%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV907-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 21:53:44 EDT 2023

% Result   : Unsatisfiable 0.50s 1.07s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16  % Problem    : SWV907-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.17  % Command    : do_cvc5 %s %d
% 0.17/0.38  % Computer : n017.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 05:30:58 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.24/0.55  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.oSFzBxqZv6/cvc5---1.0.5_2253.p...
% 0.24/0.66  ------- get file name : TPTP file name is SWV907-1
% 0.24/0.66  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2253.smt2...
% 0.24/0.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.50/1.07  % SZS status Unsatisfiable for SWV907-1
% 0.50/1.07  % SZS output start Proof for SWV907-1
% 0.50/1.09  (
% 0.50/1.09  (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom))) (let ((_let_3 (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT tptp.c_Com_Ocom_OBODY tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname))) (let ((_let_4 (tptp.c_Set_Oimage _let_3 _let_2 tptp.tc_Com_Opname _let_1))) (let ((_let_5 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_6 (tptp.c_Orderings_Obot__class_Obot _let_5))) (let ((_let_7 (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_6 _let_4 tptp.tc_Com_Ostate))) (let ((_let_8 (not _let_7))) (let ((_let_9 (= (tptp.hAPP tptp.c_Com_Obody tptp.v_pn) (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.tc_Com_Ocom) tptp.v_y)))) (let ((_let_10 (forall ((V_F $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT tptp.c_Com_Ocom_OBODY tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) _let_2 tptp.tc_Com_Opname _let_1) V_F tptp.tc_Com_Ostate) (not (tptp.c_lessequals V_F (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) _let_2 tptp.tc_Com_Opname _let_1) (tptp.tc_fun _let_1 tptp.tc_bool))) (not tptp.c_Com_OWT__bodies) (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton))))))) (let ((_let_11 (tptp.c_Finite__Set_Ofinite _let_2 tptp.tc_Com_Opname))) (let ((_let_12 (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Odom V_f T_b T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y))) (= (tptp.c_Set_Oinsert V_x _let_1 T_b) _let_1)))))) (let ((_let_13 (forall ((V_G $$unsorted) (V_Procs $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT tptp.c_Com_Ocom_OBODY tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) V_Procs tptp.tc_Com_Opname _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G _let_2 tptp.tc_Com_Ostate) (not (tptp.c_Finite__Set_Ofinite V_Procs tptp.tc_Com_Opname)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G _let_2 (tptp.tc_fun _let_1 tptp.tc_bool)) (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) V_Procs tptp.tc_Com_Opname _let_1) tptp.tc_Com_Ostate)))))))) (let ((_let_14 (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))))) (let ((_let_15 (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))))) (let ((_let_16 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_17 (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (let ((_let_18 (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname))) (let ((_let_19 (tptp.c_Set_Oimage _let_18 _let_2 tptp.tc_Com_Opname _let_1))) (let ((_let_20 (tptp.c_lessequals _let_19 _let_19 _let_5))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_4 _let_19 tptp.tc_Com_Ostate))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (forall ((V_F $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT tptp.c_Com_Ocom_OBODY tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) _let_2 tptp.tc_Com_Opname _let_1) V_F tptp.tc_Com_Ostate) (not (tptp.c_lessequals V_F (tptp.c_Set_Oimage (tptp.c_COMBB tptp.c_Hoare__Mirabelle_OMGT (tptp.c_COMBB (tptp.c_Option_Othe tptp.tc_Com_Ocom) tptp.c_Com_Obody (tptp.tc_Option_Ooption tptp.tc_Com_Ocom) tptp.tc_Com_Ocom tptp.tc_Com_Opname) tptp.tc_Com_Ocom _let_1 tptp.tc_Com_Opname) _let_2 tptp.tc_Com_Opname _let_1) (tptp.tc_fun _let_1 tptp.tc_bool))))))))) (let ((_let_25 (_let_24))) (let ((_let_26 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_6 _let_4 _let_5))) (let ((_let_27 (= _let_4 _let_26))) (let ((_let_28 (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_26 _let_19 tptp.tc_Com_Ostate))) (let ((_let_29 (not _let_22))) (let ((_let_30 (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1)))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_33 (not _let_28))) (let ((_let_34 (not _let_11))) (let ((_let_35 (or _let_7 _let_34 _let_33))) (let ((_let_36 (_let_13))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (and _let_33 _let_27))) (let ((_let_39 (_let_33 _let_27))) (let ((_let_40 (ASSUME :args (_let_33)))) (let ((_let_41 (REFL :args (_let_19)))) (let ((_let_42 (ASSUME :args (_let_27)))) (let ((_let_43 (tptp.hAPP _let_18 tptp.v_pn))) (let ((_let_44 (tptp.c_Set_Oinsert _let_43 _let_19 _let_1))) (let ((_let_45 (tptp.c_lessequals _let_19 _let_44 _let_5))) (let ((_let_46 (tptp.c_Set_Oinsert tptp.v_pn _let_2 tptp.tc_Com_Opname))) (let ((_let_47 (= (tptp.c_Set_Oimage _let_18 _let_46 tptp.tc_Com_Opname _let_1) _let_44))) (let ((_let_48 (= _let_2 _let_46))) (let ((_let_49 (_let_17))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (_let_14))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (not _let_9))) (let ((_let_54 (or _let_53 _let_48))) (let ((_let_55 (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Map_Odom V_f T_b T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y))) (= _let_1 (tptp.c_Set_Oinsert V_x _let_1 T_b))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (and _let_48 _let_47 _let_45))) (let ((_let_58 (ASSUME :args (_let_45)))) (let ((_let_59 (ASSUME :args (_let_47)))) (let ((_let_60 (ASSUME :args (_let_48)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_58 _let_59 _let_60) (SCOPE (TRUE_ELIM (TRANS (CONG _let_41 (TRANS (CONG (REFL :args (_let_18)) (SYMM (SYMM _let_60)) (REFL :args (tptp.tc_Com_Opname)) (REFL :args (_let_1)) :args (APPLY_UF tptp.c_Set_Oimage)) (SYMM (SYMM _let_59))) (REFL :args (_let_5)) :args (APPLY_UF tptp.c_lessequals)) (TRUE_INTRO _let_58))) :args (_let_45 _let_47 _let_48))) :args (_let_48 _let_47 _let_45))) :args (true _let_57)) :args ((or (not _let_48) (not _let_47) _let_20 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_48 (not _let_54)))) (ASSUME :args (_let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.c_Com_Obody tptp.v_pn tptp.tc_Com_Ocom tptp.v_y tptp.tc_Com_Opname QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP V_f V_x) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y) (tptp.c_Map_Odom V_f T_b T_a)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_48 false _let_9 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_18 tptp.v_pn _let_2 tptp.tc_Com_Opname _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a)))) :args _let_51)) _let_52 :args (_let_47 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_19 _let_43 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Set_Oinsert V_a V_B T_a)))) :args _let_49)) _let_50 :args (_let_45 false _let_17)) :args (_let_20 false _let_48 false _let_47 false _let_45)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_40 _let_42) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_42)) _let_41 (REFL :args (tptp.tc_Com_Ostate)) :args (APPLY_UF tptp.c_Hoare__Mirabelle_Ohoare__derivs)) (FALSE_INTRO _let_40))) :args _let_39)) :args _let_39)) :args (true _let_38)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_28))) (REFL :args ((not _let_27))) (REFL :args (_let_29)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_7 _let_34 _let_33 (not _let_35)))) (ASSUME :args (_let_8)) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_6 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oimage _let_3 V_Procs tptp.tc_Com_Opname _let_1) tptp.tc_Com_Ostate) true))))) :args _let_36)) _let_37 :args (_let_35 false _let_13)) :args (_let_33 true _let_7 false _let_11 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_1 _let_4 QUANTIFIERS_INST_E_MATCHING ((tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_32) V_B _let_32)))) :args (_let_30))) _let_31 :args (_let_27 false _let_30)) :args (_let_29 true _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_25) :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_4 V_F tptp.tc_Com_Ostate) true))))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args ((or (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton) (not tptp.c_Com_OWT__bodies) _let_24))) (ASSUME :args (tptp.c_Hoare__Mirabelle_Ostate__not__singleton)) (ASSUME :args (tptp.c_Com_OWT__bodies)) :args (_let_24 false tptp.c_Hoare__Mirabelle_Ostate__not__singleton false tptp.c_Com_OWT__bodies)) :args (_let_23 false _let_24)) :args (false false _let_20 true _let_22 false _let_23)) :args ((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 $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((V_com1 $$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_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_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c)) V_s) V_s)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (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 ((V_e1 $$unsorted) (V_m $$unsorted) (T_b $$unsorted) (V_u1 $$unsorted) (T_a $$unsorted) (V_e2 $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_u1))) (or (= (tptp.c_Map_Omap__add (tptp.c_Fun_Ofun__upd V_e1 V_m _let_2 T_a _let_1) V_e2 T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Omap__add V_e1 V_e2 T_a T_b) V_m _let_2 T_a _let_1)) (tptp.hBOOL (tptp.c_in V_m (tptp.c_Map_Odom V_e2 T_a T_b) T_a)))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OSemi V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f4 V_com1) V_com2) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com1 T_a)) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com2 T_a)))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_vname V_vname_H))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_pname V_pname_H))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f3 V_loc) V_fun) V_com) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com T_a)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 tptp.c_Com_Ocom_OSKIP T_a) V_f1)) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_B $$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.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_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.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f8 V_vname) V_pname) V_fun))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Map_Odom (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a (tptp.tc_Option_Ooption T_b)) T_a T_b) (tptp.c_Set_Oinsert V_x (tptp.c_Map_Odom V_f T_a T_b) T_a)) (= V_y (tptp.c_Option_Ooption_ONone T_b)))) (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 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OAss V_vname V_fun) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_vname) V_fun))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.c_Option_Ooption_ONone tptp.t_b) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P V_f1)))) (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 ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s0) V_s2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_s1) V_s2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c) V_s0) V_s1))) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_m $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Omap__add V_m (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) T_a T_b) V_m)) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_m $$unsorted)) (= (tptp.c_Map_Omap__add (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) V_m T_a T_b) V_m)) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1)) V_s) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c0) V_s) V_s1))) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c1) V_s) V_t)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2)) V_s) V_t))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__rec V_f1 V_f2 (tptp.c_Option_Ooption_ONone T_b) T_a T_b) V_f1)) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OSemi V_c0 V_c1)) V_s0) V_s2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c1) V_s1) V_s2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c0) V_s0) V_s1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_m V_k) _let_1)) (not (= (tptp.hAPP V_n V_k) (tptp.c_Option_Ooption_ONone T_a))) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_m V_k) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_n V_k) _let_1)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((V_t $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (not (= (tptp.c_Fun_Ofun__upd V_t V_k (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_x) T_a _let_1) (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) _let_1 T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_fun $$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_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_Map_Omap__add V_m V_n T_a T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Map_Odom V_n T_a T_b) (tptp.c_Map_Odom V_m T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) _let_17 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_fun_H $$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 ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_fun $$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 $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_fun V_fun_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) _let_1))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))) (tptp.c_lessequals V_C V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_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_m $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Omap__comp V_m (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_c) (tptp.tc_Option_Ooption T_c) tptp.t_a) tptp.v_x T_c T_b tptp.t_a) (tptp.c_Option_Ooption_ONone T_b))) (forall ((T_b $$unsorted) (T_c $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_b))) (= (tptp.c_Map_Omap__comp (tptp.c_COMBK _let_1 (tptp.tc_Option_Ooption T_b) T_c) V_m tptp.v_x T_c T_b tptp.t_a) _let_1))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (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 ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_m1 $$unsorted) (V_m2 $$unsorted) (V_m3 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Map_Omap__add V_m1 (tptp.c_Map_Omap__add V_m2 V_m3 T_a T_b) T_a T_b) (tptp.c_Map_Omap__add (tptp.c_Map_Omap__add V_m1 V_m2 T_a T_b) V_m3 T_a T_b))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_a V_b T_a T_b) V_c V_d T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_c V_d T_a T_b) V_a V_b T_a T_b)) (= V_a V_c))) (forall ((V_f $$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 ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 tptp.c_Com_Ocom_OSKIP T_a) V_f1)) (forall ((V_f $$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.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (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.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_m V_a) (tptp.c_Option_Ooption_ONone T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Map_Odom V_m T_a T_b) T_a))))) (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Map_Odom V_m T_a T_b) T_a)) (= (tptp.hAPP V_m V_a) (tptp.c_Option_Ooption_ONone T_b)))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_f $$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.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_f $$unsorted) (V_opt $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Option_Omap V_f V_opt T_b T_a) (tptp.c_Option_Ooption_ONone T_a))) (= V_opt (tptp.c_Option_Ooption_ONone T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$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.c_Lattices_Olower__semilattice__class_Oinf V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_Q $$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)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.c_Com_Ocom_OSemi V_c V_d) V_R T_a) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_Q V_d V_R T_a) _let_2 _let_1) T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q T_a) _let_2 _let_1) T_a)))))) (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 ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_x V_z T_a T_b) (tptp.c_Fun_Ofun__upd V_f V_x V_z T_a T_b))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((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 $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_s $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP) V_s) V_s))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_u $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Natural_Oevalc V_c) V_s))) (or (= V_u V_t) (not (tptp.hBOOL (tptp.hAPP _let_1 V_u))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_t)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((T_a $$unsorted)) (tptp.hBOOL (tptp.c_Option_Ois__none (tptp.c_Option_Ooption_ONone T_a) T_a))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.c_Option_Ooption_ONone T_b) T_a T_b) V_f1)) (= (tptp.hAPP _let_16 tptp.v_x) (tptp.c_in tptp.v_x _let_16 tptp.t_a)) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c2) V_s) V_t)) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2)) V_s) V_t))))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1)) V_s) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c1) V_s) V_s1))) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_b T_a) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_a T_b) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_aa) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_aa T_a) V_f)) (forall ((V_fun1 $$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 ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_com V_com_H))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.hBOOL (tptp.c_in V_a V_C T_a))))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_B _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C V_A _let_1) (not (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OSemi V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP V_f4 V_com1) V_com2))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_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 ((V_x $$unsorted) (T_a $$unsorted)) (or (= V_x (tptp.c_Option_Ooption_ONone T_a)) (not (tptp.hBOOL (tptp.c_Option_Ois__none V_x T_a))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f8 V_vname) V_pname) V_fun))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Omap V_f (tptp.c_Option_Ooption_ONone T_b) T_b T_a) (tptp.c_Option_Ooption_ONone T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_fun_H $$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 $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP V_m V_k) _let_1)) (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_c $$unsorted)) (= (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT V_c) (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_fequal tptp.tc_Com_Ostate) V_c (tptp.c_Natural_Oevalc V_c) tptp.tc_Com_Ostate))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (= (tptp.c_Option_Ois__none tptp.v_x tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_fequal (tptp.tc_Option_Ooption tptp.t_a)) tptp.v_x) (tptp.c_Option_Ooption_ONone tptp.t_a))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OAss V_vname V_fun) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_vname) V_fun))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_f)) (= (tptp.hAPP V_f V_x) V_y))) (forall ((V_m2 $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (V_m1 $$unsorted) (T_a $$unsorted) (T_c $$unsorted)) (or (not (= (tptp.hAPP V_m2 V_k) (tptp.c_Option_Ooption_ONone T_b))) (= (tptp.c_Map_Omap__comp V_m1 V_m2 V_k T_b T_a T_c) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((V_m2 $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_m1 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_m2 V_k) (tptp.c_Option_Ooption_ONone T_a))) (= (tptp.c_Map_Omap__comp V_m1 V_m2 V_k T_a T_c T_b) (tptp.c_Option_Ooption_ONone T_c)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (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 $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$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.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OWhile V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f6 V_fun) V_com) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com T_a)))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l2 V_m)) (not (tptp.hBOOL (tptp.c_in V_m (tptp.c_Map_Odom V_l2 T_a T_b) T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f5 V_fun) V_com1) V_com2) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com1 T_a)) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com2 T_a)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (or (= V_t V_s) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP) V_s) V_t))))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Olower__semilattice__class_Oinf V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (= (tptp.c_Map_Odom (tptp.c_Fun_Ofun__upd (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) _let_1 T_a) V_x (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_xa) T_a _let_1) T_a T_b) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_x $$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 $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) _let_15 (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$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.c_COMBB V_f V_g T_a T_c T_b) _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 ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) _let_14 (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Map_Odom V_f T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_f (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_COMBK (tptp.c_Option_Ooption_ONone T_b) (tptp.tc_Option_Ooption T_b) T_a) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f3 V_loc) V_fun) V_com))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OWhile V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP V_f6 V_fun) V_com))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (let ((_let_2 (tptp.hAPP V_n V_k))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= _let_2 (tptp.c_Option_Ooption_ONone T_a)) (= _let_2 _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_A T_a T_b) (tptp.hBOOL (tptp.c_in V_y (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_A T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_b)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_vname V_vname_H))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (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 ((V_G $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P tptp.c_Com_Ocom_OSKIP V_P T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))) (forall ((V_m_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.c_Map_Odom V_m_H T_a T_b))) (or (tptp.c_Fun_Oinj__on V_m_H _let_2 T_a _let_1) (not (tptp.c_Fun_Oinj__on (tptp.c_Map_Omap__add V_m V_m_H T_a T_b) _let_2 T_a _let_1)))))) (forall ((V_m $$unsorted) (V_m_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.c_Map_Odom V_m_H T_a T_b))) (or (tptp.c_Fun_Oinj__on (tptp.c_Map_Omap__add V_m V_m_H T_a T_b) _let_2 T_a _let_1) (not (tptp.c_Fun_Oinj__on V_m_H _let_2 T_a _let_1)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_y))) (= (tptp.c_Map_Omap__add V_f (tptp.c_Fun_Ofun__upd V_g V_x _let_2 T_a _let_1) T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Map_Omap__add V_f V_g T_a T_b) V_x _let_2 T_a _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_loc V_loc_H))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (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) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c)) V_s) V_t))))) (forall ((V_m1 $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_m2 $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_ONone T_a))) (or (not (= (tptp.hAPP V_m1 V_x) _let_1)) (not (= (tptp.hAPP V_m2 V_k) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_x))) (= (tptp.c_Map_Omap__comp V_m1 V_m2 V_k T_b T_a T_c) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_f $$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_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (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.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f5 V_fun) V_com1) V_com2))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((V_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l2 V_m)) (tptp.hBOOL (tptp.c_in V_m (tptp.c_Map_Odom V_l1 T_a T_b) T_a)))) (forall ((V_l1 $$unsorted) (V_l2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.c_Map_Omap__add V_l1 V_l2 T_a T_b) V_m) (tptp.hAPP V_l1 V_m)) (tptp.hBOOL (tptp.c_in V_m (tptp.c_Map_Odom V_l2 T_a T_b) T_a)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c2) V_s) V_t)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc V_c1) V_s) V_t)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2)) V_s) V_t))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_com1_H $$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_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_m1 $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_m2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Map_Odom V_m1 T_a T_b) (tptp.c_Map_Odom V_m2 T_a T_b) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Map_Omap__add V_m1 V_m2 T_a T_b) (tptp.c_Map_Omap__add V_m2 V_m1 T_a T_b))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Option_Ooption T_b))) (let ((_let_2 (tptp.c_Option_Ooption_OSome T_b))) (or (not (= (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_2 V_x) T_a _let_1) (tptp.c_Fun_Ofun__upd V_n V_a (tptp.hAPP _let_2 V_y) T_a _let_1))) (= V_x V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Option_Othe T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x)) V_x)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__rec V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_a) T_a T_b) (tptp.hAPP V_f2 V_a))) (forall ((V_t $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_t V_k) _let_1)) (= (tptp.c_Fun_Ofun__upd V_t V_k _let_1 T_b (tptp.tc_Option_Ooption T_a)) V_t)))) (forall ((V_m $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_xa _let_1 T_aa (tptp.tc_Option_Ooption T_a)) V_xa) _let_1))) (forall ((V_m1 $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_v $$unsorted) (V_m2 $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_v))) (or (not (= (tptp.hAPP V_m1 V_x) _let_1)) (not (= (tptp.hAPP V_m2 V_k) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_x))) (= (tptp.c_Map_Omap__comp V_m1 V_m2 V_k T_b T_a T_c) _let_1)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.t_b) V_xa) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_xa))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.t_b) V_a) tptp.t_a tptp.t_b)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_a))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_Option_Ooption_OSome T_a) V_A T_a (tptp.tc_Option_Ooption T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.c_Option_Ois__none (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted)) (not (= (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_xa) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted)) (not (= (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_a_H) (tptp.c_Option_Ooption_ONone T_a)))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP V_m V_x) _let_2)) (= V_x V_a) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2)) (= (tptp.hAPP V_m V_x) _let_2) (= V_b V_y))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_a (tptp.hAPP _let_1 V_b) T_b (tptp.tc_Option_Ooption T_a)) V_x) _let_2)) (= (tptp.hAPP V_m V_x) _let_2) (= V_x V_a))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Ooption_Ooption__case V_f1 V_f2 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_a) T_a T_b) (tptp.hAPP V_f2 V_a))) (forall ((V_b $$unsorted) (V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_aa))) (or (= V_b V_y) (not (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_m V_x (tptp.hAPP _let_1 V_b) T_a (tptp.tc_Option_Ooption T_aa)) V_x) (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_y)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted)) (not (= (tptp.c_Option_Ooption_ONone T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_a_H)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)) (= (tptp.hAPP V_m V_k) _let_1) (= (tptp.hAPP V_n V_k) _let_1)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Option_Omap V_f (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_x) T_b T_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) (tptp.hAPP V_f V_x)))) (forall ((V_m2 $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_k_H $$unsorted) (V_m1 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_m2 V_k) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_k_H))) (= (tptp.c_Map_Omap__comp V_m1 V_m2 V_k T_a T_c T_b) (tptp.hAPP V_m1 V_k_H)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Option__Xospec__1__1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x) V_P T_a)))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_n $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_xx $$unsorted) (V_m $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_xx))) (or (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_n $$unsorted) (V_k $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_m $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_x))) (or (not (= (tptp.hAPP V_n V_k) _let_1)) (= (tptp.hAPP (tptp.c_Map_Omap__add V_m V_n T_b T_a) V_k) _let_1)))) (forall ((V_pname_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_pname $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) T_a) (tptp.hAPP V_f7 V_pname))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (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.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_pname $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname)))) (forall ((V_pname_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_pname $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) T_a) (tptp.hAPP V_f7 V_pname))) (forall ((V_pname_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_t $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts (tptp.tc_Hoare__Mirabelle_Otriple T_a)) T_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted) (V_ts_H $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_ts_H (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts_H T_a)))) (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_lessequals V_G_H V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G_H V_ts T_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a) (not (tptp.c_lessequals V_ts V_G (tptp.tc_fun (tptp.tc_Hoare__Mirabelle_Otriple T_a) tptp.tc_bool))))) (forall ((T_b $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Map_Odom (tptp.c_COMBK (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) V_y) (tptp.tc_Option_Ooption T_b) T_a) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_m V_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_b) (tptp.c_Map_Osko__Map__XdomD__1__1 V_a V_m T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Map_Odom V_m T_a T_b) T_a))))) (forall ((V_pn $$unsorted) (V_s0 $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) V_s0) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn))) V_s0) V_s1))))) (forall ((V_P $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_P))) V_s) V_s1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Natural_Oevalc (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P)) V_s) V_s1))))) (forall ((V_c1 $$unsorted) (V_b $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_c2 $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (forall ((V_c1 $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((V_c2 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (tptp.c_Com_OWT tptp.c_Com_Ocom_OSKIP) (forall ((V_X $$unsorted) (V_a $$unsorted)) (tptp.c_Com_OWT (tptp.c_Com_Ocom_OAss V_X V_a))) (forall ((V_b $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c))))) (forall ((V_Y $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_Y $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c))))) (forall ((V_P $$unsorted) (V_c $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.tc_Com_Ostate) _let_2 _let_1))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_2 _let_3 tptp.tc_Com_Ostate) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids _let_2 _let_3 tptp.tc_Com_Ostate)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_2 (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT V_c) _let_2 _let_1) tptp.tc_Com_Ostate))))))) (= (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT tptp.v_c) (tptp.c_Hoare__Mirabelle_Otriple_Otriple (tptp.c_fequal tptp.tc_Com_Ostate) tptp.v_c (tptp.c_Natural_Oevalc tptp.v_c) tptp.tc_Com_Ostate)) (forall ((V_t $$unsorted)) (or (not (= (tptp.v_sko__Hoare__Mirabelle__Xsingle__stateE__1 V_t) V_t)) (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn) V_Q T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert _let_3 _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Set_Oinsert _let_3 V_G _let_1) (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn)) V_Q T_a) _let_2 _let_1) T_a))))))) (forall ((V_G $$unsorted) (V_P $$unsorted) (V_pn $$unsorted) (V_Q $$unsorted) (T_a $$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)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn) V_Q T_a) _let_2 _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn)) V_Q T_a) _let_2 _let_1) 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.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((V_c $$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)))) _let_13 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_m V_a) (tptp.hAPP (tptp.c_Option_Ooption_OSome T_a) V_b))) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Map_Odom V_m T_b T_a) T_b)))) _let_12 (forall ((V_G $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G V_ts T_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a))))) (forall ((V_G $$unsorted) (V_t $$unsorted) (T_a $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple T_a))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) T_a) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert V_t V_ts _let_1) T_a))))) (forall ((V_X $$unsorted) (V_pn $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_pn V_a)) (not (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn))))) (forall ((V_P $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P)) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_P V_a))))) _let_11 (forall ((V_G $$unsorted) (V_pn $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (let ((_let_3 (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert _let_3 _let_2 _let_1) tptp.tc_Com_Ostate) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs (tptp.c_Set_Oinsert _let_3 V_G _let_1) (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT (tptp.hAPP (tptp.c_Option_Othe tptp.tc_Com_Ocom) (tptp.hAPP tptp.c_Com_Obody V_pn))) _let_2 _let_1) tptp.tc_Com_Ostate))))))) (forall ((V_G $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)) _let_1) tptp.tc_Com_Ostate) (not (tptp.c_Com_OWT V_c)) (tptp.hBOOL (tptp.c_in (tptp.v_sko__Hoare__Mirabelle__XMGF__lemma1__1 V_G) (tptp.c_Map_Odom tptp.c_Com_Obody tptp.tc_Com_Opname tptp.tc_Com_Ocom) tptp.tc_Com_Opname)) (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton)))) (forall ((V_pn $$unsorted)) (or (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pn)) (= (tptp.hAPP tptp.c_Com_Obody V_pn) (tptp.c_Option_Ooption_ONone tptp.tc_Com_Ocom)))) (forall ((V_G $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT V_c) _let_2 _let_1) tptp.tc_Com_Ostate) (not (tptp.c_Com_OWT V_c)) (not (tptp.c_Hoare__Mirabelle_Ohoare__derivs V_G (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT (tptp.hAPP tptp.c_Com_Ocom_OBODY (tptp.v_sko__Hoare__Mirabelle__XMGF__lemma1__1 V_G))) _let_2 _let_1) tptp.tc_Com_Ostate)) (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton))))) _let_10 (forall ((V_P $$unsorted)) (or (= (tptp.hAPP tptp.c_Com_Obody V_P) (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.tc_Com_Ocom) (tptp.c_Com_Osko__Com__XWTs__elim__cases__7__1 V_P))) (not (tptp.c_Com_OWT (tptp.hAPP tptp.c_Com_Ocom_OBODY V_P))))) (forall ((V_c $$unsorted)) (let ((_let_1 (tptp.tc_Hoare__Mirabelle_Otriple tptp.tc_Com_Ostate))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_bool)))) (or (tptp.c_Hoare__Mirabelle_Ohoare__derivs _let_2 (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Hoare__Mirabelle_OMGT V_c) _let_2 _let_1) tptp.tc_Com_Ostate) (not (tptp.c_Com_OWT V_c)) (not tptp.c_Com_OWT__bodies) (not tptp.c_Hoare__Mirabelle_Ostate__not__singleton))))) (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_pn $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Com_Obody V_pn) (tptp.hAPP (tptp.c_Option_Ooption_OSome tptp.tc_Com_Ocom) V_b))) (not tptp.c_Com_OWT__bodies) (tptp.c_Com_OWT V_b))) (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.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (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 $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_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 ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_Option_Ooption_OSome T_a))) (or (not (= (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_a_H))) (= V_a V_a_H)))) (forall ((V_x $$unsorted) (V_xa $$unsorted)) (or tptp.c_Hoare__Mirabelle_Ostate__not__singleton (= V_x V_xa))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_f $$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_pname $$unsorted) (V_pname_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname) (tptp.hAPP tptp.c_Com_Ocom_OBODY V_pname_H))) (= V_pname V_pname_H))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) tptp.c_Hoare__Mirabelle_Ostate__not__singleton tptp.c_Com_OWT__bodies (tptp.c_Com_OWT tptp.v_c) _let_9 _let_8 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_Option_Ooption T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_COMBC V_P V_Q V_R T_b T_c T_a) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.50/1.09  )
% 0.50/1.09  % SZS output end Proof for SWV907-1
% 0.50/1.10  % cvc5---1.0.5 exiting
% 0.50/1.10  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------