%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL858-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 07:04:02 EDT 2023

% Result   : Unsatisfiable 0.20s 0.66s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : LCL858-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri Aug 25 04:51:02 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Cr2s6CUE4I/cvc5---1.0.5_17998.p...
% 0.20/0.54  ------- get file name : TPTP file name is LCL858-1
% 0.20/0.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17998.smt2...
% 0.20/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.66  % SZS status Unsatisfiable for LCL858-1
% 0.20/0.66  % SZS output start Proof for LCL858-1
% 0.20/0.66  (
% 0.20/0.66  (let ((_let_1 (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_t)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_t)))) (let ((_let_5 (forall ((V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) V_t)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))))) (let ((_let_6 (not _let_4))) (let ((_let_7 (or _let_2 _let_6))) (let ((_let_8 (_let_5))) (let ((_let_9 (ASSUME :args _let_8))) (let ((_let_10 (not _let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (tptp.v_t QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP _let_1 V_t)))) :args _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_2 _let_6 _let_10))) (ASSUME :args (_let_3)) (ASSUME :args (_let_4)) :args (_let_10 true _let_2 false _let_4)) _let_9 :args (false true _let_7 false _let_5)) :args ((forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_ListOrder_Ostep1 V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons V_x V_ys T_a)) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ys) V_xs)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_ListOrder_Ostep1 V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ys) V_xs)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a)) (tptp.c_List_Olist_OCons V_x V_xs T_a))))))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_ListOrder_Ostep1 V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ys) V_xs)) (= V_xs V_ys) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a)) (tptp.c_List_Olist_OCons V_x V_xs T_a))))))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_xa))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.c_List_Olist_OCons V_y V_x T_a)) (tptp.c_List_Olist_OCons V_xa V_x T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (= V_xs V_ys) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a)) (tptp.c_List_Olist_OCons V_x V_xs T_a)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_OCons V_x V_xs T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.hAPP (tptp.hAPP V_f V_a) V_x) V_xs T_a T_b))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a)) (tptp.c_List_Olist_OCons V_x V_xs T_a)))))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.tc_List_Olist T_a)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_xs))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_x)))))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OFun V_type1 V_type2) (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.c_Type_Otype_OFun V_type1 V_type2) (tptp.c_Type_Otype_OFun V_type1_H V_type2_H))) (= V_type1 V_type1_H))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_U) (not (tptp.c_Type_Otyping V_env V_t V_T)) (not (tptp.c_Type_Otyping V_env V_s (tptp.c_Type_Otype_OFun V_T V_U))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (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.c_Type_Otyping V_e V_t V_T)))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (not (tptp.c_Type_Otyping V_e_H V_u V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e_H V_i V_U tptp.tc_Type_Otype) V_t V_T)) (tptp.c_Type_Otyping V_e_H (tptp.c_Lambda_Osubst V_t V_u V_i) V_T))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) V_t) V_t_H))))) (forall ((V_rs $$unsorted) (V_n $$unsorted) (V_v $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) V_rs) (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v))) (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_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_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)) (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 $$unsorted) (V_s $$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_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_t)))) (forall ((V_s $$unsorted) (V_s_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_s_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_s $$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 $$unsorted) (V_t $$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 $$unsorted) (V_s_H $$unsorted) (V_t_H $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s_H) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_t) V_t_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s) V_s_H)))))) (forall ((V_env $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_U $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OAbs V_t) (tptp.c_Type_Otype_OFun V_T V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_env (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_T tptp.tc_Type_Otype) V_t V_U)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olistsp (tptp.c_Wellfounded_Oaccp V_r T_a) V_xs T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.tc_List_Olist T_a)) V_xs))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.tc_List_Olist T_a)) V_xs)) (not (tptp.c_List_Olistsp (tptp.c_Wellfounded_Oaccp V_r T_a) V_xs T_a)))) (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 V_r T_a) V_xs) (tptp.c_List_Olist_ONil T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 V_r T_a) (tptp.c_List_Olist_ONil T_a)) V_xs)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 V_r V_s V_t V_ts) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (= V_ts (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB) V_rs) V_ss))))) (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)) (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_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))) (= _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_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_r) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_m $$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_m $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i))) (not (tptp.c_Type_Otyping V_e V_u V_U)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) V_t V_T)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_v $$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 ((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 ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (= (tptp.c_Transitive__Closure_Ortranclp _let_1 T_a) _let_1))) (forall ((V_t $$unsorted) (V_e $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t)) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (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_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y))))) (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 ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k) V_s V_k) V_t)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_r $$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 ((V_env $$unsorted) (V_x $$unsorted)) (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OVar V_x) (tptp.hAPP V_env V_x))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup 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_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup 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_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup 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_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Opred__comp V_r V_s T_a T_b T_c) V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_s 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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otranclp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_y)))))) (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 $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) 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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_b))))) (forall ((V_s $$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_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_OwfP (tptp.c_Transitive__Closure_Otranclp V_r T_a) T_a) (not (tptp.c_Wellfounded_OwfP V_r T_a)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OVar V_i) V_T)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a) V_b))))) (forall ((V_n $$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 $$unsorted) (T_a $$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_B $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_s))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_t $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_nat $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t)) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$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))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((V_r $$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_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.c_fequal T_a) (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_bool))) T_a) (tptp.c_Transitive__Closure_Ortranclp V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_r T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_b))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp V_R T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_R T_a) V_a) V_b))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortranclp V_R T_a) (tptp.c_Transitive__Closure_Ortranclp V_S T_a) _let_1) T_a) (tptp.c_Transitive__Closure_Ortranclp (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_r $$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_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otranclp V_r T_a) (tptp.c_fequal T_a) (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Transitive__Closure_Ortranclp V_r T_a))) (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_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 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otranclp 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_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) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A V_x) V_y))))) (forall ((V_r $$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) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp 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 $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otranclp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_a))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_R (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 V_R V_x T_a)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_R T_a) V_x)))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_t) V_t_H))) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_x)) (not (tptp.c_Wellfounded_OwfP V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Predicate_Oconversep V_r T_a T_b) T_b T_a) V_r)) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i)) V_t)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 V_r V_x T_a)) V_x)))) (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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep (tptp.c_Transitive__Closure_Otranclp V_r T_a) T_a T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep (tptp.c_Transitive__Closure_Otranclp V_r T_a) T_a T_a) V_x) V_y))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_R T_a))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 V_R V_x T_a)))) (tptp.hBOOL (tptp.hAPP _let_1 V_x))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otranclp (tptp.c_Predicate_Oconversep V_r T_a T_a) T_a) (tptp.c_Predicate_Oconversep (tptp.c_Transitive__Closure_Otranclp V_r T_a) T_a T_a))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) V_r))))) _let_5 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a)))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst V_r V_t V_i)) (tptp.c_Lambda_Osubst V_s V_t V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xaccp__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r tptp.t_a) V_x))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) (tptp.v_sko__Wellfounded__Xaccp__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r tptp.t_a) V_x))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp (tptp.c_Predicate_Oconversep tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_s))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xaccp__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r tptp.t_a) V_x))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) (tptp.v_sko__Wellfounded__Xaccp__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r tptp.t_a) V_x))))) (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_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 $$unsorted) (V_a $$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_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_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP _let_1 V_ya)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_ya) (tptp.v_sko__Wellfounded__Xaccp__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP _let_1 V_ya)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_ya) (tptp.v_sko__Wellfounded__Xaccp__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun T_b (tptp.tc_fun T_a tptp.tc_bool))) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Predicate_Oconversep V_r T_b T_a) (tptp.c_Predicate_Oconversep V_s T_b T_a) (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))))) (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_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_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 V_P V_r T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Lattices_Olower__semilattice__class_Oinf V_r V_s (tptp.tc_fun T_b (tptp.tc_fun T_a tptp.tc_bool))) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Predicate_Oconversep V_r T_b T_a) (tptp.c_Predicate_Oconversep V_s T_b T_a) (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 V_r V_x T_a))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 V_r V_x T_a))))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r (tptp.c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 V_r V_x T_a)) V_x)))) (forall ((V_u $$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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 V_P V_r T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_r $$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_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) (tptp.c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp V_r T_a) V_a))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_Oconversep (tptp.c_Predicate_Opred__comp V_r V_s T_b T_c T_a) T_b T_a) (tptp.c_Predicate_Opred__comp (tptp.c_Predicate_Oconversep V_s T_c T_a) (tptp.c_Predicate_Oconversep V_r T_b T_c) T_a T_c T_b))) (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))))) _let_4 _let_3 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__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_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_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice 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)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (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))))))))))))))))))
% 0.20/0.66  )
% 0.20/0.67  % SZS output end Proof for LCL858-1
% 0.20/0.67  % cvc5---1.0.5 exiting
% 0.20/0.67  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------