TSTP Solution File: SCT080-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SCT080-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Tue Sep 20 03:41:31 EDT 2022
% Result : Unsatisfiable 0.65s 0.73s
% Output : Proof 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 51 ( 11 unt; 14 typ; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 212 ( 100 ~; 96 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 7 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 139 ( 126 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(c_COMBK_type,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(v_Lba_____type,type,
v_Lba____: $i ).
tff(c_in_type,type,
c_in: $i > $i ).
tff(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(v_F_type,type,
v_F: $i ).
tff(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin))
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(3,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_L: $i] :
refl(
( ( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
<=> ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
<=> ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_const__Lin__Prof_0) ).
tff(8,plain,
! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) )
<=> ( ~ ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_L: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(17,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
<=> hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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)))) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(20,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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)))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(
( ( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) )
<=> ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
tff(27,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) )
<=> ( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [T_b: $i,V_x: $i,V_f: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) )
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(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_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT080-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 23:49:40 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.65/0.73 % SZS status Unsatisfiable
% 0.65/0.73 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------