TSTP Solution File: SCT122+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:12:06 EDT 2023
% Result : Theorem 27.16s 27.35s
% Output : Proof 27.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.17 % Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.19 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n007.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Thu Aug 24 15:54:40 EDT 2023
% 0.18/0.40 % CPUTime :
% 0.24/0.58 %----Proving TF0_NAR, FOF, or CNF
% 27.16/27.35 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hF6c6UIiZL/cvc5---1.0.5_3871.p...
% 27.16/27.35 ------- get file name : TPTP file name is SCT122+1
% 27.16/27.35 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3871.smt2...
% 27.16/27.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.16/27.35 --- Run --no-e-matching --full-saturate-quant at 5...
% 27.16/27.35 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.16/27.35 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.16/27.35 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.16/27.35 % SZS status Theorem for SCT122+1
% 27.16/27.35 % SZS output start Proof for SCT122+1
% 27.16/27.35 (
% 27.16/27.35 (let ((_let_1 (tptp.hAPP tptp.v_P tptp.v_i))) (let ((_let_2 (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_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (tptp.c_member _let_3 _let_2 _let_1))) (let ((_let_5 (not _let_4))) (let ((_let_6 (=> (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P B_x))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) _let_1)))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (not (= B_a B_b)) (=> (tptp.c_member _let_2 _let_1 (tptp.hAPP tptp.v_P tptp.v_i)) (tptp.c_member _let_2 _let_1 (tptp.v_F tptp.v_P)))))))))) (let ((_let_7 (tptp.v_F tptp.v_P))) (let ((_let_8 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (let ((_let_9 (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt _let_7))) (let ((_let_10 (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt _let_7))) (let ((_let_11 (and _let_10 _let_9 (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt _let_8 _let_7)))) (let ((_let_12 (=> (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P B_x))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) _let_1)))) _let_11))) (let ((_let_13 (tptp.c_member _let_3 _let_2 _let_7))) (let ((_let_14 (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P B_x))) (and (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt _let_1) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) _let_1)))))) (let ((_let_15 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))))) (let ((_let_16 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (= (tptp.c_Transitive__Closure_Otrancl T_a V_r_2) V_r_2))))) (let ((_let_17 (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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))))) (let ((_let_18 (forall ((V_r_2 $$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))))))) (let ((_let_19 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (let ((_let_20 (forall ((B_x $$unsorted) (BOUND_VARIABLE_7477 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P tptp.v_i))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)))) (or (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt B_x _let_3)) (not (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7477 _let_3)) (= B_x BOUND_VARIABLE_7477) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_7477) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_7477 B_x) _let_1)))))))) (let ((_let_21 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b tptp.v_a))) (let ((_let_22 (tptp.c_member _let_3 _let_21 _let_1))) (let ((_let_23 (= tptp.v_a tptp.v_b))) (let ((_let_24 (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_b _let_8))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.c_member tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a _let_8))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_4 _let_22))) (let ((_let_29 (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt _let_8 _let_1))) (let ((_let_30 (= _let_29 _let_20))) (let ((_let_31 (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) (BOUND_VARIABLE_7477 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_member T_a B_x V_A_2)) (not (tptp.c_member T_a BOUND_VARIABLE_7477 V_A_2)) (= B_x BOUND_VARIABLE_7477) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x BOUND_VARIABLE_7477) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a BOUND_VARIABLE_7477 B_x) V_r_2)))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (forall ((BOUND_VARIABLE_10417 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10417))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (AND_ELIM _let_34 :args (2)))) (let ((_let_36 (_let_33))) (let ((_let_37 (not _let_28))) (let ((_let_38 (_let_19))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (tptp.c_member _let_3 _let_21 _let_7))) (let ((_let_41 (not _let_22))) (let ((_let_42 (or _let_23 _let_41 _let_40))) (let ((_let_43 (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))) (or (= B_a B_b) (not (tptp.c_member _let_2 _let_1 (tptp.hAPP tptp.v_P tptp.v_i))) (tptp.c_member _let_2 _let_1 (tptp.v_F tptp.v_P)))))))) (let ((_let_44 (forall ((BOUND_VARIABLE_10458 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10458))))) (let ((_let_45 (forall ((BOUND_VARIABLE_10452 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10452))))) (let ((_let_46 (forall ((BOUND_VARIABLE_10446 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10446))))) (let ((_let_47 (and _let_46 _let_45 _let_44))) (let ((_let_48 (not _let_33))) (let ((_let_49 (forall ((BOUND_VARIABLE_10411 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10411))))) (let ((_let_50 (AND_ELIM _let_34 :args (1)))) (let ((_let_51 (not _let_49))) (let ((_let_52 (forall ((BOUND_VARIABLE_10405 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10405))))) (let ((_let_53 (AND_ELIM _let_34 :args (0)))) (let ((_let_54 (not _let_52))) (let ((_let_55 (_let_43))) (let ((_let_56 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_a tptp.v_a))) (let ((_let_57 (tptp.c_member _let_3 _let_56 _let_7))) (let ((_let_58 (not _let_23))) (let ((_let_59 (ASSUME :args (_let_13)))) (let ((_let_60 (forall ((B_x $$unsorted)) (not (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_x B_x) (tptp.v_F tptp.v_P)))))) (let ((_let_61 (not _let_57))) (let ((_let_62 (= _let_9 _let_60))) (let ((_let_63 (_let_18))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (forall ((BOUND_VARIABLE_10437 $$unsorted)) (tptp.c_Relation_Ototal__on tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_HOL_Obool)) (tptp.hAPP tptp.v_P BOUND_VARIABLE_10437))))) (let ((_let_66 (forall ((BOUND_VARIABLE_10431 $$unsorted)) (tptp.c_Relation_Oirrefl tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10431))))) (let ((_let_67 (forall ((BOUND_VARIABLE_10425 $$unsorted)) (tptp.c_Relation_Otrans tptp.tc_Arrow__Order__Mirabelle_Oalt (tptp.hAPP tptp.v_P BOUND_VARIABLE_10425))))) (let ((_let_68 (and _let_67 _let_66 _let_65))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_11 (not _let_68)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_52 (= BOUND_VARIABLE_10405 BOUND_VARIABLE_10425)))) :args ((or _let_67 _let_54))) _let_53 :args (_let_67 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_49 (= BOUND_VARIABLE_10411 BOUND_VARIABLE_10431)))) :args ((or _let_66 _let_51))) _let_50 :args (_let_66 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_33 (= BOUND_VARIABLE_10417 BOUND_VARIABLE_10437)))) :args ((or _let_65 _let_48))) _let_35 :args (_let_65 false _let_33)) :args (_let_68 false _let_67 false _let_66 false _let_65)) :args (_let_11 false _let_68)))) (let ((_let_70 (not _let_11))) (let ((_let_71 (_let_60))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_71) :args (tptp.v_a QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or (not _let_9) _let_60 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_11 1)) :args ((or _let_9 _let_70))) _let_69 :args (_let_9 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_7 tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Relation_Oirrefl T_a V_r_2)))) :args _let_63)) _let_64 :args (_let_62 false _let_18)) :args (_let_60 false _let_9 false _let_62)) :args (_let_61 false _let_60)))) (let ((_let_73 (or))) (let ((_let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_57))))) (let ((_let_75 (not _let_13))) (let ((_let_76 (APPLY_UF tptp.c_member))) (let ((_let_77 (REFL :args (tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_78 (REFL :args (_let_3)))) (let ((_let_79 (ASSUME :args (_let_61)))) (let ((_let_80 (FALSE_INTRO _let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_80) (CONG _let_78 (CONG _let_77 _let_77 (REFL :args (tptp.v_a)) (SYMM (SYMM (ASSUME :args (_let_23)))) :args (APPLY_UF tptp.c_Product__Type_OPair)) (REFL :args (_let_7)) :args _let_76) (TRUE_INTRO _let_59))) :args (_let_13 _let_23 _let_61))) (CONG (REFL :args (_let_75)) (REFL :args (_let_58)) _let_74 :args _let_73)) _let_72 _let_59 :args (_let_58 true _let_57 false _let_13)))) (let ((_let_82 (tptp.c_Transitive__Closure_Otrancl tptp.tc_Arrow__Order__Mirabelle_Oalt _let_7))) (let ((_let_83 (tptp.c_member _let_3 _let_21 _let_82))) (let ((_let_84 (= _let_7 _let_82))) (let ((_let_85 (not _let_40))) (let ((_let_86 (tptp.c_member _let_3 _let_56 _let_82))) (let ((_let_87 (not _let_83))) (let ((_let_88 (or _let_75 _let_87 _let_86))) (let ((_let_89 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (not (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) _let_1)) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (not _let_86))) (let ((_let_92 (not _let_10))) (let ((_let_93 (or _let_92 _let_84))) (let ((_let_94 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Relation_Otrans T_a V_r_2)) (= V_r_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_92 _let_84 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_11 0)) :args ((or _let_10 _let_70))) _let_69 :args (_let_10 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_7 tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_Relation_Otrans T_a V_r_2) false))))) :args (_let_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_84 false _let_10 false _let_93)))) (let ((_let_97 (not _let_84))) (let ((_let_98 (REFL :args (_let_97)))) (let ((_let_99 (and _let_84 _let_61))) (let ((_let_100 (ASSUME :args (_let_84)))) (let ((_let_101 (SYMM (SYMM _let_100)))) (let ((_let_102 (and _let_84 _let_87))) (let ((_let_103 (ASSUME :args (_let_87)))) (let ((_let_104 (_let_20))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_104) :args (tptp.v_a tptp.v_b QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_4 _let_23 _let_22 _let_25 _let_27 _let_37))) (ASSUME :args (_let_5)) _let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_40 _let_23 _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_102)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_103 _let_100) (SCOPE (FALSE_ELIM (TRANS (CONG _let_78 (REFL :args (_let_21)) _let_101 :args _let_76) (FALSE_INTRO _let_103))) :args (_let_87 _let_84))) :args (_let_84 _let_87))) :args (true _let_102)) (CONG _let_98 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_83))) (REFL :args (_let_85)) :args _let_73)) :args ((or _let_85 _let_97 _let_83))) _let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_75 _let_87 _let_86 (not _let_88)))) _let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_99)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_100) (SCOPE (FALSE_ELIM (TRANS (CONG _let_78 (REFL :args (_let_56)) (SYMM _let_101) :args _let_76) _let_80)) :args (_let_61 _let_84))) :args (_let_84 _let_61))) :args (true _let_99)) (CONG _let_98 _let_74 (REFL :args (_let_91)) :args _let_73)) _let_96 _let_72 :args (_let_91 false _let_84 true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.v_a _let_7 tptp.v_b tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_CBQI_PROP)) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_87 false _let_13 true _let_86 false _let_88)) :args (_let_85 false _let_84 true _let_83)) _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (tptp.v_b tptp.v_a QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_a B_b)))) :args _let_55))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_43 (not _let_47)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_52 (= BOUND_VARIABLE_10405 BOUND_VARIABLE_10446)))) :args ((or _let_46 _let_54))) _let_53 :args (_let_46 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_49 (= BOUND_VARIABLE_10411 BOUND_VARIABLE_10452)))) :args ((or _let_45 _let_51))) _let_50 :args (_let_45 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_33 (= BOUND_VARIABLE_10417 BOUND_VARIABLE_10458)))) :args ((or _let_44 _let_48))) _let_35 :args (_let_44 false _let_33)) :args (_let_47 false _let_46 false _let_45 false _let_44)) :args (_let_43 false _let_47)) :args (_let_42 false _let_43)) :args (_let_41 true _let_40 true _let_23 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_38)) _let_39 :args (_let_24 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_CBQI_PROP)) :args _let_38)) _let_39 :args (_let_26 false _let_19)) :args (_let_37 true _let_4 true _let_23 true _let_22 false _let_24 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or (not _let_29) _let_20 (not _let_30)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (tptp.v_i QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P BOUND_VARIABLE_10417)))) :args _let_36)) _let_35 :args (_let_29 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_1 _let_8 tptp.tc_Arrow__Order__Mirabelle_Oalt QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_20 false _let_29 false _let_30)) :args (false true _let_28 false _let_20)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_19 _let_18 _let_17 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Otrans T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (forall ((B_z $$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_x B_z) V_r_2)))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) V_r_2)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_x_2))) (forall ((V_c_2 $$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 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_y_2 V_z_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L_2 V_z_2)) (and (not (= V_x_2 V_z_2)) (=> _let_3 (not (= V_x_2 V_y_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2)))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Ostrict__linear__order__on T_a V_A_2 V_r_2) (and (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Oirrefl T_a V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_x_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_A_2 $$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 $$unsorted)) (=> (= V_A_2 V_B_2) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_member T_a V_x_2 V_B_2)))) (forall ((V_y_2 $$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_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_x_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_FunDef_Oin__rel T_a T_b V_R_2 V_x_2 V_y_2) (tptp.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_P_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_y_H_2 V_y_2) (tptp.hAPP V_R_2 V_x_2)) (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_H_2) (tptp.c_Product__Type_OPair T_a T_b V_x_2 V_y_2)) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2)))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$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_a_2 V_b_2) V_r_2) (tptp.c_member T_b V_b_2 (tptp.c_Relation_ORange T_a T_b V_r_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (= V_a_2 V_b_2) (=> (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Relation_OId__on T_a V_A_2))))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.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_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.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 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$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_r_2) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_z) V_r_2)))))) (tptp.c_Relation_Otrans T_a V_r_2))) (forall ((V_b_2 $$unsorted) (V_a_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_a_2 V_b_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_b_2 V_a_2) V_L_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (not (= V_x_2 V_y_2)) (= (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2) V_L_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_y_2 V_x_2) V_L_2)))))) (forall ((V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Relation_Oinv__image T_b T_a V_r_2 V_f_2)) (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b (tptp.hAPP V_f_2 V_x_2) (tptp.hAPP V_f_2 V_y_2)) V_r_2))) (forall ((V_A_2 $$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 $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_b (tptp.c_Relation_Oinv__image T_a T_b V_r_2 V_f_2)))) (forall ((V_x_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L_2 V_x_2) tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 B_y) V_r_2)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_y V_a_2) V_r_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt 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_b_2))) (let ((_let_4 (= V_x_2 V_b_2))) (=> (not (= V_a_2 V_b_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_a_2 V_b_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_a_2 V_y_2) V_L_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_x_2 V_a_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_a_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 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_y_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_x_2 V_a_2))) (let ((_let_4 (= V_y_2 V_a_2))) (=> (not (= V_a_2 V_b_2)) (=> (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_a_2 V_b_2)) (and (not (= V_x_2 V_y_2)) (=> _let_4 (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_x_2 V_b_2) V_L_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_y_2 V_b_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_b_2 V_y_2) V_L_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_L_2))))))))))))) (forall ((V_L_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (=> (not (= V_x_2 V_y_2)) (=> (tptp.c_member _let_1 V_L_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_L_2 V_x_2 V_y_2) tptp.c_Arrow__Order__Mirabelle_OLin))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (= (tptp.c_member (tptp.tc_prod _let_1 _let_1) (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Product__Type_OPair T_a T_b V_a_H_2 V_b_H_2)) (tptp.c_Wellfounded_Olex__prod T_a T_b V_r_2 V_s_2)) (or (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_H_2) V_r_2) (and (= V_a_2 V_a_H_2) (tptp.c_member (tptp.tc_prod T_b T_b) (tptp.c_Product__Type_OPair T_b T_b V_b_2 V_b_H_2) V_s_2)))))) (forall ((V_A_2 $$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 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_ORange T_b T_a V_r_2)) (not (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2)))))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (not (forall ((B_y $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 B_y) V_r_2)))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))) (forall ((V_y_2 $$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_x_2 V_A_2)))) (forall ((V_R2_2 $$unsorted) (T_b $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_R1_2) (=> (tptp.c_Relation_Otrans T_b V_R2_2) (tptp.c_Relation_Otrans (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_R1_2 V_R2_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_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2) (tptp.c_member T_a V_y_2 V_A_2)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (and (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (tptp.c_Relation_Otrans T_a V_r_2)))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member T_a V_b_2 _let_1) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 _let_1))))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)) (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_a_2) V_r_2) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_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_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_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$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_a_2) V_r_2) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_a_2) V_x_2) (tptp.hAPP V_f_2 V_x_2)))) (forall ((V_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_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted) (B_f $$unsorted) (B_R $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) B_R) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b B_f B_R V_a_2) V_x_2) (tptp.hAPP B_f V_x_2)))) (forall ((V_A_2 $$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) (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_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 $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_x_2) V_R_2) (tptp.c_member T_a B_z (tptp.c_Wellfounded_Oacc T_a V_R_2))))))) (forall ((V_a2_2 $$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 $$unsorted) (T_b $$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_b_2 $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member T_a V_a_2 _let_1) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member T_a V_b_2 _let_1))))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member T_a V_a_2 _let_1) (tptp.c_member T_a V_b_2 _let_1))))) (forall ((V_x_2 $$unsorted) (V_Fa_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nitpick_Owf__wfrec_H T_b T_a V_R_2 V_Fa_2 V_x_2) (tptp.hAPP (tptp.hAPP V_Fa_2 (tptp.c_Recdef_Ocut T_b T_a (tptp.c_Nitpick_Owf__wfrec T_b T_a V_R_2 V_Fa_2) V_R_2 V_x_2)) V_x_2))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) (tptp.c_Relation_OId T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId T_a))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId T_a))) (forall ((V_b_2 $$unsorted) (V_a_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_a_2 V_b_2) (tptp.c_Relation_OId T_a)) (= V_a_2 V_b_2))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Relation_OId T_a))) (forall ((V_r_2 $$unsorted) (V_a_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_a_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 V_r_2) (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))) (forall ((V_y_2 $$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 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_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_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))) (forall ((V_p_2 $$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_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (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_P_2 V_ax_2) V_ay_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (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_P_2 B_a) B_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_aa) B_ba))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_bx_2) V_by_2))))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_by_2 $$unsorted) (V_bx_2 $$unsorted) (V_ay_2 $$unsorted) (V_ax_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (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_P_2 V_bx_2) V_by_2)) (=> (forall ((B_a $$unsorted) (B_b $$unsorted) (B_aa $$unsorted) (B_ba $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b 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_P_2 B_aa) B_ba)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_a) B_b))))))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_ax_2) V_ay_2))))))) (forall ((V_r_2 $$unsorted) (V_zb_2 $$unsorted) (V_za_2 $$unsorted) (V_xb_2 $$unsorted) (V_xa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2))) (let ((_let_3 (tptp.tc_prod T_a T_b))) (=> (tptp.c_member (tptp.tc_prod _let_3 _let_3) (tptp.c_Product__Type_OPair _let_3 _let_3 _let_2 _let_1) (tptp.c_Transitive__Closure_Ortrancl _let_3 V_r_2)) (=> (not (= _let_2 _let_1)) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (let ((_let_2 (tptp.c_Product__Type_OPair T_a T_b B_a B_b))) (let ((_let_3 (tptp.tc_prod _let_1 _let_1))) (=> (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_xb_2) _let_2) V_r_2) (not (tptp.c_member _let_3 (tptp.c_Product__Type_OPair _let_1 _let_1 _let_2 (tptp.c_Product__Type_OPair T_a T_b V_za_2 V_zb_2)) (tptp.c_Transitive__Closure_Ortrancl _let_1 V_r_2))))))))))))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_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_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (forall ((B_z $$unsorted)) (=> (tptp.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_P_2 B_y)) (tptp.hBOOL (tptp.hAPP V_P_2 B_z))))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)))))) (forall ((V_P_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_b_2)) (=> (forall ((B_y $$unsorted) (B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_z V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_z)) (tptp.hBOOL (tptp.hAPP V_P_2 B_y))))))) (tptp.hBOOL (tptp.hAPP V_P_2 V_a_2)))))) (forall ((V_r_2 $$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_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_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_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (not (= V_a_2 V_b_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_b_2) V_r_2))))))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))) (exists ((B_L $$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_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_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Product__Type_OPair T_a T_b V_a_H_2 V_b_H_2)) (and (= V_a_2 V_a_H_2) (= V_b_2 V_b_H_2)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_P_2 $$unsorted)) (= (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Product__Type_OPair T_a T_b B_a B_b)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$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_a_2 V_b_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) V_r_2) (= V_a_2 V_b_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.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 $$unsorted) (V_B_2 $$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_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 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_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 $$unsorted) (T_a $$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_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$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_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_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_P_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (or (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x))))))) (forall ((V_P_2 $$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_P_2 B_x)))) (and (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_B_2) (tptp.hBOOL (tptp.hAPP V_P_2 B_x))))))) (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_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)))) (forall ((V_r_2 $$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 $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_B_2 $$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 $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_r_2 $$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_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _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_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 _let_2) _let_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_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_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_R_2 V_S_2))))) (forall ((V_r_2 $$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 $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) _let_16 (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ORange T_a T_a V_r_2))) (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_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_a_2 V_b_2) V_R_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_R_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)))))) _let_15 (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))) (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 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) _let_1 (tptp.c_Relation_OId T_a)) _let_1))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))) (forall ((V_R_2 $$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 $$unsorted) (V_b_2 $$unsorted) (V_a_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_a_2 V_b_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_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_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (let ((_let_3 (= V_a_2 V_b_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_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_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_a_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 $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_z_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_z_2) _let_1)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f1_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Oprod_Oprod__rec T_b T_c T_a V_f1_2 (tptp.c_Product__Type_OPair T_b T_c V_a_2 V_b_2)) (tptp.hAPP (tptp.hAPP V_f1_2 V_a_2) V_b_2))) (forall ((V_x_2 $$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__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_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x _let_1) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a _let_1 V_x) _let_1)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_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_P_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2)) (forall ((B_y $$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_P_2))))))) (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_P_2 V_Q_2))) (=> (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_x) (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_Q_2) (= B_x B_y))))) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_P_2))))))) (forall ((V_a $$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 $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_r_2 $$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 $$unsorted) (V_y_2 $$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 $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Ointernal__split T_b T_c T_a V_c_2 (tptp.c_Product__Type_OPair T_b T_c V_a_2 V_b_2)) (tptp.hAPP (tptp.hAPP V_c_2 V_a_2) V_b_2))) (forall ((V_r_2 $$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 $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (tptp.c_Relation_Oantisym T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (tptp.c_Order__Relation_Ostrict__linear__order__on T_a V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))) (forall ((V_r_2 $$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 $$unsorted)) (= (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_a V_r_2) (tptp.c_Relation_ORange T_a T_a V_r_2)))) (forall ((V_y_2 $$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_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_a_2 V_B_2)) (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (=> (not (= V_a_2 V_b_2)) (tptp.c_member T_a 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_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) (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_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_a_2 V_b_2) V_r_2)) (tptp.c_Set_Oinsert T_a V_b_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_Groups_Ominus__class_Ominus (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) (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 (tptp.c_Groups_Ominus__class_Ominus (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_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_B_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_A_2)) (or (= V_a_2 V_b_2) (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (=> (not (tptp.c_member T_a V_x_2 V_B_2)) (= (= (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (= V_A_2 V_B_2))))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_B_2) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) V_A_2))) (forall ((V_A_2 $$unsorted) (V_B_2 $$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_B_2) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$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_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))) (let ((_let_3 (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2))) (let ((_let_4 (tptp.c_member T_a V_x_2 V_B_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Set_Oinsert T_a V_x_2 _let_2))))))))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_y_2 V_A_2) V_x_2)) (or (= V_y_2 V_x_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_x_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_B_2) _let_2)))) (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Set_Oinsert T_a V_y_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_y_2 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2))) (= (tptp.c_Set_Oinsert T_a V_x_2 _let_1) _let_1))) (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_x_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_x_2) (tptp.hAPP V_B_2 V_x_2))))) (forall ((V_C_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 (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))) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (tptp.c_Relation_Otrans T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Relation_OField T_a (tptp.c_Set_Oinsert (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_Relation_OField T_a V_r_2))))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (= (tptp.c_Wellfounded_Owf T_a (tptp.c_Set_Oinsert _let_1 (tptp.c_Product__Type_OPair T_a T_a V_y_2 V_x_2) V_r_2)) (and (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (not (tptp.c_member _let_2 _let_1 V_r_2)) (not (forall ((B_c $$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_a_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_b_2) V_r_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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 B_y) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Relation_ORange T_b T_a V_A_2) (tptp.c_Relation_ORange T_b T_a V_B_2)) (tptp.c_Relation_ORange T_b T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_x $$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 ((T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (not (tptp.c_member T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_c_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_A_2))) (forall ((V_f_2 $$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 $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_ra_2) (=> (tptp.c_Wellfounded_Owf T_b V_rb_2) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Wellfounded_Olex__prod T_a T_b V_ra_2 V_rb_2))))) (forall ((V_x_2 $$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_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))) (forall ((T_a $$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_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 ((T_a $$unsorted)) (tptp.c_Order__Relation_Opartial__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((T_a $$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_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Wellfounded_Oacc T_a V_R2_2) (tptp.c_Wellfounded_Oacc T_a V_R1_2)))) (forall ((V_r_2 $$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 ((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_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_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_p_2 V_r_2) (tptp.c_Wellfounded_Owf T_a V_p_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)) (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Obot T_a) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b T_a)) V_x_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_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_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 $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x)))))) (forall ((V_y $$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 ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((V_y_2 $$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_Q_2 $$unsorted) (T_a $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)))) (forall ((V_x_2 $$unsorted) (V_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_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_x_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))) (forall ((V_x_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_x_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_x_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))))) (forall ((V_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_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OId__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (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_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 $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x_2 V_y_2) V_z_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_z_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2 V_z_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_y)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_x)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_c V_d)))))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x))))))) (forall ((V_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_a_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_member T_a V_a_2 V_A_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Otop T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2))) (forall ((V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2))))) (forall ((V_a_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 V_D_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2))))) (forall ((V_D_2 $$unsorted) (V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (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__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _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_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_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_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1)) (tptp.c_Set_Oinsert T_a V_c_2 (tptp.c_Set_Oinsert T_a V_d_2 _let_1))) (or (and (= V_a_2 V_c_2) (= V_b_2 V_d_2)) (and (= V_a_2 V_d_2) (= V_b_2 V_c_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Set_Oinsert T_a V_a_2 _let_1) (tptp.c_Set_Oinsert T_a V_b_2 _let_1)) (= V_a_2 V_b_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_B_2 $$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 ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_r_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) _let_1))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_S_2 _let_1) (= (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2) _let_1)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_A_2) _let_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) V_A_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (= (tptp.c_Transitive__Closure_Otrancl T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Oantisym T_a V_s_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_s_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Oacyclic T_a V_s_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)))))) (forall ((V_B_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_member T_a V_x_2 V_A_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 V_B_2)) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)) (forall ((V_y_2 $$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_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_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_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))) (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_x_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) V_r_2)))))) (forall ((V_x_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_x_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_a_2) V_r_2)))))) (forall ((V_a_2 $$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_a_2 V_a_2) V_r_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) V_B_2) (and (tptp.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_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))) (forall ((V_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) V_B_2)))) (forall ((V_r_2 $$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_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_member T_a V_x_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) 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_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_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2)))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_S_2 $$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 ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Relation_OId T_a))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) V_A_2)))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_x_2 V_A_2)) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_x_2 V_A_2) (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Relation_ODomain T_a T_b V_A_2) (tptp.c_Relation_ODomain T_a T_b V_B_2)) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_r_2 $$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_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_y_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_x_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_y_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_x_2) V_y_2)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Order__Relation_Opreorder__on T_a _let_3 V_r_2) (=> (tptp.c_member T_a V_a_2 _let_3) (=> (tptp.c_member T_a V_b_2 _let_3) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_2))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) V_r_2))))))))) (forall ((V_R_2 $$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_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_B_2 $$unsorted) (T_a $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$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_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_X_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 V_X_2) V_X_2) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) V_X_2) V_X_2))) (forall ((V_A_2 $$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_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_z_2)) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a1_2 V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_a2_2)) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_a_2 V_A_2) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_b V_b_2 (tptp.c_Relation_OImage T_a T_b V_r_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (exists ((B_x $$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_b_2) V_r_2))))) (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Relation_OImage T_a T_a V_R_2 V_A_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((T_a $$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_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 (tptp.c_Set_Oinsert T_b V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_HOL_Obool))))) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_a_2 V_b_2) V_r_2))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Order__Relation_Opartial__order__on T_a _let_2 V_r_2) (=> (tptp.c_member T_a V_a_2 _let_2) (=> (tptp.c_member T_a V_b_2 _let_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1))) (= V_a_2 V_b_2)))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (let ((_let_2 (tptp.c_Relation_OField T_a V_r_2))) (=> (tptp.c_Relation_Orefl__on T_a _let_2 V_r_2) (=> (tptp.c_Relation_Oantisym T_a V_r_2) (=> (tptp.c_member T_a V_a_2 _let_2) (=> (tptp.c_member T_a V_b_2 _let_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1))) (= V_a_2 V_b_2))))))))) (forall ((V_B_2 $$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 $$unsorted)) (and (tptp.c_member T_a B_xa V_B_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))))) (forall ((V_f_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omeasure T_a V_f_2))) (forall ((V_a5_2 $$unsorted) (V_a1_2 $$unsorted) (V_a2_2 $$unsorted) (V_a4_2 $$unsorted) (V_a3_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2))) (= (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 V_a2_2 _let_1) (or (and (= V_a2_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= _let_1 V_a4_2)) (exists ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (and (= (tptp.hAPP (tptp.hAPP V_a3_2 V_a1_2) V_a5_2) (tptp.hAPP (tptp.hAPP V_a3_2 B_x) B_y)) (tptp.c_member T_a B_x V_a2_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_a3_2 V_a4_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_a2_2 (tptp.c_Set_Oinsert T_a B_x (tptp.c_Orderings_Obot__class_Obot _let_1))) B_y)))))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_d_2))))) (forall ((V_A_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Relation_OImage T_b T_a V_r_2 V_A_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2) (not (tptp.c_member T_b B_x V_A_2))))))) (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (V_P_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.c_Wellfounded_Owf T_b (tptp.hAPP V_R_2 B_x)))) (tptp.c_Wellfounded_Owf (tptp.tc_prod T_a T_b) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (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_b_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_2))) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2))))))) (forall ((V_a_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_a_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_a_2)) V_a_2))))) (forall ((V_a_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_a_2 V_A_2) (tptp.c_member T_a V_a_2 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1))))))) (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_b_2 V_A_2) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member T_a V_x_2 V_A_2) (=> (tptp.c_member T_a V_y_2 V_A_2) (= (= (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_x_2 _let_1)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_y_2 _let_1))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_x_2 V_y_2) V_r_2))))))) (forall ((V_y_2 $$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 ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (tptp.c_Equiv__Relations_Oequiv T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_a_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_2)))))))) (forall ((T_b $$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_a_2 $$unsorted) (V_H_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Recdef_Owfrec T_a T_b V_r_2 V_H_2))) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (= (tptp.hAPP _let_1 V_a_2) (tptp.hAPP (tptp.hAPP V_H_2 (tptp.c_Recdef_Ocut T_a T_b _let_1 V_r_2 V_a_2)) V_a_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (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_b_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (=> (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_a_2 _let_2)) (tptp.c_Relation_OImage T_a T_a V_r_2 (tptp.c_Set_Oinsert T_a V_b_2 _let_2)))) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_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_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 ((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_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) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Equiv__Relations_Oquotient T_a (tptp.c_Orderings_Obot__class_Obot _let_1) V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))))) (forall ((V_r_2 $$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 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Equiv__Relations_Oquotient T_a V_A_2 V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_x $$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 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_y $$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_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_y))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_y_2 $$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_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_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_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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_x)))) (forall ((V_x $$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_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_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_c V_d)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_b)) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_b))))))) (forall ((V_r_H_2 $$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 $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_H_2 V_r_2)))) (forall ((V_B_2 $$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_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_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 $$unsorted) (V_R_2 $$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_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 $$unsorted) (T_a $$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_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 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2)))))) (forall ((V_D_2 $$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) (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_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_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_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_member T_a V_a_2 V_C_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2) (tptp.c_Set_Oinsert T_a V_a_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_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_a_2 V_A_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2)) (tptp.c_Set_Oinsert T_a V_a_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_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_a_2 V_C_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_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_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_a_2 V_A_2)) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_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_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_B_2 V_C_2))) (let ((_let_3 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_B_2) V_C_2))) (let ((_let_4 (tptp.c_member T_a V_a_2 V_C_2))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_a_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.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_a_2 V_B_2)))) (let ((_let_4 (tptp.c_member T_a V_a_2 V_A_2))) (and (=> _let_4 (= _let_3 (tptp.c_Set_Oinsert T_a V_a_2 _let_2))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (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)) (= (tptp.c_Groups_Ominus__class_Ominus _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_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_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_C_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_a) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_x) V_x))) (forall ((V_b $$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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_x)))) (forall ((V_y $$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_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)) (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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y))) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x _let_1) _let_1)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a V_c)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_b V_c))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z))))) (forall ((V_c $$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 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_z) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z))))) (forall ((V_x_2 $$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_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) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2)))) (forall ((V_B_2 $$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_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_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_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_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_s_2 $$unsorted) (V_B_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_Relation_Orefl__on T_a V_B_2 V_s_2) (tptp.c_Relation_Orefl__on T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_member T_a V_c_2 V_B_2))) (forall ((V_B_2 $$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 $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (and (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Orderings_Otop__class_Otop T_a) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (=> (tptp.class_Lattices_Obounded__lattice__top T_a) (= (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x_2 V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_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_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_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_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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y)) V_x))) (forall ((V_y $$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_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (=> (tptp.c_Relation_Otrans T_a V_s_2) (tptp.c_Relation_Otrans T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2))))) (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 _let_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_C_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2)) (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_C_2 V_A_2))))) (forall ((V_A_2 $$unsorted) (V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2) V_A_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_A_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_C_2 V_A_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_C_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_C_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Orderings_Otop__class_Otop _let_1)) V_A_2))) (tptp.class_Lattices_Obounded__lattice tptp.tc_HOL_Obool) (forall ((T_2 $$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 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__top (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__bot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__sup (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$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 $$unsorted)) (=> (tptp.class_Orderings_Otop T_1) (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Obot T_1) (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))) (tptp.class_Lattices_Obounded__lattice__top tptp.tc_HOL_Obool) (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__sup tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_HOL_Obool) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Otop tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Orderings_Obot tptp.tc_HOL_Obool) (tptp.class_Groups_Ominus tptp.tc_HOL_Obool) (forall ((V_y_2 $$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_14 _let_13 _let_12 _let_6 _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.16/27.36 )
% 27.16/27.36 % SZS output end Proof for SCT122+1
% 27.16/27.36 % cvc5---1.0.5 exiting
% 27.16/27.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------