TSTP Solution File: SCT123+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:12:06 EDT 2023
% Result : Theorem 1.15s 1.31s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.20 % Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 0.20/0.21 % Command : do_cvc5 %s %d
% 0.21/0.42 % Computer : n018.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.42 % CPULimit : 300
% 0.21/0.42 % WCLimit : 300
% 0.21/0.42 % DateTime : Thu Aug 24 16:34:13 EDT 2023
% 0.21/0.42 % CPUTime :
% 0.28/0.63 %----Proving TF0_NAR, FOF, or CNF
% 1.15/1.31 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.nrY0gHSr2s/cvc5---1.0.5_23243.p...
% 1.15/1.31 ------- get file name : TPTP file name is SCT123+1
% 1.15/1.31 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23243.smt2...
% 1.15/1.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.15/1.31 % SZS status Theorem for SCT123+1
% 1.15/1.31 % SZS output start Proof for SCT123+1
% 1.15/1.31 (
% 1.15/1.31 (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_COMBK _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.v_L))) (let ((_let_3 (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1)) _let_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP _let_3 tptp.c_Arrow__Order__Mirabelle_OProf)))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.c_member _let_1))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_6 tptp.v_L) tptp.c_Arrow__Order__Mirabelle_OLin)))) (let ((_let_8 (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q) V_P)))) (let ((_let_9 (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))))) (let ((_let_10 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_11 (tptp.c_COMBK _let_10 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.c_Arrow__Order__Mirabelle_OLin))) (let ((_let_12 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_HOL_Obool)))) (let ((_let_13 (tptp.c_FuncSet_OPi tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_12 _let_11))) (let ((_let_14 (= tptp.c_Arrow__Order__Mirabelle_OProf _let_13))) (let ((_let_15 (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))))) (let ((_let_16 (tptp.hBOOL (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_OLin tptp.v_L)))) (let ((_let_17 (tptp.hAPP _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_18 (= tptp.c_Arrow__Order__Mirabelle_OLin _let_17))) (let ((_let_19 (tptp.hAPP _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_20 (= tptp.v_L _let_19))) (let ((_let_21 (tptp.hBOOL (tptp.hAPP _let_17 _let_19)))) (let ((_let_22 (= _let_7 _let_16))) (let ((_let_23 (_let_15))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 ((tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))) (let ((_let_26 (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_P (tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q)))) (let ((_let_30 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_6 _let_19) _let_17)))) (let ((_let_31 (= _let_30 _let_21))) (let ((_let_32 (not _let_21))) (let ((_let_33 (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oindi) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_12))) _let_30))) (let ((_let_34 (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oindi) B_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_HOL_Obool))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.c_COMBK _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.v_L) B_x)) (tptp.hAPP (tptp.c_COMBK (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.c_Arrow__Order__Mirabelle_OLin) B_x)))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (tptp.hBOOL (tptp.hAPP _let_3 _let_13)))) (let ((_let_37 (not _let_34))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_36))) (let ((_let_42 (ASSUME :args (_let_14)))) (let ((_let_43 (ASSUME :args (_let_5)))) (let ((_let_44 (not _let_14))) (let ((_let_45 (or))) (let ((_let_46 (and _let_14 _let_5))) (let ((_let_47 (APPLY_UF tptp.hBOOL))) (let ((_let_48 (APPLY_UF tptp.hAPP))) (let ((_let_49 (_let_37))) (let ((_let_50 (and _let_16 _let_18 _let_20))) (let ((_let_51 (_let_16 _let_18 _let_20))) (let ((_let_52 (ASSUME :args (_let_16)))) (let ((_let_53 (ASSUME :args (_let_20)))) (let ((_let_54 (ASSUME :args (_let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_54 _let_53) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (SYMM _let_54) (SYMM _let_53) :args _let_48) :args _let_47) (TRUE_INTRO _let_52))) :args _let_51)) :args _let_51)) :args (true _let_50)) :args ((or (not _let_16) _let_21 (not _let_18) (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_31)) :args ((or _let_30 _let_32 (not _let_31)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_49)) :args _let_49)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_34))) (REFL :args (_let_35)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_46)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_42) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (_let_3)) (SYMM _let_42) :args _let_48) :args _let_47) (FALSE_INTRO _let_43))) :args (_let_5 _let_14))) :args (_let_14 _let_5))) :args (true _let_46)) (CONG (REFL :args (_let_44)) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args (_let_41)) :args _let_45)) :args ((or _let_4 _let_44 _let_41))) _let_43 _let_42 :args (_let_41 true _let_4 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_11 _let_2 _let_1 _let_12 tptp.tc_Arrow__Order__Mirabelle_Oindi QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_37 true _let_36 false _let_38)) :args (_let_35 true _let_34)) :args ((not _let_30) true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_17 _let_19 _let_1 QUANTIFIERS_INST_E_MATCHING _let_25)) :args _let_23)) _let_24 :args (_let_31 false _let_15)) :args (_let_32 true _let_30 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.v_L tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 QUANTIFIERS_INST_E_MATCHING _let_29)) :args _let_28)) _let_27 :args (_let_20 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.c_Arrow__Order__Mirabelle_OLin tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 QUANTIFIERS_INST_E_MATCHING _let_29)) :args _let_28)) _let_27 :args (_let_18 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or (not _let_7) _let_16 (not _let_22)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.c_Arrow__Order__Mirabelle_OLin tptp.v_L _let_1 QUANTIFIERS_INST_E_MATCHING _let_25)) :args _let_23)) _let_24 :args (_let_22 false _let_15)) :args (_let_16 false _let_7 false _let_22)) :args (false true _let_21 false _let_20 false _let_18 false _let_16)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) (forall ((V_La_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Oabove V_La_2 V_x_2 V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_La_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_La_2 V_x_2 V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_x_2 $$unsorted) (V_La_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_La_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_x_2 $$unsorted) (V_La_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_La_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))) (=> (= V_A_2 V_B_2) (=> (=> _let_3 (not _let_2)) (not (=> (not _let_3) _let_2)))))))) (forall ((V_i_2 $$unsorted) (V_F_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Odictator V_F_2 V_i_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (= (tptp.hAPP V_F_2 B_x) (tptp.hAPP B_x V_i_2)))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (= (tptp.hAPP _let_1 V_R_2) (tptp.hAPP _let_1 V_S_2)) (= V_R_2 V_S_2)))) (exists ((B_L $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)) B_L) tptp.c_Arrow__Order__Mirabelle_OLin))) _let_15 (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (=> (= V_a_2 V_b_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_A_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (=> (= V_x_2 V_y_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_A_2)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (= V_A_2 V_B_2) (= (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.hAPP tptp.c_fequal V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_La_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_y_2)))) (let ((_let_6 (= V_x_2 V_a_2))) (let ((_let_7 (= V_y_2 V_a_2))) (=> (not (= V_a_2 V_b_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.c_Arrow__Order__Mirabelle_Obelow V_La_2 V_a_2 V_b_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_b_2)) V_La_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_y_2 V_b_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_y_2)) V_La_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_La_2))))))))))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_La_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_y_2)))) (let ((_let_6 (= V_y_2 V_b_2))) (let ((_let_7 (= V_x_2 V_b_2))) (=> (not (= V_a_2 V_b_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.c_Arrow__Order__Mirabelle_Oabove V_La_2 V_a_2 V_b_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_y_2)) V_La_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_x_2 V_a_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_a_2)) V_La_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_La_2))))))))))))))))) (forall ((V_La_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Relation_Oconverse tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_La_2)) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_La_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)) V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2)) V_La_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_a_2)) V_La_2))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_La_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)) V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (=> (not (= V_x_2 V_y_2)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) V_La_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) V_La_2))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_Oinv__imagep T_a T_b V_r_2 V_f_2 V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_f_2 V_y_2))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2) V_c_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2) V_c_2))))) (forall ((T_c $$unsorted) (T_b $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2) V_c_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2))))) (forall ((V_z_2 $$unsorted) (V_La_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_x_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_La_2 V_z_2))) (and (not (= V_y_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_La_2)))))))) (forall ((V_z_2 $$unsorted) (V_La_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_y_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_La_2 V_z_2))) (and (not (= V_x_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_La_2)))))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))))) (= (= (tptp.hAPP _let_6 V_R_2) (tptp.hAPP _let_6 V_S_2)) (= V_R_2 V_S_2))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2) V_c_2)))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2) V_c_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_Oinv__imagep T_a T_b V_r_2 V_f_2 V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_f_2 V_y_2))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_b_2) V_a_2)) V_r_2)))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_b_2) V_a_2)) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r_2))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_b_2) V_a_2)) V_r_2)))) (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_c T_a)) V_A_2) V_f_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_a) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_f_2) V_x_2))))) (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tptp.tc_fun T_c T_a)) V_A_2) V_f_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_a) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_f_2) V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FunDef_Oin__rel T_a T_b V_R_2 V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2) V_y_2)) V_R_2)))) (forall ((V_f_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_a) V_A_2))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c T_a) V_B_2))) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c T_a) T_a T_b) _let_2) V_f_2)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) T_a T_c) _let_1) (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_f_2)))))))) (forall ((V_f_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_a) V_A_2))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c T_a) V_B_2))) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c T_a) T_a T_b) _let_2) V_f_2)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) T_a T_c) _let_1) (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_f_2)))))))) (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_y_H_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) V_y_H_2) V_y_2)) (tptp.hAPP V_R_2 V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP _let_1 V_y_H_2)) (tptp.hAPP _let_1 V_y_2))) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2)))))))) (forall ((T_c $$unsorted) (T_b $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2) V_c_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)))) (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_b_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B_2 V_a_2)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_a_2) V_A_2))))))) (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_b_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_a_2) V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B_2 V_a_2))))))) (forall ((V_B_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_b) V_b_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B_2 V_a_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2))))) (forall ((T_b $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP V_B_2 B_x))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP V_B_2 B_x))))))) (forall ((V_r_2 $$unsorted) (V_S_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_b T_a))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_3) V_S_2) V_r_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2) V_S_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_S_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_b T_a))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_3) V_S_2) V_r_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_S_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_r_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r_2)) V_r_2)) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H_2) V_b_H_2))) (tptp.c_Wellfounded_Olex__prod T_a T_b V_r_2 V_s_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_a_H_2)) V_r_2)) (and (= V_a_2 V_a_H_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) V_b_2) V_b_H_2)) V_s_2)))))))) (forall ((V_r_2 $$unsorted) (V_yx_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) V_yx_2) (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (= V_yx_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_y) B_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) B_y)) V_r_2)))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_b_2) V_c_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2) V_c_2)))))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_b_2) (tptp.c_Relation_ORange T_a T_b V_r_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) (tptp.c_Relation_OId__on T_a V_A_2)))))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Relation_OId__on T_a V_A_2))) (and (= V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))) V_r_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_x_2) V_y_2)) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (let ((_let_4 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_A_2) V_B_2)) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_3 _let_1) T_c) _let_2) V_B_2)) V_C_2)))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (let ((_let_4 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_A_2) V_B_2)) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_3 _let_1) T_c) _let_2) V_B_2)) V_C_2)))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b _let_1))) (let ((_let_4 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_4) V_A_2) V_B_2)) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_c _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_3 _let_1) T_c) _let_2) V_B_2)) V_C_2)))))))) (forall ((V_P_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (forall ((B_xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_xa) (tptp.hAPP V_B_2 B_x))) (tptp.hBOOL (tptp.hAPP V_P_2 B_xa)))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2))) (let ((_let_4 (tptp.tc_fun T_c _let_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_4 _let_2) T_b) _let_3) V_B_2)) V_C_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) V_B_2)) V_C_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2))) (let ((_let_4 (tptp.tc_fun T_c _let_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_4 _let_2) T_b) _let_3) V_B_2)) V_C_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) V_B_2)) V_C_2))))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2)))))) (forall ((T_a $$unsorted)) (= (tptp.c_Predicate_Oconversep T_a T_a tptp.c_fequal) tptp.c_fequal)) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Predicate_Oconversep T_b T_a (tptp.c_Predicate_Oconversep T_a T_b V_r_2)) V_r_2)) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_b V_r_2) V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_b_2) V_a_2)))) (forall ((V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_b V_r_2) V_a2_2) V_a1_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a1_2) V_a2_2)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_b V_r_2) V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_b V_r_2) V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_b_2) V_a_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_b) V_r_2)) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2)) (tptp.c_Relation_ORange T_b T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Predicate_Oconversep T_a T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool tptp.tc_HOL_Obool T_a) tptp.c_fNot)) tptp.c_fequal)) V_x_2) V_y_2)) (not (= V_x_2 V_y_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId__on T_a V_A_2))) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (exists ((B_y $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) B_y)) V_r_2))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (exists ((B_y $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_y) V_a_2)) V_r_2))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Predicate_ORangeP T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_x_2) (tptp.c_Relation_ORange T_a T_b V_r_2)))))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Predicate_ODomainP T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Relation_ODomain T_a T_b V_r_2)))))))))) (forall ((V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_c_2) (tptp.c_Relation_OId__on T_a V_A_2))) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (not (= V_c_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (not (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) V_b_2)) V_r_2))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (not (forall ((B_y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) B_y)) V_r_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.tc_prod T_b T_c))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.c_Product__Type_OPair T_b T_c))) (let ((_let_5 (tptp.c_member _let_2))) (let ((_let_6 (tptp.tc_fun _let_3 tptp.tc_HOL_Obool))) (let ((_let_7 (tptp.tc_fun T_c _let_6))) (let ((_let_8 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (let ((_let_9 (tptp.tc_fun T_b _let_8))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_9) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_9 T_a) (tptp.hAPP (tptp.c_COMBC T_b _let_3 _let_8) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_7 (tptp.tc_fun _let_3 _let_8) T_b) (tptp.c_COMBC T_c _let_3 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c _let_2) _let_7 T_b) (tptp.hAPP (tptp.c_COMBB _let_2 _let_6 T_c) _let_5)) _let_4)))) V_r_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_x_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_3) _let_1) V_r_2)))))))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.tc_prod T_b T_c))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.c_Product__Type_OPair T_b T_c))) (let ((_let_5 (tptp.c_member _let_2))) (let ((_let_6 (tptp.tc_fun _let_3 tptp.tc_HOL_Obool))) (let ((_let_7 (tptp.tc_fun T_c _let_6))) (let ((_let_8 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (let ((_let_9 (tptp.tc_fun T_b _let_8))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_9) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_9 T_a) (tptp.hAPP (tptp.c_COMBC T_b _let_3 _let_8) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_7 (tptp.tc_fun _let_3 _let_8) T_b) (tptp.c_COMBC T_c _let_3 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c _let_2) _let_7 T_b) (tptp.hAPP (tptp.c_COMBB _let_2 _let_6 T_c) _let_5)) _let_4)))) V_r_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_x_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_3) _let_1) V_r_2)))))))))))))) (forall ((V_i_2 $$unsorted) (V_F_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 _let_1)) V_F_2) (tptp.c_FuncSet_OPi _let_2 _let_1 tptp.c_Arrow__Order__Mirabelle_OProf (tptp.c_COMBK (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) _let_2 tptp.c_Arrow__Order__Mirabelle_OLin)))) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (=> (not (= B_a B_b)) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_x V_i_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_F_2 B_x))))))))) (tptp.c_Arrow__Order__Mirabelle_Odictator V_F_2 V_i_2)))))) (forall ((V_F_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Ounanimity V_F_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (=> (forall ((B_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP B_x B_i)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP V_F_2 B_x))))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_x_2))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a_2) V_b_2)) (tptp.c_Predicate_ORangeP T_a T_b V_r_2 V_b_2))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a_2) V_b_2)) (tptp.c_Predicate_ODomainP T_a T_b V_r_2 V_a_2))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_a2_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Predicate_ORangeP T_a T_b V_r_2 V_a2_2) (exists ((B_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_a) V_a2_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A_2) V_B_2) (tptp.c_Orderings_Otop__class_Otop _let_1)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_A_2) V_B_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (let ((_let_3 (tptp.c_member T_b))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBC T_b _let_1 tptp.tc_HOL_Obool) _let_3)) V_r_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) (tptp.hAPP _let_2 V_r_2)))))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (let ((_let_3 (tptp.c_member T_b))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) (tptp.hAPP (tptp.c_COMBC T_b _let_1 tptp.tc_HOL_Obool) _let_3)) V_r_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) (tptp.hAPP _let_2 V_r_2)))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) V_B_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_a)) (tptp.c_COMBI T_a)) (tptp.c_FuncSet_OPi T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK _let_1 T_a (tptp.c_Orderings_Otop__class_Otop _let_1))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool))))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_F_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_OIIA V_F_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) B_xa) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_x B_i))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_xa B_i)))))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_F_2 B_x))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_F_2 B_xa))))))))))))) _let_14 _let_9 (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) V_B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (let ((_let_2 (tptp.c_member (tptp.tc_fun T_a T_b)))) (=> (forall ((B_w $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_w) V_A_2)) (= (tptp.hAPP V_f_2 B_w) (tptp.hAPP V_g_2 B_w)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g_2) _let_1))))))) (forall ((T_b $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)))) (forall ((V_B_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_b_2) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2))))) (forall ((V_D_2 $$unsorted) (V_h_2 $$unsorted) (T_d $$unsorted) (V_C_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_b T_c)) V_g_2) (tptp.c_FuncSet_OPi T_b T_c V_B_2 (tptp.c_COMBK (tptp.tc_fun T_c tptp.tc_HOL_Obool) T_b V_C_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_c T_d)) V_h_2) (tptp.c_FuncSet_OPi T_c T_d V_C_2 (tptp.c_COMBK (tptp.tc_fun T_d tptp.tc_HOL_Obool) T_c V_D_2)))) (= (tptp.c_FuncSet_Ocompose T_a T_c T_d V_A_2 V_h_2 (tptp.c_FuncSet_Ocompose T_a T_b T_c V_A_2 V_g_2 V_f_2)) (tptp.c_FuncSet_Ocompose T_a T_b T_d V_A_2 (tptp.c_FuncSet_Ocompose T_b T_c T_d V_B_2 V_h_2 V_g_2) V_f_2)))))) (forall ((V_f_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (= (tptp.hAPP (tptp.c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) V_x_2) (tptp.hAPP V_g_2 (tptp.hAPP V_f_2 V_x_2))))) (forall ((V_C_2 $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_b T_c)) V_g_2) (tptp.c_FuncSet_OPi T_b T_c V_B_2 (tptp.c_COMBK _let_1 T_b V_C_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_c)) (tptp.c_FuncSet_Ocompose T_a T_b T_c V_A_2 V_g_2 V_f_2)) (tptp.c_FuncSet_OPi T_a T_c V_A_2 (tptp.c_COMBK _let_1 T_a V_C_2)))))))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) (tptp.c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_f_2 V_g_2)) (tptp.c_FuncSet_Oextensional T_a T_b V_A_2)))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1))))))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) V_a_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.c_Wellfounded_Oacc T_a V_r_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP V_B_2 B_x))))))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_b_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 B_x) V_b_2)))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (forall ((B_xa $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_xa) V_A_2)) (=> (not (= B_x B_xa)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_x) B_xa)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_xa) B_x)) V_r_2)))))))))))) (forall ((V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Relation_Oinv__image T_b T_a V_r_2 V_f_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_f_2 V_y_2))) V_r_2)))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) (tptp.c_Relation_Oinv__image T_b T_a V_R_2 V_f_2)) (tptp.c_Relation_Oinv__image T_b T_a (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_b) V_R_2) V_f_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_g_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (= (tptp.c_FuncSet_Ocompose T_a T_a T_b V_A_2 V_g_2 (tptp.c_FuncSet_Orestrict T_a T_a (tptp.c_COMBI T_a) V_A_2)) V_g_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (= (tptp.c_FuncSet_Ocompose T_a T_b T_b V_A_2 (tptp.c_FuncSet_Orestrict T_b T_b (tptp.c_COMBI T_b) V_B_2) V_f_2) V_f_2))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (let ((_let_5 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Wellfounded_Oaccp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a) (tptp.c_COMBC T_a _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_1) _let_4 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_a) (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_a)))) V_r_2) V_x_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) V_x_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_y) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (forall ((V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_R_2)))) (not (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) V_x_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_z) (tptp.c_Wellfounded_Oacc T_a V_R_2)))))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))) (= (tptp.hAPP V_f_2 V_x_2) (tptp.c_HOL_Oundefined T_b))))) (forall ((V_g_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (let ((_let_2 (tptp.c_member (tptp.tc_fun T_a T_b)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g_2) _let_1)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))) (= V_f_2 V_g_2))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oaccp T_a V_r_2 V_b_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a_2) V_b_2)) (tptp.c_Wellfounded_Oaccp T_a V_r_2 V_a_2)))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oaccp T_a V_r_2 V_a_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_a_2)) (tptp.c_Wellfounded_Oaccp T_a V_r_2 B_x))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oaccp T_a V_r_2 V_a_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_a_2)) (tptp.c_Wellfounded_Oaccp T_a V_r_2 B_x))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2) V_x_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP V_f_2 V_x_2))) (=> (not _let_2) (= _let_1 (tptp.c_HOL_Oundefined T_b))))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2) V_x_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP V_f_2 V_x_2))) (=> (not _let_2) (= _let_1 (tptp.c_HOL_Oundefined T_b))))))) (forall ((V_f_2 $$unsorted) (V_g_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) (tptp.c_FuncSet_Orestrict T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_c T_b T_a) V_g_2) V_f_2) V_A_2))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (= (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2) V_f_2))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2)) (tptp.c_FuncSet_Oextensional T_a T_b V_A_2)))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2)) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) V_B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) (tptp.c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2)) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f_2) V_r_2) V_x_2) V_y_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_y_2) V_x_2)) V_r_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP V_f_2 V_y_2))) (=> (not _let_2) (= _let_1 (tptp.c_HOL_Oundefined T_b))))))) (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_S_2))) (= (tptp.hAPP V_f_2 V_x_2) (tptp.c_HOL_Oundefined T_b))))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_b_2) V_a_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1))))))) (forall ((V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_b_2) V_a_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1))))))) (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_S_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) V_T_2))))) (forall ((T_b $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (B_f $$unsorted) (B_R $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_a_2)) B_R)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) B_f) B_R) V_a_2) V_x_2) (tptp.hAPP B_f V_x_2)))) (forall ((V_g_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Ocut T_a T_b))) (= (= (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_f_2) V_r_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_1 V_g_2) V_r_2) V_x_2)) (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) V_x_2)) V_r_2)) (= (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_g_2 B_y))))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_a_2)) V_r_2)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f_2) V_r_2) V_a_2) V_x_2) (tptp.hAPP V_f_2 V_x_2)))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_a_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_p_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_y_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Relation_ODomain T_a T_a V_R_2)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= V_x_2 V_y_2)))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (= (tptp.c_Transitive__Closure_Ortrancl T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP _let_1 V_r_2)) (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_F_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.tc_fun T_a _let_1))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (tptp.c_Recdef_Oadm__wf T_a T_b V_R_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 _let_3 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_1) _let_1) (tptp.c_COMBS T_a T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 _let_1) (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) V_F_2)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) _let_2) (tptp.c_Recdef_Ocut T_a T_b)) V_R_2)))) (tptp.c_COMBI T_a))))))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (let ((_let_4 (tptp.hAPP _let_2 V_x_2))) (=> (tptp.c_Relation_Osingle__valued T_a T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_y_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_z_2)) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_z_2) V_y_2)) _let_1))))))))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_ax_2) V_ay_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (forall ((B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_2 _let_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_2 _let_2) (tptp.hAPP (tptp.hAPP _let_1 B_a) B_b)) (tptp.hAPP (tptp.hAPP _let_1 B_aa) B_ba))) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_aa) B_ba))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_bx_2) V_by_2)))))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_1 _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_1 _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_ax_2) V_ay_2)) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_bx_2) V_by_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted) (B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 B_aa) B_ba))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b)) _let_3)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_bx_2) V_by_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_a) B_b))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_ax_2) V_ay_2)))))))) (forall ((V_r_2 $$unsorted) (V_zb_2 $$unsorted) (V_za_2 $$unsorted) (V_xb_2 $$unsorted) (V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_za_2) V_zb_2))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_1 V_xa_2) V_xb_2))) (let ((_let_4 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod _let_4 _let_4)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair _let_4 _let_4) _let_3) _let_2)) (tptp.c_Transitive__Closure_Ortrancl _let_4 V_r_2))) (=> (not (= _let_3 _let_2)) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_3 (tptp.hAPP (tptp.hAPP _let_2 B_a) B_b))) (let ((_let_4 (tptp.c_Product__Type_OPair _let_1 _let_1))) (let ((_let_5 (tptp.c_member (tptp.tc_prod _let_1 _let_1)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_xa_2) V_xb_2)) _let_3)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_za_2) V_zb_2))) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))))))))))))))))))) (forall ((V_T_2 $$unsorted) (V_S_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_FuncSet_OPi T_a T_b V_S_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_T_2))) (tptp.c_FuncSet_Oextensional T_a T_b V_S_2)))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (let ((_let_3 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B_2)) V_C_2) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B_2) V_B_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A_2))) (forall ((V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.c_member T_a))) (let ((_let_4 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) _let_3))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R_2)) (tptp.hAPP _let_4 V_S_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) (tptp.hAPP (tptp.hAPP _let_2 V_R_2) V_S_2))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B_2))))))) (forall ((V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_B_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_A_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) V_B_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A_2)) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_J_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.tc_fun _let_1 _let_1))) (let ((_let_4 (tptp.tc_fun T_c _let_1))) (let ((_let_5 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_J_2))) (let ((_let_6 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I_2))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_6 V_A_2)) (tptp.hAPP _let_5 V_B_2)) (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 _let_1 T_b) _let_5) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_4 _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 (tptp.tc_fun _let_4 _let_4) T_b) (tptp.c_COMBB _let_1 _let_1 T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) _let_2) V_A_2))) V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_I_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) (tptp.hAPP _let_2 V_B_2))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted) (V_I_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_I_2) V_A_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_k_2) V_I_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.hAPP V_A_2 V_k_2)) _let_2) _let_2))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_z)) V_r_2)) (= B_y B_z))))))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_b)))) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z_2)) V_r_2)) (= V_y_2 V_z_2))))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_4 (tptp.c_member _let_1))) (let ((_let_5 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.tc_fun T_b _let_5))) (let ((_let_7 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_8 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_7) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_6 (tptp.tc_fun _let_2 _let_7) T_a) (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_6 T_a) (tptp.hAPP (tptp.c_COMBB _let_1 _let_5 T_b) _let_4)) _let_3))))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a _let_7)) (tptp.hAPP _let_8 V_R_2)) (tptp.hAPP _let_8 V_S_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_R_2) V_S_2))))))))))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Predicate_Oconversep T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b (tptp.tc_fun T_a tptp.tc_HOL_Obool))) V_r_2) V_s_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Predicate_Oconversep T_b T_a V_r_2)) (tptp.c_Predicate_Oconversep T_b T_a V_s_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_b T_a))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.hAPP _let_1 V_r_2)) (tptp.hAPP _let_1 V_s_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_F_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Recdef_Oadm__wf T_a T_b V_R_2 V_F_2) (forall ((B_f $$unsorted) (B_g $$unsorted) (B_x $$unsorted)) (=> (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) B_x)) V_R_2)) (= (tptp.hAPP B_f B_z) (tptp.hAPP B_g B_z)))) (= (tptp.hAPP (tptp.hAPP V_F_2 B_f) B_x) (tptp.hAPP (tptp.hAPP V_F_2 B_g) B_x)))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_y)) V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_z)) V_r_2)) (= B_y B_z))))) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (not (= V_a_2 V_b_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) B_y)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) V_b_2)) V_r_2))))))))))) (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_z_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (not (= V_x_2 V_z_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) B_y)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) V_z_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)) (=> (forall ((B_y $$unsorted) (B_z $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_z)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_z) V_b_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_z)) (tptp.hBOOL (tptp.hAPP V_P_2 B_y)))))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2)))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)) (=> (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) B_y)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) B_z)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_y)) (tptp.hBOOL (tptp.hAPP V_P_2 B_z))))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.c_Orderings_Otop__class_Otop _let_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a) _let_3) V_A_2)) V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.c_Orderings_Otop__class_Otop _let_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) V_B_2)))))))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_a_2)) V_r_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (forall ((B_xa $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_xa) V_B_2)) (not (= B_x B_xa))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) _let_2) _let_2)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) _let_2) V_B_2) _let_2)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_S_2 $$unsorted)) (=> (not (= V_S_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool))))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OId__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))))) (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2))) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_c_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hBOOL (tptp.hAPP _let_1 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) _let_1))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)) (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)) (forall ((V_M_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_b) (=> (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a T_b) V_A_2) (tptp.c_COMBK T_b T_a V_M_2)) V_M_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) V_B_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_c_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A_2) (tptp.c_COMBK _let_1 T_a V_c_2)))) (let ((_let_3 (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_3 (= _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (not _let_3) (= _let_2 V_c_2))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) (tptp.c_COMBK _let_1 T_b _let_2)) _let_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Orderings_Obot__class_Obot _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) V_B_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_M_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_b) (=> (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b) V_A_2) (tptp.c_COMBK T_b T_a V_M_2)) V_M_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) _let_1) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) _let_1) V_x) _let_1)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_B_2) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_c_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_A_2) (tptp.c_COMBK _let_1 T_a V_c_2)))) (let ((_let_3 (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_3 (= _let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (=> (not _let_3) (= _let_2 V_c_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) V_B_2))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 V_B_2)) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a) _let_2) V_A_2)) V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 V_A_2)) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_2) V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FuncSet_OPi T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool)))) (forall ((V_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_y_2) V_A_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2) (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_x_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))) (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage T_b T_a V_r_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (=> (tptp.c_Relation_Osingle__valued T_a T_b (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_r_2)) (=> (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_c tptp.tc_HOL_Obool)))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_3) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_B_2))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_S_2)) (tptp.c_Relation_Orefl__on T_b (tptp.hAPP V_A_2 B_x) (tptp.hAPP V_r_2 B_x)))) (tptp.c_Relation_Orefl__on T_b (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_S_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a (tptp.tc_fun (tptp.tc_prod T_b T_b) tptp.tc_HOL_Obool)) V_S_2) V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_2) V_B_2)))) (let ((_let_4 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_4 (= _let_3 (tptp.c_Orderings_Otop__class_Otop _let_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_C_2) V_B_2)))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) V_A_2) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) _let_2) V_A_2) _let_2)))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage T_b T_a V_R_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (= (tptp.c_Transitive__Closure_Otrancl T_a _let_1) _let_1))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a)) V_A_2) V_B_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.hAPP V_A_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a)) V_A_2) V_B_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.hAPP V_A_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))))))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_p_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= (tptp.c_Transitive__Closure_Otrancl T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.hAPP _let_1 V_r_2)) (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2))) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_B_2) _let_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ORange T_a T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ODomain T_a T_a V_r_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_C_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) (tptp.hAPP _let_2 V_B_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B_2)) V_C_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_C_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A_2) V_B_2)) V_C_2) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_C_2)) (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_C_2))))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_C_2)))) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_C_2)) (tptp.hAPP _let_3 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_3) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) V_B_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_b) _let_2) V_A_2)) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage T_b T_a V_r_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_3) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_B_2))))))) (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a_2))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_b_2)) V_R_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_c_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_B_2) V_A_2)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B_2)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_2) V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.c_Relation_OImage T_b T_a V_r_2) V_A_2))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) V_b_2)) V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_b_2) (tptp.hAPP (tptp.c_Relation_OImage T_a T_b V_r_2) V_A_2)))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (let ((_let_2 (= V_x_2 V_y_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (or _let_2 (and (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a_2))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_b_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_c_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))))) (forall ((V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)))) (let ((_let_2 (= V_a_2 V_b_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (or _let_2 (and (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a_2))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_b_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_c_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_b_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_c_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_x_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z_2)) _let_1))))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.hAPP _let_1 V_r_2)))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_Oconverse T_a T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.hAPP _let_1 V_r_2)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2) V_y_2)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) V_B_2))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) V_B_2))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a) _let_2) V_A_2)) V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a) _let_3) V_A_2)) V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.c_Orderings_Otop__class_Otop _let_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2)) V_B_2)))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_C_2) V_B_2)))) (let ((_let_4 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_4 (= _let_3 V_A_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_2) V_B_2)))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage T_b T_a V_R_2))) (=> (tptp.c_Relation_Osingle__valued T_a T_b (tptp.hAPP (tptp.c_Relation_Oconverse T_b T_a) V_R_2)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.hAPP _let_1 V_A_2)) (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.c_Relation_OImage T_b T_a V_r_2) V_A_2))) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) V_b_2)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)))))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))) (exists ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) B_z)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_z) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))) (exists ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) B_z)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_z) V_y_2)) V_R_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_x_2) V_y_2)))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.c_Relation_OImage T_b T_a V_r_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_a_2) V_b_2)) V_r_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (= (tptp.c_Relation_OId__on T_a V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_2 _let_2) T_a) (tptp.c_Set_Oinsert _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a T_a _let_1) (tptp.c_Product__Type_OPair T_a T_a)) (tptp.c_COMBI T_a)))) (tptp.c_Orderings_Obot__class_Obot _let_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_a_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))) (= V_a_2 V_b_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b_2) V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b_2) V_A_2))) (=> (not (= V_a_2 V_b_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1)) (= V_a_2 V_b_2))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (= (= (tptp.hAPP (tptp.hAPP _let_2 V_a_2) (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_c_2) (tptp.hAPP (tptp.hAPP _let_2 V_d_2) _let_1))) (or (and (= V_a_2 V_c_2) (= V_b_2 V_d_2)) (and (= V_a_2 V_d_2) (= V_b_2 V_c_2))))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_A_2)))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) V_r_2)) (and (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.hAPP (tptp.c_Relation_Oconverse T_a T_a) V_r_2)) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_b_2 V_a_2))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_b_2 V_a_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP _let_1 V_B_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B_2)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)))) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B_2)) V_C_2))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_C_2)))) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_B_2)) (tptp.hAPP _let_1 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_C_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_B_2)) V_C_2) (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_C_2)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B_2)) V_C_2) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2))))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2))) (let ((_let_4 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_A_2)) V_B_2))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_B_2)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 _let_2)))))))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_B_2)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2) V_A_2)) V_B_2) (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_A_2) V_A_2))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2))) (let ((_let_2 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 V_A_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 V_B_2))) (= (= (tptp.hAPP _let_1 V_A_2) (tptp.hAPP _let_1 V_B_2)) (= V_A_2 V_B_2))))))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_a_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b_2) V_A_2))) (or (= V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) V_B_2)))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.hAPP _let_1 V_y_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_A_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_A_2))))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_y_2) V_A_2) V_x_2)) (or (= V_y_2 V_x_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) V_a_2) V_b_2)) V_r_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_b_2) (tptp.c_Relation_ORange T_b T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_a_2) V_b_2)) V_r_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Relation_ODomain T_a T_b V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_A_2)) (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_2) V_C_2))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_b) _let_1) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_C_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_b) _let_3) V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2))))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_2) V_A_2) (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)))) (tptp.hAPP _let_1 V_A_2))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A_2))) (= (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (let ((_let_4 (tptp.hAPP _let_3 V_A_2))) (= (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_B_2)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_u_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_u_2) V_A_2)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2)))))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_C_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2))))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_1 _let_1) (tptp.c_Set_Oinsert T_a)) (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_C_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_2) V_C_2))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_B_2)))) (let ((_let_5 (= V_C_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (and (=> _let_5 (= _let_4 (tptp.hAPP _let_1 (tptp.c_Orderings_Obot__class_Obot _let_2)))) (=> (not _let_5) (= _let_4 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 T_a) _let_1) V_B_2))))))))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_u_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a _let_1) V_A_2))) (let ((_let_3 (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_u_2) V_A_2)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_1 T_a) _let_3) V_B_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2) V_A_2)) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.hAPP V_B_2 V_a_2)) (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_A_2))))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) (tptp.hAPP _let_2 V_A_2)) (tptp.hAPP _let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2))))) (forall ((V_B_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Relation_OImage T_b T_a V_r_2))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP _let_2 V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_3) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_1 _let_3 T_b) _let_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b _let_1 _let_1) (tptp.c_Set_Oinsert T_b)) (tptp.c_Orderings_Obot__class_Obot _let_1))))))))) (forall ((V_T_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (= (tptp.c_FuncSet_Oextensional__funcset T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_T_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_COMBK T_b T_a (tptp.c_HOL_Oundefined T_b))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))))) (forall ((T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (= (tptp.c_FuncSet_Oextensional T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert _let_1) (tptp.c_COMBK T_b T_a (tptp.c_HOL_Oundefined T_b))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_x_2)) (forall ((V_y_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2) (tptp.c_Orderings_Obot__class_Obot _let_1))) V_y_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_x_2) V_y_2)))))) (forall ((V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_T_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun T_b T_a)))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_T_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_b T_a V_S_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_2) V_T_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot _let_2)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Fun_Ofun__upd T_b T_a V_f_2 V_x_2 V_a_2)) (tptp.c_FuncSet_Oextensional__funcset T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x_2) V_S_2) V_T_2)))))))) (forall ((V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_z_2)) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a1_2 V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_a2_2)) (forall ((V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_T_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun T_b T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_y_2) V_T_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_b T_a V_S_2 V_T_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Fun_Ofun__upd T_b T_a V_f_2 V_x_2 V_y_2)) (tptp.c_FuncSet_Oextensional__funcset T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_x_2) V_S_2) V_T_2))))))) (forall ((V_T_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_S_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun T_a T_b)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_S_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2) V_S_2) V_T_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 (tptp.c_HOL_Oundefined T_b))) (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2))))))) (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 (tptp.hAPP V_f_2 V_x_2)) V_f_2)) (forall ((V_T_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_S_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_member (tptp.tc_fun T_a T_b)))) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_S_2)) (not (= (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 B_x))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_x_2) V_S_2) V_T_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 (tptp.c_HOL_Oundefined T_b))) (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_T_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.c_Orderings_Obot__class_Obot _let_1))))))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (=> (= (tptp.hAPP V_f_2 V_x_2) V_y_2) (= (tptp.c_Fun_Ofun__upd T_b T_a V_f_2 V_x_2 V_y_2) V_f_2))) (forall ((V_y_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (not (= V_z_2 V_x_2)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_z_2) (tptp.hAPP V_f_2 V_z_2)))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted)) (=> (not (= V_a_2 V_c_2)) (= (tptp.c_Fun_Ofun__upd T_a T_b (tptp.c_Fun_Ofun__upd T_a T_b V_m_2 V_a_2 V_b_2) V_c_2 V_d_2) (tptp.c_Fun_Ofun__upd T_a T_b (tptp.c_Fun_Ofun__upd T_a T_b V_m_2 V_c_2 V_d_2) V_a_2 V_b_2)))) (forall ((V_y_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_z_2))) (let ((_let_2 (= V_z_2 V_x_2))) (and (=> _let_2 (= _let_1 V_y_2)) (=> (not _let_2) (= _let_1 (tptp.hAPP V_f_2 V_z_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd T_b T_a V_f_2 V_x_2 V_y_2) V_x_2) V_y_2)) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd T_a T_b (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_x_2 V_z_2) (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_z_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_f_2) (= (tptp.hAPP V_f_2 V_x_2) V_y_2))) (forall ((V_b_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_a_2 V_b_2) V_x_2))) (let ((_let_2 (= V_x_2 V_a_2))) (and (=> _let_2 (= _let_1 V_b_2)) (=> (not _let_2) (= _let_1 (tptp.hAPP V_f_2 V_x_2))))))) (forall ((V_a5_2 $$unsorted) (V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_a4_2 $$unsorted) (V_a3_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2))) (= (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 V_a2_2 _let_1) (or (and (= V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= _let_1 V_a4_2)) (exists ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (and (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) (tptp.hAPP (tptp.hAPP V_a3_2 B_x) B_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_a2_2)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_a2_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) B_x) (tptp.c_Orderings_Obot__class_Obot _let_1))) B_y)))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert T_a))) (let ((_let_4 (tptp.c_Relation_OImage T_a T_a V_r_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_a_2) _let_2))) (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_b_2) _let_2))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) V_r_2))))))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_a_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Relation_OImage T_a T_a V_r_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.c_Relation_OImage T_a T_a V_r_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) V_r_2)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_3 (tptp.c_Set_Oinsert T_a))) (let ((_let_4 (tptp.c_Relation_OImage T_a T_a V_r_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (and (= (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) _let_2)) (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_y_2) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_A_2)))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.c_Relation_OImage T_a T_a V_r_2))) (let ((_let_4 (tptp.c_member T_a))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_x_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 V_y_2) V_A_2)) (= (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x_2) _let_1)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2))))))))))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.c_Relation_OImage T_a T_a V_r_2))) (=> (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1)) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) V_r_2))))))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (V_r2_2 $$unsorted) (V_A2_2 $$unsorted) (T_b $$unsorted) (V_r1_2 $$unsorted) (V_A1_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A1_2 V_r1_2) (=> (tptp.c_Equiv__Relations_Oequiv T_b V_A2_2 V_r2_2) (=> (tptp.c_Equiv__Relations_Ocongruent2 T_a T_b _let_1 V_r1_2 V_r2_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a1_2) V_A1_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_a2_2) V_A2_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) (tptp.hAPP (tptp.c_Relation_OImage T_a T_a V_r1_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a1_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_1 T_a) (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.hAPP (tptp.c_Relation_OImage T_b T_b V_r2_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a2_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool)))))) V_f_2)) (tptp.hAPP (tptp.hAPP V_f_2 V_a1_2) V_a2_2))))))))) (forall ((V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_Equiv__Relations_Ocongruent T_a _let_1 V_r_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) (tptp.hAPP (tptp.c_Relation_OImage T_a T_a V_r_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_a) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) V_f_2) (tptp.hAPP V_f_2 V_a_2))))))) (forall ((V_a_2 $$unsorted) (V_f_2 $$unsorted) (V_r2_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_r1_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r1_2) (=> (tptp.c_Equiv__Relations_Ocongruent2 T_a T_b T_c V_r1_2 V_r2_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.c_Equiv__Relations_Ocongruent T_b T_c V_r2_2 (tptp.hAPP V_f_2 V_a_2)))))) (forall ((V_z2_2 $$unsorted) (V_y2_2 $$unsorted) (V_z1_2 $$unsorted) (V_y1_2 $$unsorted) (V_f_2 $$unsorted) (V_r2_2 $$unsorted) (V_r1_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Ocongruent2 T_a T_b T_c V_r1_2 V_r2_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_y1_2) V_z1_2)) V_r1_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) V_y2_2) V_z2_2)) V_r2_2)) (= (tptp.hAPP (tptp.hAPP V_f_2 V_y1_2) V_y2_2) (tptp.hAPP (tptp.hAPP V_f_2 V_z1_2) V_z2_2)))))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Ocongruent T_a T_b V_r_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_y_2) V_z_2)) V_r_2)) (= (tptp.hAPP V_f_2 V_y_2) (tptp.hAPP V_f_2 V_z_2))))) (forall ((V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (V_r2_2 $$unsorted) (V_A2_2 $$unsorted) (T_b $$unsorted) (V_r1_2 $$unsorted) (V_A1_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A1_2 V_r1_2) (=> (tptp.c_Equiv__Relations_Oequiv T_b V_A2_2 V_r2_2) (=> (tptp.c_Equiv__Relations_Ocongruent2 T_a T_b _let_1 V_r1_2 V_r2_2 V_f_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_a_2) V_A2_2)) (tptp.c_Equiv__Relations_Ocongruent T_a _let_1 V_r1_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_1 T_a) (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) (tptp.hAPP (tptp.c_Relation_OImage T_b T_b V_r2_2) (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert T_b) V_a_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool)))))) V_f_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Set_Oinsert T_a))) (let ((_let_3 (tptp.c_member T_a))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_y_2) V_A_2)) (= (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.hAPP (tptp.hAPP _let_2 V_x_2) _let_1) V_r_2) (tptp.c_Equiv__Relations_Oquotient T_a (tptp.hAPP (tptp.hAPP _let_2 V_y_2) _let_1) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)))))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert T_a))) (let ((_let_4 (tptp.c_Relation_OImage T_a T_a V_r_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_b_2) _let_2)) (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_a_2) _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_b_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_a_2) V_b_2)) V_r_2)))))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= V_A_2 V_B_2))))) (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OImage T_b T_a V_r_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_3) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_2) V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 T_c) _let_1) V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_B_2))))))) (forall ((V_M_2 $$unsorted) (V_A_2 $$unsorted) (V_i_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_i_2) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b) V_A_2) V_M_2) (tptp.hAPP V_M_2 V_i_2))))) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_a_2) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP V_B_2 V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a _let_1) V_A_2) V_B_2))))) (forall ((V_r_2 $$unsorted) (V_s_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_s_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2)))) (forall ((V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (V_r_2 $$unsorted) (V_r_H_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_H_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_Relation_OImage T_a T_b V_r_H_2) V_A_H_2) (tptp.hAPP (tptp.c_Relation_OImage T_a T_b V_r_2) V_A_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP _let_2 V_R_2) (tptp.hAPP _let_2 V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_R_2 V_S_2))))) (forall ((V_u_2 $$unsorted) (V_M_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_a) V_A_2) V_M_2) V_u_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_M_2 B_x) V_u_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_I_2) V_A_2) V_B_2) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_I_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.hAPP V_A_2 B_x) V_B_2)))))) (forall ((V_M_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_u_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_u_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_a) V_A_2) V_M_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_u_2 (tptp.hAPP V_M_2 B_x))))))) (forall ((V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_1) V_I_2) V_A_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_x) V_I_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.hAPP V_A_2 B_x))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b)) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b))))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_y) V_z)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_b) V_x)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_y_2) V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2) V_x_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_D_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) V_A_2))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_S_2 _let_1) (= (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2) _let_1)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_r_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) _let_1))))) (forall ((V_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Wellfounded_Oacc T_a V_R2_2) (tptp.c_Wellfounded_Oacc T_a V_R1_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))) (forall ((V_f_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_a T_b))) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_f_2) (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_f_2)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))) (forall ((V_f_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_a T_b))) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_f_2) (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_f_2)))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((V_x_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_FuncSet_OPi T_a T_b V_A_H_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (= (tptp.hAPP (tptp.hAPP _let_2 V_B_2) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_A_2)) V_A_2)))))) (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_D_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus _let_1) V_A_2) V_B_2) V_A_2))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_2) (= V_A_2 _let_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))) (tptp.class_Lattices_Obounded__lattice tptp.tc_HOL_Obool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Complete__Lattice_Ocomplete__lattice T_1) (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__top (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__bot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__inf (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Otop T_1) (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Obot T_1) (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_HOL_Obool) (tptp.class_Lattices_Obounded__lattice__top tptp.tc_HOL_Obool) (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Otop tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Orderings_Obot tptp.tc_HOL_Obool) (tptp.class_Groups_Ominus tptp.tc_HOL_Obool) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) _let_8 (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P_2) V_Q_2) V_R_2) (tptp.hAPP V_P_2 (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_b T_c T_a) V_P_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) V_Q_2))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2)))) (forall ((V_P_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.c_fNot V_P_2))) (not (tptp.hBOOL V_P_2)))) (forall ((V_P_2 $$unsorted)) (or (not (not (tptp.hBOOL V_P_2))) (tptp.hBOOL (tptp.hAPP tptp.c_fNot V_P_2)))) _let_7 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.15/1.31 )
% 1.15/1.31 % SZS output end Proof for SCT123+1
% 1.15/1.31 % cvc5---1.0.5 exiting
% 1.15/1.32 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------