TSTP Solution File: SCT115+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 14:12:05 EDT 2023
% Result : Theorem 10.81s 11.13s
% Output : Proof 10.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% 0.18/0.18 % Command : do_cvc5 %s %d
% 0.18/0.40 % Computer : n022.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Thu Aug 24 15:36:55 EDT 2023
% 0.18/0.40 % CPUTime :
% 0.25/0.58 %----Proving TF0_NAR, FOF, or CNF
% 10.81/11.13 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Qh53GpTk9a/cvc5---1.0.5_10930.p...
% 10.81/11.13 ------- get file name : TPTP file name is SCT115+1
% 10.81/11.13 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10930.smt2...
% 10.81/11.13 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.81/11.13 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.81/11.13 % SZS status Theorem for SCT115+1
% 10.81/11.13 % SZS output start Proof for SCT115+1
% 10.81/11.13 (
% 10.81/11.13 (let ((_let_1 (not (and (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (= B_y tptp.v_x))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (= B_x tptp.v_x))) (let ((_let_5 (not _let_4))) (and (=> (and (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L) _let_5 _let_2) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (= B_z tptp.v_x))) (and (=> (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_z) tptp.v_L) (not _let_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_z) tptp.v_L)) (=> (and _let_2 (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y tptp.v_y) tptp.v_L)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x tptp.v_y) tptp.v_L))))))) (=> (and _let_1 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x tptp.v_y) tptp.v_L) _let_5) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_z) tptp.v_L) (not (= B_z tptp.v_x))) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_z) tptp.v_L))))) (=> (and _let_4 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_y) tptp.v_L) _let_2) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (= B_z tptp.v_x))) (and (=> (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_z) tptp.v_L) (not _let_2)) (or (= B_z tptp.v_y) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_z) tptp.v_L))) (=> _let_2 (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y tptp.v_y) tptp.v_L))))))))))))))) (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (= B_x tptp.v_x))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (= B_y tptp.v_x))) (let ((_let_5 (not _let_4))) (=> (not (= B_x B_y)) (or (and _let_1 (= B_y tptp.v_y)) (and (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L) _let_2 _let_5) (and _let_4 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x tptp.v_y) tptp.v_L) _let_2) (and _let_1 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_y) tptp.v_L) _let_5) (and _let_4 (= B_x tptp.v_y)) (and (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_x) tptp.v_L) _let_5 _let_2) (and _let_1 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y tptp.v_y) tptp.v_L) _let_5) (and _let_4 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_x) tptp.v_L) _let_2))))))))))))) (let ((_let_2 (forall ((B_x $$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_L))))) (let ((_let_3 (and (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_z) tptp.v_L) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_z) tptp.v_L)))))) _let_2 (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (not (= B_x B_y)) (or (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_x) tptp.v_L)))))))) (let ((_let_4 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_5 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) tptp.v_L))) (let ((_let_6 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) tptp.v_L))) (let ((_let_7 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) tptp.v_L))) (let ((_let_8 (not _let_7))) (let ((_let_9 (not _let_5))) (let ((_let_10 (or _let_9 _let_8 _let_6))) (let ((_let_11 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.v_y) tptp.v_L))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_8 (= tptp.v_x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) (= tptp.v_y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) _let_6))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (or _let_9 (= tptp.v_x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) _let_14))) (let ((_let_16 (forall ((BOUND_VARIABLE_10750 $$unsorted) (BOUND_VARIABLE_10811 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y BOUND_VARIABLE_10750) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10750) (and (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10750 BOUND_VARIABLE_10811) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10811) (= tptp.v_y BOUND_VARIABLE_10811) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y BOUND_VARIABLE_10811) tptp.v_L)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10750 tptp.v_y) tptp.v_L)))))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (forall ((BOUND_VARIABLE_10731 $$unsorted) (BOUND_VARIABLE_10790 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10731 tptp.v_y) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10731) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y BOUND_VARIABLE_10790) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10790) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10731 BOUND_VARIABLE_10790) tptp.v_L)))))) (let ((_let_19 (forall ((BOUND_VARIABLE_10705 $$unsorted) (BOUND_VARIABLE_10707 $$unsorted) (BOUND_VARIABLE_10771 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10705 BOUND_VARIABLE_10707) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10705) (= tptp.v_x BOUND_VARIABLE_10707) (and (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10707 BOUND_VARIABLE_10771) tptp.v_L)) (= tptp.v_x BOUND_VARIABLE_10771) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10705 BOUND_VARIABLE_10771) tptp.v_L)) (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10707 tptp.v_y) tptp.v_L)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt BOUND_VARIABLE_10705 tptp.v_y) tptp.v_L)))))))) (let ((_let_20 (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (= tptp.v_x B_x))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (= tptp.v_x B_y))) (let ((_let_5 (not _let_4))) (or (= B_x B_y) (and _let_1 (= tptp.v_y B_y)) (and (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L) _let_2 _let_5) (and _let_4 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x tptp.v_y) tptp.v_L) _let_2) (and _let_1 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_y) tptp.v_L) _let_5) (and _let_4 (= tptp.v_y B_x)) (and (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y B_x) tptp.v_L) _let_5 _let_2) (and _let_1 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y tptp.v_y) tptp.v_L) _let_5) (and _let_4 (tptp.c_member _let_3 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y B_x) tptp.v_L) _let_2)))))))))) (let ((_let_21 (not _let_16))) (let ((_let_22 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) tptp.v_L))) (let ((_let_23 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.v_y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) tptp.v_L))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.v_y) tptp.v_L))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 (= tptp.v_x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) _let_24 (= tptp.v_x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_22))) (let ((_let_28 (or _let_26 _let_24 _let_22))) (let ((_let_29 (or))) (let ((_let_30 (REFL :args (_let_27)))) (let ((_let_31 (forall ((B_x $$unsorted) (B_y $$unsorted) (BOUND_VARIABLE_10569 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (or (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x B_y) tptp.v_L)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_y BOUND_VARIABLE_10569) tptp.v_L)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt B_x BOUND_VARIABLE_10569) tptp.v_L)))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (AND_ELIM _let_32 :args (0)))) (let ((_let_34 (_let_31))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (not _let_18))) (let ((_let_37 (_let_36))) (let ((_let_38 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.v_y) tptp.v_L))) (let ((_let_39 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.v_y) tptp.v_L))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (tptp.c_member _let_4 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt 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_let_31)) _let_107 :args (false true _let_6 false _let_7 false _let_10 false _let_5)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) (forall ((V_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 $$unsorted) (V_La_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_xa_2 V_z_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_La_2 V_z_2)) (and (not (= V_ya_2 V_z_2)) (=> _let_3 (not (= V_xa_2 V_ya_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_La_2)))))))) (forall ((V_z_2 $$unsorted) (V_La_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_ya_2 V_z_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_La_2 V_z_2)) (and (not (= V_xa_2 V_z_2)) (=> _let_3 (not (= V_xa_2 V_ya_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_La_2)))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_FunDef_Oin__rel T_a T_b V_R_2) V_xa_2) V_ya_2)) (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_ya_2) V_R_2))) (forall ((T_a $$unsorted) (V_R_2 $$unsorted) (V_ya_2 $$unsorted) (V_y_H_2 $$unsorted) (T_b $$unsorted) (V_xa_2 $$unsorted) (V_P_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_b))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_xa_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_ya_2) (tptp.hAPP V_R_2 V_xa_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_xa_2 V_y_H_2) (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_ya_2)) (tptp.c_Recdef_Osame__fst T_a T_b V_P_2 V_R_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nitpick_Orefl_H T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2)))) (forall ((T_b $$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 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Product__Type_OPair T_a T_b B_a B_b)))))) (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Product__Type_OPair T_a T_b V_a_H_2 V_b_H_2)) (and (= V_a_2 V_a_H_2) (= V_b_2 V_b_H_2)))) (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (= (tptp.c_Product__Type_OPair T_a T_b V_a V_b) (tptp.c_Product__Type_OPair T_a T_b V_a_H V_b_H)) (not (=> (= V_a V_a_H) (not (= V_b V_b_H)))))) (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_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_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_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (=> (= V_xa_2 V_ya_2) (= (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_member T_a V_ya_2 V_A_2)))) (forall ((V_xa_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_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (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_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_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_b_2 $$unsorted) (V_a_2 $$unsorted) (V_La_2 $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (tptp.c_member (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_2 V_b_2) V_La_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_b_2 V_a_2) V_La_2)))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_La_2 $$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_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (=> (not (= V_xa_2 V_ya_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_xa_2 V_ya_2) V_La_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_ya_2 V_xa_2) V_La_2)))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_F_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_F_2 V_a1_2 (tptp.hAPP (tptp.hAPP V_F_2 V_a2_2) V_a1_2)) (exists ((B_g $$unsorted)) (and (= (tptp.hAPP (tptp.hAPP V_F_2 V_a2_2) V_a1_2) (tptp.hAPP (tptp.hAPP V_F_2 B_g) V_a1_2)) (forall ((B_z $$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_F_2 B_z (tptp.hAPP B_g B_z)))))))) (forall ((V_xa_2 $$unsorted) (V_La_2 $$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_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_La_2 V_xa_2) tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_xa_2 $$unsorted) (V_La_2 $$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_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_La_2 V_xa_2) tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2))) (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_a_2 V_b_2)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_a_2) V_r_2) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_a_2) V_xa_2) (tptp.hAPP V_f_2 V_xa_2)))) (forall ((V_g_2 $$unsorted) (V_xa_2 $$unsorted) (V_r_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Recdef_Ocut T_a T_b V_f_2 V_r_2 V_xa_2) (tptp.c_Recdef_Ocut T_a T_b V_g_2 V_r_2 V_xa_2)) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_xa_2) V_r_2) (= (tptp.hAPP V_f_2 B_y) (tptp.hAPP V_g_2 B_y)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_a_2 V_b_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.c_Product__Type_Ocurry T_a T_b tptp.tc_HOL_Obool V_f_2 V_a_2 V_b_2)) (tptp.hBOOL (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_Ocurry T_b T_c T_a V_f_2 V_a_2 V_b_2) (tptp.hAPP V_f_2 (tptp.c_Product__Type_OPair T_b T_c V_a_2 V_b_2)))) (forall ((T_b $$unsorted) (V_a_2 $$unsorted) (V_xa_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_xa_2 V_a_2) B_R) (= (tptp.hAPP (tptp.c_Recdef_Ocut T_a T_b B_f B_R V_a_2) V_xa_2) (tptp.hAPP B_f V_xa_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_La_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_ya_2 V_b_2))) (let ((_let_4 (= V_xa_2 V_b_2))) (=> (not (= V_a_2 V_b_2)) (=> (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Oabove V_La_2 V_a_2 V_b_2)) (and (not (= V_xa_2 V_ya_2)) (=> _let_4 (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_a_2 V_ya_2) V_La_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_xa_2 V_a_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_xa_2 V_a_2) V_La_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_La_2))))))))))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_La_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (= V_xa_2 V_a_2))) (let ((_let_4 (= V_ya_2 V_a_2))) (=> (not (= V_a_2 V_b_2)) (=> (tptp.c_member (tptp.tc_fun _let_2 tptp.tc_HOL_Obool) V_La_2 tptp.c_Arrow__Order__Mirabelle_OLin) (= (tptp.c_member _let_2 _let_1 (tptp.c_Arrow__Order__Mirabelle_Obelow V_La_2 V_a_2 V_b_2)) (and (not (= V_xa_2 V_ya_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_xa_2 V_b_2) V_La_2)) (=> (not _let_4) (and (=> _let_3 (or (= V_ya_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_ya_2) V_La_2))) (=> (not _let_3) (tptp.c_member _let_2 _let_1 V_La_2))))))))))))) (forall ((V_a2_2 $$unsorted) (V_a1_2 $$unsorted) (V_F_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_F_2 V_a1_2 V_a2_2) (exists ((B_g $$unsorted)) (and (= V_a2_2 (tptp.hAPP (tptp.hAPP V_F_2 B_g) V_a1_2)) (forall ((B_z $$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_F_2 B_z (tptp.hAPP B_g B_z)))))))) (forall ((V_g_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted) (V_R_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_xa_2) V_R_2) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_F_2 B_z (tptp.hAPP V_g_2 B_z)))) (tptp.c_Recdef_Owfrec__rel T_a T_b V_R_2 V_F_2 V_xa_2 (tptp.hAPP (tptp.hAPP V_F_2 V_g_2) V_xa_2)))) (forall ((V_r_2 $$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 $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x V_a_2) V_r_2) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2)))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member T_a V_b_2 _let_1) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 _let_1))))) (exists ((B_L $$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_xa_2 $$unsorted) (V_F_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nitpick_Owf__wfrec_H T_b T_a V_R_2 V_F_2 V_xa_2) (tptp.hAPP (tptp.hAPP V_F_2 (tptp.c_Recdef_Ocut T_b T_a (tptp.c_Nitpick_Owf__wfrec T_b T_a V_R_2 V_F_2) V_R_2 V_xa_2)) V_xa_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_xa_2 (tptp.c_fequal V_ya_2)) (= V_xa_2 V_ya_2))) (forall ((V_B_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 T_b V_b_2 (tptp.hAPP V_B_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) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$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) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_a_2 V_A_2) (not (tptp.c_member T_b V_b_2 (tptp.hAPP V_B_2 V_a_2))))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$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) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)) (tptp.c_member T_b V_b_2 (tptp.hAPP V_B_2 V_a_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$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) (tptp.c_Product__Type_OSigma T_a T_b 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_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) (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)) (and (tptp.c_member T_a V_a_2 V_A_2) (tptp.c_member T_b V_b_2 (tptp.hAPP V_B_2 V_a_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) V_c_2 (tptp.c_Product__Type_OSigma T_a T_b V_A_2 V_B_2)) (not (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_y $$unsorted)) (=> (tptp.c_member T_b B_y (tptp.hAPP V_B_2 B_x)) (not (= V_c_2 (tptp.c_Product__Type_OPair T_a T_b B_x B_y)))))))))) (forall ((V_R_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 (tptp.c_Wellfounded_Oacc T_a V_R_2))) (not (forall ((B_z $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_z V_xa_2) V_R_2) (tptp.c_member T_a B_z (tptp.c_Wellfounded_Oacc T_a V_R_2))))))) (forall ((V_r_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y V_xa_2) V_r_2) (tptp.c_member T_a B_y (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (tptp.c_member T_a V_xa_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc T_a V_r_2))) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_a_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member T_a V_a_2 _let_1) (tptp.c_member T_a V_b_2 _let_1))))) (forall ((V_b_2 $$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) (T_a $$unsorted)) (= (tptp.c_Relation_Oirrefl T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) V_r_2))))) (forall ((V_La_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_HOL_Obool))) (= (tptp.c_member _let_1 (tptp.c_Relation_Oconverse tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt V_La_2) tptp.c_Arrow__Order__Mirabelle_OLin) (tptp.c_member _let_1 V_La_2 tptp.c_Arrow__Order__Mirabelle_OLin)))) (forall ((V_r_2 $$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 $$unsorted) (V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) (tptp.c_Relation_OId__on T_a V_A_2)) (and (= V_xa_2 V_ya_2) (tptp.c_member T_a V_xa_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId__on T_a V_A_2))) (= (tptp.c_Relation_Oconverse T_a T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse T_b T_a (tptp.c_Relation_Oconverse T_a T_b V_r_2)) V_r_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_r_2 $$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) (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_b_2 V_a_2) V_r_2))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_b_2 V_a_2) (tptp.c_Relation_Oconverse T_a T_b V_r_2)))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a V_b_2 V_a_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_ORange T_b T_a V_r_2)) (exists ((B_y $$unsorted)) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_y V_a_2) V_r_2)))) (forall ((V_r_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 V_r_2) (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))) (forall ((V_r_2 $$unsorted) (V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ya_2 V_xa_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_ya_2 V_xa_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))) (forall ((V_c_2 $$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_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) _let_1)))))) (forall ((V_c_2 $$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_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))) (forall ((V_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 $$unsorted) (T_a $$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 $$unsorted) (T_b $$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 $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2)))))) (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$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_xa_2 V_ya_2) _let_1) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_z_2) _let_1) (or (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ya_2 V_z_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_z_2 V_ya_2) _let_1)))))))) (forall ((V_r_2 $$unsorted) (V_yx_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) V_yx_2 (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (=> (= V_yx_2 (tptp.c_Product__Type_OPair T_a T_b B_y B_x)) (not (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x B_y) V_r_2))))))) (forall ((V_ya_2 $$unsorted) (V_R_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_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_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (= V_xa_2 V_ya_2)))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_b) (tptp.c_Product__Type_OPair T_a T_b V_a_2 V_b_2) V_r_2) (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)))) (forall ((V_P_2 $$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_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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 B_y) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_b_2) V_r_2))))))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Relation_OId__on T_a V_A_2)) V_A_2)) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Relation_ODomain T_a T_b (tptp.c_Relation_Oconverse T_b T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Relation_Oconverse T_b T_a V_r_2)) (tptp.c_Relation_ORange T_b T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Relation_Oconverse T_a T_b V_r_2)) (tptp.c_Relation_ODomain T_a T_b V_r_2))) (forall ((V_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_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_b V_xa_2 V_z_2) V_r_2) (= V_ya_2 V_z_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)) (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 $$unsorted)) (=> (tptp.c_member T_a V_a_2 (tptp.c_Relation_ODomain T_a T_b V_r_2)) (not (forall ((B_y $$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_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_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_xa_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_xa_2 V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (not (= V_xa_2 V_z_2)) (not (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 B_y) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2) (forall ((B_x $$unsorted)) (=> (tptp.c_member T_a B_x V_A_2) (forall ((B_xa $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member T_a B_xa V_A_2) (=> (not (= B_x B_xa)) (or (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_xa) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_xa B_x) V_r_2)))))))))) (forall ((V_f_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) (tptp.hAPP (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_xa_2) (tptp.hAPP V_f_2 V_ya_2)) 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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a V_A_2 (tptp.c_Relation_OId__on T_a V_A_2))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse T_a T_a (tptp.hAPP (tptp.c_Relation_Oinv__image T_b T_a V_R_2) V_f_2)) (tptp.hAPP (tptp.c_Relation_Oinv__image T_b T_a (tptp.c_Relation_Oconverse T_b T_b V_R_2)) V_f_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Ototal__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) V_r_2) (tptp.c_member T_a V_ya_2 V_A_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) V_r_2) (tptp.c_member T_a V_xa_2 V_A_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_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 ((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_r_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))) (tptp.c_member _let_2 _let_1 (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))) (forall ((V_r_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 _let_1 (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2))))))) (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_ya_2 V_z_2) _let_1) (tptp.c_member _let_2 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_z_2) _let_1)))))) (forall ((V_c_2 $$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) (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_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 ((T_a $$unsorted)) (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_OId T_a))) (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 V_r_2) (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= (tptp.c_Transitive__Closure_Otrancl T_a _let_1) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ODomain T_a T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (tptp.c_Relation_ORange T_a T_a V_r_2))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_OId T_a))) (= (tptp.c_Relation_Oconverse T_a T_a _let_1) _let_1))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued T_a T_a (tptp.c_Relation_OId T_a))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) V_R_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_R_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)))))) (forall ((V_c_2 $$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)))))) (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 ((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_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Relation_OId T_a)) (= V_a_2 V_b_2))) (forall ((V_R_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (let ((_let_3 (= V_xa_2 V_ya_2))) (= (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (or _let_3 (and (not _let_3) (tptp.c_member _let_2 _let_1 (tptp.c_Transitive__Closure_Otrancl T_a V_R_2))))))))) (forall ((V_c_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_b_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_b_2 V_c_2) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_c_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_R_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (exists ((B_z $$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_xa_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_ya_2) V_R_2)))))) (forall ((V_R_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Otrancl T_a V_R_2)) (exists ((B_z $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (and (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 B_z) V_R_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_z V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))))))) (forall ((V_p_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) V_p_2 (tptp.c_Relation_OId T_a)) (not (forall ((B_x $$unsorted)) (not (= V_p_2 (tptp.c_Product__Type_OPair T_a T_a B_x B_x))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a V_r_2) (forall ((B_x $$unsorted)) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_x B_x) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_y) V_r_2) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (= B_x B_y))))) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) V_r_2) (not (= V_xa_2 V_ya_2))))) (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 B_y) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y V_z_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))))))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Oacyclic T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_r_2 $$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 $$unsorted) (V_xa_2 $$unsorted) (V_ya_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_ya_2 V_xa_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_xa_2 V_ya_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) (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 $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a)))) (forall ((V_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))))) (forall ((T_a $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) V_xa_2)))) (forall ((V_A_2 $$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_B_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (=> (not (tptp.c_member T_a V_a_2 V_B_2)) (= V_a_2 V_b_2)) (tptp.c_member T_a V_a_2 (tptp.c_Set_Oinsert T_a V_b_2 V_B_2)))) (forall ((V_B_2 $$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 $$unsorted)) (=> (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 V_A_2)) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (=> (not (tptp.c_member T_a V_c_2 V_B_2)) (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (not (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2))))) (forall ((V_s_2 $$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 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_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_xa_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_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_xa_2)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2) V_A_2)) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_A_2)))) (forall ((V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2))) (= (tptp.c_Set_Oinsert T_a V_xa_2 _let_1) _let_1))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 _let_2) _let_2)))) (forall ((V_A_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2)) (tptp.c_Set_Oinsert T_a V_ya_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (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_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_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_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_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_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_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_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_xa_2 $$unsorted) (V_A_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert T_a V_ya_2 V_A_2) V_xa_2)) (or (= V_ya_2 V_xa_2) (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_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_xa_2 V_A_2) V_B_2))) (let ((_let_4 (tptp.c_member T_a V_xa_2 V_B_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Set_Oinsert T_a V_xa_2 _let_2))))))))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_xa_2 V_B_2) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_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 $$unsorted) (V_b_2 $$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) (V_c_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)) (or (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_member T_a V_c_2 V_B_2) (tptp.c_member T_a V_c_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2)))) (forall ((V_B_2 $$unsorted) (V_a_2 $$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 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (=> (not (tptp.c_member T_a V_xa_2 V_B_2)) (= (= (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (= V_A_2 V_B_2))))) (forall ((V_b_2 $$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_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_R_2 V_S_2))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse T_b T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2)) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) (tptp.c_Relation_Oconverse T_b T_a V_r_2) (tptp.c_Relation_Oconverse T_b T_a V_s_2)))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (or (tptp.c_member _let_1 V_xa_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2)) (tptp.c_member _let_1 V_xa_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2))) (tptp.c_member _let_1 V_xa_2 (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_R_2 V_S_2)))))) (forall ((V_r_2 $$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) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R_2 (tptp.c_Relation_OId T_a))) (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) _let_1 (tptp.c_Relation_OId T_a)) _let_1))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oantisym T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))) (tptp.c_Relation_Oantisym T_a V_r_2))) (forall ((V_r_2 $$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_xa_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ominus T_a) (= (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun T_b T_a) V_A_2 V_B_2) V_xa_2) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP V_A_2 V_xa_2) (tptp.hAPP V_B_2 V_xa_2))))) (forall ((V_xa_2 $$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_xa_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_g_2 V_xa_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_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 $$unsorted) (V_xa_2 $$unsorted) (V_ya_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_ya_2 V_xa_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_xa_2 V_ya_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2))))))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_b (tptp.hAPP (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_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_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_Wellfounded_Oacyclic T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans 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_Transitive__Closure_Otrancl T_a V_r_2) 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))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Otrans T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_Otrans T_a V_r_2))) (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans T_a (tptp.c_Relation_OId T_a))) (forall ((V_A_2 $$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 $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_b (tptp.hAPP (tptp.c_Relation_Oinv__image T_a T_b V_r_2) V_f_2)))) (forall ((V_a_2 $$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_xa_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_xa_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_a_2) V_r_2)))))) (forall ((V_xa_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_xa_2) V_r_2) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_a_2) V_r_2)))))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (not (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_a_2 V_a_2) V_r_2)))) (forall ((V_xa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_r_2) (tptp.c_member T_a V_xa_2 (tptp.c_Wellfounded_Oacc T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Wellfounded_Owf T_a (tptp.c_Relation_Oconverse T_a T_a (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))) (forall ((V_c_2 $$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_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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_z) V_r_2)))))))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Relation_Otrans T_a V_r_2) (tptp.c_Relation_Otrans T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))) (forall ((V_a $$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_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_f_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Wellfounded_Owf T_a (tptp.hAPP (tptp.c_Wellfounded_Omeasure T_a) V_f_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_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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (tptp.c_Order__Relation_Ostrict__linear__order__on T_a V_A_2 (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 (tptp.c_Relation_OId T_a))))) (forall ((T_a $$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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (and (tptp.c_Relation_Orefl__on T_a V_A_2 V_r_2) (tptp.c_Relation_Otrans T_a V_r_2)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Wellfounded_Owf T_a V_r_2) (forall ((B_Q $$unsorted)) (=> (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x B_Q)) (exists ((B_x $$unsorted)) (and (tptp.c_member T_a B_x B_Q) (forall ((B_y $$unsorted)) (=> (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a B_y B_x) V_r_2) (not (tptp.c_member T_a B_y B_Q)))))))))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$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_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Olinear__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (tptp.c_Relation_Ototal__on T_a V_A_2 V_r_2)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2) (and (tptp.c_Order__Relation_Opreorder__on T_a V_A_2 V_r_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (tptp.c_Wellfounded_OwfP T_a (tptp.c_FunDef_Oin__rel T_a T_a V_R_2)))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Order__Relation_Opartial__order__on T_a V_A_2 V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (=> (forall ((B_x $$unsorted)) (tptp.c_member T_a B_x (tptp.c_Wellfounded_Oacc T_a V_r_2))) (tptp.c_Wellfounded_Owf T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Lattices_Osemilattice__sup__class_Osup (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_a V_r_2) (tptp.c_Relation_ORange T_a T_a V_r_2)))) (forall ((V_f_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_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_xa_2 V_ya_2) (tptp.hAPP (tptp.c_Wellfounded_Omeasure T_a) V_f_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_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 $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_y B_z) V_r_2) (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a B_x B_z) V_r_2)))))) (tptp.c_Relation_Otrans T_a V_r_2))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Relation_Oconverse T_a T_a V_r_2)) (tptp.c_Relation_OField T_a V_r_2))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b))))) (forall ((V_s_2 $$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) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (tptp.c_member (tptp.tc_prod T_a T_a) (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2) (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2)))) (forall ((V_d_2 $$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 T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2))))) (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 ((T_a $$unsorted)) (= (tptp.c_Wellfounded_Omeasure T_a) (tptp.c_Relation_Oinv__image tptp.tc_Nat_Onat T_a tptp.c_Wellfounded_Oless__than))) (forall ((T_a $$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)))) (tptp.c_Relation_Otrans tptp.tc_Nat_Onat tptp.c_Wellfounded_Oless__than) (tptp.c_Wellfounded_Owf tptp.tc_Nat_Onat tptp.c_Wellfounded_Oless__than) (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 ((T_a $$unsorted)) (= (tptp.c_Relation_OField T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (not (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_c_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2) (=> (tptp.c_member T_a V_c_2 V_A_2) (tptp.c_member T_a V_c_2 V_B_2)))) (forall ((T_a $$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 ((T_a $$unsorted)) (tptp.c_Order__Relation_Opreorder__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_a_2 $$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_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)) (= (exists ((B_x $$unsorted)) (tptp.c_member T_a B_x V_A_2)) (not (= V_A_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))))) (forall ((V_A_2 $$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_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (=> (= (tptp.c_Set_Oinsert T_a V_a_2 _let_1) (tptp.c_Set_Oinsert T_a V_b_2 _let_1)) (= V_a_2 V_b_2)))) (forall ((V_d_2 $$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_A_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert T_a V_a_2 V_A_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))))) (forall ((V_A_2 $$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 ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange T_b T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (= (tptp.c_Relation_ORange T_b T_a V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_HOL_Obool))))) (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Product__Type_OSigma T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_B_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_OId__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= V_r_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))))) (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain T_a T_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (= (tptp.c_Transitive__Closure_Otrancl T_a _let_1) _let_1))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (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 ((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))) (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_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) _let_2) (and (= V_A_2 _let_2) (= V_B_2 _let_2)))))) (forall ((V_A_2 $$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) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Orderings_Obot__class_Obot _let_1) V_B_2) V_B_2))) (forall ((T_a $$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 ((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_Owell__order__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool)))) (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Ototal__on T_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_r_2)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Orderings_Obot__class_Obot T_a) V_x) V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (=> (tptp.class_Lattices_Obounded__lattice__bot T_a) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) _let_1) (and (= V_xa_2 _let_1) (= V_ya_2 _let_1)))))) (forall ((V_a_2 $$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 $$unsorted)) (=> (tptp.c_member T_a V_b_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) (= V_b_2 V_a_2))) (forall ((V_A_2 $$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_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_a_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))) (tptp.c_Set_Oinsert T_a V_a_2 V_A_2)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted)) (= (tptp.c_member (tptp.tc_prod tptp.tc_Nat_Onat tptp.tc_Nat_Onat) (tptp.c_Product__Type_OPair tptp.tc_Nat_Onat tptp.tc_Nat_Onat V_xa_2 V_ya_2) tptp.c_Wellfounded_Oless__than) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_xa_2 V_ya_2))) (forall ((T_a $$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_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_A_2)))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_d_2))))) (forall ((V_f_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (tptp.c_Wellfounded_Owf T_a (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2)))) (forall ((V_xa_2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Othe__elem T_a (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_HOL_Obool)))) V_xa_2)) (forall ((V_ya_2 $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_member T_a V_xa_2 V_A_2) (=> (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_ya_2) (tptp.c_Nitpick_Ofold__graph_H T_a T_b V_f_2 V_z_2 V_A_2 (tptp.hAPP (tptp.hAPP V_f_2 V_xa_2) V_ya_2)))))) (forall ((V_xa_2 $$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_xa_2) (tptp.c_Orderings_Obot__class_Obot T_a)))) (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_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 _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_C_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) (T_a $$unsorted)) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Relation_OId T_a) V_A_2) V_A_2)) (forall ((V_B_2 $$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 $$unsorted) (V_S_2 $$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 $$unsorted)) (and (tptp.c_member T_b B_x V_A_2) (tptp.c_member (tptp.tc_prod T_b T_a) (tptp.c_Product__Type_OPair T_b T_a B_x V_b_2) V_r_2))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2))))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2) (= V_xa_2 V_ya_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))) (forall ((V_xa_2 $$unsorted) (V_ya_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_ya_2 V_xa_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_xa_2 V_ya_2)) (= V_xa_2 V_ya_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x 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V_B_2)))) (forall ((V_xa_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_xa_2 V_A_2) (tptp.c_member T_a V_xa_2 V_B_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OField T_a V_r_2) (tptp.c_Relation_OField T_a V_s_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Osingle__valued T_a T_b V_s_2) (tptp.c_Relation_Osingle__valued T_a T_b V_r_2)))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> 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(tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z) V_x))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_a V_b) V_x))))) (forall ((V_x $$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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__sup T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) V_y)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> 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T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_xa_2 V_ya_2) V_ya_2)))) (forall ((V_x $$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_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_y $$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_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y)))) (forall ((V_a_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_D_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_a_2 V_C_2) (tptp.c_Set_Oinsert T_a V_a_2 V_D_2))))) (forall ((V_b_2 $$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_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_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_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2) V_C_2))))) (forall ((V_A_2 $$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 $$unsorted) (V_A_2 $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 V_B_2)))) (forall ((V_B_2 $$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 (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_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_A_2)) V_A_2))))) (forall ((V_B_2 $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_D_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) (tptp.c_Groups_Ominus__class_Ominus _let_1 V_C_2 V_D_2)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 V_B_2) V_A_2))) (forall ((V_R2_2 $$unsorted) (V_R1_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_R1_2 V_R2_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Wellfounded_Oacc T_a V_R2_2) (tptp.c_Wellfounded_Oacc T_a V_R1_2)))) (forall ((V_Q_2 $$unsorted) (T_a $$unsorted) (V_xa_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_xa_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))) (forall ((V_xa_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_P_2 V_Q_2) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_xa_2)) (tptp.hBOOL (tptp.hAPP V_Q_2 V_xa_2))))) (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_A_2)) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= V_A_2 V_B_2) (and (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_A_2 V_B_2))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (=> (= V_A_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) V_B_2 V_A_2))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_C_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_C_2))))) (forall ((T_a $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (= V_A_2 V_B_2) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (not (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_B_2 V_A_2))))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_ODomain T_a T_b V_r_2) (tptp.c_Relation_ODomain T_a T_b V_s_2)))) (forall ((V_r_2 $$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_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool) V_r_2 V_s_2) (=> (tptp.c_Relation_Oantisym T_a V_s_2) (tptp.c_Relation_Oantisym T_a V_r_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_r_2 V_s_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_R_2 V_S_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_S_2 _let_1) (= (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2) _let_1)))))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_s_2))) (let ((_let_2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_2 V_r_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq _let_2 (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) _let_1))))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_d_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Set_Oinsert T_a V_xa_2 V_A_2) V_B_2) (and (tptp.c_member T_a V_xa_2 V_B_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (not (tptp.c_member T_a V_xa_2 V_A_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2))))) (forall ((V_xa_2 $$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_xa_2 _let_2))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 _let_3) (or (= V_A_2 _let_2) (= V_A_2 _let_3))))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (tptp.c_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 V_B_2) (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_A_2 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_B_2 V_A_2)) V_B_2)))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (=> (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_r_2)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun _let_1 tptp.tc_HOL_Obool) V_r_2 V_s_2) (tptp.c_member _let_1 V_p_2 (tptp.c_Transitive__Closure_Otrancl T_a V_s_2)))))) (forall ((V_X_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a tptp.tc_HOL_Obool) (tptp.c_Relation_OImage T_a T_a V_r_2 V_X_2) V_X_2) (= (tptp.c_Relation_OImage T_a T_a (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2) V_X_2) V_X_2))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Transitive__Closure_Ortrancl T_a V_R_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_S_2)) (tptp.c_Transitive__Closure_Ortrancl T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_R_2 V_S_2))))) (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (=> (tptp.c_Wellfounded_Owf T_a V_R_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Relation_OImage T_a T_a V_R_2 V_A_2)) (= V_A_2 (tptp.c_Orderings_Obot__class_Obot _let_1)))))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_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_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))))) (= tptp.c_Wellfounded_Oless__than (tptp.c_Transitive__Closure_Otrancl tptp.tc_Nat_Onat tptp.c_Wellfounded_Opred__nat)) (forall ((V_B_2 $$unsorted) (V_xa_2 $$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_xa_2 V_A_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_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_xa_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_B_2 $$unsorted) (V_xa_2 $$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_xa_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) V_B_2) (=> (tptp.c_member T_a V_xa_2 V_A_2) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)))))) (tptp.c_Wellfounded_Owf tptp.tc_Nat_Onat tptp.c_Wellfounded_Opred__nat) (forall ((V_B_2 $$unsorted) (V_xa_2 $$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_xa_2 V_A_2))) (let ((_let_3 (tptp.c_member T_a V_xa_2 V_B_2))) (= (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_2 V_B_2)) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless _let_1 V_A_2 V_B_2)) (=> (not _let_3) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless _let_1 (tptp.c_Groups_Ominus__class_Ominus _let_1 V_A_2 (tptp.c_Set_Oinsert T_a V_xa_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_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_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 ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x V_y))) (forall ((V_p_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.c_Wellfounded_OwfP T_a V_r_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool)) V_p_2 V_r_2) (tptp.c_Wellfounded_OwfP T_a V_p_2)))) (forall ((V_R_2 $$unsorted) (T_a $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (V_f_2 $$unsorted)) (let ((_let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_ya_2))) (let ((_let_2 (tptp.tc_prod T_a T_a))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP V_f_2 V_xa_2) (tptp.hAPP V_f_2 V_ya_2)) (=> (tptp.c_member _let_2 _let_1 V_R_2) (tptp.c_member _let_2 _let_1 (tptp.c_Wellfounded_Omlex__prod T_a V_f_2 V_R_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_member (tptp.tc_prod tptp.tc_Nat_Onat tptp.tc_Nat_Onat) (tptp.c_Product__Type_OPair tptp.tc_Nat_Onat tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Transitive__Closure_Ortrancl tptp.tc_Nat_Onat tptp.c_Wellfounded_Opred__nat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_xa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_HOL_Obool))) (=> (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_2 (tptp.c_Relation_Oconverse T_a T_a V_r_2) (tptp.c_Transitive__Closure_Ortrancl T_a V_r_2)) (tptp.c_Orderings_Obot__class_Obot _let_2)) (not (tptp.c_member _let_1 (tptp.c_Product__Type_OPair T_a T_a V_xa_2 V_xa_2) (tptp.c_Transitive__Closure_Otrancl T_a V_r_2))))))) (forall ((V_a_2 $$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 ((T_a $$unsorted) (V_B_2 $$unsorted) (V_xa_2 $$unsorted) (V_A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (=> (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_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_xa_2))))) (forall ((V_xa_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_xa_2)) (not (=> (tptp.hBOOL (tptp.hAPP V_A_2 V_xa_2)) (not (tptp.hBOOL (tptp.hAPP V_B_2 V_xa_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_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_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 (tptp.c_Relation_OImage T_b T_a V_R_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf (tptp.tc_fun T_b tptp.tc_HOL_Obool) V_A_2 V_B_2)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 (tptp.c_Relation_OImage T_b T_a V_R_2 V_A_2) (tptp.c_Relation_OImage T_b T_a V_R_2 V_B_2))))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_HOL_Obool))) (= (= (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 V_B_2) V_C_2) (tptp.c_Lattices_Osemilattice__inf__class_Oinf _let_1 V_A_2 (tptp.c_Lattices_Osemilattice__sup__class_Osup _let_1 V_B_2 V_C_2))) (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_C_2 V_A_2)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_y V_z))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Olattice T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_y V_z)) (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_y) (tptp.c_Lattices_Osemilattice__sup__class_Osup T_a V_x V_z))))) (forall ((V_y $$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 $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_x V_y) V_y))) (forall ((V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (= (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_xa_2 V_ya_2) V_xa_2)))) (forall ((V_z_2 $$unsorted) (V_ya_2 $$unsorted) (V_xa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Lattices_Osemilattice__inf T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 (tptp.c_Lattices_Osemilattice__inf__class_Oinf T_a V_ya_2 V_z_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_ya_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_xa_2 V_z_2))))) (tptp.class_Lattices_Obounded__lattice tptp.tc_HOL_Obool) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Obounded__lattice T_1) (tptp.class_Lattices_Obounded__lattice__bot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__sup (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Osemilattice__inf (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Lattices_Olattice T_1) (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Obot T_1) (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Groups_Ominus T_1) (tptp.class_Groups_Ominus (tptp.tc_fun T_2 T_1)))) (tptp.class_Lattices_Osemilattice__sup tptp.tc_Nat_Onat) (tptp.class_Lattices_Osemilattice__inf tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Lattices_Olattice tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Orderings_Obot tptp.tc_Nat_Onat) (tptp.class_Groups_Ominus tptp.tc_Nat_Onat) (tptp.class_Lattices_Obounded__lattice__bot tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__sup tptp.tc_HOL_Obool) (tptp.class_Lattices_Osemilattice__inf tptp.tc_HOL_Obool) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Lattices_Olattice tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Orderings_Obot tptp.tc_HOL_Obool) (tptp.class_Groups_Ominus tptp.tc_HOL_Obool) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_fequal V_x_2) V_y_2)))) (not (= tptp.v_x tptp.v_y)) _let_3 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.81/11.14 )
% 10.81/11.14 % SZS output end Proof for SCT115+1
% 10.81/11.14 % cvc5---1.0.5 exiting
% 10.81/11.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------