%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL822-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 : Thu Aug 31 07:03:52 EDT 2023

% Result   : Unsatisfiable 0.40s 0.68s
% Output   : Proof 0.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14  % Problem    : LCL822-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n024.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Thu Aug 24 20:39:09 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.50  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xpy9CmifTD/cvc5---1.0.5_10195.p...
% 0.22/0.55  ------- get file name : TPTP file name is LCL822-1
% 0.22/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10195.smt2...
% 0.22/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.40/0.68  % SZS status Unsatisfiable for LCL822-1
% 0.40/0.68  % SZS output start Proof for LCL822-1
% 0.40/0.68  (
% 0.40/0.68  (let ((_let_1 (tptp.c_Type_Oshift tptp.v_e____ tptp.v_i____ tptp.v_T____ tptp.tc_Type_Otype))) (let ((_let_2 (tptp.c_Type_Otyping _let_1))) (let ((_let_3 (tptp.c_List_Olistsp (tptp.c_COMBB (tptp.c_Ex tptp.tc_Type_Otype) _let_2 (tptp.tc_fun tptp.tc_Type_Otype tptp.tc_bool) tptp.tc_bool tptp.tc_Lambda_OdB) tptp.v_rs____ tptp.tc_Lambda_OdB))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.c_Type_Otypings _let_1 tptp.v_rs____ tptp.v_Ts____))) (let ((_let_6 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar tptp.v_n____) tptp.v_rs____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_7 (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (or (tptp.c_List_Olistsp (tptp.c_COMBB (tptp.c_Ex tptp.tc_Type_Otype) (tptp.c_Type_Otyping V_e) (tptp.tc_fun tptp.tc_Type_Otype tptp.tc_bool) tptp.tc_bool tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)))))) (let ((_let_8 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_9 (not _let_5))) (let ((_let_10 (or _let_3 _let_9))) (let ((_let_11 (_let_7))) (let ((_let_12 (ASSUME :args _let_11))) (let ((_let_13 (not _let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (_let_1 tptp.v_rs____ tptp.v_Ts____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Type_Otypings V_e V_ts V_Ts) false))))) :args _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_3 _let_9 _let_13))) (ASSUME :args (_let_4)) (ASSUME :args (_let_5)) :args (_let_13 true _let_3 false _let_5)) _let_12 :args (false true _let_10 false _let_7)) :args ((forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (= (tptp.c_Transitive__Closure_Ortranclp _let_1 T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_y) V_x))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_ONil T_b) V_a T_b T_a) V_a)) (forall ((V_r $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a) V_b))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_a))))) (forall ((V_r $$unsorted) (V_a2 $$unsorted) (V_a1 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a2) V_a1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_a1) V_a2))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep V_r T_a T_b) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)) (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys V_x T_a) (tptp.c_List_Oappend V_xs V_x T_a) T_a))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_vs $$unsorted) (T_a $$unsorted) (V_us $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_x V_vs T_a) (tptp.c_List_Oappend V_x V_us T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_vs V_us T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_x))) (forall ((V_r $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a))) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)))) (forall ((V_r $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_b T_a) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_t $$unsorted)) (or (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_t tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r)) (not (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_r tptp.tc_Lambda_OdB)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Oappend V_xs V_ys T_b) V_a T_b T_a) (tptp.c_List_Ofoldr V_f V_xs (tptp.c_List_Ofoldr V_f V_ys V_a T_b T_a) T_b T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_ONil T_a) V_xs T_a))) (forall ((V_r $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_fequal T_a))) (= (tptp.c_Predicate_Oconversep _let_1 T_a T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Predicate_Oconversep V_r T_a T_b) T_b T_a) V_r)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((V_r $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_y T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_a))) (not (tptp.c_Wellfounded_Oaccp V_r V_a T_a)))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_Wellfounded_Oaccp V_r V_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))) (not (tptp.c_Wellfounded_Oaccp V_r V_b T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_s_H $$unsorted) (V_t_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s_H) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_s_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s_H) V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_t_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_t)) (tptp.hAPP _let_2 V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_t_H))))))) (forall ((V_s $$unsorted) (V_s_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_s_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_t)))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_t $$unsorted) (V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) (tptp.c_Lambda_Osubst V_t V_r V_i)) (tptp.c_Lambda_Osubst V_t V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Osubst V_r V_t V_i)) (tptp.c_Lambda_Osubst V_s V_t V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_t $$unsorted) (V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Osubst V_t V_r V_i)) (tptp.c_Lambda_Osubst V_t V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_rs $$unsorted) (V_n $$unsorted) (V_v $$unsorted)) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v))))) (forall ((V_e $$unsorted) (V_u $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_u) (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) V_T)))))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t_H) V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_T))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) V_t) V_t_H)))))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T)))))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T)))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s)) (tptp.hAPP _let_1 V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t)))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____)) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k) V_s V_k) V_t)) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Olift _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T)) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun V_Ts V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))))))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_i $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 V_T V_e V_i V_ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))) (forall ((V_e $$unsorted) (V_us $$unsorted) (V_T $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_Type_Otyping V_e))) (or (tptp.c_Type_Otypings V_e V_us (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 V_T V_U V_e V_us)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_U))) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_us tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))) (forall ((V_v $$unsorted) (V_n $$unsorted) (V_rs $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_n))) (or (= V_v (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_U $$unsorted) (V_T $$unsorted) (V_e $$unsorted) (V_us $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_Type_Otyping V_e))) (or (= V_U (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 V_T V_U V_e V_us) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_U))) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_us tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u)) V_T))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) V_T)))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_m) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_r) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_Lambda_OdB_OAbs V_r))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs V_ss tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (not (tptp.c_Wellfounded_Oaccp _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)) (not (tptp.c_Wellfounded_Oaccp _let_1 V_s tptp.tc_Lambda_OdB)) (tptp.c_Wellfounded_Oaccp _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (let ((_let_2 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 V_T V_e V_i V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_T))))))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_x) V_s V_x) V_s))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______)) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubst _let_1 V_s V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst V_r V_t V_i)) (tptp.c_Lambda_Osubst V_s V_t V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k)) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_s))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_nat $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H)))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t)) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Type_Otyping V_e) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (or (= V_T V_U) (not (tptp.hBOOL (tptp.hAPP _let_1 V_U))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_T)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_n $$unsorted) (V_rs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_rs tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1)) (= V_s _let_1)))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_env))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) V_U)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_T))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U))))))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i)) V_t)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (not (tptp.c_HOL_Oord__class_Oless _let_8 _let_8 tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.c_Lambda_Osubst _let_1 V_u V_i) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_r (tptp.c_Lambda_OdB_OVar V_i) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type2 V_type2_H))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type1 V_type1_H))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k) V_u V_k) V_u)) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_m V_n))) (forall ((V_dB_H $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OVar V_nat_H))) (= V_nat V_nat_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_s V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_t V_s V_k)) (tptp.c_Lambda_Osubst V_u V_s V_k)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype)) (tptp.c_Lambda_Olift V_t V_i)) V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) V_t) V_T))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping tptp.v_e____) tptp.v_u____) tptp.v_T____)) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t_H) V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_t) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_T)))))) _let_7 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted) (T_a $$unsorted) (V_j $$unsorted)) (or (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_i V_T T_a) V_j) (tptp.hAPP V_e V_j)) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (not (tptp.c_List_Olistsp V_A V_ys T_a)) (not (tptp.c_List_Olistsp V_A V_xs T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.c_List_Osko__List__Xin__listsp__conv__set__1__1 V_A V_xs T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (or (tptp.c_List_Olistsp (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_l T_a) (not (tptp.c_List_Olistsp V_B V_l T_a)) (not (tptp.c_List_Olistsp V_A V_l T_a)))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) V_u) V_T2))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T2 tptp.tc_Type_Otype)) V_t) V_Ta))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) V_u) V_T1))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T1 tptp.tc_Type_Otype)) V_t) V_Ta))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) (forall ((V_env $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_U $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_env) (tptp.c_Lambda_OdB_OAbs V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_env (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_T tptp.tc_Type_Otype)) V_t) V_U))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_e) (tptp.c_Lambda_OdB_OVar V_i)) V_T))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_ea______ tptp.v_ia______ tptp.v_T____ tptp.tc_Type_Otype)) _let_6) tptp.v_T_Ha______)) (not (= tptp.v_n____ tptp.v_i____)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping tptp.v_ea______) tptp.v_ua______) tptp.v_T____)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_A $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olistsp V_A V_ys T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_6) tptp.v_T_H____)) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping V_env) (tptp.c_Lambda_OdB_OVar V_x)) (tptp.hAPP V_env V_x)))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.c_Type_Otyping V_e_H))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_u) V_U))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e_H V_i V_U tptp.tc_Type_Otype)) V_t) V_T))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Osubst V_t V_u V_i)) V_T))))) _let_5 _let_4 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_COMBC V_P V_Q V_R T_b T_c T_a) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y)))))))))))))))))))))
% 0.40/0.68  )
% 0.40/0.69  % SZS output end Proof for LCL822-1
% 0.40/0.69  % cvc5---1.0.5 exiting
% 0.40/0.69  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------