
( ( char_size @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_char__size) ).
thf(295,plain,
! [A: char] :
( ( char_size @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(150,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(61,axiom,
! [TA: $tType] :
( ( sgn_if @ TA )
=> ( ( sgn_sgn @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_sgn0) ).
thf(327,plain,
! [TA: $tType] :
( ( sgn_if @ TA )
=> ( ( sgn_sgn @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(56,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_dB_Osimps_I11_J) ).
thf(310,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(20,axiom,
sgn_if @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(182,plain,
sgn_if @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(127,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_of__nat__less__iff) ).
thf(359,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(98,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dB_Osimps_I12_J) ).
thf(465,plain,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(93,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_not__less0) ).
thf(450,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(495,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(112,axiom,
( ( bool_size @ fTrue )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_bool_Osize_I1_J) ).
thf(517,plain,
( ( bool_size @ fTrue )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(54,axiom,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_subst__Var__IT) ).
thf(304,plain,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_apps__eq__tail__conv) ).
thf(351,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_transfer__int__nat__relations_I2_J) ).
thf(390,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(186,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_linorder__neqE__nat) ).
thf(510,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__neq__iff) ).
thf(207,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(102,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_int__0) ).
thf(478,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(79,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_appR) ).
thf(383,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_of__nat__0__less__iff) ).
thf(346,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(119,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_nat__less__cases) ).
thf(536,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(86,axiom,
! [A: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_int__less__0__conv) ).
thf(410,plain,
! [A: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(11,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(146,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
= ( sgn_sgn @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_sgn__sgn) ).
thf(183,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
= ( sgn_sgn @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(75,axiom,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_substn__subst__0) ).
thf(373,plain,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_of__nat__less__imp__less) ).
thf(341,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(42,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_subst__preserves__beta) ).
thf(268,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(70,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(358,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sgn__0__0) ).
thf(415,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(36,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_liftn_Osimps_I2_J) ).
thf(239,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(37,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Abs__apps__eq__Abs__apps__conv) ).
thf(242,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_dB_Osimps_I1_J) ).
thf(395,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(97,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(464,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_zless__int) ).
thf(459,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(28,axiom,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( lift @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_lift__IT) ).
thf(200,plain,
! [A: nat,B: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( lift @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(90,axiom,
! [A: char] :
( ( size_size @ char @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_size__char) ).
thf(442,plain,
! [A: char] :
( ( size_size @ char @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(109,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dB_Osimps_I2_J) ).
thf(501,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(73,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_appL) ).
thf(369,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(553,plain,
$false,
inference(e,[status(thm)],[227,333,468,523,202,217,276,385,533,550,153,174,288,301,189,421,325,448,475,321,376,485,480,293,453,133,265,527,380,270,546,381,220,334,349,407,137,165,252,197,456,224,519,317,403,388,488,124,526,471,256,129,371,134,530,128,343,298,513,279,149,191,286,204,413,445,313,498,187,362,271,140,483,251,155,330,278,306,167,162,548,123,194,295,150,327,310,182,127,359,465,450,495,517,304,351,390,186,510,207,478,383,346,536,410,146,183,373,341,268,358,415,239,242,395,464,459,200,442,501,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL773_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n026.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 16:35:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.62/1.05 % [INFO] Parsing done (190ms).
% 1.62/1.06 % [INFO] Running in sequential loop mode.
% 2.00/1.27 % [INFO] eprover registered as external prover.
% 2.00/1.27 % [INFO] cvc4 registered as external prover.
% 2.00/1.27 % [INFO] Scanning for conjecture ...
% 2.29/1.37 % [INFO] Found a conjecture and 120 axioms. Running axiom selection ...
% 2.53/1.45 % [INFO] Axiom selection finished. Selected 120 axioms (removed 0 axioms).
% 3.00/1.58 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.00/1.59 % [INFO] Type checking passed.
% 3.00/1.60 % [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 ...
% 3.30/1.75 % [INFO] [Domain constraints] Detected constraint on bool
% 3.30/1.75 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 3.54/1.78 % [INFO] [Domain constraints] Detected constraint on bool
% 3.54/1.78 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 3.54/1.80 % [INFO] [Domain constraints] Detected constraint on bool
% 3.54/1.80 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 6.57/2.63 % External prover 'e' found a proof!
% 6.57/2.63 % [INFO] Killing All external provers ...
% 6.57/2.63 % Time passed: 2102ms (effective reasoning time: 1571ms)
% 6.57/2.63 % 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)>
% 6.57/2.63 % 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
% 6.57/2.63 % No. of inferences in proof: 244
% 6.57/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2102 ms resp. 1571 ms w/o parsing
% 6.92/2.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.92/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------