TSTP Solution File: SCT131+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT131+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 14:12:08 EDT 2023
% Result : Theorem 1.15s 1.35s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.19 % Problem : SCT131+1 : TPTP v8.1.2. Released v5.2.0.
% 0.20/0.20 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n023.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Thu Aug 24 16:55:42 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.45/0.61 %----Proving TF0_NAR, FOF, or CNF
% 1.15/1.35 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ubvblWCZpb/cvc5---1.0.5_14674.p...
% 1.15/1.35 ------- get file name : TPTP file name is SCT131+1
% 1.15/1.35 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14674.smt2...
% 1.15/1.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.15/1.35 % SZS status Theorem for SCT131+1
% 1.15/1.35 % SZS output start Proof for SCT131+1
% 1.15/1.35 (
% 1.15/1.35 (let ((_let_1 (tptp.hAPP tptp.v_F tptp.v_Q____))) (let ((_let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (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.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_b____) tptp.v_b_H____)) _let_1)))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2) (forall ((B_x $$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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP B_x B_i)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)) (tptp.hAPP V_Fa_2 B_x))))))))))) (let ((_let_8 (tptp.tc_fun _let_3 tptp.tc_HOL_Obool))) (let ((_let_9 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_8))) (let ((_let_10 (tptp.c_member _let_9))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_10 tptp.v_Q____) tptp.c_Arrow__Order__Mirabelle_OProf)))) (let ((_let_12 (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_a____) tptp.v_b____)))) (let ((_let_13 (forall ((V_i_2 $$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) tptp.v_b____) tptp.v_b_H____)) (tptp.hAPP tptp.v_Q____ V_i_2)))))) (let ((_let_14 (tptp.c_Arrow__Order__Mirabelle_Ounanimity tptp.v_F))) (let ((_let_15 (forall ((B_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.v_b____) tptp.v_b_H____)) (tptp.hAPP tptp.v_Q____ B_i)))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (not _let_11))) (let ((_let_18 (or _let_17 _let_16 _let_5))) (let ((_let_19 (forall ((B_x $$unsorted) (BOUND_VARIABLE_10178 $$unsorted) (BOUND_VARIABLE_10176 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10176) BOUND_VARIABLE_10178)) (tptp.hAPP B_x B_i))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10176) BOUND_VARIABLE_10178)) (tptp.hAPP tptp.v_F B_x)))))))) (let ((_let_20 (= _let_14 _let_19))) (let ((_let_21 (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_10178 $$unsorted) (BOUND_VARIABLE_10176 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) B_x) tptp.c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$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) BOUND_VARIABLE_10176) BOUND_VARIABLE_10178)) (tptp.hAPP B_x B_i))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10176) BOUND_VARIABLE_10178)) (tptp.hAPP V_Fa_2 B_x)))))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (_let_19))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_5 _let_17 _let_16 (not _let_18)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_23) :args (tptp.v_Q____ tptp.v_b_H____ tptp.v_b____ QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 BOUND_VARIABLE_10176) BOUND_VARIABLE_10178)) (tptp.hAPP tptp.v_F B_x))))) :args _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_20)) :args ((or (not _let_14) _let_19 (not _let_20)))) (ASSUME :args (_let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.v_F QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2)))) :args (_let_21))) _let_22 :args (_let_20 false _let_21)) :args (_let_19 false _let_14 false _let_20)) :args (_let_18 false _let_19)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_13 (= V_i_2 B_i)))) (ASSUME :args (_let_13)) :args (_let_15 false _let_13)) (ASSUME :args (_let_6)) (ASSUME :args (_let_11)) :args (false false _let_18 false _let_15 true _let_5 false _let_11)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_14 (tptp.c_Arrow__Order__Mirabelle_OIIA tptp.v_F) (not (= tptp.v_b____ tptp.v_b_H____)) (not (= tptp.v_b____ tptp.v_a_H____)) _let_13 (not (= tptp.v_a_H____ tptp.v_b_H____)) (not (= tptp.v_a____ tptp.v_b____)) (not (= tptp.v_a____ tptp.v_b_H____)) (tptp.hBOOL (tptp.hAPP _let_12 _let_1)) (tptp.hBOOL (tptp.hAPP _let_12 (tptp.hAPP tptp.v_F tptp.v_P____))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))) (=> (= V_A_2 V_B_2) (=> (=> _let_3 (not _let_2)) (not (=> (not _let_3) _let_2)))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_x_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_z_2))) (and (not (= V_y_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_L_2)))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_x_2) V_y_2)))) (let ((_let_2 (= V_y_2 V_z_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_z_2))) (and (not (= V_x_2 V_z_2)) (=> _let_2 (not (= V_x_2 V_y_2))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 V_L_2)))))))) (=> (not (= tptp.v_a____ tptp.v_a_H____)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 tptp.v_a_H____) tptp.v_a____)) _let_1))) (forall ((B_i $$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) tptp.v_a____) tptp.v_b____)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.v_P____ B_i))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.v_Q____ B_i)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_FunDef_Oin__rel T_a T_b V_R_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_x_2) V_y_2)) V_R_2)))) (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_y_H_2 $$unsorted) (T_b $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$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_Pa_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_Pa_2 V_R_2)))))))) (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.v_a____) tptp.v_b____)) (tptp.hAPP tptp.v_P____ B_i))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 tptp.v_a_H____) tptp.v_b_H____)) (tptp.hAPP tptp.v_P_H____ B_i))))))) (forall ((V_r_2 $$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))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_8) _let_1) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_10 tptp.v_P____) tptp.c_Arrow__Order__Mirabelle_OProf)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_10 tptp.v_P_H____) tptp.c_Arrow__Order__Mirabelle_OProf)) (forall ((V_x_2 $$unsorted) (V_L_2 $$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_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_x_2 $$unsorted) (V_L_2 $$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_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_x_2)) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_member _let_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) V_L_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_aa_2)) V_L_2))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$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_L_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_L_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) V_L_2))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a))) (=> (= V_aa_2 V_ba_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_aa_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_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) _let_11 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$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_aa_2))) (let ((_let_7 (= V_y_2 V_aa_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_aa_2 V_ba_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_ba_2)) V_L_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_y_2 V_ba_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_y_2)) V_L_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_L_2))))))))))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_y_2)))) (let ((_let_6 (= V_y_2 V_ba_2))) (let ((_let_7 (= V_x_2 V_ba_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_3 tptp.tc_HOL_Obool)) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (= (tptp.hBOOL (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2) V_aa_2) V_ba_2))) (and (not (= V_x_2 V_y_2)) (=> _let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_y_2)) V_L_2))) (=> (not _let_7) (and (=> _let_6 (or (= V_x_2 V_aa_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_2 V_aa_2)) V_L_2)))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP _let_5 V_L_2))))))))))))))))) (forall ((V_L_2 $$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_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2) V_x_2) V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_x_2 V_y_2)) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_i_2 $$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.hAPP tptp.v_P____ V_i_2))) (= (tptp.hAPP tptp.v_Q____ V_i_2) (tptp.c_HOL_OLet _let_1 _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_If _let_1 (tptp.hAPP (tptp.hAPP tptp.c_fequal tptp.v_a____) tptp.v_a_H____)) _let_2) (tptp.c_Arrow__Order__Mirabelle_Obelow _let_2 tptp.v_a_H____ tptp.v_a____)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS _let_1 _let_1 _let_1) (tptp.c_If _let_1 (tptp.hAPP (tptp.hAPP tptp.c_fequal tptp.v_b____) tptp.v_b_H____))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1)) tptp.c_Arrow__Order__Mirabelle_Oabove) tptp.v_b____)) tptp.v_b_H____))))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_b_Ha_2 $$unsorted) (V_a_Ha_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$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_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP _let_1 V_a_Ha_2) V_b_Ha_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_aa_2) V_a_Ha_2)) V_r_2)) (and (= V_aa_2 V_a_Ha_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_ba_2) V_b_Ha_2)) V_s_2)))))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (not (= V_aa_2 V_ba_2)) (exists ((B_x $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)) B_x) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_aa_2) V_ba_2)) B_x))))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_a1_2) (tptp.hAPP (tptp.hAPP V_Fa_2 V_a2_2) V_a1_2))) (exists ((B_g $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP V_Fa_2 V_a2_2) V_a1_2) (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) V_a1_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) V_a1_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z) (tptp.hAPP B_g B_z))))))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_aa_2)) V_r_2)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f_2) V_r_2) V_aa_2) V_x_2) (tptp.hAPP V_f_2 V_x_2)))) (forall ((V_g_2 $$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))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_9 _let_8)) tptp.v_F) (tptp.c_FuncSet_OPi _let_9 _let_8 tptp.c_Arrow__Order__Mirabelle_OProf (tptp.c_COMBK (tptp.tc_fun _let_8 tptp.tc_HOL_Obool) _let_9 tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_1) V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1)) (tptp.c_COMBK _let_1 tptp.tc_Arrow__Order__Mirabelle_Oindi V_L_2)) tptp.c_Arrow__Order__Mirabelle_OProf))))) (forall ((T_b $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (B_f $$unsorted) (B_R $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_aa_2)) B_R)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) B_f) B_R) V_aa_2) V_x_2) (tptp.hAPP B_f V_x_2)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a (tptp.c_COMBB _let_1 _let_3 T_b (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))))) (= (= (tptp.hAPP _let_6 V_R_2) (tptp.hAPP _let_6 V_S_2)) (= V_R_2 V_S_2))))))))) _let_7 (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_OIIA V_Fa_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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) B_a) B_b)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_x B_i))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP B_xa B_i)))))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_Fa_2 B_x))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_Fa_2 B_xa))))))))))))) (forall ((V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (let ((_let_2 (tptp.tc_fun T_a _let_1))) (let ((_let_3 (tptp.tc_fun T_a T_a))) (tptp.c_Recdef_Oadm__wf T_a T_b V_R_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 _let_3 _let_1) (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_1) _let_1 (tptp.c_COMBS T_a T_a T_b)) (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 _let_1 (tptp.c_COMBB _let_1 _let_1 T_a V_Fa_2)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) _let_2) (tptp.c_Recdef_Ocut T_a T_b)) V_R_2)))) (tptp.c_COMBI T_a))))))) (forall ((V_i_2 $$unsorted) (V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Odictator V_Fa_2 V_i_2) (forall ((B_x $$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_Fa_2 B_x) (tptp.hAPP B_x V_i_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_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_member T_a)))) (= (= (tptp.hAPP _let_1 V_R_2) (tptp.hAPP _let_1 V_S_2)) (= V_R_2 V_S_2)))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_a1_2) V_a2_2)) (exists ((B_g $$unsorted)) (and (= V_a2_2 (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) V_a1_2)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) V_a1_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z) (tptp.hAPP B_g B_z))))))))) (forall ((V_g_2 $$unsorted) (V_Fa_2 $$unsorted) (T_b $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_z $$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) V_x_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z) (tptp.hAPP V_g_2 B_z))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_x_2) (tptp.hAPP (tptp.hAPP V_Fa_2 V_g_2) V_x_2))))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))) (forall ((B_x $$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_aa_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_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.hAPP tptp.c_fequal V_y_2))) (= V_x_2 V_y_2))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_aa_2) _let_1))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_B_2 V_x_2)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)))))) (forall ((V_i_2 $$unsorted) (V_Fa_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun _let_2 _let_1)) V_Fa_2) (tptp.c_FuncSet_OPi _let_2 _let_1 tptp.c_Arrow__Order__Mirabelle_OProf (tptp.c_COMBK (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) _let_2 tptp.c_Arrow__Order__Mirabelle_OLin)))) (=> (forall ((B_x $$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_Fa_2 B_x))))))))) (tptp.c_Arrow__Order__Mirabelle_Odictator V_Fa_2 V_i_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_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (let ((_let_5 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a (tptp.c_COMBC T_a _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_1) _let_4 T_a (tptp.c_COMBB _let_1 _let_3 T_a (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_a)))) V_r_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2)))))))))) (forall ((V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) V_x_2)) V_R_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_z) (tptp.c_Wellfounded_Oacc T_a V_R_2)))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) V_x_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_y) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (forall ((V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Recdef_Oadm__wf T_a T_b V_R_2 V_Fa_2) (forall ((B_f $$unsorted) (B_g $$unsorted) (B_x $$unsorted)) (=> (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_z) B_x)) V_R_2)) (= (tptp.hAPP B_f B_z) (tptp.hAPP B_g B_z)))) (= (tptp.hAPP (tptp.hAPP V_Fa_2 B_f) B_x) (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) V_aa_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_aa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) V_aa_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_x) V_aa_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oaccp T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_aa_2)))))) (forall ((V_x_2 $$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_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 $$unsorted) (V_f_2 $$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_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_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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_w) V_A_2)) (= (tptp.hAPP V_f_2 B_w) (tptp.hAPP V_g_2 B_w)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_f_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_g_2) _let_1))))))) (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_B_2 B_x))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2))))) (forall ((V_C_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_HOL_Obool))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_B_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_b T_c)) V_g_2) (tptp.c_FuncSet_OPi T_b T_c V_B_2 (tptp.c_COMBK _let_1 T_b V_C_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_c)) (tptp.c_FuncSet_Ocompose T_a T_b T_c V_A_2 V_g_2 V_f_2)) (tptp.c_FuncSet_OPi T_a T_c V_A_2 (tptp.c_COMBK _let_1 T_a V_C_2)))))))) (forall ((V_D_2 $$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_ba_2 $$unsorted) (V_r_2 $$unsorted) (V_aa_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_aa_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_ba_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1))))))) (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_f_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2)) (= (tptp.hAPP (tptp.c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) V_x_2) (tptp.hAPP V_g_2 (tptp.hAPP V_f_2 V_x_2))))) (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_S_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) (tptp.hAPP V_f_2 V_x_2)) V_T_2))))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (let ((_let_2 (tptp.c_member T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_ba_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_aa_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) _let_1))))))) (forall ((V_r_2 $$unsorted) (V_aa_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_aa_2) V_aa_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) V_p_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_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_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_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_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_c_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_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_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_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_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_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_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.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)) (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_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_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_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_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_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (let ((_let_4 (tptp.hAPP _let_2 V_x_2))) (=> (tptp.c_Relation_Osingle__valued T_a T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_y_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_4 V_z_2)) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_z_2) V_y_2)) _let_1))))))))))) (forall ((V_y_2 $$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_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_Pa_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_Pa_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_Pa_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_a) B_b))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_ax_2) V_ay_2)))))))) (forall ((V_Pa_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_Pa_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_Pa_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_aa) B_ba))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_bx_2) V_by_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 ((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 ((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_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_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_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_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_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_B_2 $$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_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_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_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_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 $$unsorted) (V_A_2 $$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))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_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_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (exists ((B_y $$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_aa_2) B_y)) V_r_2))))) (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_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_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.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.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a (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_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 ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.c_Predicate_ODomainP T_a T_b V_r_2 V_aa_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.c_Product__Type_OPair T_a T_b))) (let ((_let_4 (tptp.c_member _let_1))) (let ((_let_5 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.tc_fun T_b _let_5))) (let ((_let_7 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_8 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_7) (tptp.hAPP (tptp.c_COMBB _let_6 (tptp.tc_fun _let_2 _let_7) T_a (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_6 T_a (tptp.c_COMBB _let_1 _let_5 T_b _let_4)) _let_3))))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a _let_7)) (tptp.hAPP _let_8 V_R_2)) (tptp.hAPP _let_8 V_S_2)) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_x_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_R_2) V_S_2))))))))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_c $$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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((V_y $$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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_b $$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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_y $$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_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_x) V_x))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_a) V_a) V_a))) (forall ((V_r_2 $$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_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (not (forall ((B_y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) B_y)) V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$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_aa_2) V_ba_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.c_Relation_ORange T_a T_b V_r_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_A_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (= V_aa_2 V_ba_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_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_aa_2) V_ba_2)) (tptp.c_Relation_OId__on T_a V_A_2)))))) (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_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_aa_2)) (=> (forall ((B_y $$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_aa_2) B_y)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) B_z)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_y)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_z))))))) (tptp.hBOOL (tptp.hAPP V_Pa_2 V_ba_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2))))))) (forall ((T_b $$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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B_2 V_x_2) V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool))) V_A_2) V_B_2) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_A_2 V_x_2) V_y_2)))) (forall ((V_A_2 $$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 $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (exists ((B_y $$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_aa_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.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.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a (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_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_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_ba_2) (tptp.c_Relation_ORange T_b T_a V_r_2))) (not (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_a) B_x) V_ba_2)) V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (not (= V_aa_2 V_ba_2)) (not (forall ((B_y $$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_aa_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_ba_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 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) B_y)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) V_z_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))))))) (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_2) V_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_ba_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_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_z)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_y)))))))) (tptp.hBOOL (tptp.hAPP V_Pa_2 V_aa_2)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.c_Predicate_ORangeP T_a T_b V_r_2 V_ba_2))) (forall ((V_a2_2 $$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_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 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (tptp.c_Relation_Oinv__image T_b T_a V_r_2 V_f_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_b T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_b) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_f_2 V_y_2))) V_r_2)))) (forall ((V_y_2 $$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_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_y_2) V_A_2))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_aa_2)) V_r_2))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_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)) (= (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_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_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_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_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_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_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_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_c_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_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_ba_2)) V_R_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ba_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_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2))))) (forall ((V_z_2 $$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_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_aa_2))) (let ((_let_4 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ba_2)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 V_ba_2) V_c_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c_2)) _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_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_ba_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_ba_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_R_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_2) V_ba_2)))) (let ((_let_2 (= V_aa_2 V_ba_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_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_aa_2))) (let ((_let_3 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_c_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (let ((_let_2 (= V_x_2 V_y_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (or _let_2 (and (not _let_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_R_2 $$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_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) (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_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_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_aa_2) V_ba_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_r_2))) (not (forall ((B_c $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) B_c)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_c) V_ba_2)) V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_z_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_r_2))) (not (forall ((B_y $$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_Otrancl T_a V_r_2))))))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.c_Set_Oinsert _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$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))))) (=> (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)) (not (= V_x_2 V_y_2))))) (forall ((V_xa_2 $$unsorted) (V_x_2 $$unsorted) (V_r_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))) (let ((_let_3 (tptp.c_member _let_2))) (let ((_let_4 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_5 (tptp.tc_fun _let_4 tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.tc_fun T_a _let_5))) (let ((_let_7 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_4 _let_7) (tptp.hAPP (tptp.c_COMBB _let_6 (tptp.tc_fun _let_4 _let_7) T_a (tptp.c_COMBC T_a _let_4 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_2) _let_6 T_a (tptp.c_COMBB _let_2 _let_5 T_a _let_3)) _let_1))) V_r_2)) V_x_2) V_xa_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_xa_2)) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (tptp.c_Relation_Oantisym T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_aa_2) V_ba_2)))) (forall ((V_ba_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_aa_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))) (= V_aa_2 V_ba_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_ba_2 V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_aa_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_ba_2 V_A_2))) (=> (not (= V_aa_2 V_ba_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))))) (forall ((V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_aa_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_ba_2 V_A_2))) (or (= V_aa_2 V_ba_2) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_x_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))) (= (= (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (= V_A_2 V_B_2)))))) (forall ((V_ba_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_aa_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_ba_2 V_B_2)))))) (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (= (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_aa_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 (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.hAPP (tptp.hAPP _let_1 V_A_2) V_B_2))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (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_aa_2) V_ba_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_ba_2 (tptp.c_Relation_ORange T_b T_a V_r_2)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otranclp T_a V_r_2))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_z_2)) (tptp.hBOOL (tptp.hAPP _let_2 V_z_2))))))) (forall ((V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_aa_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_ba_2) V_c_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_c_2)))))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otranclp T_a V_r_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_aa_2) V_ba_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_c_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_c_2)))))) (forall ((V_a3_2 $$unsorted) (V_a1_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_a1_2) V_a3_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a1_2) V_a3_2)) (exists ((B_b $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_a1_2) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_b) V_a3_2))))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_a1_2) V_a2_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 V_a1_2) V_a2_2)) (exists ((B_b $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Transitive__Closure_Otranclp T_a V_r_2) V_a1_2) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r_2 B_b) V_a2_2))))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_y_2 V_A_2) V_x_2)) (or (= V_y_2 V_x_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Set_Oinsert T_a V_y_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2))) (= (tptp.c_Set_Oinsert T_a V_x_2 _let_1) _let_1))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_C_2)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) V_C_2) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_aa_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))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_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_aa_2) V_C_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_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_aa_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_aa_2) V_A_2))) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) (tptp.hAPP _let_1 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_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.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) V_C_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_C_2)))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_aa_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 _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_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.c_Relation_Oantisym T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ba_2) V_aa_2)) V_r_2)) (= V_aa_2 V_ba_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$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 B_x) B_y)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_x)) V_r_2)) (= B_x B_y)))))))) (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.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 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_T_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_member (tptp.tc_fun T_b T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_y_2) V_T_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_f_2) (tptp.c_FuncSet_Oextensional__funcset T_b T_a V_S_2 V_T_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Fun_Ofun__upd T_b T_a V_f_2 V_x_2 V_y_2)) (tptp.c_FuncSet_Oextensional__funcset T_b T_a (tptp.c_Set_Oinsert T_b V_x_2 V_S_2) V_T_2))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Owf T_a (tptp.c_Set_Oinsert _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_x) B_y)) V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 B_y) B_x)) V_r_2)) (= B_x B_y)))))) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_ORange T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Relation_ORange T_b T_a V_A_2)) (tptp.c_Relation_ORange T_b T_a V_B_2))))) (forall ((V_B_2 $$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.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_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_b (tptp.c_Relation_Oinv__image T_a T_b V_r_2 V_f_2)))) (forall ((V_rb_2 $$unsorted) (T_b $$unsorted) (V_ra_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_ra_2) (=> (tptp.c_Wellfounded_Owf T_b V_rb_2) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_ra_2 V_rb_2))))) (forall ((V_aa_2 $$unsorted) (V_D_2 $$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_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_C_2) (tptp.c_Set_Oinsert T_a V_aa_2 V_D_2))))) (forall ((V_ba_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_A_2 (tptp.c_Set_Oinsert T_a V_ba_2 V_B_2))))) (forall ((V_aa_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2))) (forall ((V_D_2 $$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_Qa_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Qa_2) (tptp.hBOOL (tptp.hAPP V_Qa_2 V_x_2))))) (forall ((V_x_2 $$unsorted) (V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_Pa_2 V_Qa_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (tptp.hBOOL (tptp.hAPP V_Qa_2 V_x_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 ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((T_a $$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 ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((T_a $$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_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_p_2 V_r_2) (tptp.c_Wellfounded_Owf T_a V_p_2)))) (forall ((V_R2_2 $$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_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_FuncSet_OPi T_a T_b V_A_H_2 V_B_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> 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(tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_y) V_z)))))) (forall ((V_b $$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 $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.hAPP (tptp.hAPP 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(tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2))))) (forall ((V_y_2 $$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_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_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_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 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_r_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) _let_1))))) (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (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_r_H_2)))) (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_H_2) V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_s_2 $$unsorted) (V_r_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_r_2 V_s_2) (=> (tptp.c_Relation_Oantisym T_a V_s_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_s_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_s_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2)))) (forall ((V_s_2 $$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_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_aa_2)) V_r_2))))) (forall ((V_x_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_x_2)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_aa_2)) V_r_2)))))))) (forall ((V_x_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a))) (let ((_let_2 (tptp.c_member (tptp.tc_prod T_a T_a)))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_x_2)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_aa_2)) V_r_2)))))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (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) V_aa_2) V_aa_2)) V_r_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_A_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.c_Wellfounded_Oacc T_a V_r_2)))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf 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_s_2 $$unsorted) (V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member _let_1) V_p_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Otrancl T_a V_s_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_fun T_a T_b)) V_f_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_A_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_FuncSet_Oextensional T_a T_b V_B_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Relation_ODomain T_a T_b V_A_2)) (tptp.c_Relation_ODomain T_a T_b V_B_2))))) (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 (tptp.hAPP V_f_2 V_x_2)) V_f_2)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_f_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omeasure T_a V_f_2))) (forall ((V_x_2 $$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_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a _let_1) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Wellfounded_Oaccp T_a V_R2_2) (tptp.c_Wellfounded_Oaccp T_a V_R1_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_b _let_3))) (let ((_let_5 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_6 (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a (tptp.c_COMBC T_b _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b _let_1) _let_4 T_a (tptp.c_COMBB _let_1 _let_3 T_b (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_b)))))) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a _let_5) (tptp.hAPP _let_6 V_R_2) (tptp.hAPP _let_6 V_S_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2))))))))) (forall ((V_y $$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_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_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$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 $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_y $$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_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_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_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))) (forall ((V_y $$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_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_f_2) (= (tptp.hAPP V_f_2 V_x_2) V_y_2))) (forall ((V_z_2 $$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_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_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_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (not (= V_aa_2 V_c_2)) (= (tptp.c_Fun_Ofun__upd T_a T_b (tptp.c_Fun_Ofun__upd T_a T_b V_m_2 V_aa_2 V_ba_2) V_c_2 V_d_2) (tptp.c_Fun_Ofun__upd T_a T_b (tptp.c_Fun_Ofun__upd T_a T_b V_m_2 V_c_2 V_d_2) V_aa_2 V_ba_2)))) (forall ((V_y_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (not (= V_z_2 V_x_2)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_x_2 V_y_2) V_z_2) (tptp.hAPP V_f_2 V_z_2)))) (forall ((T_a $$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_ba_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Fun_Ofun__upd T_a T_b V_f_2 V_aa_2 V_ba_2) V_x_2))) (let ((_let_2 (= V_x_2 V_aa_2))) (and (=> _let_2 (= _let_1 V_ba_2)) (=> (not _let_2) (= _let_1 (tptp.hAPP V_f_2 V_x_2))))))) (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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))) (forall ((V_x_2 $$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 ((T_a $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (V_Pa_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)) (tptp.c_Wellfounded_Owf T_b (tptp.hAPP V_R_2 B_x)))) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Recdef_Osame__fst T_a T_b V_Pa_2 V_R_2)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (B_M $$unsorted) (B_R $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a B_R) (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Owfrec T_a T_b B_R B_M))) (= (tptp.hAPP _let_1 B_x) (tptp.hAPP (tptp.hAPP B_M (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) _let_1) B_R) B_x)) B_x)))))) (forall ((V_aa_2 $$unsorted) (V_H_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP _let_1 V_aa_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) _let_1) V_r_2) V_aa_2)) V_aa_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_Pa_2 V_Qa_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Qa_2 V_x_2) V_y_2))))) (forall ((V_Qa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_x_2) V_y_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_b tptp.tc_HOL_Obool)) V_Pa_2 V_Qa_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Qa_2 V_x_2) V_y_2))))) (forall ((V_aa_2 $$unsorted) (V_H_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (= V_f_2 (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP V_f_2 V_aa_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b) V_f_2) V_r_2) V_aa_2)) V_aa_2))))) (forall ((V_x_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b T_a))) (let ((_let_2 (tptp.tc_fun T_b _let_1))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (= (tptp.hAPP (tptp.c_Recdef_Owfrec T_b T_a V_R_2 V_Fa_2) V_x_2) (tptp.c_HOL_OThe T_a (tptp.c_Recdef_Owfrec__rel T_b T_a V_R_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 _let_3 _let_1) (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_1) _let_1 (tptp.c_COMBS T_b T_b T_a)) (tptp.hAPP (tptp.c_COMBB _let_2 _let_2 _let_1 (tptp.c_COMBB _let_1 _let_1 T_b V_Fa_2)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 (tptp.tc_fun (tptp.tc_prod T_b T_b) tptp.tc_HOL_Obool) _let_2) (tptp.c_Recdef_Ocut T_b T_a)) V_R_2)))) (tptp.c_COMBI T_b)) V_x_2))))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_R_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2))))))) (forall ((V_x_2 $$unsorted) (V_Fa_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_Fa_2) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_x_2) B_x)) (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_x_2) B_y)) (= B_y B_x)))))))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2)))) (forall ((V_x_2 $$unsorted) (V_Fa_2 $$unsorted) (T_b $$unsorted) (V_R_2 $$unsorted) (T_a $$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))) (let ((_let_4 (tptp.c_Nitpick_Owfrec_H T_a T_b V_R_2 V_Fa_2 V_x_2))) (let ((_let_5 (tptp.c_Wellfounded_Owf T_a V_R_2))) (and (=> _let_5 (= _let_4 (tptp.c_Nitpick_Owf__wfrec_H T_a T_b V_R_2 V_Fa_2 V_x_2))) (=> (not _let_5) (= _let_4 (tptp.c_HOL_OThe T_b (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBC _let_1 _let_3 _let_1) (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.c_COMBB _let_2 _let_2 _let_1 (tptp.c_COMBB _let_1 _let_1 T_a V_Fa_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)) V_x_2))))))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_HOL_OThe T_a (tptp.hAPP tptp.c_fequal V_x_2)) V_x_2)) (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_HOL_OThe T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_a tptp.tc_HOL_Obool) tptp.c_fequal) V_aa_2)) V_aa_2)) (forall ((V_x_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nitpick_Owf__wfrec_H T_b T_a V_R_2 V_Fa_2 V_x_2) (tptp.hAPP (tptp.hAPP V_Fa_2 (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Recdef_Ocut T_b T_a) (tptp.c_Nitpick_Owf__wfrec T_b T_a V_R_2 V_Fa_2)) V_R_2) V_x_2)) V_x_2))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.hAPP V_B_2 B_x) (tptp.hAPP V_C_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_fun T_a T_b) tptp.tc_HOL_Obool) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_B_2) (tptp.c_FuncSet_OPi T_a T_b V_A_2 V_C_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_HOL_Obool))) (let ((_let_4 (tptp.tc_fun T_a _let_3))) (let ((_let_5 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Wellfounded_OwfP T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a _let_2 _let_5) (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_5) T_a (tptp.c_COMBC T_a _let_2 tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a _let_1) _let_4 T_a (tptp.c_COMBB _let_1 _let_3 T_a (tptp.c_member _let_1))) (tptp.c_Product__Type_OPair T_a T_a)))) V_r_2)) (tptp.c_Wellfounded_Owf T_a V_r_2)))))))) (forall ((T_a $$unsorted)) (tptp.c_Wellfounded_OwfP T_a (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a (tptp.c_COMBK tptp.tc_HOL_Obool T_a tptp.c_fFalse)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_OwfP T_a V_r_2) (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) B_x1))))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_OwfP T_a V_r_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Wellfounded_Oaccp T_a V_r_2) V_x_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_OwfP T_a V_r_2) (tptp.c_Wellfounded_OwfP T_a (tptp.c_Transitive__Closure_Otranclp T_a V_r_2)))) (forall ((V_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_OwfP T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_p_2 V_r_2) (tptp.c_Wellfounded_OwfP T_a V_p_2)))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (tptp.c_Wellfounded_OwfP T_a (tptp.c_FunDef_Oin__rel T_a T_a V_R_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_Q $$unsorted)) (=> (exists ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) B_Q))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) B_Q)) (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) B_x)) V_r_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_y) B_Q))))))))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (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_aa_2) V_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_r_2 (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))) (or (= V_aa_2 V_ba_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2))))))) (forall ((V_x_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Othe__inv__into T_a T_b V_A_2 V_f_2 V_x_2) (tptp.c_HOL_OThe T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a tptp.tc_HOL_Obool tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) T_a tptp.c_fconj) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_HOL_Obool) (tptp.c_member T_a)) V_A_2))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC T_a T_b tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a tptp.c_fequal) V_f_2)) V_x_2))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_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_Otrancl T_a V_r_2) _let_1))))) (forall ((V_A_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) (tptp.c_Relation_OId__on T_a V_A_2) (tptp.c_Product__Type_OSigma 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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (and (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Product__Type_OSigma T_a T_a V_A_2 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_a V_A_2))) (forall ((B_x $$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 (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_B_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_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_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_C_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_b V_C_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_C_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) (tptp.c_Product__Type_OSigma T_b T_a V_A_2 _let_1) (tptp.c_Product__Type_OSigma T_b T_a V_B_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$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_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2)))))))) (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (=> (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H)) (not (=> (= V_a V_a_H) (not (= V_b V_b_H))))))) (forall ((V_b_Ha_2 $$unsorted) (V_a_Ha_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_aa_2) V_ba_2) (tptp.hAPP (tptp.hAPP _let_1 V_a_Ha_2) V_b_Ha_2)) (and (= V_aa_2 V_a_Ha_2) (= V_ba_2 V_b_Ha_2))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_Pa_2 $$unsorted)) (= (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x1))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP V_Pa_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_a) B_b)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (V_C_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_a tptp.tc_HOL_Obool) T_b V_C_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) V_C_2)) (= (= (tptp.c_Product__Type_OSigma T_b T_a V_A_2 _let_1) (tptp.c_Product__Type_OSigma T_b T_a V_B_2 _let_1)) (= V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Product__Type_OSigma T_a T_b V_I_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a _let_1 _let_1) (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1)) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_A_2)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_C_2))) (= (tptp.c_Product__Type_OSigma T_a T_b (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) _let_1) (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.c_Product__Type_OSigma T_a T_b V_A_2 _let_1)) (tptp.c_Product__Type_OSigma T_a T_b V_B_2 _let_1))))) (forall ((V_C_2 $$unsorted) (V_J_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_I_2) V_J_2) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_C_2)) (tptp.c_Product__Type_OSigma T_a T_b V_J_2 V_C_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) V_ba_2) (tptp.hAPP V_B_2 V_aa_2))))) (forall ((V_A_2 $$unsorted) (V_r_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_r_2 (tptp.c_Product__Type_OSigma 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 ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2)))) (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Oprod_Oprod__rec T_b T_c T_a V_f1_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_aa_2) V_ba_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_b)) V_c_2) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))) (not (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_b) B_y) (tptp.hAPP V_B_2 B_x))) (not (= V_c_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) B_x) B_y)))))))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted) (V_C_2 $$unsorted) (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_C_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.hAPP V_B_2 B_x) (tptp.hAPP V_D_2 B_x)))) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2) (tptp.c_Product__Type_OSigma T_a T_b V_C_2 V_D_2))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Ointernal__split T_b T_c T_a V_c_2 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_b T_c) V_aa_2) V_ba_2)) (tptp.hAPP (tptp.hAPP V_c_2 V_aa_2) V_ba_2))) (forall ((V_B_2 $$unsorted) (V_ba_2 $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2))) (let ((_let_3 (tptp.c_COMBK _let_1 T_a (tptp.c_Set_Oinsert T_b V_ba_2 V_B_2)))) (let ((_let_4 (tptp.tc_prod T_a T_b))) (= (tptp.c_Product__Type_OSigma T_a T_b _let_2 _let_3) (tptp.c_Set_Oinsert _let_4 (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_4 tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 _let_3)) (tptp.c_Product__Type_OSigma T_a T_b _let_2 (tptp.c_COMBK _let_1 T_a V_B_2)))))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))) (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_B_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_A_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_C_2 $$unsorted) (V_J_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_I_2) V_J_2) V_C_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_C_2)) (tptp.c_Product__Type_OSigma T_a T_b V_J_2 V_C_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_COMBK (tptp.tc_fun T_b tptp.tc_HOL_Obool) T_a V_C_2))) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 _let_1)) (tptp.c_Product__Type_OSigma T_a T_b V_B_2 _let_1))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (= (tptp.c_Product__Type_OSigma T_a T_b V_I_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_a _let_1 _let_1) (tptp.hAPP (tptp.c_COMBB _let_1 (tptp.tc_fun _let_1 _let_1) T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1)) V_A_2)) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_A_2)) (tptp.c_Product__Type_OSigma T_a T_b V_I_2 V_B_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.hAPP _let_2 V_R_2) V_S_2)))))) (forall ((V_B_2 $$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 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))) (forall ((V_B_2 $$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__sup__class_Osup _let_1) V_A_2) V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2) V_B_2)))) (forall ((V_A_2 $$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__sup__class_Osup _let_1) V_A_2) V_B_2) V_A_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))) (=> (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_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2) V_C_2))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_D_2))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup 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__sup__class_Osup T_a) V_x_2) V_y_2) V_y_2)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x_2) V_y_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_z_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup 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 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_a) V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_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__sup__class_Osup T_a) V_a) V_b))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y) V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (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__sup__class_Osup T_a) V_a) V_b) V_x))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup 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_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_y) V_z) V_x))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))))))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_a) V_b) V_x) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_x_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (let ((_let_3 (tptp.c_member T_a))) (let ((_let_4 (tptp.hAPP (tptp.c_COMBC T_a _let_1 tptp.tc_HOL_Obool) _let_3))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_R_2)) (tptp.hAPP _let_4 V_S_2)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x_2) (tptp.hAPP (tptp.hAPP _let_2 V_R_2) V_S_2))))))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.hAPP _let_1 V_R_2) V_S_2))))) (forall ((V_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) V_x) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a))) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (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 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)) V_x))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Relation_ORange T_b T_a V_A_2)) (tptp.c_Relation_ORange T_b T_a V_B_2)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2) V_x_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup (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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (let ((_let_2 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_1 _let_2) _let_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (let ((_let_3 (tptp.hAPP _let_1 V_B_2))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_C_2)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_C_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.hAPP _let_1 V_A_2))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_B_2)) V_C_2) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2)))))) (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (and (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_a) V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Osemilattice__sup 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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (=> (tptp.class_Lattices_Osemilattice__sup 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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup 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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))))))) (forall ((V_x_2 $$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__sup__class_Osup (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup 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 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b T_a)) V_f_2) V_g_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)) V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Relation_ODomain T_a T_b V_A_2)) (tptp.c_Relation_ODomain T_a T_b V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP _let_3 V_B_2) V_C_2))) (tptp.hAPP (tptp.hAPP _let_3 V_C_2) V_A_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_A_2) V_B_2)) (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_C_2))) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_A_2))))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B_2) V_C_2)) V_A_2) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_A_2)) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_A_2))))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B_2) V_C_2)) V_A_2) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_A_2)) (tptp.hAPP (tptp.hAPP _let_2 V_C_2) V_A_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B_2) V_C_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP _let_2 V_C_2))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_B_2) V_C_2)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_B_2)) (tptp.hAPP _let_2 V_C_2))))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_member T_a) V_c_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2) V_B_2))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_aa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_A_2))) (= (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.hAPP _let_1 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) V_C_2) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.hAPP (tptp.hAPP _let_1 V_B_2) V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1))) (let ((_let_3 (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2))) (= (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_B_2)) V_C_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_B_2) V_C_2))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2)))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member _let_1) V_x_2))) (=> (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)) V_R_2) V_S_2)))))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_Wellfounded_Owf T_a V_s_2) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1) (tptp.c_Relation_ODomain T_a T_a V_r_2)) (tptp.c_Relation_ORange T_a T_a V_s_2)) (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Wellfounded_Owf T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)) V_r_2) V_s_2))))))) (forall ((V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_member _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)) V_Pa_2) V_Qa_2)))) (=> (forall ((B_x $$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_ba_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2))) (forall ((B_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member (tptp.tc_prod T_a T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Product__Type_OPair T_a T_a) B_y) B_x)) V_Qa_2)) (= B_y B_x))))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2)))))))) (forall ((T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (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 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) (tptp.c_Orderings_Obot__class_Obot _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__sup__class_Osup _let_1) V_A_2) (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2) _let_2) (and (= V_A_2 _let_2) (= V_B_2 _let_2)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$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__sup__class_Osup T_a) V_x_2) V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2) (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2)))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_ba_2) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_ba_2 V_aa_2))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_ba_2) (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (= V_ba_2 V_aa_2))) (forall ((V_T_2 $$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.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.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_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (= (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_1)) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Set_Oinsert T_a V_d_2 _let_1))) (or (and (= V_aa_2 V_c_2) (= V_ba_2 V_d_2)) (and (= V_aa_2 V_d_2) (= V_ba_2 V_c_2)))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Set_Oinsert T_a V_aa_2 _let_1) (tptp.c_Set_Oinsert T_a V_ba_2 _let_1)) (= V_aa_2 V_ba_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 ((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 $$unsorted) (V_A_2 $$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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_xa) V_B_2)) (not (= B_x B_xa))))))))) (forall ((T_a $$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_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_aa_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_aa_2) V_A_2))))) (forall ((T_b $$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 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) B_x) V_A_2)) (= (tptp.hAPP V_B_2 B_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))))))) (forall ((T_b $$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 ((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_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_x $$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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a) _let_1) V_x) _let_1)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (tptp.hBOOL (tptp.hAPP _let_1 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_member T_a) V_x_2) _let_1))))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) 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)))) (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_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__sup (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_Lattices_Odistrib__lattice T_1) (tptp.class_Lattices_Odistrib__lattice (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_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)))) (tptp.class_Lattices_Osemilattice__sup tptp.tc_Nat_Onat) (tptp.class_Lattices_Osemilattice__inf tptp.tc_Nat_Onat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Lattices_Olattice tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Orderings_Obot tptp.tc_Nat_Onat) (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__sup tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool) (tptp.class_Lattices_Odistrib__lattice 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_Oord tptp.tc_HOL_Obool) (tptp.class_Orderings_Obot tptp.tc_HOL_Obool) (forall ((V_P $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (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)) (forall ((V_R_2 $$unsorted) (V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c V_Pa_2) V_Qa_2) V_R_2) (tptp.hAPP V_Pa_2 (tptp.hAPP V_Qa_2 V_R_2)))) (forall ((V_R_2 $$unsorted) (V_Qa_2 $$unsorted) (V_Pa_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_Pa_2) V_Qa_2) V_R_2) (tptp.hAPP (tptp.hAPP V_Pa_2 V_R_2) V_Qa_2))) (forall ((V_R_2 $$unsorted) (V_Qa_2 $$unsorted) (V_Pa_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_Pa_2) V_Qa_2) V_R_2) (tptp.hAPP (tptp.hAPP V_Pa_2 V_R_2) (tptp.hAPP V_Qa_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)))) (not (tptp.hBOOL tptp.c_fFalse)) (forall ((V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL V_Pa_2)) (not (tptp.hBOOL V_Qa_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Qa_2)))) (forall ((V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Qa_2))) (tptp.hBOOL V_Pa_2))) (forall ((V_Qa_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fconj V_Pa_2) V_Qa_2))) (tptp.hBOOL V_Qa_2))) _let_6 true))))))))))))))))))))))))))
% 1.15/1.35 )
% 1.15/1.35 % SZS output end Proof for SCT131+1
% 1.15/1.36 % cvc5---1.0.5 exiting
% 1.15/1.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------