%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV861-1 : 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 21:53:34 EDT 2023

% Result   : Unsatisfiable 0.54s 0.96s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.17  % Problem    : SWV861-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.18  % Command    : do_cvc5 %s %d
% 0.18/0.39  % Computer : n017.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39  % CPULimit   : 300
% 0.18/0.39  % WCLimit    : 300
% 0.18/0.39  % DateTime   : Tue Aug 29 03:04:58 EDT 2023
% 0.18/0.39  % CPUTime    : 
% 0.24/0.57  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.58  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rdTozXKApk/cvc5---1.0.5_28644.p...
% 0.24/0.70  ------- get file name : TPTP file name is SWV861-1
% 0.24/0.70  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28644.smt2...
% 0.24/0.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.54/0.96  % SZS status Unsatisfiable for SWV861-1
% 0.54/0.96  % SZS output start Proof for SWV861-1
% 0.54/0.98  (
% 0.54/0.98  (let ((_let_1 (forall ((V_Z $$unsorted) (V_s_H $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_R V_Z) V_s_H)) (not (tptp.c_Natural_Oevaln tptp.v_d V_s tptp.v_n V_s_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_Q V_Z) V_s))))))) (let ((_let_2 (forall ((V_Z $$unsorted) (V_s_H $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_Q V_Z) V_s_H)) (not (tptp.c_Natural_Oevaln tptp.v_c V_s tptp.v_n V_s_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Z) V_s))))))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_R tptp.v_Z) tptp.v_s_H)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.c_Natural_Oevaln tptp.v_d tptp.v_s1 tptp.v_n tptp.v_s_H))) (let ((_let_6 (tptp.c_Natural_Oevaln tptp.v_c tptp.v_s tptp.v_n tptp.v_s1))) (let ((_let_7 (tptp.hAPP (tptp.hAPP tptp.v_P tptp.v_Z) tptp.v_s))) (let ((_let_8 (tptp.hBOOL _let_7))) (let ((_let_9 (tptp.hAPP tptp.v_P tptp.v_R))) (let ((_let_10 (tptp.hAPP tptp.v_Q tptp.v_R))) (let ((_let_11 (not _let_8))) (let ((_let_12 (not _let_6))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_Q tptp.v_Z) tptp.v_s1)))) (let ((_let_14 (or _let_13 _let_12 _let_11))) (let ((_let_15 (_let_2))) (let ((_let_16 (ASSUME :args _let_15))) (let ((_let_17 (not _let_14))) (let ((_let_18 (not _let_13))) (let ((_let_19 (not _let_5))) (let ((_let_20 (or _let_3 _let_19 _let_18))) (let ((_let_21 (_let_1))) (let ((_let_22 (ASSUME :args _let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (tptp.v_Z tptp.v_s1 tptp.v_s QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.v_Q V_Z) V_s_H) (not (= (tptp.c_Natural_Oevaln tptp.v_c V_s tptp.v_n V_s_H) false))))) :args _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_11 _let_12 _let_13 _let_17))) (ASSUME :args (_let_8)) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_3 _let_19 _let_18 (not _let_20)))) (ASSUME :args (_let_4)) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.v_Z tptp.v_s_H tptp.v_s1 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.v_R V_Z) V_s_H) (not (= (tptp.c_Natural_Oevaln tptp.v_d V_s tptp.v_n V_s_H) false))))) :args _let_21)) _let_22 :args (_let_20 false _let_1)) :args (_let_18 true _let_3 false _let_5 false _let_20)) :args (_let_17 false _let_8 false _let_6 true _let_13)) _let_16 :args (false true _let_14 false _let_2)) :args ((forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals V_f V_g _let_1) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((T_a $$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) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_f $$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 $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_aa T_a) V_f)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B _let_1))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_C (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_f $$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 ((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_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (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_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.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 $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) V_M T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_B V_M T_b _let_1) _let_1)))) (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 ((T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.hAPP (tptp.hAPP _let_2 V_B) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_A)) V_A) (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 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (= V_A V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_f $$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_f $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A V_y T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((T_a $$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_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_A T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a _let_1) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_I $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP V_A V_x) V_B _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_I))) (not (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_b _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_a _let_1))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_A V_k) _let_2 _let_1) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_k) V_I))))))) (forall ((V_a $$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_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_COMBC (tptp.c_in T_a) T_a _let_1 tptp.tc_bool))) (or (tptp.c_lessequals V_R V_S _let_1) (not (tptp.c_lessequals (tptp.hAPP _let_2 V_R) (tptp.hAPP _let_2 V_S) _let_1)))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_COMBC (tptp.c_in T_a) T_a _let_1 tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP _let_2 V_R) (tptp.hAPP _let_2 V_S) _let_1) (not (tptp.c_lessequals V_R V_S _let_1)))))) (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oinsert V_a V_A T_b) V_B T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB V_B V_f T_c _let_1 T_b) T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oimage V_f V_A T_b T_c) V_B T_c _let_1)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oimage V_f V_A T_c T_b) V_B T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBB V_B V_f T_b _let_1 T_c) T_c _let_1)))) (forall ((V_f $$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_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Set_Oimage V_f V_A T_b T_a)) (tptp.c_Set_Oimage V_f V_B T_b T_a)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_b T_a) _let_1))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_2 V_B) (tptp.hAPP _let_2 V_C) _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A))) (= (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_2 V_B) (tptp.hAPP _let_2 V_C) _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_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_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1) (tptp.c_lessequals V_g V_f _let_1) (not (tptp.c_lessequals V_f V_g _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) (tptp.hAPP (tptp.hAPP _let_2 V_C) V_D) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_x V_z T_a T_b) (tptp.c_Fun_Ofun__upd V_f V_x V_z T_a T_b))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_m $$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_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_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_x $$unsorted) (V_z $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_x V_z) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x T_a T_b)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((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_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 ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBS (tptp.c_COMBB _let_1 V_f T_a (tptp.tc_fun T_a T_a) T_b) V_g T_b T_a T_a) V_A T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetsum V_g V_A T_b T_a)))))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_B $$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 $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (or (not (tptp.class_HOL_Oord T_b)) (not (tptp.c_lessequals V_g V_f _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$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) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A) _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_A _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_z T_a T_b)) (forall ((V_f $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_z T_a T_b)) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_A T_b T_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (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 $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)) V_C) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP _let_2 V_A) V_C) (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (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_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$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_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 ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_C _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_a 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_HOL_Oord__class_Oless V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_b T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_t $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_t))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_B)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A)))))) (forall ((V_G $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__3 V_G V_ts)) V_ts)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_A T_a T_b) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_y) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless 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.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_2) (not (tptp.c_lessequals V_A V_B _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_A)) (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)))))) (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_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B) (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))) (tptp.hBOOL (tptp.hAPP _let_2 V_B)) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_2) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_2) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_2) T_a)) V_B _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$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_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_b tptp.tc_bool)) V_A) V_B) T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Ovimage V_f V_A T_a T_b)) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))) (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_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.c_Collect V_P T_a) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (= (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B)) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP _let_2 V_A))) (= (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a V_B T_a)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a))) V_B)))))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_a $$unsorted) (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)) (tptp.c_Fun_Oinj__on (tptp.c_COMBI T_a) V_A T_a T_a)) (forall ((T_aa $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_a) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a)))) (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_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_fun_H $$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_Sup $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.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)) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_fun V_fun_H))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_A) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) _let_2) V_A) _let_2)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) _let_1) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_B _let_1)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP _let_2 V_A) V_B) V_C _let_1) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1)))) (= (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.hAPP _let_2 V_B))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Collect V_P T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_s $$unsorted)) (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_s)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_u $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (= V_u V_t) (not (tptp.c_Natural_Oevalc V_c V_s V_u)) (not (tptp.c_Natural_Oevalc V_c V_s V_t)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b))))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_A) V_B) T_a T_b) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP _let_3 V_B) V_A) T_a T_b) _let_2) (tptp.c_Orderings_Obot__class_Obot _let_2))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a T_b)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (or (= (tptp.c_Set_Oimage (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_A T_b T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_b)) T_b T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((V_G $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 V_G V_ts) (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__3 V_G V_ts) tptp.t_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (= (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_in T_b) V_f T_b (tptp.tc_fun _let_1 tptp.tc_bool) T_a) T_a _let_1 tptp.tc_bool) V_B) T_a)))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Nitpick_Ofold__graph_H V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.c_Nitpick_Ofold__graph_H V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_y T_a T_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_B _let_1))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Osetsum V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a tptp.tc_nat) (tptp.c_Finite__Set_Osetsum V_f V_A T_a tptp.tc_nat)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_f $$unsorted) (V_z $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofold__graph V_f V_z V_A (tptp.hAPP (tptp.hAPP V_f V_x) V_y) T_a T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Finite__Set_Ofold__graph V_f V_z (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_y T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) _let_1)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard _let_1 T_a)))))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.hAPP V_M V_i) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_a T_b) T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) V_A))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((V_c $$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.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) V_B) V_A)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Collect V_P T_a) (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y 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_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1)) V_A))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B))) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_B) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevalc _let_1 V_s0 V_s2) (not (tptp.c_Natural_Oevalc _let_1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c V_s0 V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_xa $$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 ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x))) (= V_xa V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (= V_x_H V_y_H)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (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 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_s2) (not (tptp.c_Natural_Oevalc V_c1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c0 V_s0 V_s1)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_y $$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.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_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.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))) (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_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_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_B) V_A) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Collect V_P T_a) (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_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 ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_x V_A T_a)) V_B) (tptp.c_Set_Oinsert V_x (tptp.hAPP (tptp.hAPP _let_1 V_A) V_B) T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) (tptp.c_Set_Oinsert V_x V_A T_a)) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) V_A) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_t)))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexCI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_Q $$unsorted) (V_xb $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xb)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xb) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a))))))) (forall ((V_P $$unsorted) (V_xb $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xb) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a))))))) (forall ((V_Q $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)) V_A))))) (forall ((V_P $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)) V_A))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexCI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanLessThan V_less V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_l) V_i))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanAtMost V_less__eq V_less V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_l) V_i))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexCI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexE__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y 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_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b 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_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$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_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$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_b V_d)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (tptp.c_Natural_Oevalc V_c1 V_s V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_c) V_A)))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun1 V_fun1_H))) (forall ((V_fun1 $$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_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 V_A V_B V_P T_b T_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b)))))) (forall ((T_a $$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) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Collect V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (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 ((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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_t)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus _let_1) V_A) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)) T_a) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((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 $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless 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_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_fequal T_a) T_a T_a tptp.tc_bool) V_a) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) V_C) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.hAPP (tptp.hAPP _let_2 V_B) V_C) _let_1))))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Collect V_P T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_fequal T_a) V_a) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Collect (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_A) T_a) V_A)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$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 ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_less $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanAtMost V_less__eq V_less V_l V_u T_a)))))) (forall ((V_less__eq $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanAtMost V_less__eq V_less V_l V_u T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_HOL_Oord__class_Oless V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_a V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_B T_a)))) (forall ((V_Q $$unsorted) (V_xc $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_xc)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xc) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)))))) (forall ((V_P $$unsorted) (V_xc $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xc)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xc) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)) V_A)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)) V_A))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_Q T_a)) V_A)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 V_A V_P T_a)) V_A))))) (forall ((V_Q $$unsorted) (V_xf $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xf)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xf) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q _let_1))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_P $$unsorted) (V_xg $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xg)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xg) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q _let_1))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XballE__1__1 V_A V_P T_a)) V_A))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexCI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_less $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanLessThan V_less V_l V_u T_a)))))) (forall ((V_less $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThanLessThan V_less V_l V_u T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Collect V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Collect V_P T_a)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatMost V_less__eq V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_k))))) (forall ((V_less__eq $$unsorted) (V_i $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatMost V_less__eq V_k T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_B))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_Q $$unsorted) (V_xd $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xd)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xd) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a)) V_A))))) (forall ((V_P $$unsorted) (V_xe $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xe)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xe) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a)) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XballE__1__1 V_A V_P T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_b) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThan V_less V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_k) V_i))))) (forall ((V_less $$unsorted) (V_k $$unsorted) (V_i $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_k) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThan V_less V_k T_a)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 V_A V_B V_P T_b T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_A))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a)))))) (forall ((V_less__eq $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexE__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OlessThan V_less V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_k))))) (forall ((V_less $$unsorted) (V_i $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OlessThan V_less V_k T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_bool))) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B V_x) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_bool))) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B V_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_less $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a)))))) (forall ((V_less__eq $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_aa $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_aa T_a))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_m $$unsorted) (V_t $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s V_m V_t) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_t)))) (forall ((V_s $$unsorted) (V_n $$unsorted)) (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_s)) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c1 V_s V_n V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s_H $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s (tptp.c_Suc V_n) V_s_H) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)))) (forall ((V_c2 $$unsorted) (V_s2 $$unsorted) (V_c1 $$unsorted) (V_s1 $$unsorted) (V_t1 $$unsorted) (V_t2 $$unsorted) (V_n2 $$unsorted) (V_n1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s2 (tptp.c_Natural_Osko__Natural__Xevaln__max2__1__1 V_c1 V_c2 V_s1 V_s2 V_t1 V_t2) V_t2) (not (tptp.c_Natural_Oevaln V_c2 V_s2 V_n2 V_t2)) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n1 V_t1)))) (forall ((V_c1 $$unsorted) (V_s1 $$unsorted) (V_c2 $$unsorted) (V_s2 $$unsorted) (V_t1 $$unsorted) (V_t2 $$unsorted) (V_n2 $$unsorted) (V_n1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c1 V_s1 (tptp.c_Natural_Osko__Natural__Xevaln__max2__1__1 V_c1 V_c2 V_s1 V_s2 V_t1 V_t2) V_t1) (not (tptp.c_Natural_Oevaln V_c2 V_s2 V_n2 V_t2)) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n1 V_t1)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c0 V_s V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevaln _let_1 V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln _let_1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c V_s0 V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c0 V_s0 V_n V_s1)))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_x $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_x V_t)))) (= (tptp.hAPP (tptp.c_COMBI tptp.t_a) tptp.v_P) tptp.v_P) (forall ((V_n $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_t T_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) V_t T_a)))) (forall ((V_n $$unsorted) (V_na $$unsorted) (V_ts $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_na tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_na) V_ts))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 V_G V_n)) V_G)) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a))))) (forall ((V_n $$unsorted) (V_xa $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_xa tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_xa) V_ts))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) (tptp.v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 V_n V_ts) tptp.t_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (V_x $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a) (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 V_G V_ts) V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_x) V_G))))) (forall ((V_n $$unsorted) (V_nb $$unsorted) (V_ts $$unsorted) (V_G $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_nb tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_nb) V_ts))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 V_G V_n) tptp.t_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a)))) (= (tptp.c_Hoare__Mirabelle_Opeek__and tptp.v_P tptp.v_p tptp.v_Z tptp.v_s tptp.t_a) (tptp.c_and _let_7 (tptp.hAPP tptp.v_p tptp.v_s))) (forall ((V_P $$unsorted) (V_p $$unsorted)) (= (tptp.c_Hoare__Mirabelle_Opeek__and V_P V_p tptp.v_Z tptp.v_s tptp.t_a) (tptp.c_and (tptp.hAPP (tptp.hAPP V_P tptp.v_Z) tptp.v_s) (tptp.hAPP V_p tptp.v_s)))) (forall ((V_Q $$unsorted) (V_Z $$unsorted) (V_s_H $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q V_Z) V_s_H)) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_Z) V_s))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a) tptp.t_a)))) (= (tptp.hAPP (tptp.c_COMBK tptp.v_P tptp.t_a tptp.t_b) tptp.v_Q) tptp.v_P) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ts))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 V_n V_ts)) V_ts))))) (= (tptp.hAPP (tptp.c_COMBB tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP tptp.v_P _let_10)) (= (tptp.hAPP (tptp.c_COMBS tptp.v_P tptp.v_Q tptp.t_a tptp.t_b tptp.t_c) tptp.v_R) (tptp.hAPP _let_9 _let_10)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC tptp.v_P tptp.t_a tptp.t_b tptp.t_c) tptp.v_Q) tptp.v_R) (tptp.hAPP _let_9 tptp.v_Q)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) _let_8 _let_6 _let_5 _let_4 (forall ((V_x $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_n V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_x) tptp.v_Ga))))) _let_2 _let_1 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y))))))))))))))))))))))))))))))
% 0.54/0.98  )
% 0.54/0.98  % SZS output end Proof for SWV861-1
% 0.54/0.98  % cvc5---1.0.5 exiting
% 0.82/0.99  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------