%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT086-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Tue Sep 29 12:36:53 PM UTC 2026
% Result : Unsatisfiable 3.26s 1.44s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 11 unt; 3 def)
% Number of atoms : 77 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 95 ( 51 ~; 41 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-6 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f261,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f588,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2) ).
fof(f589,axiom,
! [X0] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X0),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X0),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f590,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f591,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f592,negated_conjecture,
! [X0] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,X0)),X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f593,negated_conjecture,
! [X0] :
( v_thesis____
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),hAPP(v_n,X0)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f633,definition,
( spl0_1
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),hAPP(v_n,X0)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f634,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),hAPP(v_n,X0)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f636,definition,
( spl0_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f639,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f593,f636,f633]) ).
fof(f641,definition,
( spl0_3
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,X0)),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f642,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,X0)),X0))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f643,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f592,f636,f641]) ).
fof(f644,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f591,f636]) ).
fof(f2346,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_Suc(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))),
inference(forward_demodulation,[],[f588,f261]) ).
fof(f2349,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,X0)),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) )
| ~ spl0_1 ),
inference(resolution,[],[f589,f634]) ).
fof(f2352,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,X0)),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_Suc(X0)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2349,f261]) ).
fof(f2435,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_Suc(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ spl0_1 ),
inference(resolution,[],[f2352,f590]) ).
fof(f2436,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(v_n,v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f2435,f2346]) ).
fof(f2437,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f2436,f642]) ).
fof(f2445,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Oplus__class_Oplus(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2437,f590]) ).
fof(f2447,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_Suc(v_sko__CHAINED__1(v_F,v_Lab____,v_Lba____,v_a____,v_b____,v_h____))),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f2445,f261]) ).
fof(f2449,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f2447,f2346]) ).
fof(f2450,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f2449]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f639]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f643]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f644]) ).
cnf(s21,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f2450]) ).
cnf(s25,plain,
spl0_3,
inference(rat,[],[s2,s3]) ).
cnf(s26,plain,
~ spl0_1,
inference(rat,[],[s21,s25]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s1,s3,s26]) ).
fof(f2451,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT086-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 % Computer : n026.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sun Sep 27 23:42:42 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.46 Running first-order theorem proving
% 0.11/0.46 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.26/1.44 % (3334568)Input is clausal, will run a generic CNF schedule.
% 3.26/1.44 % (3334577)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4147772716:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.26/1.44 % (3334576)lrs+10_1_sil=8000:sp=occurrence:random_seed=3917470081:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.26/1.44 % (3334575)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1767708922:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.26/1.44 % (3334574)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3560865201:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.26/1.44 % (3334573)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3381026264:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.26/1.44 % (3334577)Instruction limit reached!
% 3.26/1.44 % (3334577)------------------------------
% 3.26/1.44 % (3334577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (3334577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (3334577)CaDiCaL version: 2.1.3
% 3.26/1.44 % (3334577)Termination reason: Instruction limit
% 3.26/1.44 % (3334577)Termination phase: Saturation
% 3.26/1.44 % (3334577)Time elapsed: 0.041 s
% 3.26/1.44 % (3334577)Peak memory usage: 89 MB
% 3.26/1.44 % (3334577)Instructions burned: 115 (million)
% 3.26/1.44 % (3334579)dis-21_1_sil=8000:lcm=predicate:random_seed=450617369:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.26/1.44 % (3334578)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2383221043:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.26/1.44 % (3334576)Instruction limit reached!
% 3.26/1.44 % (3334576)------------------------------
% 3.26/1.44 % (3334576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (3334576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (3334576)CaDiCaL version: 2.1.3
% 3.26/1.44 % (3334576)Termination reason: Instruction limit
% 3.26/1.44 % (3334576)Termination phase: Saturation
% 3.26/1.44 % (3334576)Time elapsed: 0.060 s
% 3.26/1.44 % (3334576)Peak memory usage: 89 MB
% 3.26/1.44 % (3334576)Instructions burned: 108 (million)
% 3.26/1.44 % (3334579)Instruction limit reached!
% 3.26/1.44 % (3334579)------------------------------
% 3.26/1.44 % (3334579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (3334579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (3334579)CaDiCaL version: 2.1.3
% 3.26/1.44 % (3334579)Termination reason: Instruction limit
% 3.26/1.44 % (3334579)Termination phase: Saturation
% 3.26/1.44 % (3334579)Time elapsed: 0.069 s
% 3.26/1.44 % (3334579)Peak memory usage: 89 MB
% 3.26/1.44 % (3334579)Instructions burned: 118 (million)
% 3.26/1.44 % (3334578)First to succeed.
% 3.26/1.44 % (3334578)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3334568"
% 3.26/1.44 % (3334586)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3942076606:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.26/1.44 % (3334586)Refutation not found, incomplete strategy
% 3.26/1.44 % (3334586)------------------------------
% 3.26/1.44 % (3334586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.44 % (3334586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.44 % (3334586)CaDiCaL version: 2.1.3
% 3.26/1.44 % (3334586)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.44 % (3334586)Time elapsed: 0.006 s
% 3.26/1.44 % (3334586)Peak memory usage: 89 MB
% 3.26/1.44 % (3334586)Instructions burned: 19 (million)
% 3.26/1.44 % (3334588)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2331144773:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.26/1.44 % (3334589)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1397341786:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.26/1.44 % (3334588)Also succeeded, but the first one will report.
% 3.26/1.44 % (3334589)Also succeeded, but the first one will report.
% 3.26/1.44 % (3334586)------------------------------
% 3.26/1.44 % (3334586)------------------------------
% 3.26/1.44 % (3334578)Refutation found. Thanks to Tanya!
% 3.26/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.26/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.27/1.64 % (3334578)------------------------------
% 4.27/1.64 % (3334578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.64 % (3334578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.64 % (3334578)CaDiCaL version: 2.1.3
% 4.27/1.64 % (3334578)Termination reason: Refutation
% 4.27/1.64 % (3334578)Time elapsed: 0.082 s
% 4.27/1.64 % (3334578)Peak memory usage: 91 MB
% 4.27/1.64 % (3334578)Instructions burned: 128 (million)
% 4.27/1.64 % (3334578)------------------------------
% 4.27/1.64 % (3334578)------------------------------
% 4.27/1.64 % (3334568)Success in time 0.543 s
% 4.27/1.64 % Vampire exiting
%------------------------------------------------------------------------------