%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV959-1 : 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 05:36:24 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV959-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:06:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(c_WellTypeRT_OWTrt_type, type, (
% 0.20/0.48 c_WellTypeRT_OWTrt: ( $i * $i * $i * $i * $i ) > $o)).
% 0.20/0.48 tff(c_Type_Oty_OClass_type, type, (
% 0.20/0.48 c_Type_Oty_OClass: $i > $i)).
% 0.20/0.48 tff(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1_type, type, (
% 0.20/0.48 c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.48 tff(v_e_092_060_094isub_0622_____type, type, (
% 0.20/0.48 v_e_092_060_094isub_0622____: $i)).
% 0.20/0.48 tff(v_ha_____type, type, (
% 0.20/0.48 v_ha____: $i)).
% 0.20/0.48 tff(v_ea_____type, type, (
% 0.20/0.48 v_ea____: $i)).
% 0.20/0.48 tff(v_P_type, type, (
% 0.20/0.48 v_P: $i)).
% 0.20/0.48 tff(v_F_____type, type, (
% 0.20/0.48 v_F____: $i)).
% 0.20/0.48 tff(v_E_____type, type, (
% 0.20/0.48 v_E____: $i)).
% 0.20/0.48 tff(v_D_____type, type, (
% 0.20/0.48 v_D____: $i)).
% 0.20/0.48 tff(c_Type_Oty_ONT_type, type, (
% 0.20/0.48 c_Type_Oty_ONT: $i)).
% 0.20/0.48 tff(hBOOL_type, type, (
% 0.20/0.48 hBOOL: $i > $o)).
% 0.20/0.48 tff(hAPP_type, type, (
% 0.20/0.48 hAPP: ( $i * $i ) > $i)).
% 0.20/0.48 tff(v_T_____type, type, (
% 0.20/0.48 v_T____: $i)).
% 0.20/0.48 tff(v_sko__CHAINED__1_type, type, (
% 0.20/0.48 v_sko__CHAINED__1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.48 tff(v_h_Ha_____type, type, (
% 0.20/0.48 v_h_Ha____: $i)).
% 0.20/0.48 tff(v_e_Ha_____type, type, (
% 0.20/0.48 v_e_Ha____: $i)).
% 0.20/0.48 tff(c_TypeRel_Owiden_type, type, (
% 0.20/0.48 c_TypeRel_Owiden: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tc_prod_type, type, (
% 0.20/0.48 tc_prod: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tc_Expr_Oexp_type, type, (
% 0.20/0.48 tc_Expr_Oexp: $i > $i)).
% 0.20/0.48 tff(tc_List_Olist_type, type, (
% 0.20/0.48 tc_List_Olist: $i > $i)).
% 0.20/0.48 tff(tc_String_Ochar_type, type, (
% 0.20/0.48 tc_String_Ochar: $i)).
% 0.20/0.48 tff(c_Expr_Oexp_OFAss_type, type, (
% 0.20/0.48 c_Expr_Oexp_OFAss: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.48 tff(c_Type_Oty_OVoid_type, type, (
% 0.20/0.48 c_Type_Oty_OVoid: $i)).
% 0.20/0.48 tff(c_TypeRel_Ohas__field_type, type, (
% 0.20/0.48 c_TypeRel_Ohas__field: ( $i * $i * $i * $i * $i * $i ) > $o)).
% 0.20/0.48 tff(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2_type, type, (
% 0.20/0.48 c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2: ( $i * $i * $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.48 tff(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3_type, type, (
% 0.20/0.48 c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3: ( $i * $i * $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 (^[V_x: $i] : refl(((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), V_x))) <=> ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), V_x))) <=> ![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), V_x)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,(
% 0.20/0.49 ![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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____))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.49 tff(11,assumption,(~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))), introduced(assumption)).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 ((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(13,axiom,(c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_0_03')).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[18, 11])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 ((v_T____ = c_Type_Oty_OVoid) <=> (v_T____ = c_Type_Oty_OVoid)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(21,axiom,(v_T____ = c_Type_Oty_OVoid), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_void_0')).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (v_T____ = c_Type_Oty_OVoid),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (c_Type_Oty_OVoid = v_T____),
% 0.20/0.49 inference(symmetry,[status(thm)],[22])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid) <=> c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____) <=> c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)),
% 0.20/0.49 inference(symmetry,[status(thm)],[24])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____) <=> c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(27,axiom,(c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_wt_0')).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_T____)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (^[V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT)) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT)) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT)) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (^[V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.49 tff(35,axiom,(![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_WTrt__elim__cases_I8_J_4')).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.49 tff(38,plain,(
% 0.20/0.49 ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(skolemize,[status(sab)],[37])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT)) <=> (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[46, 29])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 19])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (^[V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,plain,
% 0.20/0.50 (^[V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.50 tff(54,axiom,(![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_WTrt__elim__cases_I8_J_7')).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.50 tff(57,plain,(
% 0.20/0.50 ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[56])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(V_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_F, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v), V_D, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[62, 29])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[63, 19])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (^[V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (^[V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.50 tff(70,axiom,(![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_WTrt__elim__cases_I8_J_10')).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.50 tff(73,plain,(
% 0.20/0.50 ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[72])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_v, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[78, 29])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[79, 19])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (^[V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) <=> ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (^[V_F: $i, V_D: $i, V_E: $i, V_T: $i, V_v: $i, V_h: $i, V_e: $i, V_P: $i] : trans(monotonicity(rewrite((c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) <=> (c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))), (((c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))))), rewrite(((c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))), (((c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T))) <=> ((~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(85,plain,
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% 0.20/0.51 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.51 tff(86,axiom,(![V_F: $i, V_D: $i, 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_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v)))) | (~c_WellTypeRT_OWTrt(V_P, V_h, V_E, c_Expr_Oexp_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_WTrt__elim__cases_I8_J_13')).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.51 tff(89,plain,(
% 0.20/0.51 ![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[88])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | 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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) <=> (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | 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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))) <=> ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.51 tff(94,plain,
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% 0.20/0.51 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | ((~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), c_Type_Oty_OVoid)) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | 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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 ((~![V_F: $i, V_D: $i, 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_OFAss(V_e, V_F, V_D, V_v, tc_List_Olist(tc_String_Ochar)), V_T)) | c_WellTypeRT_OWTrt(V_P, V_h, V_E, V_e, c_Type_Oty_ONT) | 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__8__3(V_D, V_E, V_F, V_P, V_e, V_h, V_v)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(V_D, V_E, V_F, V_P, V_e, V_h, V_v))))) | c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, c_Expr_Oexp_OFAss(v_ea____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[96, 90])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT) | 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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[97, 29])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[98, 19])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (^[V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : refl((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (^[V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF))))), (((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) <=> ((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))))), rewrite(((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), (((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))))), ((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> ((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))))), rewrite(((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), ((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))))), (((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> ((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))))), rewrite(((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), (((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : ((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.52 tff(105,axiom,(![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : ((((c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~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_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_0_01')).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : (c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~hBOOL(hAPP(hAPP(c_TypeRel_Owiden(v_P, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))), V_T_092_060_094isub_0622), V_TF))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.52 tff(107,plain,
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% 0.20/0.52 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.52 tff(108,plain,(
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% 0.20/0.52 tff(109,plain,
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% 0.20/0.52 tff(110,plain,
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% 0.20/0.52 tff(111,plain,
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% 0.20/0.53 tff(112,plain,
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% 0.20/0.53 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.53 tff(113,plain,
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% 0.20/0.53 tff(116,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[115, 109, 11, 99, 80, 64, 48])).
% 0.20/0.53 tff(117,plain,(c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(118,plain,
% 0.20/0.53 (((~![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))) | (~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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____))))) <=> ((~![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))) | (~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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(119,plain,
% 0.20/0.53 ((~![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))) | (~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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(120,plain,
% 0.20/0.53 ((~![V_x: $i] : ((~c_WellTypeRT_OWTrt(v_P, v_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, 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_h_Ha____, v_E____, c_Expr_Oexp_OFAss(v_e_Ha____, v_F____, v_D____, v_e_092_060_094isub_0622____, tc_List_Olist(tc_String_Ochar)), v_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____))) | (~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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.53 tff(121,plain,
% 0.20/0.53 (~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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[120, 117, 10])).
% 0.20/0.53 tff(122,plain,
% 0.20/0.53 ((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(123,axiom,(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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_1_02')).
% 0.20/0.53 tff(124,plain,
% 0.20/0.53 (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.53 tff(125,plain,
% 0.20/0.53 (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.20/0.53 tff(126,plain,
% 0.20/0.53 (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.20/0.53 tff(127,plain,
% 0.20/0.53 (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.20/0.54 tff(129,plain,
% 0.20/0.54 (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_ONT)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[128, 121])).
% 0.20/0.54 tff(130,plain,
% 0.20/0.54 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[47, 129])).
% 0.20/0.54 tff(131,plain,
% 0.20/0.54 (c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[63, 129])).
% 0.20/0.54 tff(132,plain,
% 0.20/0.54 (c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[79, 129])).
% 0.20/0.54 tff(133,plain,
% 0.20/0.54 (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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[98, 129])).
% 0.20/0.54 tff(134,plain,
% 0.20/0.54 (^[V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_sko__CHAINED__1(v_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(135,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.54 tff(136,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(137,plain,
% 0.20/0.54 (^[V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $i] : trans(monotonicity(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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), ((((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> ((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))))), 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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), ((((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))))), (((((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> ((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))))), 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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))), (((((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(138,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C)))) <=> ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.54 tff(139,axiom,(![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_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_T_092_060_094isub_0622), V_TF)))) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_CHAINED_1')).
% 0.20/0.54 tff(140,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.54 tff(141,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.54 tff(142,plain,(
% 0.20/0.54 ![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[141])).
% 0.20/0.54 tff(143,plain,
% 0.20/0.54 (![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.20/0.54 tff(144,plain,
% 0.20/0.54 (((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))) <=> ((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | 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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(145,plain,
% 0.20/0.55 ((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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))) <=> (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(146,plain,
% 0.20/0.55 (((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))) <=> ((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.55 tff(147,plain,
% 0.20/0.55 (((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))) <=> ((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | 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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.55 tff(148,plain,
% 0.20/0.55 ((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | (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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(149,plain,
% 0.20/0.55 ((~![V_T_092_060_094isub_0622: $i, V_TF: $i, V_C: $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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(V_C))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, V_T_092_060_094isub_0622)) | (~c_TypeRel_Ohas__field(v_P, V_C, v_F____, V_TF, v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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_092_060_094isub_0622), V_TF))))) | 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_D____, v_E____, v_F____, v_P, v_T____, v_e_Ha____, v_e_092_060_094isub_0622____, v_h_Ha____)), v_T____)) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_e_092_060_094isub_0622____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))) | (~c_WellTypeRT_OWTrt(v_P, v_ha____, v_E____, v_ea____, c_Type_Oty_OClass(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)))) | (~c_TypeRel_Ohas__field(v_P, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_F____, c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____), v_D____, tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)), tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))) | (~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__8__3(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____)), c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2(v_D____, v_E____, v_F____, v_P, v_ea____, v_ha____, v_e_092_060_094isub_0622____))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.57 tff(150,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[149, 143, 121, 133, 132, 131, 130])).
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % E exiting
%------------------------------------------------------------------------------