%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 14:11:55 EDT 2023

% Result   : Unsatisfiable 1.88s 2.19s
% Output   : Proof 1.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19  % Command    : do_cvc5 %s %d
% 0.20/0.40  % Computer : n022.cluster.edu
% 0.20/0.40  % Model    : x86_64 x86_64
% 0.20/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.40  % Memory   : 8042.1875MB
% 0.20/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.40  % CPULimit   : 300
% 0.20/0.40  % WCLimit    : 300
% 0.20/0.40  % DateTime   : Thu Aug 24 15:11:25 EDT 2023
% 0.20/0.40  % CPUTime    : 
% 0.27/0.60  %----Proving TF0_NAR, FOF, or CNF
% 0.27/0.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qqUuWkoVTr/cvc5---1.0.5_17008.p...
% 0.27/0.74  ------- get file name : TPTP file name is SCT058-1
% 0.27/0.74  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17008.smt2...
% 0.27/0.74  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.88/2.19  % SZS status Unsatisfiable for SCT058-1
% 1.88/2.19  % SZS output start Proof for SCT058-1
% 1.88/2.20  (
% 1.88/2.20  (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.c_Relation_Oconverse tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.hAPP (tptp.c_Fun_Ocomp _let_3 tptp.v_P____ _let_2 _let_2 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.v_x))) (let ((_let_5 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_6 (tptp.hBOOL (tptp.c_in _let_5 _let_4 _let_1)))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_b____ tptp.v_c____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P_H____ tptp.v_x) _let_1)))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (or _let_8 _let_6))) (let ((_let_12 (not (= tptp.v_a____ tptp.v_b____)))) (let ((_let_13 (not (= tptp.v_b____ tptp.v_c____)))) (let ((_let_14 (not (= tptp.v_a____ tptp.v_c____)))) (let ((_let_15 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2))) (let ((_let_16 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))))) (let ((_let_17 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r)) V_r)))) (let ((_let_18 (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_b____ tptp.v_c____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P_H____ V_i) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P____ V_i) _let_1)))))))) (let ((_let_19 (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P____ V_i) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_b____ tptp.v_c____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P_H____ V_i) _let_1)))))))) (let ((_let_20 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) (tptp.tc_prod T_a T_b)))))))) (let ((_let_21 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))))))) (let ((_let_22 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_23 (tptp.c_Orderings_Obot__class_Obot _let_22))) (let ((_let_24 (tptp.hAPP tptp.v_P____ tptp.v_x))) (let ((_let_25 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_26 (tptp.hBOOL (tptp.c_in _let_25 _let_24 _let_1)))) (let ((_let_27 (or _let_26 _let_9))) (let ((_let_28 (_let_19))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (not _let_27))) (let ((_let_31 (tptp.hAPP _let_3 _let_24))) (let ((_let_32 (= _let_24 (tptp.hAPP _let_3 _let_31)))) (let ((_let_33 (= _let_4 _let_31))) (let ((_let_34 (tptp.hAPP _let_3 _let_4))) (let ((_let_35 (tptp.hBOOL (tptp.c_in _let_25 _let_34 _let_1)))) (let ((_let_36 (not _let_26))) (let ((_let_37 (forall ((T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= V_r (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt _let_24 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r)))) :args (_let_37))) _let_38 :args (_let_32 false _let_37)))) (let ((_let_40 (_let_16))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_3 tptp.v_P____ tptp.v_x _let_2 _let_2 tptp.tc_Arrow__Order__Mirabelle_Oindi QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v)))) :args _let_40))) _let_41 :args (_let_33 false _let_16)))) (let ((_let_43 (not _let_35))) (let ((_let_44 (tptp.hBOOL (tptp.c_in _let_5 (tptp.hAPP _let_3 _let_34) _let_1)))) (let ((_let_45 (or _let_44 _let_43))) (let ((_let_46 (_let_21))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 (not _let_44))) (let ((_let_49 (or _let_8 _let_36))) (let ((_let_50 (tptp.hBOOL (tptp.c_in _let_5 _let_31 _let_1)))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_26 _let_51))) (let ((_let_53 (_let_18))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (_let_20))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (and _let_6 _let_33))) (let ((_let_58 (_let_6 _let_33))) (let ((_let_59 (ASSUME :args (_let_6)))) (let ((_let_60 (APPLY_UF tptp.hBOOL))) (let ((_let_61 (APPLY_UF tptp.c_in))) (let ((_let_62 (REFL :args (_let_1)))) (let ((_let_63 (ASSUME :args (_let_33)))) (let ((_let_64 (SYMM _let_63))) (let ((_let_65 (REFL :args (_let_5)))) (let ((_let_66 (CONG _let_65 _let_64 _let_62 :args _let_61))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_59 _let_63) (SCOPE (TRUE_ELIM (TRANS (CONG _let_66 :args _let_60) (TRUE_INTRO _let_59))) :args _let_58)) :args _let_58)) :args (true _let_57)) _let_42 (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_26 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt _let_24 QUANTIFIERS_INST_E_MATCHING ((tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))))) :args _let_55)) _let_56 :args (_let_52 false _let_20)) (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_8 _let_36 (not _let_49)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.v_x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P_H____ V_i)))) :args _let_53)) _let_54 :args (_let_49 false _let_18)) (ASSUME :args (_let_11)) :args (_let_8 false _let_33 true _let_50 false _let_52 true _let_26 false _let_49 false _let_6)))) (let ((_let_68 (not _let_32))) (let ((_let_69 (not _let_33))) (let ((_let_70 (or))) (let ((_let_71 (REFL :args (_let_68)))) (let ((_let_72 (REFL :args (_let_69)))) (let ((_let_73 (and _let_7 _let_33 _let_32))) (let ((_let_74 (_let_7 _let_33 _let_32))) (let ((_let_75 (ASSUME :args (_let_7)))) (let ((_let_76 (APPLY_UF tptp.hAPP))) (let ((_let_77 (ASSUME :args (_let_32)))) (let ((_let_78 (SYMM (SYMM _let_77)))) (let ((_let_79 (REFL :args (_let_3)))) (let ((_let_80 (and _let_33 _let_43 _let_32))) (let ((_let_81 (ASSUME :args (_let_43)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (tptp.v_x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P____ V_i)))) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_9 _let_26 _let_30))) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_63 _let_77) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (_let_25)) (TRANS _let_78 (CONG _let_79 _let_64 :args _let_76)) _let_62 :args _let_61) :args _let_60) (FALSE_INTRO _let_81))) :args (_let_43 _let_33 _let_32))) :args (_let_33 _let_43 _let_32))) :args (true _let_80)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_35))) _let_71 (REFL :args (_let_36)) :args _let_70)) :args ((or _let_35 _let_36 _let_69 _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_43 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_63 _let_77) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG _let_65 (CONG _let_79 (TRANS (CONG _let_79 _let_63 :args _let_76) (SYMM _let_78)) :args _let_76) _let_62 :args _let_61) _let_66) :args _let_60) (FALSE_INTRO _let_75))) :args _let_74)) :args _let_74)) :args (true _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) _let_72 _let_71 (REFL :args (_let_48)) :args _let_70)) :args ((or _let_6 _let_69 _let_48 _let_68))) (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_10)) _let_67 :args (_let_7 false _let_8)) _let_42 _let_39 :args (_let_48 true _let_6 false _let_33 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt _let_34 QUANTIFIERS_INST_E_MATCHING ((tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))))) :args _let_46)) _let_47 :args (_let_45 false _let_21)) :args (_let_43 true _let_44 false _let_45)) _let_42 _let_39 :args (_let_36 true _let_35 false _let_33 false _let_32)) :args (_let_30 false _let_8 true _let_26)) _let_29 :args (false true _let_27 false _let_19)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((V_P $$unsorted) (V_Rb $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Rb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_A T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_S V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r_H $$unsorted) (V_s_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r_H V_s_H T_a T_b T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s_H V_s (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.c_Relation_ODomain V_B T_a T_b) _let_1) (tptp.c_Relation_ODomain (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) T_a T_b) _let_1))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ORange V_A T_b T_a) (tptp.c_Relation_ORange V_B T_b T_a) _let_1) (tptp.c_Relation_ORange (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_1) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a) _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Osym V_s T_a)) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Transitive__Closure_Ortrancl V_s T_a) _let_1) (not (tptp.c_lessequals V_r V_s _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) _let_1))) (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))) (tptp.c_lessequals V_C V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_I $$unsorted) (V_J $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.c_HOL_Ominus__class_Ominus V_I V_J (tptp.tc_fun T_a tptp.tc_bool)) V_C T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a) (not (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_R V_S T_a T_a T_a) V_R _let_1)) (not (tptp.c_Wellfounded_Owf V_S T_a)) (not (tptp.c_Wellfounded_Owf V_R T_a))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Orefl__on (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Orefl__on V_B V_s T_a)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_B _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) T_a))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((V_P $$unsorted) (V_xb $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_s T_a))) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_2 _let_1) (not (tptp.c_lessequals V_r _let_2 _let_1)))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((V_S $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (or (= (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_2) (not (tptp.c_lessequals V_S _let_2 _let_1)) (not (tptp.c_lessequals V_R V_S _let_1)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Relation_OField (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) T_a) (tptp.c_Relation_OField V_r T_a) _let_1)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_I $$unsorted) (V_J $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.c_Lattices_Oupper__semilattice__class_Osup V_I V_J (tptp.tc_fun T_a tptp.tc_bool)) V_C T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((V_S $$unsorted) (V_T $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S V_T (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) V_R T_a T_c T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_S V_R T_a T_c T_b) (tptp.c_Relation_Orel__comp V_T V_R T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (V_T $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S V_T (tptp.tc_fun (tptp.tc_prod T_c T_b) tptp.tc_bool)) T_a T_c T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_S T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R V_T T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OField V_r T_a) (tptp.c_Relation_OField V_s T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (= (tptp.c_Relation_OField tptp.v_r tptp.t_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain tptp.v_r tptp.t_a tptp.t_a) (tptp.c_Relation_ORange tptp.v_r tptp.t_a tptp.t_a) _let_22)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.c_Relation_ODomain V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((V_R2 $$unsorted) (T_a $$unsorted) (V_R1 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Wellfounded_Oacc V_R2 T_a) (tptp.c_Wellfounded_Oacc V_R1 T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_R1 V_R2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_1) T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a)) (tptp.hBOOL (tptp.c_in V_x V_B T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b))) (or (not (= (tptp.hAPP V_f _let_1) (tptp.hAPP V_g _let_1))) (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Ocomp V_f V_g T_c T_a T_b) V_r T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_r T_b T_c) T_c T_a))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_b T_a))) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool))) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_r) (tptp.hAPP _let_1 V_s) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_OField (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (tptp.c_Relation_OField V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a) _let_2 _let_1)) (= V_x V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) _let_2 _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_OField V_r T_a) (tptp.c_Relation_OField V_s T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ORange V_A T_b T_a) (tptp.c_Relation_ORange V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField V_r T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain V_r T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_p $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf V_p T_a) (not (tptp.c_lessequals V_p V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym V_s T_a)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Oacyclic V_s T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Osingle__valued V_r T_a T_b) (not (tptp.c_Relation_Osingle__valued V_s T_a T_b)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_ODomain V_r T_a T_b) (tptp.c_Relation_ODomain V_s T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r_H $$unsorted) (V_A_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_OImage V_r_H V_A_H T_a T_b) (tptp.c_Relation_OImage V_r V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A_H V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Oirrefl V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.c_Wellfounded_Oacyclic V_r T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 V_P V_b V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a) T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 V_P V_a V_r T_a) T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_Q $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_Q $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun _let_1 tptp.tc_bool)) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S (tptp.tc_fun _let_1 tptp.tc_bool)) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_S T_a) _let_1)))))) (forall ((V_p $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_s T_a) _let_1)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun _let_1 tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_R T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) _let_1 T_a))) (tptp.hBOOL (tptp.c_in V_x _let_1 T_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_x _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) _let_1 T_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a) _let_1) V_S _let_1) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a))))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (or (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a) _let_1) V_S _let_1) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_ODomain V_r T_a T_a) (tptp.c_Relation_ORange V_s T_a T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (not (tptp.c_Wellfounded_Owf V_s T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)) (tptp.c_Wellfounded_Owf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (= _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) _let_1))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Relation_OId__on V_A T_a) V_B T_a T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 V_r V_x V_z T_a) T_a T_a) V_r _let_1)) (= V_x V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 V_P V_b V_r T_a) V_b T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a) T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 V_P V_a V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xrtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a) _let_2 _let_1)) (= V_a2 V_a1) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) _let_2 _let_1))))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_b)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 V_P V_a V_r T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xrtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a) V_r _let_1)) (= V_a2 V_a1) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) (tptp.c_Transitive__Closure_Ortrancl V_r tptp.t_a) _let_1)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 V_P V_b V_r T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P V_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) T_a T_a) _let_2 _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_P $$unsorted) (V_Ra $$unsorted) (V_y $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Ra)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r _let_1))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_2 _let_2 T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (let ((_let_3 (tptp.c_Pair V_x V_z T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) T_a T_a) V_R _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a))) (let ((_let_3 (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (let ((_let_3 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in _let_3 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 _let_1)))))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) V_y T_a T_a) V_R _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_z T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.t_a tptp.t_a))) (let ((_let_2 (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a) _let_1))))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) V_c T_c T_b) V_s (tptp.tc_prod T_c T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) T_a T_c) V_r (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a))) (or (= V_p (tptp.c_Pair _let_1 _let_1 T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)) T_a T_b) (tptp.c_Set_Oinsert V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.c_Relation_OImage V_R V_A T_a T_a) _let_1)) (not (tptp.c_Wellfounded_Owf V_R T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)) T_b T_a) (tptp.c_Set_Oinsert V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a))) (or (= V_c (tptp.c_Pair _let_1 _let_1 T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OId T_a) (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (= (tptp.c_Relation_ORange tptp.v_r tptp.t_a tptp.t_b) (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Relation_Oconverse tptp.t_a tptp.t_b) tptp.v_r) tptp.t_b tptp.t_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a))) (or (tptp.c_Relation_Oirrefl V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_1 _let_1 T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_R $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Relation_OImage V_R (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_R V_A T_b T_a) (tptp.c_Relation_OImage V_R V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Relation_Osingle__valued (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_R) T_a T_b)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a))) (or (tptp.c_Nitpick_Orefl_H V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair _let_1 _let_1 T_a T_a) V_r (tptp.tc_prod T_a T_a))))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)) (not (tptp.c_Relation_Oirrefl V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.hAPP V_f V_a) V_b) (tptp.c_Set_Oimage (tptp.c_split V_f T_a T_b T_c) V_A _let_1 T_c) T_c)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_A _let_1)))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomainE__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) V_x T_a T_a) V_R (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_R T_a) T_a)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya _let_1 tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x _let_1 tptp.t_a)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r tptp.t_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya _let_1 tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x _let_1 tptp.t_a)))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.c_Wellfounded_Owf (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.c_Wellfounded_Owf V_r T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRangeE__1__1 V_b V_r T_a T_b) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Equiv__Relations_Oquotient (tptp.c_Set_Oinsert V_x _let_1 T_a) V_r T_a) (tptp.c_Equiv__Relations_Oquotient (tptp.c_Set_Oinsert V_y _let_1 T_a) V_r T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Equiv__Relations_Oquotient (tptp.c_Set_Oinsert V_x _let_1 T_a) V_r T_a) (tptp.c_Equiv__Relations_Oquotient (tptp.c_Set_Oinsert V_y _let_1 T_a) V_r T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (tptp.c_lessequals (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_2 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_2 T_a) T_a T_a) _let_1) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Relation_OField V_r T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_2 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_2 T_a) T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a))) (not (tptp.c_Relation_Oantisym V_r T_a)) (not (tptp.c_Relation_Orefl__on _let_1 V_r T_a)) (= V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_lessequals (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_2 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_2 T_a) T_a T_a) _let_1)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_2 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_2 T_a) T_a T_a) _let_1) T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_b T_a) T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y _let_1 T_a) T_a T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y _let_1 T_a) T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y _let_1 T_a) T_a T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))) (forall ((V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_y _let_1 T_a) T_a T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_a _let_1 T_a) T_a T_a) (tptp.c_Relation_OImage V_r (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a))))) (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Relation_Osym (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Relation_Osym (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Relation_Orefl__on V_A (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r)) (tptp.c_Relation_Osym V_r T_a))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a)) (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Relation_Oconverse T_c T_a) V_s) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_c) V_r) T_a T_c T_b))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId T_a))) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) _let_1) _let_1))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) (tptp.c_Relation_Oinv__image V_R V_f T_b T_a)) (tptp.c_Relation_Oinv__image (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_b) V_R) V_f T_b T_a))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (= (tptp.c_Transitive__Closure_Otrancl (tptp.hAPP _let_1 V_r) T_a) (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl V_r T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId__on V_A T_a))) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) _let_1) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP _let_1 V_r) T_a) (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_p V_r _let_1)))))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in V_p V_r _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1))) (= V_x V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_R T_a) _let_1))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_z V_y T_a T_a) _let_2 _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) _let_2 _let_1))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_b T_c T_a) (tptp.c_Pair V_a V_b T_b T_c)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_a T_b T_c) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))) (forall ((V_R $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_R V_a) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_split V_R T_a T_b (tptp.tc_fun T_c tptp.tc_bool)) (tptp.c_Pair V_a V_b T_a T_b)) V_c))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId__on V_A T_a) T_a T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) V_r) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ODomain V_r T_a T_a))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a))))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((T_a $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_OId T_a) V_R T_a T_a T_b) V_R)) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_OId T_b) T_a T_b T_b) V_R)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (or (tptp.c_Wellfounded_Owf (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl V_r T_a)) T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP _let_1 V_r) T_a))))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf V_R T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_R T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Relation_OId T_a) V_A T_a T_a) V_A)) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId T_a) T_a T_a)) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= (tptp.c_Relation_Orel__comp V_r _let_1 T_a T_a T_a) (tptp.c_Relation_Orel__comp _let_1 V_r T_a T_a T_a)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Osym V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Transitive__Closure_Otrancl _let_1 T_a) _let_1))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Orel__comp V_R V_S T_a T_d T_c) V_T T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_Orel__comp V_S V_T T_d T_c T_b) T_a T_d T_b))) (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Otrans V_r T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r T_a T_a T_a) V_r)) (tptp.c_Equiv__Relations_Oequiv (tptp.c_Relation_ODomain V_r T_a T_a) V_r T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId T_a) T_a)) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r) T_b T_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) T_a T_c) (not (tptp.c_Relation_Osingle__valued V_s T_b T_c)) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId T_a) T_a)) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) V_r T_a T_a T_a) V_r) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Relation_Orel__comp _let_1 _let_1 T_a T_a T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a)) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_r2 $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted)) (or (tptp.c_Equiv__Relations_Ocongruent V_r2 (tptp.hAPP V_f V_a) T_b T_c) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r1 T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) T_a T_b) (tptp.c_Relation_ORange V_r T_b T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange V_r T_b T_a) (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) T_a T_b))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Otrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= (tptp.c_Transitive__Closure_Ortrancl _let_1 T_a) _let_1))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 V_a V_r T_a T_b) V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a))))) (forall ((V_r $$unsorted) (V_yx $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XconverseE__1__1 V_r V_yx T_b T_a) (tptp.c_ATP__Linkup_Osko__Relation__XconverseE__1__2 V_r V_yx T_b T_a) T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_yx (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) (tptp.tc_prod T_a T_b)))))) (forall ((V_yx $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= V_yx (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XconverseE__1__2 V_r V_yx T_b T_a) (tptp.c_ATP__Linkup_Osko__Relation__XconverseE__1__1 V_r V_yx T_b T_a) T_a T_b)) (not (tptp.hBOOL (tptp.c_in V_yx (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r) (tptp.tc_prod T_a T_b)))))) (forall ((V_z $$unsorted) (V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.c_split V_c T_b T_c (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Pair V_a V_b T_b T_c)) T_a)) (not (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.hAPP V_c V_a) V_b) T_a))))) (forall ((V_f $$unsorted) (V_y1 $$unsorted) (V_y2 $$unsorted) (V_z1 $$unsorted) (V_z2 $$unsorted) (T_b $$unsorted) (V_r2 $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted) (T_c $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_f V_y1) V_y2) (tptp.hAPP (tptp.hAPP V_f V_z1) V_z2)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y2 V_z2 T_b T_b) V_r2 (tptp.tc_prod T_b T_b)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y1 V_z1 T_a T_a) V_r1 (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (or (= V_y V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_b) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_r _let_1))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b))))) (forall ((V_f $$unsorted) (V_R $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_R V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_R (tptp.tc_prod T_a T_a)))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_r V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b))) (not (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Otrans V_r T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Otrans V_r T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_r _let_1))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_a) V_r _let_1))) (not (tptp.c_Wellfounded_Owf V_r T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Oantisym V_r T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Oantisym V_r T_a))))) (forall ((V_f $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_y) (tptp.hAPP V_f V_z)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent V_r V_f T_a T_b)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))) (= (tptp.hAPP V_f V_y) (tptp.hAPP V_g V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.c_Nitpick_Orefl_H V_r T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Osym V_r T_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r _let_1))) (not (tptp.c_Relation_Osym V_r T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_b T_c) V_s (tptp.tc_prod T_b T_c)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_R _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_R _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) _let_2 _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))) (= (tptp.hAPP _let_23 tptp.v_x) (tptp.c_in tptp.v_x _let_23 tptp.t_a)) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp (tptp.c_COMBK V_c T_b T_c) V_f T_c T_b tptp.t_a) tptp.v_x) V_c)) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_y) (= V_x V_z))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_y V_z) (= V_x V_z))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1)) (= V_y V_z) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (or (= V_x V_y) (= V_y V_x) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_y) (= V_y V_z))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1))) (= V_x V_z) (= V_y V_z))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (let ((_let_1 (= V_xa V_x))) (or _let_1 _let_1 (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in _let_2 V_L _let_1)) (= V_x V_z) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 V_a V_b) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= V_a V_b))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_b _let_1 T_a)))))) (forall ((V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (or (tptp.hBOOL (tptp.c_in V_y _let_1 T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a _let_1 T_a)))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) (forall ((V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x T_a T_a) V_r _let_1)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_xa T_a T_a) V_r _let_1)) (= V_x V_xa) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Relation_Oconverse T_a T_a))) (let ((_let_3 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Transitive__Closure_Otrancl (tptp.hAPP _let_2 V_r) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a)) _let_1)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Relation_Oconverse T_a T_a))) (let ((_let_3 (tptp.c_Pair V_x V_y T_a T_a))) (or (tptp.hBOOL (tptp.c_in _let_3 (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a)) _let_1)) (not (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Transitive__Closure_Otrancl (tptp.hAPP _let_2 V_r) T_a) _let_1)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) _let_1)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r) T_a) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))))) _let_12 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_b V_b_H))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_a V_a_H))) _let_21 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r) (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))) _let_20 (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_c T_b tptp.t_a) tptp.v_x) (tptp.hAPP V_f (tptp.hAPP V_g tptp.v_x)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) _let_19 _let_18 _let_13 _let_17 _let_16 (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) _let_14 (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P____ V_i) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_b____ tptp.v_c____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P_H____ V_i) _let_1)))))) (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_b____ tptp.v_c____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P_H____ V_i) _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P____ V_i) _let_1)))))) (tptp.hBOOL (tptp.c_in tptp.v_P_H____ tptp.c_Arrow__Order__Mirabelle_OProf _let_15)) (tptp.hBOOL (tptp.c_in tptp.v_P____ tptp.c_Arrow__Order__Mirabelle_OProf _let_15)) _let_14 _let_13 _let_12 _let_11 _let_10 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.88/2.20  )
% 1.88/2.21  % SZS output end Proof for SCT058-1
% 1.88/2.21  % cvc5---1.0.5 exiting
% 1.88/2.22  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------