%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL830-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 07:03:55 EDT 2023

% Result   : Unsatisfiable 0.82s 1.00s
% Output   : Proof 0.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17  % Problem    : LCL830-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.18  % Command    : do_cvc5 %s %d
% 0.19/0.40  % Computer : n012.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Thu Aug 24 20:02:56 EDT 2023
% 0.19/0.40  % CPUTime    : 
% 0.25/0.57  %----Proving TF0_NAR, FOF, or CNF
% 0.25/0.58  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2ibANDNRde/cvc5---1.0.5_15316.p...
% 0.25/0.66  ------- get file name : TPTP file name is LCL830-1
% 0.25/0.66  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15316.smt2...
% 0.25/0.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.82/1.00  % SZS status Unsatisfiable for LCL830-1
% 0.82/1.00  % SZS output start Proof for LCL830-1
% 0.82/1.01  (
% 0.82/1.01  (let ((_let_1 (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_COMBC tptp.c_Lambda_Osubst tptp.v_u____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB _let_1))) (let ((_let_3 (tptp.c_COMBC _let_2 tptp.v_i____ tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB))) (let ((_let_4 (tptp.c_List_Omap _let_3 (tptp.c_List_Olist_OCons tptp.v_a____ tptp.v_as____ tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_5 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT _let_4 tptp.tc_Lambda_OdB))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.c_List_Omap _let_3 tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_8 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_a____) tptp.v_u____))) (let ((_let_9 (tptp.hAPP _let_8 tptp.v_i____))) (let ((_let_10 (tptp.c_List_Olist_OCons _let_9 _let_7 tptp.tc_Lambda_OdB))) (let ((_let_11 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT _let_10 tptp.tc_Lambda_OdB))) (let ((_let_12 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xa T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xa T_b T_a) T_a))))) (let ((_let_13 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))))) (let ((_let_14 (forall ((V_x $$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)))) (let ((_let_15 (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))))) (let ((_let_16 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_17 (= _let_10 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) _let_10 tptp.tc_Lambda_OdB)))) (let ((_let_18 (tptp.hAPP _let_3 tptp.v_a____))) (let ((_let_19 (tptp.c_List_Olist_OCons _let_18 _let_7 tptp.tc_Lambda_OdB))) (let ((_let_20 (= _let_4 _let_19))) (let ((_let_21 (= _let_7 (tptp.c_List_Oremove1 _let_18 _let_19 tptp.tc_Lambda_OdB)))) (let ((_let_22 (tptp.hAPP _let_2 tptp.v_a____))) (let ((_let_23 (= _let_18 (tptp.hAPP _let_22 tptp.v_i____)))) (let ((_let_24 (= _let_8 _let_22))) (let ((_let_25 (ASSUME :args (_let_11)))) (let ((_let_26 (ASSUME :args (_let_6)))) (let ((_let_27 (_let_15))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (_let_12))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_13))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 ((tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R)))) (let ((_let_36 (not _let_24))) (let ((_let_37 (not _let_23))) (let ((_let_38 (not _let_21))) (let ((_let_39 (not _let_20))) (let ((_let_40 (not _let_17))) (let ((_let_41 (not _let_11))) (let ((_let_42 (APPLY_UF tptp.c_List_Olistsp))) (let ((_let_43 (REFL :args (tptp.tc_Lambda_OdB)))) (let ((_let_44 (ASSUME :args (_let_17)))) (let ((_let_45 (REFL :args (tptp.c_InductTermi_OIT)))) (let ((_let_46 (APPLY_UF tptp.c_List_Olist_OCons))) (let ((_let_47 (ASSUME :args (_let_21)))) (let ((_let_48 (ASSUME :args (_let_24)))) (let ((_let_49 (ASSUME :args (_let_23)))) (let ((_let_50 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_48 _let_49 _let_47 _let_50 _let_44 _let_26 _let_25) :args (_let_11 _let_6 _let_17 _let_20 _let_21 _let_23 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_26)) (CONG _let_45 (TRANS (TRANS (SYMM (SYMM _let_50)) (CONG (TRANS (SYMM (SYMM _let_49)) (CONG (SYMM _let_48) (REFL :args (tptp.v_i____)) :args (APPLY_UF tptp.hAPP))) _let_47 _let_43 :args _let_46) (CONG (REFL :args (_let_9)) (SYMM _let_47) _let_43 :args _let_46)) _let_44) _let_43 :args _let_42) (CONG _let_45 (SYMM _let_44) _let_43 :args _let_42) (TRUE_INTRO _let_25))) :args (_let_24 _let_23 _let_21 _let_20 _let_17 _let_6 _let_11)) :args ((not (and _let_11 _let_6 _let_17 _let_20 _let_21 _let_23 _let_24)) SB_LITERAL))) (CONG (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) (REFL :args (_let_40)) (REFL :args (_let_39)) (REFL :args (_let_38)) (REFL :args (_let_37)) (REFL :args (_let_36)) :args (or))) :args ((or _let_5 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.c_Lambda_Osubst tptp.v_u____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB _let_1 tptp.v_a____ QUANTIFIERS_INST_E_MATCHING _let_35)) :args _let_33))) _let_34 :args (_let_24 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_2 tptp.v_i____ tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB tptp.v_a____ QUANTIFIERS_INST_E_MATCHING _let_35)) :args _let_33)) _let_34 :args (_let_23 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_18 _let_7 tptp.tc_Lambda_OdB QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_List_Olist_OCons V_x V_xs T_a)))) :args (_let_31))) _let_32 :args (_let_21 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_3 tptp.v_a____ tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB QUANTIFIERS_INST_E_MATCHING ((tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xa T_b) T_b T_a)))) :args _let_29)) _let_30 :args (_let_20 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_9 _let_7 tptp.tc_Lambda_OdB QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_List_Olist_OCons V_x V_xs T_a)))) :args _let_27)) _let_28 :args (_let_17 false _let_15)) _let_26 _let_25 :args (false false _let_24 false _let_23 false _let_21 false _let_20 false _let_17 true _let_5 false _let_11)) :args ((forall ((V_i $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_i (tptp.c_List_Oreplicate V_k V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ominus__class_Ominus V_k V_i tptp.tc_nat) V_x T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate V_n V_xs T_a) (tptp.c_List_Orotate (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_xs T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Otake V_m V_xs T_a) T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_List_Odrop V_n V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_OdropWhile V_P V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_xs) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat)))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_U) (not (tptp.c_Type_Otyping V_env V_t V_T)) (not (tptp.c_Type_Otyping V_env V_s (tptp.c_Type_Otype_OFun V_T V_U))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Odrop V_n V_xs T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs _let_1) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_zs T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted _let_1 T_a)) (not (tptp.c_lessequals V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_OCons V_y V_zs T_a) T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Ofilter V_P V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otake V_n V_xs T_a) V_xs) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_ys T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_ys _let_1) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (= (tptp.c_List_Orotate V_n (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Orev (tptp.c_List_Orotate (tptp.c_HOL_Ominus__class_Ominus _let_1 (tptp.c_Divides_Odiv__class_Omod V_n _let_1 tptp.tc_nat) tptp.tc_nat) V_xs T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_n))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_n)))) (tptp.c_lessequals _let_16 _let_16 tptp.tc_nat) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OFun V_type1 V_type2) (tptp.c_Type_Otype_OFun V_type1_H V_type2_H))) (= V_type1 V_type1_H))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OFun V_type1 V_type2) (tptp.c_Type_Otype_OFun V_type1_H V_type2_H))) (= V_type2 V_type2_H))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) _let_1)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) _let_1)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_l tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat) _let_1))) (forall ((T_a $$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) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$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) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_k tptp.tc_nat) V_j tptp.tc_nat))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) 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_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a 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_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x 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_lessequals V_x V_y T_a) (not (tptp.c_lessequals 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_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) V_i) (not (tptp.c_lessequals V_i V_n tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Odrop _let_2 _let_1 T_a) _let_1))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Olist_ONil T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= (tptp.c_List_Otake _let_2 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= V_xs_092_060_094isub_0622 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_xs_092_060_094isub_0621 T_a) V_xs_092_060_094isub_0622 T_a) V_ys_092_060_094isub_0622) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Odrop (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Orotate V_n V_xs T_a) V_xs))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Odistinct V_ys T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_xs $$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 $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a) V_xs)) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OdropWhile V_P _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= V_xs (tptp.c_List_Otake (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_f $$unsorted) (V_P $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap__filter V_f V_P V_xs T_b T_a) (tptp.c_List_Omap V_f (tptp.c_List_Ofilter V_P V_xs T_b) T_b T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_b) T_a T_b)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t)) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_k)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_k)))) (forall ((V_n $$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_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_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_e $$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_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Odrop V_n _let_1 T_a) _let_1))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))) (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_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_P $$unsorted)) (or (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_ys (tptp.tc_List_Olist T_b))) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_ONil T_a) V_xs T_a))) (forall ((V_r $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_r $$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.hAPP (tptp.hAPP (tptp.hAPP 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_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 $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.c_Type_Otype_OFun V_T1 V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i))) (not (tptp.c_Type_Otyping V_e V_u V_T1)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T1 tptp.tc_Type_Otype) V_t V_Ta)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.c_Type_Otype_OFun V_T1 V_T2))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i))) (not (tptp.c_Type_Otyping V_e V_u V_T2)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T2 tptp.tc_Type_Otype) V_t V_Ta)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_us $$unsorted) (V_T $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (tptp.c_Type_Otypings V_e V_us (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 V_T V_U V_e V_us)) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_us tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T))))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_i $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 V_T V_e V_i V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (= (tptp.c_List_Orotate V_n V_xs T_a) (tptp.c_List_Oappend (tptp.c_List_Odrop _let_1 V_xs T_a) (tptp.c_List_Otake _let_1 V_xs T_a) T_a)))) (tptp.c_Type_Otyping tptp.v_ea______ tptp.v_ua______ tptp.v_T____) (forall ((V_env $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_U $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OAbs V_t) (tptp.c_Type_Otype_OFun V_T V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_env (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_T tptp.tc_Type_Otype) V_t V_U)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Odrop V_i V_xs T_a) T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Otake V_i V_xs T_a) T_a) (tptp.c_List_Odrop (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat) (tptp.c_List_Orev V_xs T_a) T_a))) (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ tptp.v_T____) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a))) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a) T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_ys_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Otake _let_2 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621)) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_xs_092_060_094isub_0621 T_a) V_xs_092_060_094isub_0622 T_a) T_a)))))) (forall ((V_v $$unsorted) (V_n $$unsorted) (V_rs $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_n))) (or (= V_v (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_v))))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Otake _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a))))) (forall ((T_a $$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 $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_OtakeWhile V_P V_xs T_a))) (= _let_1 (tptp.c_List_Otake (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.tc_List_Olist T_a)) V_xs T_a)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Otake V_n _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Otake V_n V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_m $$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_P $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (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 ((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 $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_P $$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 ((T_a $$unsorted) (V_n $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Odrop V_n V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Otake V_n V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)))) (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_OremoveAll V_x _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= V_xs V_ys) (not (tptp.c_List_Olist__all2 (tptp.c_fequal T_a) V_xs V_ys T_a T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_xs T_a) V_xs)) (forall ((V_r $$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) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a)))) (forall ((V_A $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (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 ((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 $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_a V_c T_a) (tptp.c_List_Oappend V_b V_d T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_c V_d T_a T_b)) (not (tptp.c_List_Olist__all2 V_P V_a V_b T_a T_b)))) (forall ((V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_b))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xa _let_2) (tptp.c_Nat_Osize__class_Osize V_zs _let_1))) (not (= (tptp.c_Nat_Osize__class_Osize V_x _let_2) (tptp.c_Nat_Osize__class_Osize V_ys _let_1))) (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_x V_xa T_a) (tptp.c_List_Oappend V_ys V_zs T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xa V_zs T_a T_b)) (not (tptp.c_List_Olist__all2 V_P V_x V_ys T_a T_b)))))) (forall ((V_xa $$unsorted) (T_b $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_List_Olist T_b))) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xa _let_2) (tptp.c_Nat_Osize__class_Osize V_ys _let_1))) (not (= (tptp.c_Nat_Osize__class_Osize V_x _let_2) (tptp.c_Nat_Osize__class_Osize V_xs _let_1))) (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_x V_xa T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_ys V_xa T_a T_b)) (not (tptp.c_List_Olist__all2 V_P V_xs V_x T_a T_b)))))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Odrop (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (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 ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Otake V_n V_xs T_a) _let_1)) (= V_xs _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$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 ((T_a $$unsorted) (V_P $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_r $$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_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Odrop V_n V_xs T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s) (tptp.hAPP _let_1 V_t)) (not (tptp.c_Lambda_Obeta V_s V_t))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((V_ys $$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 ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Oreplicate _let_1 V_x T_a) (tptp.c_List_Oreplicate _let_1 V_y T_a)))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Odrop V_i V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) 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_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_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_us $$unsorted) (V_vs $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_ys (tptp.tc_List_Olist T_b)))) (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_xs V_us T_a) (tptp.c_List_Oappend V_ys V_vs T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_us V_vs T_a T_b)) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_r) V_i) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (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_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_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)))) _let_15 (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_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_x V_y) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (not (tptp.c_Type_Otyping V_e_H V_u V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e_H V_i V_U tptp.tc_Type_Otype) V_t V_T)) (tptp.c_Type_Otyping V_e_H (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i) V_T))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__all V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (not (tptp.c_List_Olist__all V_P V_ys T_a)) (not (tptp.c_List_Olist__all V_P V_xs T_a)))) (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) (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_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Otake V_i V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s) (tptp.c_Lambda_OdB_OAbs V_t)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((V_i $$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 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrelp V_r _let_1 _let_1 T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (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 $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_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 ((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_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) V_ys T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs (tptp.c_List_Orev V_ys T_b) T_a T_b)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__all2 V_P V_xs (tptp.c_List_Orev V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) V_ys T_a T_b)))) (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_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_xa V_xb tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xa) V_xb))))) (forall ((V_P $$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 $$unsorted) (V_x $$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_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Olist__all V_P V_xs T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_x V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_OremoveAll V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_OremoveAll V_x V_xs T_a))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_f $$unsorted) (V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Omap__filter V_f V_P (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap__filter V_f V_P V_xs T_b T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (= (tptp.c_List_OdropWhile V_P _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OdropWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_OdropWhile V_P V_xs T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a))) (or (not (= (tptp.c_List_OdropWhile V_P V_xs T_a) _let_1)) (= V_xs (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1 T_a))))) (forall ((V_xs $$unsorted) (V_P $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a))) (or (not (= V_xs (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1 T_a))) (= (tptp.c_List_OdropWhile V_P V_xs T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_y))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (not (= V_xs (tptp.c_List_Otake _let_1 V_zs T_a))) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Odrop _let_1 V_zs T_a) T_a) V_zs)))) (forall ((V_nat $$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_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Oremove1 V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_m $$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_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_us $$unsorted) (V_vs $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_ys (tptp.tc_List_Olist T_b)))) (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_xs V_us T_a) (tptp.c_List_Oappend V_ys V_vs T_b) T_a T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (V_us $$unsorted) (V_vs $$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_List_Olist__all2 V_P V_us V_vs T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Oappend V_xs V_us T_a) (tptp.c_List_Oappend V_ys V_vs T_b) T_a T_b)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_OremoveAll V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_OremoveAll V_x V_xs T_a) (tptp.c_List_OremoveAll V_x V_ys T_a) T_a))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_n $$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 ((V_P $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_l T_a) T_a) T_a) (tptp.c_List_OtakeWhile V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (forall ((V_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 ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Odrop V_n V_as T_a) (tptp.c_List_Odrop V_n V_bs T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_as V_bs T_a T_b)))) (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 $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1)) (= V_s _let_1)))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i) V_t))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x V_xs T_a) (tptp.c_List_OremoveAll V_x V_xs T_a)) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_x $$unsorted) (V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Ofilter V_P V_xs T_a))) (or (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oreplicate V_n V_x T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) V_xs)) (forall ((V_ys $$unsorted) (T_b $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (= V_ys (tptp.c_List_Olist_ONil T_b)) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_ONil T_a) V_ys T_a T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (T_b $$unsorted)) (or (= V_xs (tptp.c_List_Olist_ONil T_a)) (not (tptp.c_List_Olist__all2 V_P V_xs (tptp.c_List_Olist_ONil T_b) T_a T_b)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (= V_y V_x) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Orotate V_n V_xs T_a) T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Orotate V_n V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.c_List_Olist_ONil T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) (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 ((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 $$unsorted) (V_x $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_n $$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 ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_OdropWhile V_P V_xs T_a) (tptp.c_List_Odrop (tptp.c_Nat_Osize__class_Osize (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.tc_List_Olist T_a)) V_xs T_a))) (forall ((V_xs $$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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OtakeWhile V_P _let_1 T_a) _let_1))) (forall ((T_a $$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 $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_ys_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_xs_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (let ((_let_3 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a))) (let ((_let_4 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend (tptp.c_List_Odrop _let_4 V_xs_092_060_094isub_0621 T_a) _let_3 T_a) V_ys_092_060_094isub_0622)) (not (= (tptp.c_List_Otake _let_4 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621)) (not (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a))) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 _let_3 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a)))))))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_m V_n))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.c_Lambda_Obeta V_t V_t_H)) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_ys T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_dB_H $$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_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 ((V_f $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap__filter V_f V_P (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (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_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__all V_P V_xs T_a) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Orev V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__all V_P (tptp.c_List_Orev V_xs T_a) T_a) (not (tptp.c_List_Olist__all V_P V_xs T_a)))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend _let_1 V_xs T_a) T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OremoveAll V_x _let_1 T_a) _let_1))) (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_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_ONil T_b) T_a T_b)) (forall ((V_A $$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 ((T_a $$unsorted) (V_x $$unsorted)) (tptp.c_List_Olist__all2 (tptp.c_fequal T_a) V_x V_x 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 $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olist__all V_P V_xs T_a) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_P $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olist__all V_P V_ys T_a) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (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_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i) V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((V_x $$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_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistrelp V_r (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (not (tptp.c_List_Olistrelp V_r V_xs V_ys T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Olist__ex V_P V_xs T_a) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$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_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xa V_ys T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_x) V_y))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_xa V_xb T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_xb T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_x) V_xa))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_x) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OremoveAll 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_OremoveAll V_x V_xs T_a) T_a)) (= V_x V_y))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_OdropWhile V_P V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_y))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f $$unsorted) (V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Omap__filter V_f V_P (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Omap__filter V_f V_P V_xs T_b T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_OListMem V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b)))) (forall ((V_P $$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_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 $$unsorted)) (or (= V_x V_y) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$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) (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_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 ((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 ((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_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_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))) _let_14 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_x) V_y)) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b)))) (forall ((V_x $$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_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 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((T_a $$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_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile 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_OtakeWhile V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Olist__all V_P V_xs T_a) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_OListMem V_x (tptp.c_List_Olist_OCons V_y V_xs T_a) T_a) (not (tptp.c_List_OListMem V_x V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_List_Osko__List__Xmap__eq__Cons__conv__1__1 V_f V_xs V_y V_ys T_b T_a) (tptp.c_List_Osko__List__Xmap__eq__Cons__conv__1__2 V_f V_xs V_y V_ys T_b T_a) T_b)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_ys (tptp.c_List_Olist_OCons (tptp.c_List_Osko__List__XCons__eq__map__conv__1__1 V_f V_x V_xs V_ys T_b T_a) (tptp.c_List_Osko__List__XCons__eq__map__conv__1__2 V_f V_x V_xs V_ys T_b T_a) T_b)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_List_Osko__List__Xmap__eq__Cons__D__1__1 V_f V_xs V_y V_ys T_b T_a) (tptp.c_List_Osko__List__Xmap__eq__Cons__D__1__2 V_f V_xs V_y V_ys T_b T_a) T_b)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_ys (tptp.c_List_Olist_OCons (tptp.c_List_Osko__List__XCons__eq__map__D__1__1 V_f V_x V_xs V_ys T_b T_a) (tptp.c_List_Osko__List__XCons__eq__map__D__1__2 V_f V_x V_xs V_ys T_b T_a) T_b)))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i) (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (or (tptp.c_Type_Otypings (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_Ts) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_ONil T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop 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_Odrop V_n V_xs T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__Xmap__idI__1__1 V_f V_xs T_a))) (or (not (= (tptp.hAPP V_f _let_1) _let_1)) (= (tptp.c_List_Omap V_f V_xs T_a T_a) V_xs)))) (forall ((V_xs $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_b) (not (tptp.c_List_Odistinct (tptp.c_List_Omap V_f V_xs T_b T_a) T_a)))) (forall ((V_f $$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_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) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f V_xs T_b T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_f $$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_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_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orotate V_n V_xs T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orev V_xs T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__Xmap__ext__1__1 V_f V_g V_xs T_a T_b))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1))) (= (tptp.c_List_Omap V_f V_xs T_a T_b) (tptp.c_List_Omap V_g V_xs T_a T_b))))) (forall ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Otake V_n V_xs T_b) T_b T_a))) (forall ((V_f $$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 ((V_f $$unsorted) (V_g $$unsorted) (V_xs $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Omap V_g V_xs T_c T_b) T_b T_a) (tptp.c_List_Omap (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_xs T_c T_a))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__Xmap__cong__1__1 V_f V_g V_x T_a T_b))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1))) (= (tptp.c_List_Omap V_f V_x T_a T_b) (tptp.c_List_Omap V_g V_x T_a T_b))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__Xmap__eq__conv__1__1 V_f V_g V_xs T_b T_a))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1))) (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_g V_xs T_b 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 ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) V_s) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_k)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_s) V_k)))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k)) V_u) V_k) V_u)) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) V_t) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_k)) V_s) V_k) V_t)) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______)) (forall ((V_r $$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_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) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_A $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olistsp V_A V_ys T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_ua $$unsorted) (V_ia $$unsorted) (V_ea $$unsorted) (V_T_H $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_a____) V_ua) V_ia))) (not (tptp.c_Type_Otyping V_ea V_ua tptp.v_T____)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_ua))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_ea V_ia tptp.v_T____ tptp.tc_Type_Otype) tptp.v_a____ V_T_H)))) (forall ((V_u $$unsorted) (V_ia $$unsorted) (V_ea $$unsorted) (V_T_H $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_a____) V_u) V_ia))) (not (tptp.c_Type_Otyping V_ea V_u tptp.v_T____)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_ea V_ia tptp.v_T____ tptp.tc_Type_Otype) tptp.v_a____ V_T_H)))) (not (= tptp.v_n____ tptp.v_i____)) (forall ((V_e $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otypings V_e (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst V_u tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_Ts) (not (tptp.c_Type_Otypings (tptp.c_Type_Oshift V_e V_i V_T tptp.tc_Type_Otype) V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e V_u V_T)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= (tptp.c_List_Omap V_f (tptp.c_List_Osko__List__Xmap__eq__Cons__D__1__2 V_f V_xs V_y V_ys T_b T_a) T_b T_a) V_ys))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_xs (tptp.c_List_Omap V_f (tptp.c_List_Osko__List__XCons__eq__map__conv__1__2 V_f V_x V_xs V_ys T_b T_a) T_b T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= (tptp.hAPP V_f (tptp.c_List_Osko__List__Xmap__eq__Cons__D__1__1 V_f V_xs V_y V_ys T_b T_a)) V_y))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= (tptp.hAPP V_f (tptp.c_List_Osko__List__Xmap__eq__Cons__conv__1__1 V_f V_xs V_y V_ys T_b T_a)) V_y))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= (tptp.c_List_Omap V_f (tptp.c_List_Osko__List__Xmap__eq__Cons__conv__1__2 V_f V_xs V_y V_ys T_b T_a) T_b T_a) V_ys))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_x (tptp.hAPP V_f (tptp.c_List_Osko__List__XCons__eq__map__conv__1__1 V_f V_x V_xs V_ys T_b T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_x (tptp.hAPP V_f (tptp.c_List_Osko__List__XCons__eq__map__D__1__1 V_f V_x V_xs V_ys T_b T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= V_xs (tptp.c_List_Omap V_f (tptp.c_List_Osko__List__XCons__eq__map__D__1__2 V_f V_x V_xs V_ys T_b T_a) T_b T_a)))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP 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_ts $$unsorted)) (or (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_ts tptp.tc_Lambda_OdB)))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i) (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst V_u tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) _let_13 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT _let_7 tptp.tc_Lambda_OdB) _let_12 (forall ((V_f $$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_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xs T_b T_a) T_a))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____)) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) _let_11 _let_6 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Lattices_Olower__semilattice tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Lattices_Olattice tptp.tc_Int_Oint) (tptp.class_Divides_Oring__div tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted)) (= (tptp.c_COMBB V_P V_Q V_R T_b T_a T_c) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.82/1.02  )
% 0.82/1.02  % SZS output end Proof for LCL830-1
% 0.82/1.02  % cvc5---1.0.5 exiting
% 0.82/1.02  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------