TSTP Solution File: SCT156+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT156+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 14:12:13 EDT 2023
% Result : Theorem 1.65s 1.90s
% Output : Proof 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : SCT156+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.19 % Command : do_cvc5 %s %d
% 0.18/0.40 % Computer : n006.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Thu Aug 24 16:42:07 EDT 2023
% 0.18/0.41 % CPUTime :
% 0.25/0.60 %----Proving TF0_NAR, FOF, or CNF
% 1.65/1.90 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tSGusLHFI7/cvc5---1.0.5_16434.p...
% 1.65/1.90 ------- get file name : TPTP file name is SCT156+1
% 1.65/1.90 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16434.smt2...
% 1.65/1.90 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.65/1.90 % SZS status Theorem for SCT156+1
% 1.65/1.90 % SZS output start Proof for SCT156+1
% 1.65/1.90 (
% 1.65/1.90 (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a_H____ tptp.v_b_H____))) (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 _let_1 (tptp.hAPP tptp.v_F tptp.v_P_H____)))) (let ((_let_4 (tptp.hAPP tptp.v_F tptp.v_P____))) (let ((_let_5 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a____ tptp.v_b____))) (let ((_let_6 (tptp.c_member _let_2 _let_5 _let_4))) (let ((_let_7 (= _let_6 _let_3))) (let ((_let_8 (not _let_7))) (let ((_let_9 (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))) (=> (not (= V_aa_2 V_ba_2)) (=> (not (= V_ba_2 V_c_2)) (=> (not (= V_aa_2 V_c_2)) (=> (tptp.c_member _let_2 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (tptp.c_member _let_2 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP V_Pa_2 B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_c_2) (tptp.hAPP V_P_Ha_2 B_i))))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP tptp.v_F V_Pa_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_c_2) (tptp.hAPP tptp.v_F V_P_Ha_2)))))))))))))) (let ((_let_10 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_2 tptp.tc_HOL_Obool)))) (let ((_let_11 (tptp.c_member _let_10 tptp.v_P_H____ tptp.c_Arrow__Order__Mirabelle_OProf))) (let ((_let_12 (tptp.c_member _let_10 tptp.v_P____ tptp.c_Arrow__Order__Mirabelle_OProf))) (let ((_let_13 (= tptp.v_b____ tptp.v_a_H____))) (let ((_let_14 (not _let_13))) (let ((_let_15 (= tptp.v_a____ tptp.v_b_H____))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a____ tptp.v_b____) (tptp.hAPP tptp.v_P____ B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a_H____ tptp.v_b_H____) (tptp.hAPP tptp.v_P_H____ B_i))))))) (let ((_let_18 (and _let_15 _let_14))) (let ((_let_19 (not (= tptp.v_a_H____ tptp.v_b_H____)))) (let ((_let_20 (not (= tptp.v_a____ tptp.v_b____)))) (let ((_let_21 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b_H____ tptp.v_b____))) (let ((_let_22 (tptp.c_member _let_2 _let_21 _let_4))) (let ((_let_23 (ASSUME :args (_let_18)))) (let ((_let_24 (AND_ELIM _let_23 :args (0)))) (let ((_let_25 (= _let_3 _let_22))) (let ((_let_26 (not _let_3))) (let ((_let_27 (ASSUME :args (_let_8)))) (let ((_let_28 (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b_H____ tptp.v_b____) (tptp.hAPP tptp.v_P____ B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a_H____ tptp.v_b_H____) (tptp.hAPP tptp.v_P_H____ B_i))))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_12))) (let ((_let_31 (not _let_11))) (let ((_let_32 (= tptp.v_b____ tptp.v_b_H____))) (let ((_let_33 (= tptp.v_b_H____ tptp.v_a_H____))) (let ((_let_34 (or _let_33 _let_32 _let_13 _let_31 _let_30 _let_29 _let_25))) (let ((_let_35 (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))) (or (= V_ba_2 V_aa_2) (= V_c_2 V_ba_2) (= V_c_2 V_aa_2) (not (tptp.c_member _let_2 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf)) (not (tptp.c_member _let_2 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf)) (not (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP V_Pa_2 B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_c_2) (tptp.hAPP V_P_Ha_2 B_i)))))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP tptp.v_F V_Pa_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_c_2) (tptp.hAPP tptp.v_F V_P_Ha_2))))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (tptp.c_member _let_2 _let_1 (tptp.hAPP tptp.v_P_H____ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_38 (tptp.hAPP tptp.v_P____ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_39 (tptp.c_member _let_2 _let_21 _let_38))) (let ((_let_40 (= _let_39 _let_37))) (let ((_let_41 (tptp.c_member _let_2 _let_5 _let_38))) (let ((_let_42 (= _let_37 _let_41))) (let ((_let_43 (not _let_37))) (let ((_let_44 (_let_40))) (let ((_let_45 (_let_17))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P____ B_i)))) :args _let_45))) _let_46 :args (_let_42 false _let_17)))) (let ((_let_48 (not _let_42))) (let ((_let_49 (_let_42))) (let ((_let_50 (or))) (let ((_let_51 (not _let_41))) (let ((_let_52 (not _let_39))) (let ((_let_53 (REFL :args (_let_16)))) (let ((_let_54 (and _let_15 _let_52))) (let ((_let_55 (ASSUME :args (_let_52)))) (let ((_let_56 (APPLY_UF tptp.c_member))) (let ((_let_57 (APPLY_UF tptp.c_Product__Type_OPair))) (let ((_let_58 (REFL :args (tptp.v_b____)))) (let ((_let_59 (ASSUME :args (_let_15)))) (let ((_let_60 (SYMM _let_59))) (let ((_let_61 (SYMM _let_60))) (let ((_let_62 (REFL :args (tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_63 (REFL :args (_let_2)))) (let ((_let_64 (CONG _let_63 (CONG _let_62 _let_62 _let_61 _let_58 :args _let_57) (REFL :args (_let_38)) :args _let_56))) (let ((_let_65 (and _let_15 _let_39))) (let ((_let_66 (ASSUME :args (_let_39)))) (let ((_let_67 (_let_29))) (let ((_let_68 (= tptp.v_b____ tptp.v_a____))) (let ((_let_69 (not _let_32))) (let ((_let_70 (SYMM (ASSUME :args (_let_20))))) (let ((_let_71 (not _let_68))) (let ((_let_72 (and _let_15 _let_71))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_13 _let_33 _let_30 _let_31 _let_32 _let_25 _let_29 (not _let_34)))) (AND_ELIM _let_23 :args (1)) (SYMM (ASSUME :args (_let_19))) (ASSUME :args (_let_12)) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_70 _let_59) (SCOPE (FALSE_ELIM (TRANS (CONG _let_58 _let_60 :args (=)) (FALSE_INTRO _let_70))) :args (_let_71 _let_15))) :args (_let_15 _let_71))) :args (true _let_72)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_68))) (REFL :args (_let_69)) :args _let_50)) _let_24 _let_70 :args (_let_69 false _let_15 true _let_68)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_67)) :args _let_67)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) (REFL :args ((not _let_40))) :args _let_50)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_65)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_59) (SCOPE (TRUE_ELIM (TRANS _let_64 (TRUE_INTRO _let_66))) :args (_let_39 _let_15))) :args (_let_15 _let_39))) :args (true _let_65)) _let_24 (REORDERING (CNF_EQUIV_POS2 :args _let_49) :args ((or _let_37 _let_51 _let_48))) _let_47 (REORDERING (CNF_EQUIV_NEG1 :args _let_44) :args ((or _let_39 _let_37 _let_40))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_55 _let_59) (SCOPE (FALSE_ELIM (TRANS _let_64 (FALSE_INTRO _let_55))) :args (_let_52 _let_15))) :args (_let_15 _let_52))) :args (true _let_54)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_39))) (REFL :args (_let_51)) :args _let_50)) _let_24 (REORDERING (CNF_EQUIV_POS1 :args _let_49) :args ((or _let_43 _let_41 _let_48))) _let_47 (CNF_EQUIV_NEG2 :args _let_44) :args ((or _let_40 _let_43) false _let_15 false _let_41 false _let_42 true _let_39)) :args (_let_40 false _let_15 true _let_41 false _let_42 false _let_39 true _let_37)) :args (_let_28 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.v_P____ tptp.v_P_H____ tptp.v_b____ tptp.v_b_H____ tptp.v_a_H____ QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_member _let_10 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf) false)) (not (= (tptp.c_member _let_10 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf) false)) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_c_2)))) :args (_let_35)))) _let_36 :args (_let_34 false _let_35)) :args (_let_25 true _let_13 true _let_33 false _let_12 false _let_11 true _let_32 false _let_28 false _let_34)))) (let ((_let_74 (not _let_25))) (let ((_let_75 (_let_25))) (let ((_let_76 (not _let_22))) (let ((_let_77 (not _let_6))) (let ((_let_78 (and _let_15 _let_77))) (let ((_let_79 (ASSUME :args (_let_77)))) (let ((_let_80 (REFL :args (_let_4)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_59) (SCOPE (FALSE_ELIM (TRANS (CONG _let_63 (CONG _let_62 _let_62 (SYMM _let_61) _let_58 :args _let_57) _let_80 :args _let_56) (FALSE_INTRO _let_79))) :args (_let_77 _let_15))) :args (_let_15 _let_77))) :args (true _let_78)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_6))) (REFL :args (_let_76)) :args _let_50)) _let_24 (REORDERING (CNF_EQUIV_POS1 :args _let_75) :args ((or _let_26 _let_22 _let_74))) _let_73 (NOT_EQUIV_ELIM2 _let_27) :args (_let_26 false _let_15 false _let_22 false _let_25 true _let_6)))) (let ((_let_82 (and _let_15 _let_6))) (let ((_let_83 (ASSUME :args (_let_6)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_82)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_83 _let_59) (SCOPE (TRUE_ELIM (TRANS (CONG _let_63 (CONG _let_62 _let_62 _let_60 _let_58 :args _let_57) _let_80 :args _let_56) (TRUE_INTRO _let_83))) :args (_let_6 _let_15))) :args (_let_15 _let_6))) :args (true _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_75) :args ((or _let_3 _let_76 _let_74))) _let_81 _let_73 :args (_let_76 true _let_3 false _let_25)) (MACRO_RESOLUTION_TRUST (NOT_EQUIV_ELIM1 _let_27) _let_81 :args (_let_6 true _let_3)) _let_24 :args (false true _let_22 false _let_6 false _let_15)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) (tptp.c_Arrow__Order__Mirabelle_OIIA tptp.v_F) (tptp.c_Arrow__Order__Mirabelle_Ounanimity tptp.v_F) _let_20 _let_19 _let_18 _let_17 (=> (and _let_16 _let_14) _let_7) _let_12 _let_11 (forall ((V_c_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.c_member T_a V_c_2 V_B_2))) (let ((_let_2 (tptp.c_member T_a V_c_2 V_A_2))) (=> (= V_A_2 V_B_2) (=> (=> _let_2 (not _let_1)) (not (=> (not _let_2) _let_1))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_x_2 V_z_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_z_2)) (and (not (= V_y_2 V_z_2)) (=> _let_3 (not (= V_x_2 V_y_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2)))))))) (forall ((V_z_2 $$unsorted) (V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_y_2 V_z_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_z_2)) (and (not (= V_x_2 V_z_2)) (=> _let_3 (not (= V_x_2 V_y_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2)))))))) (forall ((V_y_2 $$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.c_member (tptp.tc_prod T_a T_b) (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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_x_2)) (=> (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_y_H_2 V_y_2) (tptp.hAPP V_R_2 V_x_2)) (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_H_2) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2)) (tptp.c_Recdef_Osame__fst T_a T_b V_Pa_2 V_R_2)))))) _let_9 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_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.c_Product__Type_OPair T_a T_b B_a B_b)))))) (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)) (= (= (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) (tptp.c_Product__Type_OPair T_a T_b V_a_Ha_2 V_b_Ha_2)) (and (= V_aa_2 V_a_Ha_2) (= V_ba_2 V_b_Ha_2)))) (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Product__Type_OPair T_a T_b V_a V_b) (tptp.c_Product__Type_OPair T_a T_b V_a_H V_b_H)) (not (=> (= V_a V_a_H) (not (= V_b V_b_H)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (= V_aa_2 V_ba_2) (=> (tptp.c_member T_a V_ba_2 V_A_2) (tptp.c_member T_a V_aa_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (= V_x_2 V_y_2) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_y_2 V_A_2)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.c_member _let_2 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (tptp.c_member _let_2 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP V_Pa_2 B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_aa_2) (tptp.hAPP V_P_Ha_2 B_i))))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP tptp.v_F V_Pa_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_aa_2) (tptp.hAPP tptp.v_F V_P_Ha_2)))))))))) (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_b_Ha_2 $$unsorted) (V_a_Ha_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))) (=> (not (= V_aa_2 V_ba_2)) (=> (not (= V_a_Ha_2 V_b_Ha_2)) (=> (not (= V_aa_2 V_b_Ha_2)) (=> (not (= V_ba_2 V_a_Ha_2)) (=> (tptp.c_member _let_2 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (tptp.c_member _let_2 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP V_Pa_2 B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_Ha_2 V_b_Ha_2) (tptp.hAPP V_P_Ha_2 B_i))))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP tptp.v_F V_Pa_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_Ha_2 V_b_Ha_2) (tptp.hAPP tptp.v_F V_P_Ha_2))))))))))))) (forall ((V_P_Ha_2 $$unsorted) (V_Pa_2 $$unsorted) (V_b_Ha_2 $$unsorted) (V_a_Ha_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)))) (=> (not (= V_aa_2 V_ba_2)) (=> (not (= V_a_Ha_2 V_b_Ha_2)) (=> (not (= V_aa_2 V_b_Ha_2)) (=> (not (= V_ba_2 V_a_Ha_2)) (=> (tptp.c_member _let_2 V_Pa_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (tptp.c_member _let_2 V_P_Ha_2 tptp.c_Arrow__Order__Mirabelle_OProf) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP V_Pa_2 B_i)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_Ha_2 V_b_Ha_2) (tptp.hAPP V_P_Ha_2 B_i))))) (= (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) (tptp.hAPP tptp.v_F V_Pa_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_Ha_2 V_b_Ha_2) (tptp.hAPP tptp.v_F V_P_Ha_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.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_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_OIIA V_Fa_2) (forall ((B_x $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.c_member (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool)) B_xa tptp.c_Arrow__Order__Mirabelle_OProf) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (forall ((B_i $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.c_member _let_2 _let_1 (tptp.hAPP B_x B_i)) (tptp.c_member _let_2 _let_1 (tptp.hAPP B_xa B_i)))))) (= (tptp.c_member _let_2 _let_1 (tptp.hAPP V_Fa_2 B_x)) (tptp.c_member _let_2 _let_1 (tptp.hAPP V_Fa_2 B_xa))))))))))))) (forall ((V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2) (forall ((B_x $$unsorted)) (=> (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 $$unsorted)) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP B_x B_i))) (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b) (tptp.hAPP V_Fa_2 B_x)))))))) (forall ((V_s_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) (tptp.c_Product__Type_OPair T_a T_b V_a_Ha_2 V_b_Ha_2)) (tptp.c_Wellfounded_Olex__prod T_a T_b V_r_2 V_s_2)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_a_Ha_2) V_r_2) (and (= V_aa_2 V_a_Ha_2) (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_ba_2 V_b_Ha_2) V_s_2)))))) (forall ((V_i_2 $$unsorted) (V_Fa_2 $$unsorted)) (= (tptp.c_Arrow__Order__Mirabelle_Odictator V_Fa_2 V_i_2) (forall ((B_x $$unsorted)) (=> (tptp.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_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.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_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (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.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_a1_2) V_R_2) (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_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) V_L_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_aa_2) V_L_2)))))) (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_x_2) tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_x_2) tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (not (= V_x_2 V_y_2)) (= (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_y_2 V_x_2) V_L_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_y_2 V_ba_2))) (let ((_let_4 (= V_x_2 V_ba_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_aa_2 V_ba_2)) (and (not (= V_x_2 V_y_2)) (=> _let_4 (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_y_2) V_L_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_x_2 V_aa_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_aa_2) V_L_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2))))))))))))) (forall ((V_y_2 $$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 V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_x_2 V_aa_2))) (let ((_let_4 (= V_y_2 V_aa_2))) (=> (not (= V_aa_2 V_ba_2)) (=> (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_aa_2 V_ba_2)) (and (not (= V_x_2 V_y_2)) (=> _let_4 (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_ba_2) V_L_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_y_2 V_ba_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ba_2 V_y_2) V_L_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2))))))))))))) (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Oabove V_L_2 V_x_2 V_y_2) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_L_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.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.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _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_ba_2 $$unsorted) (V_aa_2 $$unsorted)) (=> (not (= V_aa_2 V_ba_2)) (exists ((B_x $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (and (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) B_x tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_aa_2 V_ba_2) B_x)))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 V_a1_2 V_a2_2) (exists ((B_g $$unsorted)) (and (= V_a2_2 (tptp.hAPP (tptp.hAPP V_Fa_2 B_g) V_a1_2)) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_a1_2) V_R_2) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_Fa_2 B_z (tptp.hAPP B_g B_z)))))))) (forall ((V_g_2 $$unsorted) (V_Fa_2 $$unsorted) (T_b $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_x_2) V_R_2) (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.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 $$unsorted)) (= (tptp.c_member T_a V_aa_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_aa_2) V_r_2) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_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))) (=> (tptp.c_member T_a V_ba_2 _let_1) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (tptp.c_member T_a V_aa_2 _let_1))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2))) (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_aa_2 V_ba_2)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_aa_2 V_ba_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_aa_2 V_ba_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Ocurry T_b T_c T_a V_f_2 V_aa_2 V_ba_2) (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_b T_c V_aa_2 V_ba_2)))) (forall ((V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_R_2))) (not (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_x_2) V_R_2) (tptp.c_member T_a B_z (tptp.c_Wellfounded_Oacc T_a V_R_2))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_x_2) V_r_2) (tptp.c_member T_a B_y (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_aa_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member T_a V_aa_2 _let_1) (tptp.c_member T_a V_ba_2 _let_1))))) (forall ((V_ba_2 $$unsorted) (V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member T_a V_aa_2 _let_1) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_aa_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member T_a V_ba_2 _let_1))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_aa_2) V_r_2) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_aa_2) V_x_2) (tptp.hAPP V_f_2 V_x_2)))) (forall ((V_g_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_x_2) (tptp.c_Recdef_Ocut T_a T_b V_g_2 V_r_2 V_x_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_x_2) V_r_2) (= (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_g_2 B_y)))))) (forall ((T_b $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (B_f $$unsorted) (B_R $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_aa_2) B_R) (= (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)))) (exists ((B_L $$unsorted)) (tptp.c_member (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool) B_L tptp.c_Arrow__Order__Mirabelle_OLin)) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_x_2 (tptp.c_fequal V_y_2)) (= V_x_2 V_y_2))) (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_aa_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 V_r_2) (tptp.c_member _let_1 V_p_2 (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 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$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.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) V_r_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (= (tptp.c_Transitive__Closure_Ortrancl T_a _let_1) _let_1))) (forall ((V_x_2 $$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.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_y_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 (tptp.c_Relation_ODomain T_a T_a V_R_2))) (= (tptp.c_member (tptp.tc_prod T_a T_a) (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_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Relation_Osingle__valued T_a T_a V_r_2) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) _let_1) (or (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_z_2 V_y_2) _let_1)))))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) V_r_2) (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.c_member T_a V_aa_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 B_y) V_r_2)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_z_2) V_r_2) (= V_y_2 V_z_2)))))) (forall ((V_r_2 $$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.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_z) V_r_2) (= B_y B_z))))))) (forall ((V_Pa_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_ax_2) V_ay_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b B_a B_b)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2)) (forall ((B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b B_a B_b) (tptp.c_Product__Type_OPair T_a T_b B_aa B_ba)) V_r_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_aa) B_ba))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_bx_2) V_by_2))))))) (forall ((V_Pa_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_ax_2 V_ay_2) (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_bx_2) V_by_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted) (B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b B_aa B_ba))) (let ((_let_3 (tptp.tc_prod _let_1 _let_1))) (=> (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b B_a B_b) _let_2) V_r_2) (=> (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 _let_2 (tptp.c_Product__Type_OPair T_a T_b V_bx_2 V_by_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 B_a) B_b))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_ax_2) V_ay_2))))))) (forall ((V_r_2 $$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 V_za_2 V_zb_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2))) (let ((_let_3 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_3 _let_3) (tptp.c_Product__Type_OPair _let_3 _let_3 _let_2 _let_1) (tptp.c_Transitive__Closure_Ortrancl _let_3 V_r_2)) (=> (not (= _let_2 _let_1)) (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 B_a B_b))) (let ((_let_3 (tptp.tc_prod _let_1 _let_1))) (=> (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2) _let_2) V_r_2) (not (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 _let_2 (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))))))))))))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_aa_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (not (forall ((B_y $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 B_y) V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (not (= V_aa_2 V_ba_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_ba_2) V_r_2))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) V_r_2) (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.c_member (tptp.tc_prod T_a T_a) (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.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.c_member T_a V_aa_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (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 $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b B_x B_y) V_r_2) (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (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 $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 V_aa_2)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (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 $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (=> (tptp.hBOOL (tptp.hAPP V_Pa_2 B_y)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_z))))))) (tptp.hBOOL (tptp.hAPP V_Pa_2 V_ba_2)))))) (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (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.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a 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 ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_y) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))))) (forall ((V_A_2 $$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 $$unsorted)) (= (tptp.c_member T_a V_aa_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_y V_aa_2) V_r_2)))) (forall ((V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_c_2 (tptp.c_Relation_OId__on T_a V_A_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (not (= V_c_2 (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.c_member T_a V_ba_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_ba_2) V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a 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.c_member (tptp.tc_prod T_a T_a) (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.c_member (tptp.tc_prod T_b T_b) (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 $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (tptp.c_member T_a V_y_2 V_A_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (tptp.c_member T_a V_x_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.c_member T_a V_aa_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (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.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member _let_2 _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.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 V_r_2) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 V_r_2) (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (forall ((V_R_2 $$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.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_R_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) V_R_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) (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 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$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.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) V_r_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (let ((_let_3 (= V_x_2 V_y_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (or _let_3 (and (not _let_3) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_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.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (let ((_let_3 (= V_aa_2 V_ba_2))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (or _let_3 (and (not _let_3) (tptp.c_member _let_2 _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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_c_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_c_2) _let_1)))))) (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) _let_1)))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (exists ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_z) V_R_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_z V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))))) (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_z) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_z V_y_2) V_R_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (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_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (not (= V_x_2 V_y_2))))) (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (not (tptp.c_member _let_2 _let_1 V_r_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_y) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_z_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.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (not (tptp.c_member _let_2 _let_1 V_r_2)) (not (forall ((B_c $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 B_c) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_c V_ba_2) V_r_2))))))))))) (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_aa_2) (tptp.c_Relation_OId T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId T_a))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) (tptp.c_Relation_OId T_a)) (= V_aa_2 V_ba_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (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_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Relation_OId T_a)) (not (forall ((B_x $$unsorted)) (not (= V_p_2 (tptp.c_Product__Type_OPair T_a T_a B_x B_x))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.c_Set_Oinsert _let_1 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (tptp.c_Relation_Oantisym T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_aa_2) V_r_2) (= V_aa_2 V_ba_2)))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))) (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)))) (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 V_A_2)) (=> (not (= V_aa_2 V_ba_2)) (tptp.c_member T_a V_aa_2 V_A_2)))) (forall ((V_ba_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_aa_2 V_B_2)) (= V_aa_2 V_ba_2)) (tptp.c_member T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (=> (not (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_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_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 V_A_2 V_B_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 _let_2) _let_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_B_2 $$unsorted) (V_aa_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 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.c_Lattices_Osemilattice__sup__class_Osup _let_1 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.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _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.c_Lattices_Osemilattice__sup__class_Osup _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))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _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 $$unsorted)) (and (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (forall ((V_Pa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x (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 $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_Pa_2 B_x))))))) (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_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.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.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_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (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.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_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))) (forall ((V_r_2 $$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.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 $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_aa_2 V_ba_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_ba_2 (tptp.c_Relation_ORange T_b T_a V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (or (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (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)) (= (tptp.c_member T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 V_A_2)) (or (= V_aa_2 V_ba_2) (tptp.c_member T_a V_aa_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (=> (not (tptp.c_member T_a V_x_2 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)) (=> (tptp.c_member T_a V_aa_2 V_B_2) (tptp.c_member T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_aa_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2) V_A_2))) (forall ((V_S_2 $$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_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _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.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_R_2 V_S_2))))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId T_a))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (or (tptp.c_member _let_1 V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_member _let_1 V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_member _let_1 V_x_2 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_R_2 V_S_2)))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) _let_1 (tptp.c_Relation_OId T_a)) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (= B_x B_y))))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_x_2) (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_Q_2 $$unsorted) (V_Pa_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_Pa_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 B_x) (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_Q_2) (= B_x B_y))))) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2))))))) (forall ((V_Q_2 $$unsorted) (V_Pa_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 V_aa_2 V_ba_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_Pa_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_ba_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_Q_2) (= B_y B_x))))) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_Pa_2))))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Owf T_a (tptp.c_Set_Oinsert _let_1 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member _let_1 (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))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (= B_x B_y))))) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_a V_r_2) (tptp.c_Relation_ORange T_a T_a V_r_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_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_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_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_aa_2) V_r_2)))) (forall ((V_x_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_x_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_aa_2) V_r_2)))))) (forall ((V_x_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_x_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_aa_2) V_r_2)))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_aa_2) V_r_2)))) (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_x) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y))) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_f_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omeasure T_a V_f_2))) (forall ((V_aa_2 $$unsorted) (V_H_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (= V_f_2 (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP V_f_2 V_aa_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_aa_2)) V_aa_2))))) (forall ((V_aa_2 $$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.c_Recdef_Ocut T_a T_b _let_1 V_r_2 V_aa_2)) V_aa_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 $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Owfrec T_a T_b B_R B_M))) (= (tptp.hAPP _let_1 B_x) (tptp.hAPP (tptp.hAPP B_M (tptp.c_Recdef_Ocut T_a T_b _let_1 B_R B_x)) B_x)))))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Relation_OField T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Set_Oinsert T_a V_ba_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_Relation_OField T_a V_r_2))))) (forall ((T_a $$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.c_member T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$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 $$unsorted) (T_b $$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 ((T_a $$unsorted)) (= (tptp.c_Relation_OId__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$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 ((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 ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (not (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 $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_c_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_c_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_aa_2 $$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.c_member T_a V_aa_2 V_A_2)))) (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))) (= (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.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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) _let_2) (and (= V_A_2 _let_2) (= V_B_2 _let_2)))))) (forall ((T_a $$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 ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((V_y_2 $$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.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_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_ba_2 (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_ba_2 V_aa_2))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.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_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_aa_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2)))) (forall ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Relation_OId T_a))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_x_2)) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (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 ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_Wellfounded_Owf T_a V_s_2) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Relation_ODomain T_a T_a V_r_2) (tptp.c_Relation_ORange T_a T_a V_s_2)) (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_Q $$unsorted)) (=> (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x B_Q)) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x B_Q) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (not (tptp.c_member T_a B_y B_Q)))))))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2))))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (not (tptp.c_member T_a V_c_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a _let_1 V_x) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 _let_2 V_B_2) _let_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.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 $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (=> (tptp.c_member T_a B_xa V_B_2) (not (= B_x B_xa))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _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.c_Lattices_Osemilattice__inf__class_Oinf _let_1 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.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_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))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_C_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))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 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))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 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))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_A_2))))) (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_r_H_2)))) (forall ((V_r_H_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.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_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_B_2 V_x_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))))) (forall ((V_B_2 $$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_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))) (= (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_B_2))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.hAPP (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b T_a) V_f_2 V_g_2) V_x_2) (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_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_c) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y))) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (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.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_a) V_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_z V_x))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Odistrib__lattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z) V_x) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_x) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_z V_x))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_aa_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _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.c_Lattices_Osemilattice__inf__class_Oinf _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.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_aa_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 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.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_aa_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _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.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_aa_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_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 V_B_2 V_C_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2) V_C_2))) (let ((_let_4 (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.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_aa_2 V_B_2)))) (let ((_let_4 (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_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_x_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_ba_2 (tptp.c_Relation_OImage T_b T_a V_r_2 (tptp.c_Set_Oinsert T_b V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))))) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_aa_2 V_ba_2) V_r_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_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Relation_Orefl__on T_a _let_2 V_r_2) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (=> (tptp.c_member T_a V_aa_2 _let_2) (=> (tptp.c_member T_a V_ba_2 _let_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_1))) (= V_aa_2 V_ba_2))))))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Osingle__valued T_a T_b (tptp.c_Relation_Oconverse T_b T_a V_R_2)) (= (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse T_b T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) (tptp.c_Relation_Oconverse T_b T_a V_r_2) (tptp.c_Relation_Oconverse T_b T_a V_s_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) (tptp.c_Relation_Oconverse T_b T_a V_r_2) (tptp.c_Relation_Oconverse T_b T_a V_s_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Relation_OId T_a) V_A_2) V_A_2)) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_OField T_a V_r_2))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId T_a))) (= (tptp.c_Relation_Oconverse T_a T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId__on T_a V_A_2))) (= (tptp.c_Relation_Oconverse T_a T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse T_b T_a (tptp.c_Relation_Oconverse T_a T_b V_r_2)) V_r_2)) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2)))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Relation_Oinv__image T_b T_a V_R_2 V_f_2)) (tptp.c_Relation_Oinv__image T_b T_a (tptp.c_Relation_Oconverse T_b T_b V_R_2) V_f_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_ba_2 V_aa_2) V_r_2))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) V_r_2) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_ba_2 V_aa_2) (tptp.c_Relation_Oconverse T_a T_b V_r_2)))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_ba_2 V_aa_2) V_r_2))) (forall ((V_A_2 $$unsorted) (V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_OImage T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_R_2 V_S_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_S_2 V_A_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Relation_OId__on T_a V_A_2) V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Relation_Oconverse T_b T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_Relation_ORange T_b T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Relation_Oconverse T_a T_b V_r_2)) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (forall ((V_L_2 $$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.c_member _let_1 (tptp.c_Relation_Oconverse tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_L_2) tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_ba_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (exists ((B_x $$unsorted)) (and (tptp.c_member T_b B_x V_A_2) (tptp.c_member (tptp.tc_prod T_b T_a) (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) (T_b $$unsorted) (V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_aa_2 V_A_2) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_aa_2 V_ba_2) V_r_2) (tptp.c_member T_b V_ba_2 (tptp.c_Relation_OImage T_a T_b V_r_2 V_A_2))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))) (tptp.c_member _let_2 _let_1 (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Order__Relation_Opartial__order__on T_a _let_2 V_r_2) (=> (tptp.c_member T_a V_aa_2 _let_2) (=> (tptp.c_member T_a V_ba_2 _let_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_1))) (= V_aa_2 V_ba_2)))))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_ba_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_ba_2) V_r_2) (not (tptp.c_member T_b B_x V_A_2))))))) (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Owell__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2))) (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Opartial__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_2)))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2))) (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_aa_2 V_A_2) (tptp.c_member T_a V_aa_2 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_1))))))) (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Opreorder__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_member T_a V_y_2 V_A_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_y_2 _let_1))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2))))))) (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_ba_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (and (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_y_2 _let_1))) (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_y_2 V_A_2)))))) (forall ((T_a $$unsorted)) (tptp.c_Order__Relation_Olinear__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Order__Relation_Opreorder__on T_a _let_3 V_r_2) (=> (tptp.c_member T_a V_aa_2 _let_3) (=> (tptp.c_member T_a V_ba_2 _let_3) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_2))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_ba_2 V_aa_2) V_r_2))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_member T_a V_y_2 V_A_2) (= (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Set_Oinsert T_a V_x_2 _let_1) V_r_2) (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Set_Oinsert T_a V_y_2 _let_1) V_r_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2))))))) (forall ((V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2))) (=> (tptp.c_member T_a V_ba_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_x))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= V_A_2 V_B_2))))) (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_A_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool)) (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Orderings_Obot__class_Obot _let_1) V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (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.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.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_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)))))) (forall ((V_A_2 $$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.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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_A_2)))) (forall ((V_B_2 $$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.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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_A_2))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> 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V_y V_z)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)))))) (forall ((V_x $$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.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) V_x)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y_2 V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.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 $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x))) (forall ((V_A_2 $$unsorted) (V_A_H_2 $$unsorted) (V_r_2 $$unsorted) (V_r_H_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_H_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_H_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_b tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_b V_r_H_2 V_A_H_2) (tptp.c_Relation_OImage T_a T_b V_r_2 V_A_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$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_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_x_2 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.c_member T_a V_x_2 V_B_2)))) (forall ((V_x_2 $$unsorted) (V_B_2 $$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_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_y $$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.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_x $$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.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) V_y_2)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_z_2))))) (forall 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(=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_g_2 V_x_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (forall ((B_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))) (forall ((V_B_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_2) (= V_A_2 _let_2))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert T_a V_x_2 _let_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_3) (or (= V_A_2 _let_2) (= V_A_2 _let_3))))))) (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_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 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_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_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.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_s_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2))))) (forall ((V_X_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 V_X_2) V_X_2) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) V_X_2) V_X_2))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_R_2 V_S_2))))) (forall ((V_A_2 $$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_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Relation_OImage T_a T_a V_R_2 V_A_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (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.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.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_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.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.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_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) (= (tptp.c_Equiv__Relations_Oquotient T_a _let_2 V_r_2) (tptp.c_Set_Oinsert _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 _let_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))))) (forall ((V_Y_2 $$unsorted) (V_X_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member _let_1 V_X_2 _let_2) (=> (tptp.c_member _let_1 V_Y_2 _let_2) (or (= V_X_2 V_Y_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_X_2 V_Y_2) (tptp.c_Orderings_Obot__class_Obot _let_1))))))))) (forall ((V_r_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_member T_a V_x_2 V_A_2) (tptp.c_member _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2))))) (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_aa_2 V_ba_2) V_r_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_aa_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_ba_2 _let_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Y_2 $$unsorted) (V_X_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member _let_2 V_X_2 _let_1) (=> (tptp.c_member _let_2 V_Y_2 _let_1) (=> (tptp.c_member T_a V_x_2 V_X_2) (=> (tptp.c_member T_a V_y_2 V_Y_2) (= (= V_X_2 V_Y_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2)))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Y_2 $$unsorted) (V_X_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member _let_2 V_X_2 _let_1) (=> (tptp.c_member _let_2 V_Y_2 _let_1) (=> (tptp.c_member T_a V_x_2 V_X_2) (=> (tptp.c_member T_a V_y_2 V_Y_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (= V_X_2 V_Y_2)))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Order__Relation_Opreorder__on T_a _let_2 V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 _let_2) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 V_A_2) (tptp.c_Relation_OImage T_a T_a V_r_2 V_B_2)) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (exists ((B_xa $$unsorted)) (and (tptp.c_member T_a B_xa V_B_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_X_2 (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2)) (not (forall ((B_x $$unsorted)) (=> (= V_X_2 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a B_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (not (tptp.c_member T_a B_x V_A_2))))))) (forall ((V_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_OwfP T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_p_2 V_r_2) (tptp.c_Wellfounded_OwfP T_a V_p_2)))) (forall ((V_z_2 $$unsorted) (V_y_2 $$unsorted) (V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Ocongruent T_a T_b V_r_2 V_f_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) V_r_2) (= (tptp.hAPP V_f_2 V_y_2) (tptp.hAPP V_f_2 V_z_2))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (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.c_member _let_2 _let_1 V_R_2) (tptp.c_member _let_2 _let_1 (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2))))))) (forall ((V_Q_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_Q_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_2 V_x_2) V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_Q_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_Q_2) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Pa_2 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q_2 V_x_2) V_y_2))))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2)))) (forall ((V_aa_2 $$unsorted) (V_f_2 $$unsorted) (V_r2_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_r1_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r1_2) (=> (tptp.c_Equiv__Relations_Ocongruent2 T_a T_b T_c V_r1_2 V_r2_2 V_f_2) (=> (tptp.c_member T_a V_aa_2 V_A_2) (tptp.c_Equiv__Relations_Ocongruent T_b T_c V_r2_2 (tptp.hAPP V_f_2 V_aa_2)))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Owell__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (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)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 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_Groups_Ominus__class_Ominus _let_1 (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_b) 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.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_Groups_Ominus__class_Ominus _let_1 V_B_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_A_2)) V_A_2))))) (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_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_Groups_Ominus__class_Ominus _let_1 (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)) (tptp.c_Relation_ORange T_b T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 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_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_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))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2))))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_x_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_x_2) (tptp.hAPP V_B_2 V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_B_2) _let_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_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_C_2))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 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.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_B_2))))) (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)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))) (tptp.class_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_Groups_Ominus 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) (tptp.class_Groups_Ominus tptp.tc_HOL_Obool) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (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.c_fequal V_x_2) V_y_2)))) _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.65/1.91 )
% 1.65/1.91 % SZS output end Proof for SCT156+1
% 1.65/1.91 % cvc5---1.0.5 exiting
% 1.65/1.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------