TSTP Solution File: SWV834-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV834-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 21:53:28 EDT 2023
% Result : Unsatisfiable 4.58s 4.79s
% Output : Proof 4.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : SWV834-1 : TPTP v8.1.2. Released v4.1.0.
% 0.17/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n001.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Tue Aug 29 06:18:06 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.23/0.59 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.uDfrB3BGkR/cvc5---1.0.5_23333.p...
% 0.23/0.74 ------- get file name : TPTP file name is SWV834-1
% 0.23/0.74 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23333.smt2...
% 0.23/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.58/4.79 % SZS status Unsatisfiable for SWV834-1
% 4.58/4.79 % SZS output start Proof for SWV834-1
% 4.62/4.81 (
% 4.62/4.81 (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_5 (tptp.tc_fun tptp.tc_Com_Ostate _let_4))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_5 (tptp.tc_fun _let_3 _let_3) tptp.t_a) (tptp.c_COMBS tptp.tc_Com_Ostate tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_5 tptp.t_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_4 tptp.tc_Com_Ostate) tptp.c_and)) tptp.v_P)) tptp.t_a _let_3 _let_3) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool tptp.tc_Com_Ostate) tptp.c_Not) tptp.v_b)))) (let ((_let_7 (tptp.c_COMBK tptp.c_False tptp.tc_bool tptp.tc_Com_Ostate))) (let ((_let_8 (tptp.c_COMBK _let_7 _let_3 tptp.t_a))) (let ((_let_9 (tptp.c_Set_Oinsert _let_1))) (let ((_let_10 (tptp.c_Hoare__Mirabelle_Ohoare__derivs tptp.v_G (tptp.hAPP (tptp.hAPP _let_9 (tptp.c_Hoare__Mirabelle_Otriple_Otriple _let_8 tptp.v_c _let_6 tptp.t_a)) _let_2) tptp.t_a))) (let ((_let_11 (not _let_10))) (let ((_let_12 (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)))) (let ((_let_13 (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)))))) (let ((_let_14 (forall ((T_a $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect (tptp.c_COMBK tptp.c_False tptp.tc_bool T_a) T_a))))) (let ((_let_15 (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))))))) (let ((_let_16 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_17 (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.c_Collect V_P T_a) V_P)))) (let ((_let_18 (tptp.c_Collect _let_7 tptp.tc_Com_Ostate))) (let ((_let_19 (tptp.c_Orderings_Obot__class_Obot _let_3))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 tptp.v_G _let_8 _let_6 tptp.v_c))) (let ((_let_22 (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 tptp.v_G _let_8 _let_6 tptp.v_c))) (let ((_let_23 (tptp.hAPP _let_8 _let_22))) (let ((_let_24 (tptp.hBOOL (tptp.hAPP _let_23 _let_21)))) (let ((_let_25 (= _let_7 _let_18))) (let ((_let_26 (= _let_7 _let_23))) (let ((_let_27 (tptp.hBOOL (tptp.hAPP _let_19 _let_21)))) (let ((_let_28 (_let_14))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (or _let_10 _let_24))) (let ((_let_31 (_let_15))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (forall ((V_P $$unsorted) (T_a $$unsorted)) (= V_P (tptp.c_Collect V_P T_a))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= V_P (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (not _let_27))) (let ((_let_38 (_let_13))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (ASSUME :args (_let_37)))) (let ((_let_41 (ASSUME :args (_let_20)))) (let ((_let_42 (ASSUME :args (_let_25)))) (let ((_let_43 (ASSUME :args (_let_26)))) (let ((_let_44 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_40 _let_41 _let_42 _let_43 _let_44) :args (_let_24 _let_20 _let_25 _let_26 _let_37)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_44)) (CONG (CONG (TRANS (SYMM _let_43) (SYMM (SYMM _let_42)) (SYMM _let_41)) (REFL :args (_let_21)) :args (APPLY_UF tptp.hAPP)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_40))) :args (_let_37 _let_20 _let_25 _let_26 _let_24)) :args ((not (and _let_24 _let_20 _let_25 _let_26 _let_37)) SB_LITERAL))) (CONG (REFL :args ((not _let_24))) (REFL :args ((not _let_20))) (REFL :args ((not _let_25))) (REFL :args ((not _let_26))) (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_27))) :args (or))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.tc_Com_Ostate _let_21 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) :args _let_38)) _let_39 :args (_let_37 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_7 _let_3 tptp.t_a _let_22 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q)))) :args (_let_35))) _let_36 :args (_let_26 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_7 tptp.tc_Com_Ostate QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Collect V_P T_a)))) :args (_let_33))) _let_34 :args (_let_25 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_10 _let_24 (not _let_30)))) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.v_G _let_8 tptp.v_c _let_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_9 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) true))))) :args _let_31)) _let_32 :args (_let_30 false _let_15)) :args (_let_24 true _let_10 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (tptp.tc_Com_Ostate QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tc_fun T_a tptp.tc_bool)))) :args _let_28)) _let_29 :args (_let_20 false _let_14)) :args (false true _let_27 false _let_26 false _let_25 false _let_24 false _let_20)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (tptp.c_Fun_Oinj__on V_f (tptp.hAPP _let_2 V_A) T_a T_b) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (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))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((V_g $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_c) T_c T_b) (not (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ocomp V_g V_f T_c T_b T_a) V_A T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_A)))) (forall ((V_pname_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not) V_P) T_a) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool tptp.tc_bool T_a) tptp.c_Not) V_P) T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a)) V_B))))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) V_B) (tptp.c_Set_Oimage V_f V_A T_a T_b)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_lessequals _let_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)))) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_1 V_B))))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_B)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_A) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_B)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 V_f V_A T_a) (tptp.c_The (tptp.c_Finite__Set_Ofold1Set V_f V_A T_a) T_a))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_M V_i)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))) (forall ((T_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP V_B V_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a _let_1))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_c T_b) V_f) V_g) _let_1 T_b T_c) T_c) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_g _let_1 T_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_xa)) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A T_a)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_OInf__class_OInf T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) (tptp.hAPP _let_1 V_A)))))) _let_17 (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_OSup__class_OSup T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) _let_2) _let_2)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP V_B V_x) T_b) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$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_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP _let_1 V_A)) (tptp.hAPP V_f V_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP _let_1 V_A)) (tptp.hAPP V_f V_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)) (= V_A V_B))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted) (V_i $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_B))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP V_A V_i))) (not (tptp.hBOOL (tptp.c_in V_i V_I T_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_b _let_1)))))))) (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.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP V_A V_x)) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_I T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_b _let_1)) V_B))))))) (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_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) V_a)) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_a _let_1))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_A V_k)) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_fun V_fun_H))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_C) V_A)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_I $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_a (tptp.tc_fun T_b tptp.tc_bool)) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP V_A V_x) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_I T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_c T_b) V_B T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_c) V_B) V_f) T_c _let_1)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_c V_d T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1)) V_B) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP _let_1 V_A)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c T_a T_b) V_f) V_g) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) _let_1) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b)) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b)) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a T_b))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x))) (= V_xa V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (= V_x_H V_y_H)))) (forall ((T_a $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Olinorder__class_OMax V_M T_a)) (tptp.c_Finite__Set_Olinorder__class_OMax V_N T_a))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a))) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_b) _let_1) V_f)) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (let ((_let_3 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (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.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) 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.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (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_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f 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_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (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 ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_y) V_z)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (forall ((V_a $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Collect V_P T_a) T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) 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 $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) 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_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) (tptp.hAPP V_f V_x)) _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B)))) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) 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 ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) V_A) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) (tptp.hAPP _let_2 V_B))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun tptp.t_a T_b)) V_A) V_B) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP V_A tptp.v_x)) (tptp.hAPP V_B tptp.v_x))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a)) V_B))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_pname $$unsorted) (V_pname_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OBODY V_pname_H))) (= V_pname V_pname_H))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_b) V_f))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_b) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ocomp V_g V_f T_b T_c T_a) V_A T_a T_c) (not (tptp.c_Fun_Oinj__on V_g (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_c)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_A $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c _let_1 T_b) V_B) V_f) T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oimage V_f V_A T_b T_c) V_B T_c _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2) V_A) V_B) _let_3)) (= V_B _let_3) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_3) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= (tptp.c_Finite__Set_Ofold1 _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2) V_A) V_B) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Ofold1 _let_1 V_A T_a)) (tptp.c_Finite__Set_Ofold1 _let_1 V_B T_a)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_a T_b)) (tptp.hAPP V_M V_i))) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a _let_1)) (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_C))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) V_C) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_D) V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)) (tptp.hAPP _let_3 V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_l T_a)) (not (tptp.hBOOL (tptp.c_List_Olistsp V_B V_l T_a))) (not (tptp.hBOOL (tptp.c_List_Olistsp V_A V_l T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_Finite__Set_Ofold1 _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_Finite__Set_Ofold1 _let_1 V_A T_a))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((V_A $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c _let_1 T_b) V_B) V_f) T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_b T_c) V_B T_c _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_A V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_B) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) V_B)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) V_B))))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (= (tptp.hAPP _let_16 tptp.v_x) (tptp.c_in tptp.v_x _let_16 tptp.t_a)) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Olinorder__class_OMin V_N T_a)) (tptp.c_Finite__Set_Olinorder__class_OMin V_M T_a))) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_M) V_N)))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A) V_B T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP V_B V_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Ofold1 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_A T_a)) V_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) V_A)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_y)) V_x)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_A)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B)) V_B)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals _let_1) V_C))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) (tptp.c_Orderings_Otop__class_Otop _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a))))) (forall ((T_a $$unsorted) (V_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))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_Finite__Set_Ofold1 _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) T_a) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Finite__Set_Ofold1 _let_3 V_A T_a)) (tptp.c_Finite__Set_Ofold1 _let_3 V_B T_a))) (= V_B _let_2) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (= V_A _let_2) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a))) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B) V_C)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_A)) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A))))))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP _let_1 V_B))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2))) T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP _let_1 V_A) T_a T_b)))))) (forall ((V_pname_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) V_B) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x))))) (forall ((T_c $$unsorted) (T_b $$unsorted) (V_h $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_c)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_c) V_h) (tptp.c_Set_Oimage V_f V_B T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_a T_c) (tptp.c_Fun_Ocomp V_h V_f T_b T_c T_a)) V_B)) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Set_Oimage V_f V_A T_a T_a)))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x $$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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((T_a $$unsorted) (V_F $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_F) V_G) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_b) (tptp.hAPP V_f V_x)) (tptp.hAPP V_g V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a T_b)) V_f) V_g))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_f) V_g) V_A T_c T_a))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_f) T_b T_a T_a) V_r)) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_A) V_B) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) _let_2) _let_2) _let_2)))) (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_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$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_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_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 ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) _let_2) _let_2))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_2))))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Collect V_P T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) V_x)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (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.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) _let_2) V_A) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_B) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A) _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$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 ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_P $$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 ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_B _let_2))))) (forall ((T_a $$unsorted) (V_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))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_2) V_f)) V_g)) V_A) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_g) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_3 (tptp.c_lessequals _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_4 V_B))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_B))))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_C)) (tptp.hAPP _let_2 V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_C) V_D))))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_B) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) (tptp.hAPP V_f V_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_A) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a)))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A)) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B)) V_C) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b) V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A)) V_B)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) T_a T_b)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_B) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (or (not (= (tptp.hAPP _let_1 V_A) (tptp.hAPP _let_1 V_B))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_X $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Ocontents V_X T_a) (tptp.c_The (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_a) (tptp.hAPP (tptp.c_fequal _let_1) V_X)) (tptp.hAPP (tptp.c_COMBC (tptp.c_Set_Oinsert T_a) T_a _let_1 _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q) T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_Q T_a) T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a)))) (forall ((V_Q $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_Q T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q) T_a) T_a)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_Q $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q) T_a) T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_or) V_P)) V_Q) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a)) (tptp.c_Collect V_Q T_a)))) (forall ((T_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_B) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A))) (or (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_B)) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.hAPP _let_1 V_B) T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Ocomp V_f V_g T_c T_a T_b) V_r T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_r T_b T_c) T_c T_a))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_x) V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_x))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) V_a) V_b)) V_x)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_A) V_B)) V_C))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_Finite__Set_Ofold1 _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_Finite__Set_Ofold1 _let_1 V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun tptp.t_a T_b)) V_f) V_g) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf T_b) (tptp.hAPP V_f tptp.v_x)) (tptp.hAPP V_g tptp.v_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_x) V_x))) (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.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.hBOOL (tptp.c_in V_x 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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_C)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_P) V_Q))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oimage V_f V_A T_c T_b) V_B T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b _let_1 T_c) V_B) V_f) T_c _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B)) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_D))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) V_B) V_C)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_A))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) V_C) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C))) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_M T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_B V_M T_b _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Collect V_P T_a)) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_a _let_1))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP V_A V_k)) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))) (forall ((V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) V_B) V_C)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 V_B)) (tptp.hAPP _let_2 V_C)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) (tptp.c_Lattices_Oupper__semilattice__class_Osup T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a) (tptp.c_Orderings_Obot__class_Obot T_a) T_a))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) V_M T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_b _let_1)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_B V_M T_b _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.c_fequal T_a) V_x) T_a) V_x)) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a)) V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_lessequals _let_1))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.hAPP (tptp.hAPP _let_3 V_B) (tptp.hAPP (tptp.hAPP _let_3 V_C) V_A)) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_H) V_x_H))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_2 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_b tptp.tc_bool)) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_x T_b T_a)) (tptp.c_Set_Oimage V_f V_A T_b T_a))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))) (forall ((T_b $$unsorted) (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_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a) V_A) V_B T_b _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1) (tptp.hAPP V_B V_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) V_A))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OWhile V_b V_c) (tptp.c_Hoare__Mirabelle_Opeek__and V_P (tptp.c_Fun_Ocomp tptp.c_Not V_b tptp.tc_bool tptp.tc_bool tptp.tc_Com_Ostate) T_a) T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_Hoare__Mirabelle_Opeek__and V_P V_b T_a) V_c V_P T_a)) _let_2) T_a))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OBODY V_pn) V_Q T_a)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_4 _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.hAPP _let_4 V_G) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Option_Othe (tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom) V_Q T_a)) _let_2) T_a)))))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OCond V_b V_c V_d) V_Q T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_Hoare__Mirabelle_Opeek__and V_P (tptp.c_Fun_Ocomp tptp.c_Not V_b tptp.tc_bool tptp.tc_bool tptp.tc_Com_Ostate) T_a) V_d V_Q T_a)) _let_2) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_Hoare__Mirabelle_Opeek__and V_P V_b T_a) V_c V_Q T_a)) _let_2) T_a))))))) (forall ((V_c $$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.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Fun_Oinj__on (tptp.hAPP (tptp.c_COMBC (tptp.c_Set_Oinsert T_a) T_a _let_1 _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Otop__class_Otop _let_1) T_a _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (= (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.t_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) tptp.t_a) tptp.c_and) V_A)) V_B) tptp.v_x tptp.t_a) (tptp.hAPP (tptp.hAPP tptp.c_and (tptp.c_List_Olistsp V_A tptp.v_x tptp.t_a)) (tptp.c_List_Olistsp V_B tptp.v_x tptp.t_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q) T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_Q T_a) T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q) T_a) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_P)) V_Q) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a)) (tptp.c_Collect V_Q T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_a T_b))) (let ((_let_3 (tptp.tc_fun tptp.tc_bool tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 tptp.tc_bool T_b) (tptp.c_Ex T_a)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_4 T_b) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool _let_3 T_a) tptp.c_and)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b tptp.tc_bool) (tptp.tc_fun _let_2 _let_1) T_b) (tptp.c_COMBB T_b tptp.tc_bool T_a)) (tptp.c_fequal T_b)) T_b _let_2 _let_1) V_f))) T_b _let_1 _let_1) V_P)) T_b) T_b) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Collect V_P T_a) T_a)))))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_fequal T_a) V_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) _let_2))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals _let_1) V_A) _let_3)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OSup__class_OSup T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_The (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x)) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Inf (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (or (= (tptp.hAPP V_Sup (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A))) (= (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A))) (= (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_B)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Finite__Set_Ofold1Set V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Set_Ocontents (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_x)) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (or (= V_y (tptp.c_Nitpick_Osko__Nitpick__XEx1__def__1__3 _let_1 T_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Finite__Set_Ofold1 V_f (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP _let_1 V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastAtMost V_a V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a))) (= (tptp.hAPP _let_2 V_A) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.hAPP (tptp.c_Complete__Lattice_OInf__class_OInf T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_a))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun _let_1 _let_1) T_b) (tptp.c_Set_Oinsert T_a)) V_f) T_b _let_1 _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) T_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a))) V_P) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP V_P V_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK _let_2 _let_1 T_b) T_b _let_1) _let_2)))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))))) (forall ((T_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBK V_c _let_1 T_b) T_b _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (= (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_bool) tptp.v_P) (tptp.hAPP tptp.c_and (tptp.hAPP tptp.c_Not tptp.v_P))) (= (tptp.hAPP (tptp.c_COMBK tptp.v_P tptp.t_a tptp.t_b) tptp.v_Q) tptp.v_P) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.tc_fun tptp.tc_Com_Ostate tptp.tc_bool))) (let ((_let_4 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_COMBK (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal tptp.tc_Com_Ostate) tptp.tc_Com_Ostate tptp.tc_Com_Ostate tptp.tc_bool) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)) _let_3 tptp.t_a) V_c (tptp.c_COMBK (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) _let_3 tptp.t_a) tptp.t_a)) _let_2) tptp.t_a)))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted) (V_Z_H $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_xa $$unsorted) (V_Z_H $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_xa V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_x V_Z_H) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 V_G V_P V_Q V_c)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) _let_15 (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 V_G V_P V_Q V_c)))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_H (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__2 V_P V_P_H V_Q V_Q_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 V_G V_P V_Q V_c V_x V_xa)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_x V_c V_xa tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_H (tptp.v_sko__Hoare__Mirabelle__Xconseq1__1 V_P V_P_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq1__2 V_P V_P_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_P_H $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq12__1 V_P V_P_H V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq12__3 V_P V_P_H V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P_H V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted) (V_Q_H $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) _let_2) tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q (tptp.v_sko__Hoare__Mirabelle__Xconseq2__1 V_Q V_Q_H)) (tptp.v_sko__Hoare__Mirabelle__Xconseq2__2 V_Q V_Q_H)))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q_H tptp.t_a)) _let_2) tptp.t_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P (tptp.v_sko__Hoare__Mirabelle__Xescape__1 V_G V_P V_Q V_c)) (tptp.v_sko__Hoare__Mirabelle__Xescape__2 V_G V_P V_Q V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a))) V_P) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_g $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_c T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.tc_fun T_a T_a))) (let ((_let_5 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_6 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_6 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_5 V_g) V_B)) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_1 T_a) T_b) _let_5) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_2) T_b) (tptp.c_COMBB T_a T_a T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a _let_4 T_b) _let_3) V_f)) T_b _let_2 _let_2) V_g)) T_b _let_1 T_a) V_B)) V_A)))))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_3 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_4 (tptp.tc_fun T_c tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c T_a) (tptp.tc_fun _let_4 T_a) T_b) _let_3) V_f) T_b _let_4 T_a) V_B)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) (tptp.tc_fun _let_1 T_a) T_c) _let_2) (tptp.c_COMBC V_f T_b T_c T_a)) T_c _let_1 T_a) V_A)) V_B)))))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.hAPP (tptp.c_COMBC (tptp.c_Set_Oinsert T_a) T_a _let_1 _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)) T_a _let_1) V_A))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Ofilter V_Q V_xs T_a) T_a) (tptp.c_List_Ofilter (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) V_Q)) V_P) V_xs T_a))) _let_14 (forall ((T_a $$unsorted)) (tptp.c_Wellfounded_OwfP (tptp.c_COMBK (tptp.c_COMBK tptp.c_False tptp.tc_bool T_a) (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_a))) V_P) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP V_P V_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P tptp.c_Com_Ocom_OSKIP V_P T_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) T_a))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OSemi V_c V_d) V_R T_a)) _let_2) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_Q V_d V_R T_a)) _let_2) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q T_a)) _let_2) T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (= (tptp.c_Collect (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_bool tptp.tc_bool) T_a) tptp.c_and) (tptp.hAPP (tptp.c_fequal T_a) V_a))) V_P) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert _let_1) V_t))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_2 V_ts) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool))) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x) V_A) V_x))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_G_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_G_H T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A)))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_com V_com_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun1 V_fun1_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_b V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_b V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_b V_c) (= V_a V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)))) (= V_a V_d) (= V_a V_c))))) _let_13 (forall ((V_G $$unsorted) (T_a $$unsorted)) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool)) T_a)) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_A))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) _let_12 (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_xa))) (let ((_let_4 (tptp.hAPP _let_2 V_x))) (= (tptp.hAPP _let_3 (tptp.hAPP _let_4 _let_1)) (tptp.hAPP _let_4 (tptp.hAPP _let_3 _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (= V_a V_b))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) _let_11 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.c_COMBI V_P T_a) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.62/4.81 )
% 4.62/4.81 % SZS output end Proof for SWV834-1
% 4.62/4.82 % cvc5---1.0.5 exiting
% 4.62/4.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------