%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL771-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 07:03:36 EDT 2023

% Result   : Unsatisfiable 0.52s 0.78s
% Output   : Proof 0.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem    : LCL771-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Thu Aug 24 17:39:37 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.54  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bo7Gilek3C/cvc5---1.0.5_17099.p...
% 0.23/0.61  ------- get file name : TPTP file name is LCL771-1
% 0.23/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17099.smt2...
% 0.23/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.52/0.78  % SZS status Unsatisfiable for LCL771-1
% 0.52/0.78  % SZS output start Proof for LCL771-1
% 0.52/0.79  (
% 0.52/0.79  (let ((_let_1 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)))) (let ((_let_4 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_5 (_let_3))) (let ((_let_6 (ASSUME :args _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_6 :args (tptp.c_InductTermi_OIT tptp.tc_Lambda_OdB QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a) true))))) :args _let_5)) :args ((or _let_1 (not _let_3)))) (ASSUME :args (_let_2)) _let_6 :args (false true _let_1 false _let_3)) :args ((forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oremdups V_xs T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize__class_Osize _let_1 _let_2) (tptp.c_Nat_Osize__class_Osize V_xs _let_2))) (= _let_1 V_xs))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (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 $$unsorted) (V_x $$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_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_a) V_a))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_m V_n))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_xa))) (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_x T_a) (tptp.c_List_Olist_OCons V_xa V_x T_a) T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc _let_1) tptp.tc_nat))))) (forall ((V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Suc (tptp.c_Nat_Osize__class_Osize V_xa _let_1)) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_xa T_a) _let_1)))) (forall ((V_r $$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 $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)) (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys V_x T_a) (tptp.c_List_Oappend V_xs V_x T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_xa T_a) _let_1) (tptp.c_Suc (tptp.c_Nat_Osize__class_Osize V_xa _let_1))))) (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)))) (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 ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_Suc V_n) V_x T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oreplicate V_n V_x T_a) T_a))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate (tptp.c_Suc V_n) V_xs T_a) (tptp.c_List_Orotate1 (tptp.c_List_Orotate V_n V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Oreplicate V_n V_x T_a) T_a) V_x) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Oreplicate _let_1 V_x T_a) (tptp.c_List_Oreplicate _let_1 V_y T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist__update V_xs V_i V_x T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_x V_y) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_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 ((T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast _let_1 T_a) _let_1))) (forall ((V_r $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_r $$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_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orotate1 V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orotate1 _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Oremdups V_xs T_a))) (or (not (= _let_2 V_xs)) (= (tptp.c_Nat_Osize__class_Osize _let_2 _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_b)))) (forall ((V_f $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Oreplicate V_n V_x T_b) T_b T_a) (tptp.c_List_Oreplicate V_n (tptp.hAPP V_f V_x) T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Ortranclp V_r T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (tptp.c_HOL_Oord__class_Oless _let_4 (tptp.c_Suc _let_4) tptp.tc_nat) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (or (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP V_P V_x)))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_b))) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= (tptp.c_Nat_Osize__class_Osize V_xs _let_1) (tptp.c_Nat_Osize__class_Osize V_ys _let_1))))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs V_ys T_a) V_n V_x T_a) (tptp.c_List_Oappend (tptp.c_List_Olist__update V_xs V_n V_x T_a) V_ys T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs V_ys T_a) V_i V_x T_a) (tptp.c_List_Oappend (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_ys T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Orotate V_n V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Orotate1 V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (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_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_y $$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 ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (let ((_let_2 (tptp.c_List_Oreplicate V_k V_x T_a))) (= (tptp.c_List_Oappend _let_1 _let_2 T_a) (tptp.c_List_Oappend _let_2 _let_1 T_a))))) (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 ((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_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.c_List_Olist_ONil T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_t V_k) V_t)) (not (tptp.c_HOL_Oord__class_Oless _let_4 _let_4 tptp.tc_nat)) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.tc_List_Olist T_a)) V_n)) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate V_n V_x T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_x V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Orev V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate1 (tptp.c_List_Orotate V_n V_xs T_a) T_a) (tptp.c_List_Orotate V_n (tptp.c_List_Orotate1 V_xs T_a) T_a))) (forall ((T_a $$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 ((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 ((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 $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= (tptp.c_List_Oappend (tptp.c_List_Obutlast V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Olast V_xs T_a) _let_1 T_a) T_a) V_xs) (= V_xs _let_1)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= V_r (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_xa tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_s (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Oappend V_ts (tptp.c_List_Olist_OCons V_u (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_x $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_s _let_1 tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (or (= _let_2 _let_1) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_x tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t _let_2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.c_Lambda_Osubstn (tptp.c_Lambda_OdB_OVar V_x) V_s V_x) (tptp.c_Lambda_Oliftn V_x V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) _let_1))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) V_x)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Obutlast V_xs T_a) T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) _let_1)) (= (tptp.c_List_Oappend (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a) V_xs) (= V_zs _let_1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_ys V_zs T_a))) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a) V_ys) (= _let_1 V_zs)))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) _let_1)) (= V_ys (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a)) (= V_zs _let_1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_ys V_zs T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a)) (= _let_1 V_zs)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend _let_1 V_xs T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Obutlast V_xs T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Olast V_ys T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olast V_xs T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Obutlast V_ys T_a) T_a)) (= V_ys (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_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oreplicate V_n V_x T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (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 $$unsorted)) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_y T_a) (tptp.c_List_Olist_OCons V_y V_xs T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_Suc V_i) V_y T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist__update V_xs V_i V_y T_a) T_a))) (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_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubst _let_1 V_s V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_j $$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_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_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_Olift V_r V_i)) (tptp.c_Lambda_Olift V_s V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_s)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_m $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_ys (tptp.tc_List_Olist T_b)))) (= (tptp.c_Map_Omap__upds V_m (tptp.c_List_Oappend V_xs V_zs T_a) V_ys T_a T_b) (tptp.c_Map_Omap__upds V_m V_xs V_ys T_a T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_m $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_ys (tptp.tc_List_Olist T_b)))) (= (tptp.c_Map_Omap__upds V_m V_xs (tptp.c_List_Oappend V_ys V_zs T_b) T_a T_b) (tptp.c_Map_Omap__upds V_m V_xs V_ys T_a T_b)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Olift _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Oliftn V_n _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (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 ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a) T_a))) (forall ((T_a $$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_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_ONil T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= V_xs (tptp.c_List_Olist_ONil T_a)) (not (tptp.c_List_Onull V_xs T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oremdups _let_1 T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$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_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_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oremdups V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orotate V_n V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((T_a $$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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_xs $$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 ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_a $$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 ((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 ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremdups _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f V_xs T_b T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$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 $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_r $$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_v $$unsorted) (V_n $$unsorted) (V_rs $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_n))) (or (= V_v (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v)))))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t)) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xconcat__Xinduct__1 V_P) (tptp.v_sko__List__Xconcat__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xtake__Xinduct__1 V_P) (tptp.v_sko__List__Xtake__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xmap__Xinduct__1 V_P) (tptp.v_sko__List__Xmap__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlist__Xinduct__1 V_P) (tptp.v_sko__List__Xlist__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__XdropWhile__Xinduct__1 V_P) (tptp.v_sko__List__XdropWhile__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xzip__Xinduct__1 V_P) (tptp.v_sko__List__Xzip__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistset__Xinduct__1 V_P) (tptp.v_sko__List__Xlistset__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xremove1__Xinduct__1 V_P) (tptp.v_sko__List__Xremove1__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xdistinct__Xinduct__1 V_P) (tptp.v_sko__List__Xdistinct__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (= (tptp.c_Lambda_Osubstn V_t V_s V_n) (tptp.c_Lambda_Osubst V_t (tptp.c_Lambda_Oliftn V_n V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_y T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a))) (forall ((V_r $$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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs V_ss tptp.tc_Lambda_OdB)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__XCons__eq__filter__iff__1__3 V_P V_xa T_a))) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Ofilter V_P V_xb T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 V_P V_xa T_a))) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Ofilter V_P V_xb T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Oappend V_ys V_zs T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= V_ys (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_x)) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_xs)) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (= V_y V_x) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (= V_y V_x) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a) V_xs) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Oappend V_ys V_zs T_a))) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a) V_ys) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Orotate1 (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_b) T_b) T_b))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_i V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_x _let_1 T_a)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB))) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ts (tptp.c_List_Oappend (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 V_r V_s V_t V_ts) (tptp.c_List_Olist_OCons V_s _let_1 tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)) (= V_ts _let_1)))) (forall ((V_n $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn (tptp.c_Suc V_n) V_t V_k) (tptp.c_Lambda_Olift (tptp.c_Lambda_Oliftn V_n V_t V_k) V_k))) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubstn _let_1 V_s V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Lambda_Osubstn V_t V_s _let_1) (tptp.c_Lambda_Osubst V_t V_s _let_1)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) (tptp.c_List_Ofoldr (tptp.c_COMBC V_f T_a T_b T_a) (tptp.c_List_Orev V_xs T_b) V_a T_b T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_k $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist__update V_xs V_k V_y T_b) T_b T_a) (tptp.c_List_Olist__update (tptp.c_List_Omap V_f V_xs T_b T_a) V_k (tptp.hAPP V_f V_y) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_r $$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 $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xinducts__1 V_A V_P) (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_t $$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_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xinduct__1 V_A V_P) (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_xs T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs1 $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_xs)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list T_b) T_a T_b) (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xs T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_xa) (tptp.c_List_Omap V_f V_xb T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_xa V_xb T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xa T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xa T_b T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs T_a) V_ys T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a))) (forall ((V_r $$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 $$unsorted) (V_y $$unsorted) (V_zs $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_zs T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted _let_1 T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a))))) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_f $$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_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremdups (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Oremdups V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Ofilter V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_dB) T_a) (tptp.hAPP V_f3 V_dB))) (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_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orev V_xs T_b) T_b T_a))) (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_P $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orotate V_n V_xs T_b) T_b T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_ys T_a) T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a) V_xs)) (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 ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Olist__ex V_P V_xs T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Olist__ex V_P V_xs T_a) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistrelp V_r (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (not (tptp.c_List_Olistrelp V_r V_xs V_ys T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_y V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Oremove1 V_x V_xs T_a) T_a)) (= V_x V_y))) (forall ((V_r $$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_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Oappend V_xs V_ys T_b) T_b T_a) (tptp.c_List_Oappend (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a) T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted)) (or (= V_a (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xcases__1 V_A V_a) (tptp.v_sko__List__Xlistsp__Xcases__2 V_A V_a) tptp.t_a)) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_r $$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_x $$unsorted) (V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Ofilter V_P V_xs T_a))) (or (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__rec V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list T_b) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list) (tptp.c_List_Olist_Olist__rec V_f1 V_f2 V_list T_a T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f V_xs V_a T_b T_a) (tptp.c_List_Ofoldl (tptp.c_COMBC V_f T_b T_a T_a) V_a (tptp.c_List_Orev V_xs T_b) T_a T_b))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_dB) T_a) (tptp.hAPP (tptp.hAPP V_f3 V_dB) (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 V_dB T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_List_Onull (tptp.c_List_Olist_OCons V_x V_xs 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_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) V_a T_b T_a) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_List_Ofoldr V_f V_xs V_a T_b T_a)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_dB) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f3 V_dB))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_xa) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f3 V_xa))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (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_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$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_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 ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_xs T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_ys T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_i_H $$unsorted) (V_x_H $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i_H V_x_H T_a) (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i_H V_x_H T_a) V_i V_x T_a)) (= V_i V_i_H))) (forall ((T_a $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oremdups V_l T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_l T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Ofilter V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (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 ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_xa V_xb tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xa) V_xb))))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i V_y T_a) (tptp.c_List_Olist__update V_xs V_i V_y T_a))) (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_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oremove1 V_a V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (not (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted)) (tptp.c_List_Onull (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_ONil tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P V_f1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_ONil T_b) V_a T_b T_a) V_a)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xzip__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Osublist _let_1 V_A T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistset__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__rec V_f1 V_f2 (tptp.c_List_Olist_ONil T_b) T_a T_b) V_f1)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__XdropWhile__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xtake__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofiltermap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oremdups V_x T_a))) (= V_x _let_1)))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_k V_x T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_y T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_v T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xconcat__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_x $$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) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xdistinct__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_m $$unsorted) (V_as $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Omap__upds V_m V_as (tptp.c_List_Olist_ONil T_b) T_a T_b) V_m)) (forall ((V_m $$unsorted) (T_a $$unsorted) (V_bs $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Omap__upds V_m (tptp.c_List_Olist_ONil T_a) V_bs T_a T_b) V_m)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xremove1__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_ONil T_b) T_a T_b) V_f1)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orotate V_n _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlist__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrelp V_r _let_1 _let_1 T_a))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xmap__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Olist__update V_xs V_k V_x T_a) _let_1)) (= V_xs _let_1)))) (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_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_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_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xb $$unsorted) (V_xc $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_xb) V_xc) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xb) V_xc))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_dB1) V_dB2))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k)) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_dB1) V_dB2))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f2 V_dB1) V_dB2) (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 V_dB1 T_a)) (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 V_dB2 T_a)))) (forall ((V_r $$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_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_n $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn V_n (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_Oliftn V_n V_s V_k)) (tptp.c_Lambda_Oliftn V_n V_t V_k)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubstn (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_Osubstn V_t V_s V_k)) (tptp.c_Lambda_Osubstn V_u V_s V_k)))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xd $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_xd) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_xd))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_nat $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_nat))))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k) V_u V_k) V_u)) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i)) V_t)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__rec V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (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_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OVar V_i) V_T)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (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 ((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_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_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_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 $$unsorted)) (or (tptp.c_List_Olistsp (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_l T_a) (not (tptp.c_List_Olistsp V_B V_l T_a)) (not (tptp.c_List_Olistsp V_A V_l T_a)))) (forall ((V_A $$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 $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_r $$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_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_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 $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xinducts__1 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xinduct__1 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted)) (or (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xcases__2 V_A V_a) tptp.t_a) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xcases__1 V_A V_a))) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_r $$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_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_r (tptp.c_Lambda_OdB_OVar V_i) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_m $$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 $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_m) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_n $$unsorted) (V_rs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_rs tptp.tc_Lambda_OdB)))) (forall ((V_nat $$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 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_nat $$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_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) _let_3 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_dB1_H $$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)))) (tptp.c_List_Olistsp tptp.c_InductTermi_OIT tptp.v_rs tptp.tc_Lambda_OdB) (tptp.c_List_Olistsp (tptp.c_COMBB tptp.c_InductTermi_OIT (tptp.hAPP (tptp.c_COMBC tptp.c_Lambda_OdB_OApp tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_Lambda_OdB_OVar tptp.v_i)) tptp.tc_Lambda_OdB tptp.tc_bool tptp.tc_Lambda_OdB) tptp.v_rs tptp.tc_Lambda_OdB) _let_2 (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_Lattices_Olower__semilattice 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 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (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 ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))
% 0.52/0.79  )
% 0.52/0.79  % SZS output end Proof for LCL771-1
% 0.52/0.80  % cvc5---1.0.5 exiting
% 0.52/0.80  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------