%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SCT146+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 14:12:10 EDT 2023

% Result   : Theorem 0.64s 1.22s
% Output   : Proof 0.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.21  % Problem    : SCT146+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.22  % Command    : do_cvc5 %s %d
% 0.23/0.43  % Computer : n023.cluster.edu
% 0.23/0.43  % Model    : x86_64 x86_64
% 0.23/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43  % Memory   : 8042.1875MB
% 0.23/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43  % CPULimit   : 300
% 0.23/0.43  % WCLimit    : 300
% 0.23/0.43  % DateTime   : Thu Aug 24 15:11:12 EDT 2023
% 0.23/0.44  % CPUTime    : 
% 0.30/0.65  %----Proving TF0_NAR, FOF, or CNF
% 0.64/1.22  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.srZnA3v6je/cvc5---1.0.5_29982.p...
% 0.64/1.22  ------- get file name : TPTP file name is SCT146+1
% 0.64/1.22  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29982.smt2...
% 0.64/1.22  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.64/1.22  % SZS status Theorem for SCT146+1
% 0.64/1.22  % SZS output start Proof for SCT146+1
% 0.64/1.22  (
% 0.64/1.22  (let ((_let_1 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P____ B_i))) (let ((_let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_b____) tptp.v_a____)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_1) tptp.v_c____) tptp.v_b____)) tptp.v_b____) tptp.v_a____)) tptp.v_a____) tptp.v_c____))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_a____) tptp.v_b____)) _let_1))))))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.tc_fun _let_3 tptp.tc_HOL_Obool))) (let ((_let_5 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_4))) (let ((_let_6 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt _let_4))) (let ((_let_7 (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt _let_6) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.c_Arrow__Order__Mirabelle_Obelow))) (let ((_let_8 (tptp.c_COMBC tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt _let_6))) (let ((_let_9 (tptp.c_COMBC tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_Arrow__Order__Mirabelle_Oalt _let_4))) (let ((_let_10 (tptp.hAPP (tptp.hAPP _let_9 (tptp.hAPP (tptp.hAPP _let_8 (tptp.hAPP _let_7 tptp.v_P____)) tptp.v_c____)) tptp.v_b____))) (let ((_let_11 (tptp.hAPP (tptp.hAPP _let_9 (tptp.hAPP (tptp.hAPP _let_8 (tptp.hAPP _let_7 _let_10)) tptp.v_b____)) tptp.v_a____))) (let ((_let_12 (tptp.c_member _let_5))) (let ((_let_13 (tptp.hAPP (tptp.hAPP _let_9 (tptp.hAPP (tptp.hAPP _let_8 (tptp.hAPP _let_7 _let_11)) tptp.v_a____)) tptp.v_c____))) (let ((_let_14 (tptp.c_List_Olist_OCons tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_15 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_16 (tptp.hAPP _let_15 tptp.v_b____))) (let ((_let_17 (tptp.c_member _let_3))) (let ((_let_18 (tptp.hAPP _let_17 (tptp.hAPP _let_16 tptp.v_a____)))) (let ((_let_19 (tptp.hAPP _let_17 (tptp.hAPP _let_16 tptp.v_c____)))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP _let_19 (tptp.hAPP tptp.v_F _let_11))))) (let ((_let_21 (tptp.hAPP _let_15 tptp.v_a____))) (let ((_let_22 (tptp.hAPP _let_17 (tptp.hAPP _let_21 tptp.v_c____)))) (let ((_let_23 (tptp.hBOOL (tptp.hAPP _let_22 (tptp.hAPP tptp.v_F _let_10))))) (let ((_let_24 (tptp.hAPP _let_17 (tptp.hAPP _let_21 tptp.v_b____)))) (let ((_let_25 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow (tptp.hAPP tptp.v_P____ B_i)) tptp.v_c____) tptp.v_b____)) tptp.v_b____) tptp.v_a____))) (let ((_let_2 (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.v_b____))) (let ((_let_3 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 tptp.v_c____)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 tptp.v_a____)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_1) tptp.v_a____) tptp.v_c____)))))))))) (let ((_let_26 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow (tptp.hAPP tptp.v_P____ B_i)) tptp.v_c____) tptp.v_b____))) (let ((_let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_a____) tptp.v_c____)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_b____) tptp.v_c____)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_1) tptp.v_b____) tptp.v_a____)))))))))) (let ((_let_27 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P____ B_i))) (let ((_let_2 (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.v_a____))) (let ((_let_3 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 tptp.v_b____)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 tptp.v_c____)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_1) tptp.v_c____) tptp.v_b____)))))))))) (let ((_let_28 (tptp.hAPP tptp.v_P____ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_28) tptp.v_c____) tptp.v_b____))) (let ((_let_30 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_29) tptp.v_b____) tptp.v_a____))) (let ((_let_31 (tptp.hBOOL (tptp.hAPP _let_19 _let_30)))) (let ((_let_32 (tptp.hBOOL (tptp.hAPP _let_22 _let_29)))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (_let_26))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P____ B_i)))) :args _let_34)) _let_35 :args (_let_33 false _let_26)))) (let ((_let_37 (tptp.hBOOL (tptp.hAPP _let_24 _let_28)))) (let ((_let_38 (= _let_37 _let_32))) (let ((_let_39 (not _let_32))) (let ((_let_40 (_let_27))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P____ B_i)))) :args _let_40)) _let_41 :args (_let_38 false _let_27)))) (let ((_let_43 (tptp.hBOOL (tptp.hAPP _let_18 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow _let_30) tptp.v_a____) tptp.v_c____))))) (let ((_let_44 (= _let_43 _let_37))) (let ((_let_45 (= _let_43 _let_31))) (let ((_let_46 (not _let_37))) (let ((_let_47 (not _let_44))) (let ((_let_48 (_let_2))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_47)) :args (or))) _let_49 :args (_let_47 true _let_1)))) (let ((_let_51 (_let_44))) (let ((_let_52 (not _let_38))) (let ((_let_53 (_let_38))) (let ((_let_54 (_let_25))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P____ B_i)))) :args _let_54))) _let_55 :args (_let_45 false _let_25)))) (let ((_let_57 (not _let_45))) (let ((_let_58 (not _let_31))) (let ((_let_59 (_let_45))) (let ((_let_60 (not _let_33))) (let ((_let_61 (_let_33))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_61) :args ((or _let_31 _let_39 _let_60))) _let_36 (REORDERING (CNF_EQUIV_POS2 :args _let_59) :args ((or _let_43 _let_58 _let_57))) _let_56 (REORDERING (CNF_EQUIV_POS1 :args _let_53) :args ((or _let_46 _let_32 _let_52))) _let_42 (CNF_EQUIV_NEG2 :args _let_51) _let_50 :args (_let_46 false _let_33 true _let_31 false _let_45 false _let_32 false _let_38 true _let_43 true _let_44)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_61) :args ((or _let_32 _let_58 _let_60))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_59) :args ((or (not _let_43) _let_31 _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_51) :args ((or _let_43 _let_37 _let_44))) _let_62 _let_50 :args (_let_43 true _let_37 true _let_44)) _let_56 :args (_let_31 false _let_43 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_53) :args ((or _let_37 _let_39 _let_52))) _let_62 _let_42 :args (_let_39 true _let_37 false _let_38)) _let_36 :args (false false _let_31 true _let_32 false _let_33)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) (not (= tptp.v_a____ tptp.v_b____)) (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.v_a____) tptp.v_b____)) (tptp.hAPP tptp.v_P____ B_i))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.v_b____) tptp.v_a____)) (tptp.hAPP tptp.v_P_H____ B_i))))))) _let_27 _let_26 _let_25 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_12 tptp.v_P____) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((V_ca_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))) (=> (= V_A_2 V_B_2) (=> (=> _let_3 (not _let_2)) (not (=> (not _let_3) _let_2)))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_x_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_z_2))) (and (not (= V_y_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_L_2)))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_y_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_z_2))) (and (not (= V_x_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_L_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FunDef_Oin__rel T_a T_b V_R_2 V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2) V_y_2)) V_R_2)))) (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_y_H_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) V_y_H_2) V_y_2)) (tptp.hAPP V_R_2 V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP _let_1 V_y_H_2)) (tptp.hAPP _let_1 V_y_2))) (tptp.c_Recdef_Osame__fst T_a T_b V_Pa_2 V_R_2)))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2))))) (= (tptp.hBOOL (tptp.hAPP _let_24 (tptp.hAPP tptp.v_F tptp.v_P____))) _let_23) (= _let_23 _let_20) (= _let_20 (tptp.hBOOL (tptp.hAPP _let_18 (tptp.hAPP tptp.v_F _let_13)))) (tptp.c_List_Odistinct tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP (tptp.hAPP _let_14 tptp.v_a____) (tptp.hAPP (tptp.hAPP _let_14 tptp.v_b____) (tptp.hAPP (tptp.hAPP _let_14 tptp.v_c____) (tptp.c_List_Olist_ONil tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_Pa_2 $$unsorted)) (= (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x1))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_a) B_b)))))) (tptp.c_Arrow__Order__Mirabelle_Ounanimity tptp.v_F) (tptp.c_Arrow__Order__Mirabelle_OIIA tptp.v_F) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_12 tptp.v_P_H____) tptp.c_Arrow__Order__Mirabelle_OProf)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_12 _let_10) tptp.c_Arrow__Order__Mirabelle_OProf)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_12 _let_13) tptp.c_Arrow__Order__Mirabelle_OProf)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_12 _let_11) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (=> (= V_aa_2 V_ba_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_A_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (=> (= V_x_2 V_y_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_A_2)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (= V_A_2 V_B_2) (= (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (=> (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H)) (not (=> (= V_a V_a_H) (not (= V_b V_b_H))))))) (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2) (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2)) (and (= V_aa_2 V_a_H_2) (= V_ba_2 V_b_H_2))))) (not (forall ((B_c $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.c_List_Odistinct tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP (tptp.hAPP _let_1 tptp.v_a____) (tptp.hAPP (tptp.hAPP _let_1 tptp.v_b____) (tptp.hAPP (tptp.hAPP _let_1 B_c) (tptp.c_List_Olist_ONil tptp.tc_Arrow__Order__Mirabelle_Oalt))))))))) (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))))) (=> (not (= V_aa_2 V_ba_2)) (=> (not (= V_a_H_2 V_b_H_2)) (=> (not (= V_aa_2 V_b_H_2)) (=> (not (= V_ba_2 V_a_H_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_Pa_2) tptp.c_Arrow__Order__Mirabelle_OProf)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_P_Ha_2) tptp.c_Arrow__Order__Mirabelle_OProf)) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) (tptp.hAPP V_Pa_2 B_i))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2)) (tptp.hAPP V_P_Ha_2 B_i))))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) (tptp.hAPP tptp.v_F V_Pa_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2)) (tptp.hAPP tptp.v_F V_P_Ha_2)))))))))))))))) (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))))) (=> (not (= V_aa_2 V_ba_2)) (=> (not (= V_a_H_2 V_b_H_2)) (=> (not (= V_aa_2 V_b_H_2)) (=> (not (= V_ba_2 V_a_H_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_Pa_2) tptp.c_Arrow__Order__Mirabelle_OProf)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_P_Ha_2) tptp.c_Arrow__Order__Mirabelle_OProf)) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) (tptp.hAPP V_Pa_2 B_i))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2)) (tptp.hAPP V_P_Ha_2 B_i))))))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) (tptp.hAPP tptp.v_F V_Pa_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2)) (tptp.hAPP tptp.v_F V_P_Ha_2)))))))))))))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))))) (= (= (tptp.hAPP _let_6 V_R_2) (tptp.hAPP _let_6 V_S_2)) (= V_R_2 V_S_2))))))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Oprod_Oprod__rec T_b T_c T_a V_f1_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_aa_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_5 _let_4)) tptp.v_F) (tptp.c_FuncSet_OPi _let_5 _let_4 tptp.c_Arrow__Order__Mirabelle_OProf (tptp.c_COMBK (tptp.tc_fun _let_4 tptp.tc_HOL_Obool) _let_5 tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct T_a (tptp.c_List_Olist_ONil T_a))) (forall ((V_list_H $$unsorted) (V_a_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_a_H) V_list_H)))) (forall ((V_list_H $$unsorted) (V_a_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_a_H) V_list_H) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2))) (tptp.c_Wellfounded_Olex__prod T_a T_b V_r_2 V_s_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_a_H_2)) V_r_2)) (and (= V_aa_2 V_a_H_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) V_ba_2) V_b_H_2)) V_s_2)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (not (= V_a V_b)) (exists ((B_c $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_List_Odistinct tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.hAPP (tptp.hAPP _let_1 B_c) (tptp.c_List_Olist_ONil tptp.tc_Arrow__Order__Mirabelle_Oalt))))))))) (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2) V_x_2) V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.hAPP tptp.c_fequal V_y_2))) (= V_x_2 V_y_2))) (forall ((V_list_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_list_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_list_2) (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_list_H_2)) (and (= V_aa_2 V_a_H_2) (= V_list_2 V_list_H_2))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_xs) V_xs))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (= V_xs (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_xs)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (=> (not (= V_x_2 V_y_2)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) V_L_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) V_L_2))))))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) V_L_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_aa_2)) V_L_2))))))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (= (tptp.hAPP _let_1 V_R_2) (tptp.hAPP _let_1 V_S_2)) (= V_R_2 V_S_2)))) (forall ((V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1)) (tptp.c_COMBK _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi V_L_2)) tptp.c_Arrow__Order__Mirabelle_OProf))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_y_2)))) (let ((_let_6 (= V_x_2 V_aa_2))) (let ((_let_7 (= V_y_2 V_aa_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2) V_aa_2) V_ba_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_ba_2)) V_L_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_y_2 V_ba_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_y_2)) V_L_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_L_2))))))))))))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) V_B_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_y_2)))) (let ((_let_6 (= V_y_2 V_ba_2))) (let ((_let_7 (= V_x_2 V_ba_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_aa_2 V_ba_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_y_2)) V_L_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_x_2 V_aa_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_aa_2)) V_L_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_L_2))))))))))))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_a)) (tptp.c_COMBI T_a)) (tptp.c_FuncSet_OPi T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))))) (forall ((V_i_2 $$unsorted) (V_Fa_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 _let_1)) V_Fa_2) (tptp.c_FuncSet_OPi _let_2 _let_1 tptp.c_Arrow__Order__Mirabelle_OProf (tptp.c_COMBK (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) _let_2 tptp.c_Arrow__Order__Mirabelle_OLin)))) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (=> (not (= B_a B_b)) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_x V_i_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_Fa_2 B_x))))))))) (tptp.c_Arrow__Order__Mirabelle_Odictator V_Fa_2 V_i_2)))))) (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (forall ((B_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP B_x B_i)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP V_Fa_2 B_x))))))))) (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_OIIA V_Fa_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_xa) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_x B_i))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_xa B_i)))))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_Fa_2 B_x))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_Fa_2 B_xa))))))))))))) (forall ((V_i_2 $$unsorted) (V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Odictator V_Fa_2 V_i_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (= (tptp.hAPP V_Fa_2 B_x) (tptp.hAPP B_x V_i_2)))))) (forall ((V_va $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_v) V_va))) (= (tptp.c_List_Osplice T_a _let_1 (tptp.c_List_Olist_ONil T_a)) _let_1))) (forall ((V_ys $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_x))) (= (tptp.c_List_Osplice T_a (tptp.hAPP _let_3 V_xs) (tptp.hAPP _let_2 V_ys)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 (tptp.c_List_Osplice T_a V_xs V_ys)))))))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osplice T_a (tptp.c_List_Olist_ONil T_a) V_ys) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osplice T_a V_xs (tptp.c_List_Olist_ONil T_a)) V_xs)) (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_x_2 V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) (forall ((V_f2_2 $$unsorted) (V_f1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case T_a T_b V_f1_2 V_f2_2 (tptp.c_List_Olist_ONil T_b)) V_f1_2)) (forall ((V_list_2 $$unsorted) (V_aa_2 $$unsorted) (V_f2_2 $$unsorted) (V_f1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__case T_a T_b V_f1_2 V_f2_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_b) V_aa_2) V_list_2)) (tptp.hAPP (tptp.hAPP V_f2_2 V_aa_2) V_list_2))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ointernal__split T_b T_c T_a) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_ca_2 V_aa_2) V_ba_2))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) V_B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (not (= V_aa_2 V_ba_2)) (exists ((B_x $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)) B_x) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_aa_2) V_ba_2)) B_x))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ocurry T_b T_c T_a V_ca_2) V_x_2) V_y_2) (tptp.hAPP V_ca_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_x_2) V_y_2)))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_ba_2 $$unsorted) (V_x_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olexord T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (let ((_let_5 (tptp.c_List_Olist_OCons T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_5 V_aa_2) V_x_2)) (tptp.hAPP (tptp.hAPP _let_5 V_ba_2) V_y_2))) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) V_r_2)) (and (= V_aa_2 V_ba_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_y_2)) _let_1))))))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oinsert T_a V_x _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) _let_1)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2) V_aa_2) V_ba_2)))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_x_2) (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olexord T_a V_r_2)))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2) V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2) V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (=> (tptp.c_List_Odistinct T_a V_xs) (tptp.c_List_Odistinct T_a (tptp.c_List_Oinsert T_a V_x V_xs)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Ocurry T_b T_c T_a V_f_2) V_aa_2) V_ba_2) (tptp.hAPP V_f_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.c_List_Olist_ONil T_a)) V_y_2)) (tptp.c_List_Olexord T_a V_r_2))) (exists ((B_a $$unsorted) (B_x $$unsorted)) (= V_y_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_a) B_x)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olexord T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_a) B_b)) V_r_2)) (= B_a B_b) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_b) B_a)) V_r_2)))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_y_2)) _let_1)) (= V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_y_2) V_x_2)) _let_1))))))))) (forall ((V_y_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_y_2) V_y_2)) (tptp.c_List_Olexord T_a V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olex T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.c_List_Olist_ONil T_a)) V_ys_2)) (tptp.c_List_Olex T_a V_r_2)))))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel T_a V_r_2))) (let ((_let_2 (tptp.c_List_Olist_OCons T_a))) (let ((_let_3 (tptp.tc_List_Olist T_a))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_3 _let_3))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_3 _let_3)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_xs_2) V_ys_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_ys_2))) _let_1)))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_u_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Oappend T_a) V_u_2))) (let ((_let_3 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_3 _let_3)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_3 _let_3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_x_2))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_y_2)))) (tptp.c_List_Olexord T_a V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_y_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel1 T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (let ((_let_5 (tptp.c_List_Olist_OCons T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_5 V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP _let_5 V_y_2) V_ys_2))) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (= V_xs_2 V_ys_2)) (and (= V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_xs_2) V_ys_2)) _let_1))))))))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) _let_1) V_xs_2)) (tptp.c_List_Olistrel T_a V_r_2))) (= V_xs_2 _let_1))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) V_xs_2) _let_1)) (tptp.c_List_Olistrel T_a V_r_2))) (= V_xs_2 _let_1))))) (forall ((V_us $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted) (V_xs1 $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_xs))) (=> (= (tptp.hAPP _let_2 V_xs1) V_zs) (=> (= V_ys (tptp.hAPP (tptp.hAPP _let_1 V_xs1) V_us)) (= (tptp.hAPP _let_2 V_ys) (tptp.hAPP (tptp.hAPP _let_1 V_zs) V_us))))))) (forall ((V_zs_2 $$unsorted) (V_xs_2 $$unsorted) (V_ys_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_ys_2) V_xs_2) (tptp.hAPP (tptp.hAPP _let_1 V_zs_2) V_xs_2)) (= V_ys_2 V_zs_2)))) (forall ((V_zs_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2))) (= (= (tptp.hAPP _let_1 V_ys_2) (tptp.hAPP _let_1 V_zs_2)) (= V_ys_2 V_zs_2)))) (forall ((V_ts_2 $$unsorted) (V_zs_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_xs_2) V_ys_2) (tptp.hAPP (tptp.hAPP _let_1 V_zs_2) V_ts_2)) (exists ((B_us $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (let ((_let_2 (tptp.hAPP _let_1 B_us))) (or (and (= V_xs_2 (tptp.hAPP (tptp.hAPP _let_1 V_zs_2) B_us)) (= (tptp.hAPP _let_2 V_ys_2) V_ts_2)) (and (= (tptp.hAPP (tptp.hAPP _let_1 V_xs_2) B_us) V_zs_2) (= V_ys_2 (tptp.hAPP _let_2 V_ts_2)))))))))) (forall ((V_zs $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_xs))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ys)) V_zs) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ys) V_zs)))))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_xs)) V_ys) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_xs) V_ys)))))) (forall ((V_zs $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (V_xs1 $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x))) (=> (= (tptp.hAPP _let_2 V_xs1) V_ys) (=> (= V_xs (tptp.hAPP (tptp.hAPP _let_1 V_xs1) V_zs)) (= (tptp.hAPP _let_2 V_xs) (tptp.hAPP (tptp.hAPP _let_1 V_ys) V_zs))))))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.c_List_Olist_ONil T_a)) V_ys) V_ys)) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2)) (and (= V_xs_2 _let_1) (= V_ys_2 _let_1))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) (tptp.c_List_Olist_ONil T_a)) V_xs)) (forall ((V_ys_2 $$unsorted) (T_a $$unsorted) (V_xs_2 $$unsorted)) (= (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2)) (= V_ys_2 (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted) (V_ys_2 $$unsorted)) (= (= V_ys_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2)) (= V_xs_2 (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2) _let_1) (and (= V_xs_2 _let_1) (= V_ys_2 _let_1))))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2) V_xs_2) (= V_ys_2 (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2) V_ys_2) (= V_xs_2 (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (=> (= V_xs V_ys) (= V_xs (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.c_List_Olist_ONil T_a)) V_ys)))) (forall ((V_vs_2 $$unsorted) (V_us_2 $$unsorted) (V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel1 T_a V_r_2))) (let ((_let_2 (tptp.c_List_Oappend T_a))) (let ((_let_3 (tptp.tc_List_Olist T_a))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_3 _let_3))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_3 _let_3)))) (=> (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_xs_2) V_ys_2)) _let_1)) (= V_us_2 V_vs_2)) (and (= V_xs_2 V_ys_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_us_2) V_vs_2)) _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_xs_2) V_us_2)) (tptp.hAPP (tptp.hAPP _let_2 V_ys_2) V_vs_2))) _let_1))))))))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (V_zs_2 $$unsorted) (V_ys_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_ys_2) V_zs_2) _let_1) (or (and (= V_ys_2 (tptp.c_List_Olist_ONil T_a)) (= V_zs_2 _let_1)) (exists ((B_ys_H $$unsorted)) (and (= V_ys_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) B_ys_H)) (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) B_ys_H) V_zs_2) V_xs_2))))))) (forall ((V_zs_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2))) (= (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_ys_2) V_zs_2)) (or (and (= V_ys_2 (tptp.c_List_Olist_ONil T_a)) (= _let_1 V_zs_2)) (exists ((B_ys_H $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) B_ys_H) V_ys_2) (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) B_ys_H) V_zs_2)))))))) (forall ((V_y_2 $$unsorted) (V_ys_2 $$unsorted) (V_x_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.c_List_Olist_OCons T_a))) (let ((_let_3 (tptp.c_List_Oappend T_a))) (= (= (tptp.hAPP (tptp.hAPP _let_3 V_xs_2) (tptp.hAPP (tptp.hAPP _let_2 V_x_2) _let_1)) (tptp.hAPP (tptp.hAPP _let_3 V_ys_2) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) _let_1))) (and (= V_xs_2 V_ys_2) (= V_x_2 V_y_2))))))) (forall ((V_ys_2 $$unsorted) (V_vs_2 $$unsorted) (V_us_2 $$unsorted) (V_xs_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olist_OCons T_a))) (let ((_let_3 (tptp.hAPP (tptp.c_List_Oappend T_a) V_us_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (=> (= V_xs_2 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_vs_2))) (=> (= V_ys_2 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_vs_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olistrel1 T_a V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_ys_2 $$unsorted) (V_x_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel1 T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (let ((_let_5 (tptp.c_List_Olist_ONil T_a))) (let ((_let_6 (tptp.c_List_Olist_OCons T_a))) (let ((_let_7 (tptp.c_List_Oappend T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_7 V_xs_2) (tptp.hAPP (tptp.hAPP _let_6 V_x_2) _let_5))) (tptp.hAPP (tptp.hAPP _let_7 V_ys_2) (tptp.hAPP (tptp.hAPP _let_6 V_y_2) _let_5)))) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_xs_2) V_ys_2)) _let_1)) (= V_x_2 V_y_2)) (and (= V_xs_2 V_ys_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2))))))))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_v_2 $$unsorted) (V_u_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olexord T_a V_r_2))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Oappend T_a) V_x_2))) (let ((_let_3 (tptp.tc_List_Olist T_a))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_3 _let_3))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_3 _let_3)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_u_2) V_v_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_u_2)) (tptp.hAPP _let_2 V_v_2))) _let_1))))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel1 T_a V_r_2))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2))) (let ((_let_3 (tptp.tc_List_Olist T_a))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_3 _let_3))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_3 _let_3)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_xs_2) V_ys_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_xs_2)) (tptp.hAPP _let_2 V_ys_2))) _let_1))))))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.c_List_Olist_ONil T_a)) V_xs_2)) (tptp.c_List_Olistrel1 T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrel1 T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) _let_1) _let_1)) (tptp.c_List_Olistrel T_a V_r_2)))))) (forall ((V_xs_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_xs_2))) (tptp.c_List_Olistrel1 T_a V_r_2))))))) (forall ((V_xa_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun _let_3 tptp.tc_HOL_Obool))) (let ((_let_5 (tptp.tc_fun T_a _let_4))) (let ((_let_6 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_List_Olistrelp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_3 _let_6) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_3 _let_6) T_a) (tptp.c_COMBC T_a _let_3 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_2) _let_5 T_a) (tptp.hAPP (tptp.c_COMBB _let_2 _let_4 T_a) (tptp.c_member _let_2))) (tptp.c_Product__Type_OPair T_a T_a)))) V_r_2) V_x_2 V_xa_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_x_2) V_xa_2)) (tptp.c_List_Olistrel T_a V_r_2))))))))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (V_ys_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_y_2) V_ys_2)) V_xs_2)) (tptp.c_List_Olistrel T_a V_r_2))) (not (forall ((B_y $$unsorted) (B_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_y) B_ys)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_y_2) B_y)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_ys_2) B_ys)) (tptp.c_List_Olistrel T_a V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_y_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_y_2) V_ys_2))) (tptp.c_List_Olistrel T_a V_r_2))) (not (forall ((B_x $$unsorted) (B_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_x) B_xs)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) V_y_2)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) B_xs) V_ys_2)) (tptp.c_List_Olistrel T_a V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olistrel1 T_a V_r_2))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_y)) V_r_2)) (forall ((B_us $$unsorted) (B_vs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_List_Oappend T_a) B_us))) (=> (= V_xs_2 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_x) B_vs))) (not (= V_ys_2 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_vs)))))))))))))) (forall ((V_r_2 $$unsorted) (V_v_2 $$unsorted) (V_u_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olexord T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (let ((_let_5 (tptp.hAPP (tptp.c_List_Oappend T_a) V_x_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_5 V_u_2)) (tptp.hAPP _let_5 V_v_2))) _let_1)) (=> (forall ((B_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_a) B_a)) V_r_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_u_2) V_v_2)) _let_1)))))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (exists ((B_b $$unsorted) (B_z $$unsorted)) (= V_y_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_b) B_z))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_x_2) V_y_2))) (tptp.c_List_Olexord T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_y_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olex T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (let ((_let_5 (tptp.c_List_Olist_OCons T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_5 V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP _let_5 V_y_2) V_ys_2))) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (= (tptp.c_Nat_Osize__class_Osize _let_2 V_xs_2) (tptp.c_Nat_Osize__class_Osize _let_2 V_ys_2))) (and (= V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_xs_2) V_ys_2)) _let_1))))))))))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (= (tptp.c_List_Orotate1 T_a V_xs_2) (tptp.c_List_Olist_Olist__case _let_2 T_a _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_2 _let_2) T_a) (tptp.hAPP (tptp.c_COMBC _let_2 _let_2 _let_2) (tptp.c_List_Oappend T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_2) (tptp.c_List_Olist_OCons T_a)) _let_1)) V_xs_2))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.c_List_Orotate1 T_a V_xs)) (tptp.c_Nat_Osize__class_Osize _let_1 V_xs)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (not (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys))) (not (= V_xs V_ys))))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (= (tptp.c_List_Orotate1 T_a V_xs_2) _let_1) (= V_xs_2 _let_1)))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odistinct T_a (tptp.c_List_Orotate1 T_a V_xs_2)) (tptp.c_List_Odistinct T_a V_xs_2))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_x_2) V_y_2)) (=> (tptp.c_List_Olistrelp T_a V_r_2 V_xs_2 V_ys_2) (tptp.c_List_Olistrelp T_a V_r_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_xs_2) (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_ys_2)))))) (forall ((V_a4_2 $$unsorted) (V_a2_2 $$unsorted) (V_a3_2 $$unsorted) (V_a1_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons T_a))) (= (tptp.c_List_Olistrelp T_a V_r_2 (tptp.hAPP (tptp.hAPP _let_1 V_a1_2) V_a3_2) (tptp.hAPP (tptp.hAPP _let_1 V_a2_2) V_a4_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a1_2) V_a2_2)) (tptp.c_List_Olistrelp T_a V_r_2 V_a3_2 V_a4_2))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrelp T_a V_r_2 _let_1 _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (tptp.c_List_Olistrelp T_a V_r_2 _let_1 _let_1))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olistrel1 T_a V_r_2))) (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys_2))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olistrel T_a V_r_2))) (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys_2))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_x_2) V_y_2)))) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olex T_a V_r_2))) (and (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olexord T_a V_r_2))) (= (tptp.c_Nat_Osize__class_Osize _let_1 V_x_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_y_2))))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Olist_OCons T_b) V_x))) (let ((_let_2 (tptp.c_List_Olist_ONil T_a))) (and (= (tptp.c_List_Orotate1 T_a _let_2) _let_2) (= (tptp.c_List_Orotate1 T_b (tptp.hAPP _let_1 V_xs)) (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_b) V_xs) (tptp.hAPP _let_1 (tptp.c_List_Olist_ONil T_b)))))))) (forall ((V_n_2 $$unsorted) (V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olexn T_a V_r_2 V_n_2))) (and (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2) V_n_2) (= (tptp.c_Nat_Osize__class_Osize _let_1 V_ys_2) V_n_2))))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Omaps T_b T_a V_f_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_b) V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.c_List_Omaps T_b T_a V_f_2 V_xs_2)))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (= (tptp.c_List_Opartition T_a V_Pa_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) _let_1) _let_1))))) (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olexord T_a V_r_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_3 V_x_2))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_4 V_y_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_3 V_y_2) V_z_2)) _let_1)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_4 V_z_2)) _let_1))))))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olistrel T_a V_r_2))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olistrel1 T_a V_r_2))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olistrel T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2)) V_ys_2)) (tptp.c_List_Olistrel1 T_a V_r_2))) (=> (forall ((B_y $$unsorted)) (=> (= V_ys_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_y) V_xs_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) B_y)) V_r_2))))) (not (forall ((B_zs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (= V_ys_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) B_zs)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) B_zs)) (tptp.c_List_Olistrel1 T_a V_r_2)))))))))))) (forall ((V_R2_2 $$unsorted) (T_b $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_R1_2) (=> (tptp.c_Relation_Otrans T_b V_R2_2) (tptp.c_Relation_Otrans (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_R1_2 V_R2_2))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_xs_2)) (tptp.c_List_Olistrel T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans (tptp.tc_List_Olist T_a) (tptp.c_List_Olistrel T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans (tptp.tc_List_Olist T_a) (tptp.c_List_Olexord T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olistrel T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Transitive__Closure_Ortrancl (tptp.tc_List_Olist T_a) (tptp.c_List_Olistrel1 T_a V_r_2)))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))) (let ((_let_3 (tptp.c_List_Olist_OCons T_a))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_xs_2) V_ys_2)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_xs_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y_2) V_ys_2))) _let_2)))))))))) (forall ((V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Omaps T_b T_a V_f_2 (tptp.c_List_Olist_ONil T_b)) (tptp.c_List_Olist_ONil T_a))) (forall ((V_zs_2 $$unsorted) (V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistrel T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.hAPP _let_3 V_xs_2))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_2 _let_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_4 V_ys_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_3 V_ys_2) V_zs_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_4 V_zs_2)) _let_1)))))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))) (let ((_let_3 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_xs_2) V_ys_2)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_xs_2)) (tptp.hAPP _let_3 V_ys_2))) _let_2))))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))) (= (tptp.c_Nat_Osize__class_Osize _let_1 V_x_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_y_2))))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_p_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_aa_2))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_ca_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ca_2)) V_r_2))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Otrans T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_z)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_x) B_z)) V_r_2)))))))))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_ca_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ca_2)) _let_1))))))))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_ca_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ca_2)) _let_1))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (= (tptp.c_Transitive__Closure_Ortrancl T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_ca_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ca_2)) _let_1))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2)))))) (forall ((V_ba_2 $$unsorted) (V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_aa_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_ba_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1))))))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_ba_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_aa_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1))))))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (let ((_let_4 (tptp.hAPP _let_2 V_x_2))) (=> (tptp.c_Relation_Osingle__valued T_a T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_y_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_z_2)) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_z_2) V_y_2)) _let_1))))))))))) (forall ((V_y_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Relation_ODomain T_a T_a V_R_2)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= V_x_2 V_y_2)))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.c_Relation_ORange T_a T_b V_r_2))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))))) (forall ((V_xs_2 $$unsorted) (V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Wellfounded_Oacc _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))) (let ((_let_3 (tptp.c_member _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_xs_2) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2)) _let_2)))))))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_b)))) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z_2)) V_r_2)) (= V_y_2 V_z_2))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_z)) V_r_2)) (= B_y B_z))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (exists ((B_y $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) B_y)) V_r_2))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (exists ((B_y $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_y) V_aa_2)) V_r_2))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_aa_2) _let_1))))))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) V_aa_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.c_Wellfounded_Oacc T_a V_r_2))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Predicate_ORangeP T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_x_2) (tptp.c_Relation_ORange T_a T_b V_r_2)))))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Predicate_ODomainP T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Relation_ODomain T_a T_b V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_ba_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (not (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) V_ba_2)) V_r_2))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (not (forall ((B_y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) B_y)) V_r_2))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (let ((_let_5 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_a _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_a) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_a)))) V_r_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2)))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.c_Predicate_ORangeP T_a T_b V_r_2 V_ba_2))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.c_Predicate_ODomainP T_a T_b V_r_2 V_aa_2))) (forall ((V_a2_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_ORangeP T_a T_b V_r_2 V_a2_2) (exists ((B_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_a) V_a2_2))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) V_aa_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_aa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) V_aa_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_aa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_aa_2)))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member _let_1) V_xs_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olists T_a (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Wellfounded_Oacc _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member _let_1) V_xs_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Wellfounded_Oacc _let_1 (tptp.c_List_Olistrel1 T_a V_r_2)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_List_Olists T_a (tptp.c_Wellfounded_Oacc T_a V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) V_x_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_y) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (forall ((V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_R_2)))) (not (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) V_x_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_z) (tptp.c_Wellfounded_Oacc T_a V_R_2)))))))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Relation_OId__on T_a V_A_2))) (and (= V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_List_Olist T_a)) (tptp.c_List_Olist_ONil T_a)) (tptp.c_List_Olists T_a V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_A_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olists T_a V_A_2))) (let ((_let_2 (tptp.c_member (tptp.tc_List_Olist T_a)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2)) _let_1)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_xs_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ys_2) _let_1))))))) (forall ((V_A_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olists T_a V_A_2))) (let ((_let_2 (tptp.c_member (tptp.tc_List_Olist T_a)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2)) _let_1)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_xs_2) _let_1))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (= V_aa_2 V_ba_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (tptp.c_Relation_OId__on T_a V_A_2)))))) (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_List_Olist T_a)) V_aa_2) (tptp.c_List_Olists T_a V_A_2))) (or (= V_aa_2 (tptp.c_List_Olist_ONil T_a)) (exists ((B_a $$unsorted) (B_l $$unsorted)) (and (= V_aa_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_a) B_l)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_a) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_List_Olist T_a)) B_l) (tptp.c_List_Olists T_a V_A_2)))))))) (forall ((V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_ca_2) (tptp.c_Relation_OId__on T_a V_A_2))) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (not (= V_ca_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)))))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_member T_a)) V_A_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_List_Olist T_a)) V_x_2) (tptp.c_List_Olists T_a V_A_2))))) (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_ax_2) V_ay_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (forall ((B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP (tptp.hAPP _let_1 B_a) B_b)) (tptp.hAPP (tptp.hAPP _let_1 B_aa) B_ba))) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_aa) B_ba))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_bx_2) V_by_2)))))))) (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_bx_2) V_by_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted) (B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 B_aa) B_ba))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b)) _let_3)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_a) B_b))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_ax_2) V_ay_2)))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_HOL_Obool tptp.tc_HOL_Obool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) T_a) tptp.c_fconj) V_A_2)) V_B_2)) V_x_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_B_2) V_x_2))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistsp T_a V_A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_a1_2) V_a2_2))) (and (tptp.hBOOL (tptp.hAPP V_A_2 V_a1_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_a2_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olistsp T_a V_A_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) V_ys_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_xs_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_ys_2)))))) (forall ((V_r_2 $$unsorted) (V_zb_2 $$unsorted) (V_za_2 $$unsorted) (V_xb_2 $$unsorted) (V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_za_2) V_zb_2))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_1 V_xa_2) V_xb_2))) (let ((_let_4 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_4 _let_4)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_4 _let_4) _let_3) _let_2)) (tptp.c_Transitive__Closure_Ortrancl _let_4 V_r_2))) (=> (not (= _let_3 _let_2)) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xb_2)) _let_3)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_za_2) V_zb_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))))))))))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_l_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (let ((_let_3 (tptp.hAPP (tptp.c_member (tptp.tc_List_Olist T_a)) V_l_2))) (=> (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_List_Olists T_a V_A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_List_Olists T_a V_B_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.hAPP _let_2 V_A_2)) (tptp.hAPP _let_2 V_B_2))) V_l_2)))))))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_y_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_y_2) V_ys_2))) (tptp.c_List_Olistrel1 T_a V_r_2))) (=> (forall ((B_x $$unsorted)) (=> (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_x) V_ys_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) V_y_2)) V_r_2))))) (not (forall ((B_zs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_y_2) B_zs)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) B_zs) V_ys_2)) (tptp.c_List_Olistrel1 T_a V_r_2)))))))))))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (let ((_let_3 (tptp.c_Product__Type_OPair _let_2 _let_2))) (let ((_let_4 (tptp.tc_prod _let_2 _let_2))) (let ((_let_5 (tptp.tc_fun _let_2 _let_4))) (let ((_let_6 (tptp.tc_fun _let_2 _let_2))) (let ((_let_7 (tptp.tc_fun _let_4 _let_4))) (let ((_let_8 (tptp.tc_fun _let_2 _let_7))) (= (tptp.c_List_Opartition T_a V_Pa_2 (tptp.hAPP _let_1 V_xs_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case _let_2 _let_2 _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS _let_2 _let_5 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_5 _let_5) _let_2) (tptp.c_COMBS _let_2 _let_4 _let_4)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 _let_8 _let_2) (tptp.hAPP (tptp.c_COMBB _let_4 _let_7 _let_2) (tptp.c_If _let_4 (tptp.hAPP V_Pa_2 V_x_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_5 _let_2) _let_3) _let_1)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_2 _let_6 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_6 _let_5) _let_2) (tptp.c_COMBB _let_2 _let_4 _let_2)) _let_3)) _let_1))) (tptp.c_List_Opartition T_a V_Pa_2 V_xs_2)))))))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_z)) V_r_2)) (= B_y B_z))))) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_List_Olist T_a) tptp.tc_HOL_Obool)) (tptp.c_List_Olistsp T_a V_A_2)) (tptp.c_List_Olistsp T_a V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))))) (forall ((V_p_2 $$unsorted) (V_g_2 $$unsorted) (T_e $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_c T_a) V_f_2))) (let ((_let_2 (tptp.tc_prod T_b T_c))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_d T_e _let_2) V_g_2) V_p_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_d T_e T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_e _let_2) (tptp.tc_fun T_e T_a) T_d) (tptp.hAPP (tptp.c_COMBB _let_2 T_a T_e) _let_1)) V_g_2)) V_p_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_ca_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_q_2 $$unsorted) (V_p_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c) V_ca_2))) (=> (= V_p_2 V_q_2) (= (tptp.hAPP _let_1 V_p_2) (tptp.hAPP _let_1 V_q_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B_2)) V_C_2) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2)))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (let ((_let_3 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_A_2) V_A_2)) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_c T_a) V_f1_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_aa_2) V_ba_2))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_c T_a) V_f_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_f_2 V_aa_2) V_ba_2))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_Relation_Otrans T_a V_s_2) (tptp.c_Relation_Otrans T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2))))) (forall ((V_B_2 $$unsorted) (V_l_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) V_l_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_B_2) V_l_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2)) V_l_2))))) (forall ((V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.c_member T_a))) (let ((_let_4 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) _let_3))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R_2)) (tptp.hAPP _let_4 V_S_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) (tptp.hAPP (tptp.hAPP _let_2 V_R_2) V_S_2))))))))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) (tptp.tc_fun T_b T_c) T_a) (tptp.hAPP (tptp.c_COMBB _let_1 T_c T_b) V_f_2)) (tptp.c_Product__Type_OPair T_a T_b))) V_f_2))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c) (tptp.c_Product__Type_Ocurry T_a T_b T_c V_f_2)) V_f_2)) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_Ocurry T_a T_b T_c (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c) V_f_2)) V_f_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.hAPP (tptp.c_COMBC _let_1 _let_2 tptp.tc_HOL_Obool) (tptp.c_member _let_1)))) (let ((_let_4 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBC T_a _let_4 tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (tptp.c_List_Olistsp T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_4) (tptp.hAPP _let_5 V_A_2)) (tptp.hAPP _let_5 V_B_2))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2) (tptp.hAPP _let_3 (tptp.c_List_Olists T_a V_A_2))) (tptp.hAPP _let_3 (tptp.c_List_Olists T_a V_B_2)))))))))) (forall ((T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_Ointernal__split T_a T_b T_c) (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_c) (tptp.hAPP (tptp.hAPP V_f_2 V_aa_2) V_ba_2)) (tptp.c_Set_Oimage _let_1 T_c (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b T_c) V_f_2) V_A_2)))))) (forall ((V_aa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) V_aa_2)) (or (= V_aa_2 (tptp.c_List_Olist_ONil T_a)) (exists ((B_a $$unsorted) (B_l $$unsorted)) (and (= V_aa_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) B_a) B_l)) (tptp.hBOOL (tptp.hAPP V_A_2 B_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_List_Olistsp T_a V_A_2) B_l))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_f_2 V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b tptp.tc_HOL_Obool) V_f_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f1_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_f1_2 V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b tptp.tc_HOL_Obool) V_f1_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))))) (forall ((T_c $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_ca_2 $$unsorted) (V_z_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_z_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_ca_2 V_aa_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_c (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2))))))) (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_ba_2 $$unsorted)) (=> (= V_ba_2 (tptp.hAPP V_f_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_ba_2) (tptp.c_Set_Oimage T_b T_a V_f_2 V_A_2)))))) (forall ((V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_R_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool)) V_R_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_ca_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_R_2 V_aa_2) V_ba_2) V_ca_2)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b tptp.tc_HOL_Obool) V_f_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_f_2 V_aa_2) V_ba_2)))) (forall ((V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage T_b T_a V_f_2 (tptp.c_Set_Oimage T_c T_b V_g_2 V_A_2)) (tptp.c_Set_Oimage T_c T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_f_2) V_g_2) V_A_2))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_z_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_z_2) (tptp.c_Set_Oimage T_b T_a V_f_2 V_A_2))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (= V_z_2 (tptp.hAPP V_f_2 B_x)))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.c_Set_Oimage T_a T_b V_f_2 V_A_2))))) (forall ((T_b $$unsorted) (V_f_2 $$unsorted) (V_ba_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (=> (= V_ba_2 (tptp.hAPP V_f_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.c_Set_Oimage T_a T_b V_f_2 V_A_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun T_a _let_1))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Relation_OId__on T_a V_A_2) (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_a tptp.tc_HOL_Obool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_HOL_Obool _let_3) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun tptp.tc_HOL_Obool _let_3) T_a) (tptp.c_COMBC T_a tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool _let_1 T_a) tptp.c_fconj)) tptp.c_fequal))) V_A_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_4 (tptp.c_member _let_1))) (let ((_let_5 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.tc_fun T_b _let_5))) (let ((_let_7 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_8 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_7) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 (tptp.tc_fun _let_2 _let_7) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_6 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_b) _let_4)) _let_3))))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a _let_7)) (tptp.hAPP _let_8 V_R_2)) (tptp.hAPP _let_8 V_S_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_R_2) V_S_2))))))))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_x) V_x))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_a) V_a))) (forall ((V_Y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage T_a T_a (tptp.c_COMBI T_a) V_Y_2) V_Y_2)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) (tptp.c_List_Olist_ONil T_a)))) V_x)) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (let ((_let_2 (tptp.c_member (tptp.tc_fun T_a T_b)))) (=> (forall ((B_w $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_w) V_A_2)) (= (tptp.hAPP V_f_2 B_w) (tptp.hAPP V_g_2 B_w)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g_2) _let_1))))))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_xs)))) (let ((_let_2 (= V_xs (tptp.c_List_Olist_ONil T_a)))) (and (=> _let_2 (= _let_1 V_x)) (=> (not _let_2) (= _let_1 (tptp.c_List_Olast T_a V_xs))))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (=> (not (= V_xs (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_xs)) (tptp.c_List_Olast T_a V_xs)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (=> (= V_xs (tptp.c_List_Olist_ONil T_a)) (= (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_xs)) V_x))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) V_ys)))) (let ((_let_2 (= V_ys (tptp.c_List_Olist_ONil T_a)))) (and (=> _let_2 (= _let_1 (tptp.c_List_Olast T_a V_xs))) (=> (not _let_2) (= _let_1 (tptp.c_List_Olast T_a V_ys))))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (=> (not (= V_ys (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) V_ys)) (tptp.c_List_Olast T_a V_ys)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (=> (= V_ys (tptp.c_List_Olist_ONil T_a)) (= (tptp.c_List_Olast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) V_ys)) (tptp.c_List_Olast T_a V_xs)))) (forall ((V_ys_2 $$unsorted) (V_x_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) _let_1)) V_ys_2) (and (not (= V_ys_2 _let_1)) (= (tptp.c_List_Obutlast T_a V_ys_2) V_xs_2) (= (tptp.c_List_Olast T_a V_ys_2) V_x_2))))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (=> (not (= V_xs _let_1)) (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.c_List_Obutlast T_a V_xs)) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) (tptp.c_List_Olast T_a V_xs)) _let_1)) V_xs)))) (forall ((V_p_2 $$unsorted) (V_ca_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_z_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_c (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_ca_2) V_p_2))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (= V_p_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) B_x) B_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_z_2) (tptp.hAPP (tptp.hAPP V_ca_2 B_x) B_y))))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast T_a _let_1) _let_1))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x))) (let ((_let_2 (tptp.c_List_Obutlast T_a (tptp.hAPP _let_1 V_xs)))) (let ((_let_3 (tptp.c_List_Olist_ONil T_a))) (let ((_let_4 (= V_xs _let_3))) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= _let_2 (tptp.hAPP _let_1 (tptp.c_List_Obutlast T_a V_xs)))))))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs))) (let ((_let_2 (tptp.c_List_Obutlast T_a (tptp.hAPP _let_1 V_ys)))) (let ((_let_3 (= V_ys (tptp.c_List_Olist_ONil T_a)))) (and (=> _let_3 (= _let_2 (tptp.c_List_Obutlast T_a V_xs))) (=> (not _let_3) (= _let_2 (tptp.hAPP _let_1 (tptp.c_List_Obutlast T_a V_ys))))))))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (=> (not (= V_xs (tptp.c_List_Olist_ONil T_a))) (=> (tptp.c_List_Odistinct T_a V_xs) (tptp.c_List_Odistinct T_a (tptp.c_List_Obutlast T_a V_xs))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) (tptp.c_List_Olist_ONil T_a)))) V_xs)) (forall ((T_a $$unsorted) (V_xs_2 $$unsorted)) (=> (not (= V_xs_2 (tptp.c_List_Olist_ONil T_a))) (=> (tptp.c_List_Odistinct T_a V_xs_2) (= (tptp.c_List_OtakeWhile T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool tptp.tc_HOL_Obool T_a) tptp.c_fNot) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_HOL_Obool) tptp.c_fequal) (tptp.c_List_Olast T_a V_xs_2))) V_xs_2) (tptp.c_List_Obutlast T_a V_xs_2))))) (forall ((V_ca_2 $$unsorted) (V_z_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_p_2 $$unsorted)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (= V_p_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_c) V_z_2) (tptp.hAPP (tptp.hAPP V_ca_2 B_a) B_b))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_c) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_a T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool)) V_ca_2) V_p_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_List_Omeasures T_a (tptp.c_List_Olist_ONil (tptp.tc_fun T_a tptp.tc_Nat_Onat))))))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OtakeWhile T_a V_Pa_2 _let_1) _let_1))) (forall ((V_Pa_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_List_Odistinct T_a V_xs_2) (tptp.c_List_Odistinct T_a (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2))) (let ((_let_2 (tptp.c_List_OtakeWhile T_a V_Pa_2 (tptp.hAPP _let_1 V_xs_2)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)))) (and (=> _let_3 (= _let_2 (tptp.hAPP _let_1 (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)))) (=> (not _let_3) (= _let_2 (tptp.c_List_Olist_ONil T_a)))))))) (forall ((V_l_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2))) (= (tptp.c_List_OtakeWhile T_a V_Pa_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs_2) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_l_2))) (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)))) (forall ((V_ys_2 $$unsorted) (V_y_2 $$unsorted) (V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_y_2) V_ys_2))) (= (= (tptp.c_List_OdropWhile T_a V_Pa_2 V_xs_2) _let_1) (and (= V_xs_2 (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)) _let_1)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 V_y_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_z)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_x) B_z)) V_r_2)))))))) (tptp.c_Relation_Otrans T_a V_r_2))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Fun_Ooverride__on T_a T_b V_f_2 V_g_2 V_A_2 V_aa_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP V_g_2 V_aa_2))) (=> (not _let_2) (= _let_1 (tptp.hAPP V_f_2 V_aa_2))))))) (forall ((V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OdropWhile T_a V_Pa_2 _let_1) _let_1))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x_2) V_xs_2))) (let ((_let_2 (tptp.c_List_OdropWhile T_a V_Pa_2 _let_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)))) (and (=> _let_3 (= _let_2 (tptp.c_List_OdropWhile T_a V_Pa_2 V_xs_2))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((V_Pa_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_List_Odistinct T_a V_xs_2) (tptp.c_List_Odistinct T_a (tptp.c_List_OdropWhile T_a V_Pa_2 V_xs_2)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (= (tptp.c_Fun_Ooverride__on T_a T_b V_f_2 V_g_2 V_A_2 V_aa_2) (tptp.hAPP V_g_2 V_aa_2)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2))) (= (tptp.c_Fun_Ooverride__on T_a T_b V_f_2 V_g_2 V_A_2 V_aa_2) (tptp.hAPP V_f_2 V_aa_2)))) (forall ((V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)) (tptp.c_List_OdropWhile T_a V_Pa_2 V_xs_2)) V_xs_2)) (forall ((V_D_2 $$unsorted) (V_h_2 $$unsorted) (T_d $$unsorted) (V_C_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_b T_c)) V_g_2) (tptp.c_FuncSet_OPi T_b T_c V_B_2 (tptp.c_COMBK (tptp.tc_fun T_c tptp.tc_HOL_Obool) T_b V_C_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_c T_d)) V_h_2) (tptp.c_FuncSet_OPi T_c T_d V_C_2 (tptp.c_COMBK (tptp.tc_fun T_d tptp.tc_HOL_Obool) T_c V_D_2)))) (= (tptp.c_FuncSet_Ocompose T_a T_c T_d V_A_2 V_h_2 (tptp.c_FuncSet_Ocompose T_a T_b T_c V_A_2 V_g_2 V_f_2)) (tptp.c_FuncSet_Ocompose T_a T_b T_d V_A_2 (tptp.c_FuncSet_Ocompose T_b T_c T_d V_B_2 V_h_2 V_g_2) V_f_2)))))) (forall ((V_C_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_b T_c)) V_g_2) (tptp.c_FuncSet_OPi T_b T_c V_B_2 (tptp.c_COMBK _let_1 T_b V_C_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_c)) (tptp.c_FuncSet_Ocompose T_a T_b T_c V_A_2 V_g_2 V_f_2)) (tptp.c_FuncSet_OPi T_a T_c V_A_2 (tptp.c_COMBK _let_1 T_a V_C_2)))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod _let_1 _let_1) tptp.tc_HOL_Obool) (tptp.c_List_Olistrel T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= V_A_2 V_B_2))))) (forall ((V_ca_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_C_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (= (tptp.c_Set_Oimage T_b T_a V_f_2 V_A_2) V_B_2) (=> (= (tptp.c_Set_Oimage T_a T_c V_g_2 V_B_2) V_C_2) (= (tptp.c_Set_Oimage T_b T_c (tptp.c_FuncSet_Ocompose T_b T_a T_c V_A_2 V_g_2 V_f_2) V_A_2) V_C_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_List_Olist T_a) tptp.tc_HOL_Obool) (tptp.c_List_Olistsp T_a V_A_2) (tptp.c_List_Olistsp T_a V_B_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_S_2 _let_1) (= (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2) _let_1)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_r_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) _let_1))))) (forall ((V_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Wellfounded_Oacc T_a V_R2_2) (tptp.c_Wellfounded_Oacc T_a V_R1_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_x_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_FuncSet_OPi T_a T_b V_A_H_2 V_B_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod _let_1 _let_1) tptp.tc_HOL_Obool) (tptp.c_List_Olistrel T_a V_r_2) (tptp.c_List_Olistrel T_a V_s_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod _let_1 _let_1) tptp.tc_HOL_Obool) (tptp.c_List_Olistrel1 T_a V_r_2) (tptp.c_List_Olistrel1 T_a V_s_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_List_Olist T_a) tptp.tc_HOL_Obool) (tptp.c_List_Olists T_a V_A_2) (tptp.c_List_Olists T_a V_B_2)))) (forall ((V_f_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (= (tptp.hAPP (tptp.c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) V_x_2) (tptp.hAPP V_g_2 (tptp.hAPP V_f_2 V_x_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP _let_2 V_R_2) (tptp.hAPP _let_2 V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_R_2 V_S_2))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.c_Set_Oimage T_a T_b V_f_2 V_A_2) (tptp.c_Set_Oimage T_a T_b V_f_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oimage T_b T_a V_f_2 V_A_2)) (exists ((B_AA $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) B_AA V_A_2) (= V_B_2 (tptp.c_Set_Oimage T_b T_a V_f_2 B_AA)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_A_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2)))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_D_2))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> 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((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_y_2) V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2) V_x_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP 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(tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Relation_ODomain T_a T_b V_A_2)) (tptp.c_Relation_ODomain T_a T_b V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_ORange T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Relation_ORange T_b T_a V_A_2)) (tptp.c_Relation_ORange T_b T_a V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK _let_1 T_a V_B_2)))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oimage T_a T_b V_f_2 V_A_2) V_B_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod _let_1 _let_1) tptp.tc_HOL_Obool) (tptp.c_List_Olistrel1 T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 (tptp.c_List_Olistrel1 T_a V_r_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a _let_1) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Wellfounded_Oaccp T_a V_R2_2) (tptp.c_Wellfounded_Oaccp T_a V_R1_2))))) (forall ((V_x $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_Osize__class_Osize _let_1 V_xs) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys)) (not (= V_xs (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_ys)))))) (forall ((V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)) (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2)))) (forall ((V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.c_List_OdropWhile T_a V_Pa_2 V_xs_2)) (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))))) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a _let_5) (tptp.hAPP _let_6 V_R_2) (tptp.hAPP _let_6 V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2))))))))) (forall ((V_fs_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Omeasures T_a V_fs_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Omeasures T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons (tptp.tc_fun T_a tptp.tc_Nat_Onat)) V_f_2) V_fs_2)))))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_R_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.hAPP V_B_2 B_x) (tptp.hAPP V_C_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_C_2)))) (forall ((V_Q_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_x_2) V_y_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_Pa_2 V_Q_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_2 V_x_2) V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_Pa_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_2 V_x_2) V_y_2))))) (forall ((V_fs_2 $$unsorted) (V_f_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (let ((_let_2 (tptp.hAPP V_f_2 V_y_2))) (let ((_let_3 (tptp.hAPP V_f_2 V_x_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Omeasures T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons (tptp.tc_fun T_a tptp.tc_Nat_Onat)) V_f_2) V_fs_2)))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_3 _let_2) (and (= _let_3 _let_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Omeasures T_a V_fs_2)))))))))) (forall ((V_fs_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_List_Omeasures T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons (tptp.tc_fun T_a tptp.tc_Nat_Onat)) V_f_2) V_fs_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (= V_x_2 V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_y V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2))))) (forall ((V_f_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Wellfounded_Omeasure T_a V_f_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_f_2 V_g_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_f_2 V_g_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_g_2 V_f_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (or (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (= V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (= V_A_2 V_B_2)))))) (forall ((V_ca_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_ca_2))) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_n_2) V_m_2)))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (=> (=> (= V_m_2 V_n_2) _let_1) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) _let_1) _let_1))))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_r_2 $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) V_xs_2) V_ys_2)) (tptp.c_List_Olistrel T_a V_r_2))) (and (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys_2)) (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_n (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) (tptp.c_List_Onth T_a V_xs_2 B_n)) (tptp.c_List_Onth T_a V_ys_2 B_n))) V_r_2)))))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_r_2 (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))) (or (= V_aa_2 V_ba_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2))))))) (forall ((V_B_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_2))))) (forall ((T_a $$unsorted) (V_ys_2 $$unsorted) (V_xs_2 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (= V_xs_2 V_ys_2) (and (= (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2) (tptp.c_Nat_Osize__class_Osize _let_1 V_ys_2)) (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs_2)) (= (tptp.c_List_Onth T_a V_xs_2 B_i) (tptp.c_List_Onth T_a V_ys_2 B_i)))))))) (forall ((V_ys $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onth T_a (tptp.hAPP (tptp.hAPP (tptp.c_List_Oappend T_a) V_xs) (tptp.hAPP (tptp.hAPP (tptp.c_List_Olist_OCons T_a) V_x) V_ys)) (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs)) V_x)) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted) (V_xs_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs_2))) (=> (tptp.c_List_Odistinct T_a V_xs_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 _let_1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j_2 _let_1) (= (= (tptp.c_List_Onth T_a V_xs_2 V_i_2) (tptp.c_List_Onth T_a V_xs_2 V_j_2)) (= V_i_2 V_j_2))))))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odistinct T_a V_xs_2) (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs_2)) (forall ((B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) V_xs_2)) (=> (not (= B_i B_j)) (not (= (tptp.c_List_Onth T_a V_xs_2 B_i) (tptp.c_List_Onth T_a V_xs_2 B_j)))))))))) (forall ((V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_2 (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2)) (not (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_List_Onth T_a V_xs_2 _let_2)))))))) (forall ((V_xs_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted) (V_j_2 $$unsorted)) (let ((_let_1 (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j_2 (tptp.c_Nat_Osize__class_Osize (tptp.tc_List_Olist T_a) _let_1)) (= (tptp.c_List_Onth T_a _let_1 V_j_2) (tptp.c_List_Onth T_a V_xs_2 V_j_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_C_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_b V_C_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_C_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) (tptp.c_Product__Type_OSigma T_b T_a V_A_2 _let_1) (tptp.c_Product__Type_OSigma T_b T_a V_B_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olists T_a V_A_2))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod _let_2 _let_2) tptp.tc_HOL_Obool) (tptp.c_List_Olistrel T_a V_r_2) (tptp.c_Product__Type_OSigma _let_2 _let_2 _let_1 (tptp.c_COMBK (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) _let_2 _let_1))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Relation_OId__on T_a V_A_2) (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_C_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_b V_C_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_C_2)) (= (= (tptp.c_Product__Type_OSigma T_b T_a V_A_2 _let_1) (tptp.c_Product__Type_OSigma T_b T_a V_B_2 _let_1)) (= V_A_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_J_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_I_2) V_J_2) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_C_2)) (tptp.c_Product__Type_OSigma T_a T_b V_J_2 V_C_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_C_2))) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 _let_1)) (tptp.c_Product__Type_OSigma T_a T_b V_B_2 _let_1))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Product__Type_OSigma T_a T_b V_I_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1)) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_A_2)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.c_Set_Oimage (tptp.tc_prod T_b T_a) _let_1 (tptp.hAPP (tptp.c_Product__Type_Oprod_Oprod__case T_b T_a _let_1) (tptp.hAPP (tptp.c_COMBC T_a T_b _let_1) (tptp.c_Product__Type_OPair T_a T_b))) (tptp.c_Product__Type_OSigma T_b T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_b V_B_2))) (tptp.c_Product__Type_OSigma T_a T_b V_B_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_A_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2)))))) (forall ((V_xs_2 $$unsorted) (T_a $$unsorted) (V_Pa_2 $$unsorted) (V_j_2 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_j_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.c_List_Onth T_a V_xs_2 B_i))))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Nat_Osize__class_Osize _let_1 V_xs_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.c_List_OtakeWhile T_a V_Pa_2 V_xs_2))))))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__inf (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (tptp.class_Lattices_Osemilattice__inf tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Lattices_Olattice tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q) V_P)) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_Pa_2) V_Q_2) V_R_2) (tptp.hAPP V_Pa_2 (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_Pa_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_Pa_2 V_R_2) V_Q_2))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_Pa_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_Pa_2 V_R_2) (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2)))) (forall ((V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.c_fNot V_Pa_2))) (not (tptp.hBOOL V_Pa_2)))) (forall ((V_Pa_2 $$unsorted)) (or (not (not (tptp.hBOOL V_Pa_2))) (tptp.hBOOL (tptp.hAPP tptp.c_fNot V_Pa_2)))) (forall ((V_Q_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL V_Pa_2)) (not (tptp.hBOOL V_Q_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Q_2)))) (forall ((V_Q_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Q_2))) (tptp.hBOOL V_Pa_2))) (forall ((V_Q_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Q_2))) (tptp.hBOOL V_Q_2))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.64/1.22  )
% 0.64/1.22  % SZS output end Proof for SCT146+1
% 0.64/1.23  % cvc5---1.0.5 exiting
% 0.64/1.23  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------