%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV948-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:36:22 AM UTC 2025
% Result : Unsatisfiable 1.83s 2.00s
% Output : Proof 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 65
% Syntax : Number of formulae : 155 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 749 ( 88 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1060 ( 503 ~; 478 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-5 aty)
% Number of functors : 27 ( 27 usr; 14 con; 0-5 aty)
% Number of variables : 771 ( 686 !; 0 ?; 771 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_WellTypeRT_OWTrt_type,type,
c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o ).
tff(c_Type_Oty_OVoid_type,type,
c_Type_Oty_OVoid: $i ).
tff(c_Expr_Oexp_OLAss_type,type,
c_Expr_Oexp_OLAss: ( $i * $i * $i ) > $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
tff(v_e_Ha_______type,type,
v_e_Ha______: $i ).
tff(v_V_______type,type,
v_V______: $i ).
tff(v_E_____type,type,
v_E____: $i ).
tff(v_aa_______type,type,
v_aa______: $i ).
tff(v_P_type,type,
v_P: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(c_TypeRel_Owiden_type,type,
c_TypeRel_Owiden: ( $i * $i ) > $i ).
tff(tc_prod_type,type,
tc_prod: ( $i * $i ) > $i ).
tff(tc_Expr_Oexp_type,type,
tc_Expr_Oexp: $i > $i ).
tff(v_ea_______type,type,
v_ea______: $i ).
tff(v_a_______type,type,
v_a______: $i ).
tff(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1_type,type,
c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2_type,type,
c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_TypeSafe__Mirabelle_Osconf_type,type,
c_TypeSafe__Mirabelle_Osconf: ( $i * $i * $i ) > $o ).
tff(c_Pair_type,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
tff(tc_Value_Oval_type,type,
tc_Value_Oval: $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_b_______type,type,
v_b______: $i ).
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: ( $i * $i ) > $i ).
tff(tc_Type_Oty_type,type,
tc_Type_Oty: $i ).
tff(1,plain,
( c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
<=> c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRed_I4_J_0) ).
tff(3,plain,
c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
rewrite(( ( ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( V_T = c_Type_Oty_OVoid )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_0) ).
tff(10,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) )
<=> ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( V_T = c_Type_Oty_OVoid ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( v_T____ = c_Type_Oty_OVoid ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
v_T____ = c_Type_Oty_OVoid,
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____) = hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [V_T: $i,T_a: $i,V_P: $i] :
refl(( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
<=> ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).
tff(25,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [V_T: $i,T_a: $i,V_P: $i] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),c_Type_Oty_OVoid)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)),
inference(modus_ponens,[status(thm)],[29,20]) ).
tff(31,plain,
^ [V_x: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [V_x: $i] :
rewrite(( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [V_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x) )
<=> ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [V_x: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(37,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) )
<=> ( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_x: $i] :
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),V_x)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x),v_T____)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_Type_Oty_OVoid),v_T____)) ),
inference(unit_resolution,[status(thm)],[43,40]) ).
tff(45,plain,
~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid),
inference(unit_resolution,[status(thm)],[44,30]) ).
tff(46,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
rewrite(( ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_2) ).
tff(52,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) )
<=> ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),
inference(unit_resolution,[status(thm)],[58,55,3]) ).
tff(60,plain,
^ [V_E: $i,V_T: $i] :
refl(( ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
^ [V_E: $i,V_T: $i] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) )),
( ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) )),
rewrite(( ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) )),
( ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V_E: $i,V_T: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [V_E: $i,V_T: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
tff(66,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
<=> c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRed_I3_J_0) ).
tff(72,plain,
c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)),V_T)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))),
inference(unit_resolution,[status(thm)],[78,72,69,59]) ).
tff(80,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
rewrite(( ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v)))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v)))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v)))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_3) ).
tff(86,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(V_E,V_P,V_e,V_h,V_v)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v))) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))),
inference(unit_resolution,[status(thm)],[92,89,3]) ).
tff(94,plain,
^ [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
<=> ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
<=> ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
^ [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
rewrite(( ( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U)) )
<=> ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__trans_0) ).
tff(100,plain,
! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ( ~ ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) )
<=> ( ~ ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [V_U: $i,V_T: $i,V_S: $i,T_a: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T)) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______))),
inference(unit_resolution,[status(thm)],[106,103,93,79]) ).
tff(108,plain,
^ [V_E: $i,V_T: $i] :
refl(( ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
( ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
^ [V_E: $i,V_T: $i] :
trans(monotonicity(rewrite(( ( c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) )),
( ( c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) )),
rewrite(( ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) )),
( ( c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [V_E: $i,V_T: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) )
<=> ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,axiom,
! [V_E: $i,V_T: $i] :
( c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(114,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ( ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) )
<=> ( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [V_E: $i,V_T: $i] :
( ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,V_E,v_ea______,V_T)
| c_WellTypeRT_OWTrt(v_P,v_aa______,V_E,v_e_Ha______,v_sko__CHAINED__1(V_E,v_P,V_T,v_aa______,v_e_Ha______)) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,v_ea______,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______))
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_a______,v_b______,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval))))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),
inference(unit_resolution,[status(thm)],[123,72,117,59]) ).
tff(125,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
rewrite(( ( ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) )
<=> ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_1) ).
tff(131,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) )
<=> ( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V_E: $i,V_T: $i,V_v: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_v,V_e,tc_List_Olist(tc_String_Ochar)),V_T)
| ( hAPP(V_E,V_v) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(V_E,V_P,V_e,V_h,V_v),tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_a______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_ea______,tc_List_Olist(tc_String_Ochar)),v_T____)
| ( hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
hAPP(v_E____,v_V______) = c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty),
inference(unit_resolution,[status(thm)],[137,134,3]) ).
tff(139,plain,
^ [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
refl(( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
<=> ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
<=> ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
^ [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
trans(monotonicity(rewrite(( ( ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) )),
( ( ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) ) )),
rewrite(( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) )),
( ( ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) )
<=> ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) )
<=> ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,axiom,
! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) )
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtLAss_0) ).
tff(145,plain,
! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) )
<=> ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) )
<=> ( ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) )
<=> ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) )
<=> ( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [V_E: $i,V_V: $i,V_T_H: $i,V_T: $i,V_h: $i,V_e: $i,V_P: $i] :
( ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_T_H),V_T))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T_H)
| c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OLAss(V_V,V_e,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ( hAPP(V_E,V_V) != c_Option_Ooption_OSome(V_T,tc_Type_Oty) ) )
| ~ c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,v_e_Ha______,v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______))
| c_WellTypeRT_OWTrt(v_P,v_aa______,v_E____,c_Expr_Oexp_OLAss(v_V______,v_e_Ha______,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OVoid)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__2(v_E____,v_P,v_ea______,v_a______,v_V______),v_aa______,v_e_Ha______)),c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______)))
| ( hAPP(v_E____,v_V______) != c_Option_Ooption_OSome(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__1__1(v_E____,v_P,v_ea______,v_a______,v_V______),tc_Type_Oty) ) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
$false,
inference(unit_resolution,[status(thm)],[154,148,138,124,107,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SWV948-1 : TPTP v9.0.0. Released v4.1.0.
% 0.14/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 11:06:25 EDT 2025
% 0.15/0.37 % CPUTime :
% 1.83/2.00 % SZS status Unsatisfiable
% 1.83/2.00 % SZS output start Proof
% See solution above
% 1.83/2.05 % E exiting
%------------------------------------------------------------------------------