TSTP Solution File: LCL839_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL839_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:32:17 EDT 2023
% Result : Theorem 5.04s 2.20s
% Output : Refutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 61
% Syntax : Number of formulae : 97 ( 26 unt; 27 typ; 0 def)
% Number of atoms : 188 ( 78 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1090 ( 32 ~; 0 |; 19 &; 986 @)
% ( 7 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 19 con; 0-5 aty)
% Number of variables : 183 ( 0 ^; 178 !; 0 ?; 183 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(type_type,type,
type: $tType ).
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(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(shift_type,type,
shift:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > nat > TA > ( fun @ nat @ TA ) ) ).
thf(fun1_type,type,
fun1: fun @ type @ ( fun @ type @ type ) ).
thf(typing_type,type,
typing: ( fun @ nat @ type ) > dB > type > $o ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(t1_type,type,
t1: type ).
thf(t_a_type,type,
t_a: type ).
thf(t_type,type,
t: type ).
thf(ua1_type,type,
ua1: type ).
thf(a_type,type,
a: dB ).
thf(as_type,type,
as: list @ dB ).
thf(e_type,type,
e: fun @ nat @ type ).
thf(ea_type,type,
ea: fun @ nat @ type ).
thf(i_type,type,
i: nat ).
thf(ia_type,type,
ia: nat ).
thf(r_type,type,
r: dB ).
thf(thesis_type,type,
thesis: $o ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(19,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_45_beta__cases_I2_J) ).
thf(115,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)],[19]) ).
thf(3,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_47_apps__preserves__beta) ).
thf(37,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)],[3]) ).
thf(31,axiom,
typing @ e @ u @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uT) ).
thf(157,plain,
typing @ e @ u @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,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_28_Abs__apps__eq__Abs__apps__conv) ).
thf(78,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)],[12]) ).
thf(11,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_dB_Osimps_I7_J) ).
thf(74,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [A: type] :
( ( typing @ ( shift @ type @ e @ i @ t ) @ a @ A )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(165,plain,
! [A: type] :
( ( typing @ ( shift @ type @ e @ i @ t ) @ a @ A )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
typing @ ea @ ua @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Beta_I7_J) ).
thf(156,plain,
typing @ ea @ ua @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(21,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_73_ext) ).
thf(128,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)],[21]) ).
thf(8,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_92_Var__apps__neq__Abs__apps) ).
thf(59,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)],[8]) ).
thf(10,axiom,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_beta__cases_I1_J) ).
thf(71,plain,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type_Osimps_I2_J) ).
thf(39,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
= ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,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_42_dB_Osimps_I8_J) ).
thf(135,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)],[23]) ).
thf(33,axiom,
typing @ ( shift @ type @ e @ i @ t ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ ua1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
thf(162,plain,
typing @ ( shift @ type @ e @ i @ t ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ ua1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_abs) ).
thf(154,plain,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,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_81_Var__apps__eq__Var__apps__conv) ).
thf(87,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)],[13]) ).
thf(20,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_32_dB_Osimps_I2_J) ).
thf(119,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)],[20]) ).
thf(16,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_35_appR) ).
thf(107,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)],[16]) ).
thf(18,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_43_dB_Osimps_I9_J) ).
thf(111,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)],[18]) ).
thf(26,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(142,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)],[26]) ).
thf(28,axiom,
typing @ ( shift @ type @ e @ i @ t ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_T) ).
thf(153,plain,
typing @ ( shift @ type @ e @ i @ t ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) )
=> ( ( typing @ E @ A @ C )
=> ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_App) ).
thf(109,plain,
! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
( ( typing @ E @ D @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) )
=> ( ( typing @ E @ A @ C )
=> ( typing @ E @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,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_34_apps__eq__tail__conv) ).
thf(96,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)],[14]) ).
thf(15,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_86_dB_Osimps_I5_J) ).
thf(103,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)],[15]) ).
thf(25,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_36_appL) ).
thf(140,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)],[25]) ).
thf(5,axiom,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ B )
=> ( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_var__app__type__eq) ).
thf(48,plain,
! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ B )
=> ( ( typing @ E @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_dB_Osimps_I1_J) ).
thf(63,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)],[9]) ).
thf(27,axiom,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ~ ! [E: type] :
( ( typing @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) )
=> ~ ( typing @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_typing__elims_I2_J) ).
thf(150,plain,
! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ~ ! [E: type] :
( ( typing @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) )
=> ~ ( typing @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(158,plain,
~ ! [A: type] :
~ ( typing @ ( shift @ type @ e @ i @ t ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,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_91_Abs__App__neq__Var__apps) ).
thf(55,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)],[7]) ).
thf(24,axiom,
typing @ ( shift @ type @ ea @ ia @ t ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Beta_I5_J) ).
thf(139,plain,
typing @ ( shift @ type @ ea @ ia @ t ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ a ) @ as ) @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dB_Osimps_I6_J) ).
thf(51,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,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_87_dB_Osimps_I4_J) ).
thf(131,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)],[22]) ).
thf(34,axiom,
! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ C @ B )
=> ( ( beta @ C @ A )
=> ( typing @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_subject__reduction) ).
thf(163,plain,
! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
( ( typing @ D @ C @ B )
=> ( ( beta @ C @ A )
=> ( typing @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(168,plain,
$false,
inference(e,[status(thm)],[115,37,157,78,74,165,156,128,59,71,39,135,162,154,87,119,107,111,142,153,109,96,103,140,48,63,150,158,55,139,36,51,131,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL839_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 16:24:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.67/1.10 % [INFO] Parsing done (203ms).
% 1.67/1.11 % [INFO] Running in sequential loop mode.
% 2.28/1.31 % [INFO] eprover registered as external prover.
% 2.28/1.31 % [INFO] cvc4 registered as external prover.
% 2.28/1.31 % [INFO] Scanning for conjecture ...
% 2.56/1.42 % [INFO] Found a conjecture and 109 axioms. Running axiom selection ...
% 2.93/1.49 % [INFO] Axiom selection finished. Selected 33 axioms (removed 76 axioms).
% 3.17/1.56 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.17/1.57 % [INFO] Type checking passed.
% 3.17/1.57 % [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 ...
% 5.04/2.19 % External prover 'e' found a proof!
% 5.04/2.19 % [INFO] Killing All external provers ...
% 5.04/2.20 % Time passed: 1671ms (effective reasoning time: 1086ms)
% 5.04/2.20 % 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)>
% 5.04/2.20 % Axioms used in derivation (33): fact_20_App, fact_15_Beta_I5_J, fact_14_Beta_I7_J, fact_28_Abs__apps__eq__Abs__apps__conv, fact_90_var__app__type__eq, fact_35_appR, fact_26_typing__elims_I2_J, fact_41_subject__reduction, fact_32_dB_Osimps_I2_J, fact_34_apps__eq__tail__conv, fact_36_appL, fact_92_Var__apps__neq__Abs__apps, fact_37_abs, fact_87_dB_Osimps_I4_J, fact_86_dB_Osimps_I5_J, fact_17_type_Osimps_I2_J, fact_47_apps__preserves__beta, fact_2_uT, fact_81_Var__apps__eq__Var__apps__conv, fact_33_dB_Osimps_I3_J, fact_42_dB_Osimps_I8_J, fact_4__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_91_Abs__App__neq__Var__apps, fact_73_ext, fact_83_dB_Osimps_I6_J, fact_80_beta__cases_I1_J, fact_3__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096, fact_45_beta__cases_I2_J, fact_77_dB_Osimps_I1_J, fact_43_dB_Osimps_I9_J, fact_84_dB_Osimps_I7_J, conj_0, fact_5_T
% 5.04/2.20 % No. of inferences in proof: 70
% 5.04/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1671 ms resp. 1086 ms w/o parsing
% 5.44/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.44/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------