%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL764-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 07:03:34 EDT 2023

% Result   : Unsatisfiable 0.23s 0.75s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : LCL764-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n029.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Thu Aug 24 23:17:54 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.54  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.54  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ooj3htldnJ/cvc5---1.0.5_4384.p...
% 0.23/0.60  ------- get file name : TPTP file name is LCL764-1
% 0.23/0.60  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4384.smt2...
% 0.23/0.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.75  % SZS status Unsatisfiable for LCL764-1
% 0.23/0.75  % SZS output start Proof for LCL764-1
% 0.23/0.75  (
% 0.23/0.75  (let ((_let_1 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)))) (let ((_let_4 (_let_3))) (let ((_let_5 (ASSUME :args _let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_5 :args (tptp.c_InductTermi_OIT tptp.tc_Lambda_OdB QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a) true))))) :args _let_4)) :args ((or _let_1 (not _let_3)))) (ASSUME :args (_let_2)) _let_5 :args (false true _let_1 false _let_3)) :args ((forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_Suc V_n) V_xs T_a) (tptp.c_List_Odrop V_n (tptp.c_List_Otl V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Otl V_xs T_a) T_a) (tptp.c_List_Otl (tptp.c_List_Otake (tptp.c_Suc V_n) V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_Suc V_i) V_y T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist__update V_xs V_i V_y T_a) T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Odrop V_n V_xs T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Otake V_n V_xs T_a) T_a))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate (tptp.c_Suc V_n) V_xs T_a) (tptp.c_List_Orotate1 (tptp.c_List_Orotate V_n V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xdrop__Xinduct__1 V_P) (tptp.v_sko__List__Xdrop__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xrev__Xinduct__1 V_P) (tptp.v_sko__List__Xrev__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xfoldl__Xinduct__1 V_P) (tptp.v_sko__List__Xfoldl__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xconcat__Xinduct__1 V_P) (tptp.v_sko__List__Xconcat__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ohd (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_x)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Ohd V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Ohd (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) T_a) (tptp.c_List_Ohd V_ys T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otake (tptp.c_Suc V_n) V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Ohd V_xs T_a) (tptp.c_List_Otake V_n (tptp.c_List_Otl V_xs T_a) T_a) T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_OdropWhile V_P V_xs T_a))) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Ohd _let_1 T_a)))) (= _let_1 (tptp.c_List_Olist_ONil T_a))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xhd__Xinduct__1 V_P) (tptp.v_sko__List__Xhd__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xtake__Xinduct__1 V_P) (tptp.v_sko__List__Xtake__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xset__Xinduct__1 V_P) (tptp.v_sko__List__Xset__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xmap__Xinduct__1 V_P) (tptp.v_sko__List__Xmap__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlist__Xinducts__1 V_P) (tptp.v_sko__List__Xlist__Xinducts__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlist__Xinduct__1 V_P) (tptp.v_sko__List__Xlist__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlist__update__Xinduct__1 V_P) (tptp.v_sko__List__Xlist__update__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xremdups__Xinduct__1 V_P) (tptp.v_sko__List__Xremdups__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__XremoveAll__Xinduct__1 V_P) (tptp.v_sko__List__XremoveAll__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__XtakeWhile__Xinduct__1 V_P) (tptp.v_sko__List__XtakeWhile__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__XdropWhile__Xinduct__1 V_P) (tptp.v_sko__List__XdropWhile__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xzip__Xinduct__1 V_P) (tptp.v_sko__List__Xzip__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistset__Xinduct__1 V_P) (tptp.v_sko__List__Xlistset__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xremove1__Xinduct__1 V_P) (tptp.v_sko__List__Xremove1__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xsplice__Xinduct__1 V_P) (tptp.v_sko__List__Xsplice__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xdistinct__Xinduct__1 V_P) (tptp.v_sko__List__Xdistinct__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsum__Xinduct__1 V_P) (tptp.v_sko__List__Xlistsum__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlast__Xinduct__1 V_P) (tptp.v_sko__List__Xlast__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xtl__Xinduct__1 V_P) (tptp.v_sko__List__Xtl__Xinduct__2 V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (= (tptp.c_List_Osplice (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_Olist_OCons (tptp.c_List_Ohd V_ys T_a) (tptp.c_List_Osplice V_xs (tptp.c_List_Otl V_ys T_a) T_a) T_a) T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xs)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Oappend (tptp.c_List_Osko__List__Xrev__induct__1__2 V_P T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Osko__List__Xrev__induct__1__1 V_P T_a) _let_1 T_a) T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= (tptp.c_List_Orotate1 V_xs T_a) (tptp.c_List_Oappend (tptp.c_List_Otl V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Ohd V_xs T_a) _let_1 T_a) T_a)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Omap V_f (tptp.c_List_Olinorder__class_Osort__key V_f V_xs T_b T_a) T_b T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Otl V_xs T_a) T_a) (tptp.c_List_Otl (tptp.c_List_Odrop V_n V_xs 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_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Ofilter V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((T_a $$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_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Otake V_n V_xs T_b) T_b T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremdups (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Oremdups V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_n $$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 $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$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 $$unsorted)) (or (= V_xs V_ys) (not (tptp.c_List_Olist__all2 (tptp.c_fequal T_a) V_xs V_ys T_a T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_OCons V_x V_xs T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.hAPP (tptp.hAPP V_f V_a) V_x) V_xs T_a T_b))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otl (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Odrop V_n (tptp.c_List_Otl V_xs 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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_zs $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_zs T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted _let_1 T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a))))) (forall ((V_P $$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_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_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Orotate1 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_Orotate1 V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xa T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xa T_b T_a) T_a))) (forall ((V_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))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list T_b) T_a T_b) (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_xs)) (forall ((V_P $$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 $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Odrop V_n V_xs T_a) T_a) V_xs)) (forall ((T_a $$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_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((V_i $$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_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_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oremdups V_xs T_a) V_xs)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups V_xs T_a) V_xs) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xinduct__1 V_A V_P) (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xinducts__1 V_A V_P) (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P) tptp.t_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Orotate1 (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_b) T_b) T_b))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_k $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist__update V_xs V_k V_y T_b) T_b T_a) (tptp.c_List_Olist__update (tptp.c_List_Omap V_f V_xs T_b T_a) V_k (tptp.hAPP V_f V_y) T_a))) (forall ((V_x $$unsorted) (T_a $$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_ys $$unsorted) (V_xs $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_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_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Otake V_i V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_xs $$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_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a) T_a))) (forall ((V_P $$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 $$unsorted)) (or (tptp.c_List_Olist__all2 V_P V_xs (tptp.c_List_Orev V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) V_ys T_a T_b)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_ONil T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_ONil T_b) T_a T_b)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= V_xs (tptp.c_List_Olist_ONil T_a)) (not (tptp.c_List_Onull V_xs T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oremdups _let_1 T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oremdups V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$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_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orev V_xs T_b) T_b T_a))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Otake V_n V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((T_b $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Olinorder__class_Osort__key V_f V_xs T_a T_b) T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (tptp.c_List_Odistinct (tptp.c_List_Olinorder__class_Osort__key V_f V_xs T_a T_b) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_P $$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_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b) (not (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b)))) (forall ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orotate V_n V_xs T_b) T_b T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_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 $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_P $$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 $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oconcat__map V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Oappend (tptp.hAPP V_f V_x) (tptp.c_List_Oconcat__map V_f V_xs T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Oappend V_xs V_ys T_b) V_a T_b T_a) (tptp.c_List_Ofoldr V_f V_xs (tptp.c_List_Ofoldr V_f V_ys V_a T_b T_a) T_b T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_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 $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_P $$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) (V_y $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_xs V_ys T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_x) V_y))))) (forall ((V_P $$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_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 $$unsorted)) (or (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Olist__ex V_P V_xs T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Olist__ex V_P V_xs T_a) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistrelp V_r (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (not (tptp.c_List_Olistrelp V_r V_xs V_ys T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_y V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Oremove1 V_x V_xs T_a) T_a)) (= V_x V_y))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Osplice (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_OCons V_y (tptp.c_List_Osplice V_xs V_ys T_a) T_a) T_a))) (forall ((V_xs $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Osublist V_xs V_I T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Omember V_x (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (not (tptp.c_List_Omember V_x V_ys T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otl (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Otl V_xs T_a) V_ys T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Oremove1 V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OdropWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_OdropWhile V_P V_xs T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (= (tptp.c_List_OdropWhile V_P _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otl (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Osplice _let_1 (tptp.c_List_Olist_ONil T_a) T_a) _let_1))) (forall ((V_f $$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_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (tptp.c_List_Omember V_x (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a)) (forall ((V_a $$unsorted) (V_A $$unsorted)) (or (= V_a (tptp.c_List_Olist_OCons (tptp.v_sko__List__Xlistsp__Xcases__1 V_A V_a) (tptp.v_sko__List__Xlistsp__Xcases__2 V_A V_a) tptp.t_a)) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted) (T_b $$unsorted)) (or (tptp.c_List_Olist__all2 V_P (tptp.c_List_Odrop V_n V_as T_a) (tptp.c_List_Odrop V_n V_bs T_b) T_a T_b) (not (tptp.c_List_Olist__all2 V_P V_as V_bs T_a T_b)))) (forall ((V_x $$unsorted) (V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Ofilter V_P V_xs T_a))) (or (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__rec V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list T_b) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list) (tptp.c_List_Olist_Olist__rec V_f1 V_f2 V_list T_a T_b)))) (forall ((V_xs $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_b) (not (tptp.c_List_Odistinct (tptp.c_List_Omap V_f V_xs T_b T_a) T_a)))) (forall ((V_xs $$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_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_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_List_Onull (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) V_a T_b T_a) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_List_Ofoldr V_f V_xs V_a T_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oremdups V_xs T_a) T_a)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_x V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)))) (forall ((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_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_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_i_H $$unsorted) (V_x_H $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i_H V_x_H T_a) (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i_H V_x_H T_a) V_i V_x T_a)) (= V_i V_i_H))) (forall ((T_a $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oremdups V_l T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_l T_a)))) (forall ((V_P $$unsorted) (V_xs $$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_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Odrop V_n V_xs T_b) T_b T_a))) (forall ((V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (tptp.c_List_Omember V_x V_ys T_a) (= V_x V_y) (not (tptp.c_List_Omember V_x (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Ofilter V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((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 ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate1 (tptp.c_List_Orotate V_n V_xs T_a) T_a) (tptp.c_List_Orotate V_n (tptp.c_List_Orotate1 V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted) (V_list $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_a V_list tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_a) V_list))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_OCons V_xa V_xb tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xa) V_xb))))) (forall ((T_a $$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_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osplice V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Osplice (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Otl _let_1 T_a) _let_1))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orotate V_n V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xrev__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.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 ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xsplice__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xset__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xtl__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (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_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_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlist__Xinducts__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xhd__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((T_a $$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 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oconcat__map V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xremdups__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_List_Omember V_x (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xs)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xrev__induct__1__2 V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil T_a)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_List_Olinorder__class_Osort__key V_f _let_1 T_a T_b) _let_1)))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xdrop__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistsum__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_r $$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 $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_ONil T_a) V_xs T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremdups _let_1 T_a) _let_1))) (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 ((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_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__XremoveAll__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted) (V_bs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__inter _let_1 V_bs T_a) _let_1))) (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_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orotate1 V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlast__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.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 ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__XtakeWhile__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlist__update__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xfoldl__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olist__all V_P (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orotate1 _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (not (tptp.c_List_Olist__ex V_P (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted)) (tptp.c_List_Onull (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_ONil tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P V_f1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_ONil T_b) V_a T_b T_a) V_a)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xzip__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Osublist _let_1 V_A T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistset__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__rec V_f1 V_f2 (tptp.c_List_Olist_ONil T_b) T_a T_b) V_f1)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__XdropWhile__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xtake__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofiltermap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oremdups V_x T_a))) (= V_x _let_1)))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_k V_x T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_y T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_v T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xconcat__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xdistinct__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_m $$unsorted) (V_as $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Omap__upds V_m V_as (tptp.c_List_Olist_ONil T_b) T_a T_b) V_m)) (forall ((V_m $$unsorted) (T_a $$unsorted) (V_bs $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Omap__upds V_m (tptp.c_List_Olist_ONil T_a) V_bs T_a T_b) V_m)) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xremove1__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case V_f1 V_f2 (tptp.c_List_Olist_ONil T_b) T_a T_b) V_f1)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orotate V_n _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlist__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrelp V_r _let_1 _let_1 T_a))) (forall ((V_P $$unsorted) (V_list $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_list)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xmap__Xinduct__2 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Olist__update V_xs V_k V_x T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (not (tptp.c_List_Olistsp V_A V_ys T_a)) (not (tptp.c_List_Olistsp V_A V_xs T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.c_List_Osko__List__Xin__listsp__conv__set__1__1 V_A V_xs T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (or (tptp.c_List_Olistsp (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_l T_a) (not (tptp.c_List_Olistsp V_B V_l T_a)) (not (tptp.c_List_Olistsp V_A V_l T_a)))) (forall ((V_A $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olistsp V_A V_ys T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xinducts__1 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xinduct__1 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted)) (or (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xcases__2 V_A V_a) tptp.t_a) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.v_sko__List__Xlistsp__Xcases__1 V_A V_a))) (= V_a (tptp.c_List_Olist_ONil tptp.t_a)) (not (tptp.c_List_Olistsp V_A V_a tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xinducts__2 V_A V_P) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.c_List_Olistsp V_A (tptp.v_sko__List__Xlistsp__Xinduct__2 V_A V_P) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Olist_ONil tptp.t_a)))) (not (tptp.c_List_Olistsp V_A V_x tptp.t_a)))) _let_3 _let_2 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y)))))))))))))
% 0.23/0.75  )
% 0.23/0.76  % SZS output end Proof for LCL764-1
% 0.23/0.76  % cvc5---1.0.5 exiting
% 0.23/0.76  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------