%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL839_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 : n007.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 07:53:11 AM UTC 2026
% Result : Theorem 7.75s 3.22s
% Output : Refutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 70 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 78 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1064 ( 32 ~; 0 |; 19 &; 960 @)
% ( 7 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 19 con; 0-5 aty)
% Number of variables : 178 ( 0 ^; 178 !; 0 ?; 178 :)
% 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_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(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(shift_decl,type,
shift:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > nat > TA > ( TA @ ( nat @ fun ) ) ) ).
thf(fun1_decl,type,
fun1: type @ ( type @ fun ) @ ( type @ fun ) ).
thf(typing_decl,type,
typing: ( type @ ( nat @ fun ) ) > dB > type > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(t1_decl,type,
t1: type ).
thf(t_a_decl,type,
t_a: type ).
thf(t_decl,type,
t: type ).
thf(ua1_decl,type,
ua1: type ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(e_decl,type,
e: type @ ( nat @ fun ) ).
thf(ea_decl,type,
ea: type @ ( nat @ fun ) ).
thf(i_decl,type,
i: nat ).
thf(ia_decl,type,
ia: nat ).
thf(r_decl,type,
r: dB ).
thf(thesis_decl,type,
thesis: $o ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(14,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_34_apps__eq__tail__conv) ).
thf(101,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)],[14]) ).
thf(17,axiom,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typing ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_App) ).
thf(115,plain,
! [A: dB,B: type,C: type,D: dB,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( D @ ( E @ typing ) ) )
=> ( ( C @ ( A @ ( E @ typing ) ) )
=> ( B @ ( A @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( E @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,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_91_Abs__App__neq__Var__apps) ).
thf(56,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)],[7]) ).
thf(6,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_dB_Osimps_I6_J) ).
thf(52,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,axiom,
~ ! [A: type] :
~ ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
file('/export/starexec/sandbox2/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(169,plain,
~ ! [A: type] :
~ ( A @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(33,axiom,
ua1 @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox2/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(173,plain,
ua1 @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(35,axiom,
! [A: type] :
( ( A @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(176,plain,
! [A: type] :
( ( A @ ( a @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5,axiom,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_var__app__type__eq) ).
thf(49,plain,
! [A: type,B: type,C: dB @ list,D: nat,E: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( ( A @ ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( E @ typing ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,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_81_Var__apps__eq__Var__apps__conv) ).
thf(91,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)],[13]) ).
thf(30,axiom,
t @ ( ua @ ( ea @ typing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Beta_I7_J) ).
thf(167,plain,
t @ ( ua @ ( ea @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(26,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(150,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)],[26]) ).
thf(23,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_42_dB_Osimps_I8_J) ).
thf(143,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)],[23]) ).
thf(22,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_87_dB_Osimps_I4_J) ).
thf(139,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)],[22]) ).
thf(34,axiom,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( A @ ( C @ beta ) )
=> ( B @ ( A @ ( D @ typing ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_subject__reduction) ).
thf(174,plain,
! [A: dB,B: type,C: dB,D: type @ ( nat @ fun )] :
( ( B @ ( C @ ( D @ typing ) ) )
=> ( ( A @ ( C @ beta ) )
=> ( B @ ( A @ ( D @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,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_47_apps__preserves__beta) ).
thf(37,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)],[3]) ).
thf(28,axiom,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_T) ).
thf(164,plain,
t1 @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( i @ ( e @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,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_45_beta__cases_I2_J) ).
thf(121,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)],[19]) ).
thf(24,axiom,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Beta_I5_J) ).
thf(147,plain,
t_a @ ( as @ ( a @ ( r @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( t @ ( ia @ ( ea @ ( type @ shift ) ) ) @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_beta__cases_I1_J) ).
thf(74,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,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_92_Var__apps__neq__Abs__apps) ).
thf(60,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)],[8]) ).
thf(18,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_43_dB_Osimps_I9_J) ).
thf(117,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)],[18]) ).
thf(27,axiom,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typing ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_typing__elims_I2_J) ).
thf(160,plain,
! [A: type,B: dB,C: dB,D: type @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ typing ) ) )
=> ~ ! [E: type] :
( ( A @ ( E @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) @ ( C @ ( D @ typing ) ) )
=> ~ ( E @ ( B @ ( D @ typing ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_abs) ).
thf(165,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,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_86_dB_Osimps_I5_J) ).
thf(109,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)],[15]) ).
thf(11,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_dB_Osimps_I7_J) ).
thf(77,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,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_36_appL) ).
thf(148,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)],[25]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_dB_Osimps_I1_J) ).
thf(64,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)],[9]) ).
thf(16,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_35_appR) ).
thf(113,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)],[16]) ).
thf(12,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_28_Abs__apps__eq__Abs__apps__conv) ).
thf(81,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)],[12]) ).
thf(4,axiom,
! [A: type,B: type,C: type,D: type] :
( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_type_Osimps_I2_J) ).
thf(39,plain,
! [A: type,B: type,C: type,D: type] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) )
= ( A @ ( B @ ( fun1 @ ( type @ ( type @ fun ) @ ( type @ aa ) ) ) @ ( type @ ( type @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox2/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(31,axiom,
t @ ( u @ ( e @ typing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uT) ).
thf(168,plain,
t @ ( u @ ( e @ typing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,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_32_dB_Osimps_I2_J) ).
thf(126,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)],[20]) ).
thf(21,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_73_ext) ).
thf(136,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)],[21]) ).
thf(179,plain,
$false,
inference(e,[status(thm)],[101,115,56,52,169,173,176,49,91,167,150,143,139,174,37,164,121,147,74,60,117,160,165,109,77,148,64,113,81,39,36,168,126,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL839_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
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Fri Sep 25 23:39:54 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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 ...
% 1.89/1.32 % [INFO] Parsing done (327ms).
% 1.89/1.33 % [INFO] Running in sequential loop mode.
% 2.77/1.73 % [INFO] eprover registered as external prover.
% 2.77/1.74 % [INFO] Scanning for conjecture ...
% 3.20/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 3.62/2.05 % [INFO] Axiom selection finished. Selected 33 axioms (removed 76 axioms).
% 4.10/2.18 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.10/2.19 % [INFO] Type checking passed.
% 4.40/2.20 % [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 ...
% 7.75/3.21 % External prover 'e' found a proof!
% 7.75/3.21 % [INFO] Killing All external provers ...
% 7.75/3.22 % Time passed: 2679ms (effective reasoning time: 1876ms)
% 7.75/3.22 % 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)>
% 7.75/3.22 % 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
% 7.75/3.22 % No. of inferences in proof: 70
% 7.75/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2679 ms resp. 1876 ms w/o parsing
% 8.04/3.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.04/3.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------