TSTP Solution File: LAT320+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT320+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:04:00 EDT 2023
% Result : Theorem 259.35s 249.68s
% Output : Proof 259.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LAT320+1 : TPTP v8.1.2. Released v3.4.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 04:58:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.18/0.46 %----Proving TF0_NAR, FOF, or CNF
% 259.35/249.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.GuQZOfW6yZ/cvc5---1.0.5_31934.p...
% 259.35/249.68 ------- get file name : TPTP file name is LAT320+1
% 259.35/249.68 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31934.smt2...
% 259.35/249.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 259.35/249.68 --- Run --no-e-matching --full-saturate-quant at 5...
% 259.35/249.68 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 259.35/249.68 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 259.35/249.68 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 259.35/249.68 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 259.35/249.68 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 259.35/249.68 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 259.35/249.68 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 259.35/249.68 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 259.35/249.68 --- Run --relevant-triggers --full-saturate-quant at 5...
% 259.35/249.68 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 259.35/249.68 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 259.35/249.68 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 259.35/249.68 --- Run --no-cbqi --full-saturate-quant at 10...
% 259.35/249.68 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 259.35/249.68 % SZS status Theorem for LAT320+1
% 259.35/249.68 % SZS output start Proof for LAT320+1
% 259.35/249.68 (
% 259.35/249.68 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (forall ((C $$unsorted)) (=> (tptp.m1_filter_0 C A) (= (tptp.k3_filter_0 A (tptp.k4_subset_1 (tptp.u1_struct_0 A) B C)) (tptp.k7_filter_0 A B C)))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((D $$unsorted)) (=> (and (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.k8_filter_2 A E))) (let ((_let_3 (tptp.k8_filter_2 A D))) (let ((_let_4 (tptp.k7_filter_2 A C))) (let ((_let_5 (tptp.k7_filter_2 A B))) (=> (and (not (tptp.v1_xboole_0 E)) (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 (tptp.u1_struct_0 _let_1)))) (and (= (tptp.k20_filter_2 A B C) (tptp.k5_filter_0 _let_1 _let_5 _let_4)) (= (tptp.k20_filter_2 _let_1 _let_5 _let_4) (tptp.k5_filter_0 A B C)) (= (tptp.k20_filter_2 _let_1 D E) (tptp.k5_filter_0 A _let_3 _let_2)) (= (tptp.k20_filter_2 A _let_3 _let_2) (tptp.k5_filter_0 _let_1 D E)))))))))))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.k8_filter_2 A C))) (let ((_let_2 (tptp.k1_lattice2 A))) (let ((_let_3 (tptp.k7_filter_2 A B))) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 _let_2)))) (and (= (tptp.k3_filter_2 _let_2 _let_3) (tptp.k19_filter_2 A B)) (= (tptp.k3_filter_2 A B) (tptp.k19_filter_2 _let_2 _let_3)) (= (tptp.k3_filter_2 A _let_1) (tptp.k19_filter_2 _let_2 C)) (= (tptp.k3_filter_2 _let_2 C) (tptp.k19_filter_2 A _let_1)))))))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.r1_filter_2 A B C) (= B C))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (= (tptp.k7_filter_0 A B C) (tptp.k5_filter_0 A B C)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B C) (tptp.k2_xboole_0 B C))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k3_filter_2 A B) (tptp.k3_filter_0 A B)))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A) (tptp.m2_filter_2 C A)) (= (tptp.k21_filter_2 A B C) (tptp.k20_filter_2 A B C)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (= (tptp.k15_filter_2 A B) (tptp.k7_filter_2 A B)))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m1_relset_1 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))))) (let ((_let_15 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.v12_lattices _let_1) (tptp.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.v17_lattices _let_1))))))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 (tptp.k2_xboole_0 A B))))))) (let ((_let_17 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_18 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_19 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (tptp.l2_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_20 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_21 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))))) (let ((_let_22 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))))) (let ((_let_23 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_24 (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))))) (let ((_let_25 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_subset_1 (tptp.k7_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A)))))))) (let ((_let_26 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_subset_1 A B C) _let_1)))))) (let ((_let_27 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k20_filter_2 A B C) _let_1)))))) (let ((_let_28 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_29 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m2_filter_2 (tptp.k19_filter_2 A B) A))))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (tptp.m1_filter_2 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A)))))) (let ((_let_31 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A)))) (= (tptp.k8_filter_2 A B) B))))))) (let ((_let_32 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (= (tptp.k7_filter_2 A B) B))))))) (let ((_let_33 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_tarski A B) (tptp.k2_tarski (tptp.k2_tarski A B) (tptp.k1_tarski A)))))) (let ((_let_34 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B C) (tptp.k4_subset_1 A C B))))))) (let ((_let_36 (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v17_lattices A)) (and _let_1 (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)))))))) (let ((_let_37 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))))) (let ((_let_38 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m2_filter_2 C A) (tptp.r1_filter_2 _let_1 (tptp.k19_filter_2 A (tptp.k4_subset_1 _let_1 B C)) (tptp.k21_filter_2 A B C)))))))))))) (let ((_let_39 (tptp.k20_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_40 (tptp.k21_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (tptp.k4_subset_1 _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (= _let_43 (tptp.k4_subset_1 _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_45 (tptp.k7_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43))) (let ((_let_46 (= _let_43 _let_45))) (let ((_let_47 (tptp.k19_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43))) (let ((_let_48 (= _let_47 _let_40))) (let ((_let_49 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (tptp.u1_struct_0 _let_49))) (let ((_let_51 (= _let_42 _let_50))) (let ((_let_52 (tptp.k8_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_53 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_52))) (let ((_let_54 (tptp.k7_filter_0 _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_55 (= (tptp.k3_filter_0 _let_49 (tptp.k4_subset_1 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_54))) (let ((_let_56 (tptp.k3_filter_2 _let_49 _let_43))) (let ((_let_57 (= (tptp.k3_filter_0 _let_49 _let_43) _let_56))) (let ((_let_58 (tptp.k8_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_59 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_58))) (let ((_let_60 (= _let_47 (tptp.k3_filter_2 _let_49 _let_45)))) (let ((_let_61 (tptp.k5_filter_0 _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_62 (= _let_54 _let_61))) (let ((_let_63 (= _let_61 (tptp.k20_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_52 _let_58)))) (let ((_let_64 (tptp.m2_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.m2_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.v11_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_75 (or _let_74 _let_73 _let_71 _let_69 _let_67 _let_65 _let_41))) (let ((_let_76 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v11_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 B A)) (not (tptp.m2_filter_2 C A)) (= (tptp.k21_filter_2 A B C) (tptp.k20_filter_2 A B C)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (not _let_74))) (let ((_let_79 (and _let_78 _let_70 (tptp.v13_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v14_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v15_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v16_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_80 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_69 _let_74 _let_81 _let_79))) (let ((_let_83 (forall ((A $$unsorted)) (let ((_let_1 (tptp.v3_struct_0 A))) (or (not (tptp.l3_lattices A)) _let_1 (not (tptp.v17_lattices A)) (and (not _let_1) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (tptp.r1_filter_2 _let_42 _let_47 _let_40))) (let ((_let_86 (or _let_74 _let_73 _let_81 _let_69 _let_67 _let_65 _let_85))) (let ((_let_87 (forall ((A $$unsorted) (BOUND_VARIABLE_2727 $$unsorted) (BOUND_VARIABLE_2725 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 BOUND_VARIABLE_2725 A)) (not (tptp.m2_filter_2 BOUND_VARIABLE_2727 A)) (tptp.r1_filter_2 _let_1 (tptp.k19_filter_2 A (tptp.k4_subset_1 _let_1 BOUND_VARIABLE_2725 BOUND_VARIABLE_2727)) (tptp.k21_filter_2 A BOUND_VARIABLE_2725 BOUND_VARIABLE_2727))))))) (let ((_let_88 (not _let_86))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (or))) (let ((_let_91 (not _let_87))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_89) :args (_let_91))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_87))) (REFL :args (_let_88)) :args _let_90)) _let_89 :args (_let_88 true _let_87)))) (let ((_let_93 (REFL :args (_let_86)))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 3)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_90)) :args ((or _let_68 _let_86))) _let_92 :args (_let_68 true _let_86)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 2)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_80))) :args _let_90)) :args ((or _let_80 _let_86))) _let_92 :args (_let_80 true _let_86)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_86 0)) _let_92 :args (_let_78 true _let_86)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 5)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_90)) :args ((or _let_64 _let_86))) _let_92 :args (_let_64 true _let_86)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 4)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_90)) :args ((or _let_66 _let_86))) _let_92 :args (_let_66 true _let_86)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 1)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_72))) :args _let_90)) :args ((or _let_72 _let_86))) _let_92 :args (_let_72 true _let_86)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_73 _let_69 _let_67 _let_65 _let_71 _let_41 (not _let_75)))) _let_96 _let_99 _let_94 _let_98 _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_70 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_74 _let_81 _let_69 _let_79 (not _let_82)))) _let_96 _let_95 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_79 true _let_74 false _let_80 false _let_68 false _let_82)) :args (_let_70 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k21_filter_2 A B C)))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_41 true _let_74 false _let_72 false _let_68 false _let_66 false _let_64 false _let_70 false _let_75)))) (let ((_let_101 (tptp.k1_zfmisc_1 _let_42))) (let ((_let_102 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_101))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_101))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_103 _let_44))) (let ((_let_107 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B C) (tptp.k4_subset_1 A C B))))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (tptp.m2_lattice4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_74 _let_73 _let_69 _let_110 _let_102))) (let ((_let_112 (forall ((A $$unsorted) (BOUND_VARIABLE_3403 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_lattice4 BOUND_VARIABLE_3403 A)) (tptp.m1_subset_1 BOUND_VARIABLE_3403 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (_let_112))) (let ((_let_115 (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_116 (not _let_115))) (let ((_let_117 (and _let_116 _let_109))) (let ((_let_118 (or _let_74 _let_73 _let_69 _let_65 _let_117))) (let ((_let_119 (forall ((A $$unsorted) (BOUND_VARIABLE_3377 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 BOUND_VARIABLE_3377 A)) (and (not (tptp.v1_xboole_0 BOUND_VARIABLE_3377)) (tptp.m2_lattice4 BOUND_VARIABLE_3377 A)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (_let_119))) (let ((_let_122 ((not (= (tptp.m2_filter_2 BOUND_VARIABLE_3377 A) false))))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_74 _let_73 _let_69 _let_65 _let_117 (not _let_118)))) _let_96 _let_99 _let_94 _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_121)) _let_120 :args (_let_118 false _let_119)) :args (_let_117 true _let_74 false _let_72 false _let_68 false _let_64 false _let_118)))) (let ((_let_124 (not _let_117))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_74 _let_73 _let_69 _let_102 _let_110 (not _let_111)))) _let_96 _let_99 _let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_117 1)) :args ((or _let_109 _let_124))) _let_123 :args (_let_109 false _let_117)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_114)) _let_113 :args (_let_111 false _let_112)) :args (_let_102 true _let_74 false _let_72 false _let_68 false _let_109 false _let_111)))) (let ((_let_126 (tptp.m2_lattice4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_127 (not _let_126))) (let ((_let_128 (or _let_74 _let_73 _let_69 _let_127 _let_104))) (let ((_let_129 (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_130 (not _let_129))) (let ((_let_131 (and _let_130 _let_126))) (let ((_let_132 (or _let_74 _let_73 _let_69 _let_67 _let_131))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_74 _let_73 _let_69 _let_67 _let_131 (not _let_132)))) _let_96 _let_99 _let_94 _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_121)) _let_120 :args (_let_132 false _let_119)) :args (_let_131 true _let_74 false _let_72 false _let_68 false _let_66 false _let_132)))) (let ((_let_134 (not _let_131))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_74 _let_73 _let_69 _let_104 _let_127 (not _let_128)))) _let_96 _let_99 _let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_131 1)) :args ((or _let_126 _let_134))) _let_133 :args (_let_126 false _let_131)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_114)) _let_113 :args (_let_128 false _let_112)) :args (_let_104 true _let_74 false _let_72 false _let_68 false _let_126 false _let_128)))) (let ((_let_136 (tptp.m1_subset_1 _let_43 _let_101))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_74 _let_73 _let_69 _let_137 _let_46))) (let ((_let_139 (forall ((A $$unsorted) (BOUND_VARIABLE_3046 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_3046 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= BOUND_VARIABLE_3046 (tptp.k7_filter_2 A BOUND_VARIABLE_3046)))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (_let_139))) (let ((_let_142 (or _let_105 _let_103 _let_136))) (let ((_let_143 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_subset_1 A B C) _let_1)))))) (let ((_let_144 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_142)) :args ((or _let_105 _let_103 _let_136 (not _let_142)))) _let_135 _let_125 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_144 :args (_let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k4_subset_1 A B C)))) :args (_let_143))) _let_144 :args (_let_142 false _let_143)) :args (_let_136 false _let_104 false _let_102 false _let_142)))) (let ((_let_146 (= _let_85 _let_48))) (let ((_let_147 (not _let_48))) (let ((_let_148 (tptp.m1_subset_1 _let_40 _let_101))) (let ((_let_149 (not _let_148))) (let ((_let_150 (tptp.m1_subset_1 _let_47 _let_101))) (let ((_let_151 (not _let_150))) (let ((_let_152 (tptp.v1_xboole_0 _let_42))) (let ((_let_153 (or _let_152 _let_151 _let_149 _let_146))) (let ((_let_154 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (tptp.v1_xboole_0 A) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.r1_filter_2 A B C) (= B C))))))) (let ((_let_155 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_156 (tptp.m1_subset_1 _let_39 _let_101))) (let ((_let_157 (or _let_74 _let_73 _let_69 _let_129 _let_105 _let_115 _let_103 _let_156))) (let ((_let_158 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (tptp.v1_xboole_0 B) (not (tptp.m1_subset_1 B _let_1)) 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_let_268))) (let ((_let_271 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (or (not (tptp.l2_lattices A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m1_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_272 (AND_INTRO (TRUST_SUBS_EQ (ASSUME :args (_let_3)) :args ((= tptp.r1_tarski (lambda ((BOUND_VARIABLE_4430 $$unsorted) (BOUND_VARIABLE_4431 $$unsorted)) (tptp.m1_subset_1 BOUND_VARIABLE_4430 (tptp.k1_zfmisc_1 BOUND_VARIABLE_4431)))))) (TRUST_SUBS_EQ (ASSUME :args (_let_7)) :args ((= tptp.m2_relset_1 (lambda ((BOUND_VARIABLE_4418 $$unsorted) (BOUND_VARIABLE_4419 $$unsorted) (BOUND_VARIABLE_4420 $$unsorted)) (tptp.m1_relset_1 BOUND_VARIABLE_4418 BOUND_VARIABLE_4419 BOUND_VARIABLE_4420))))) (TRUST_SUBS_EQ (ASSUME :args (_let_33)) :args ((= tptp.k4_tarski (lambda ((BOUND_VARIABLE_4407 $$unsorted) (BOUND_VARIABLE_4408 $$unsorted)) (tptp.k2_tarski 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(tptp.k5_filter_0 A B C)))))) (let ((_let_397 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_398 (tptp.k7_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42))) (let ((_let_399 (and (= (tptp.k20_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42 _let_42) (tptp.k5_filter_0 _let_49 _let_398 _let_398)) (= (tptp.k20_filter_2 _let_49 _let_398 _let_398) (tptp.k5_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42 _let_42)) (= (tptp.k20_filter_2 _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.k5_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_52 _let_58)) _let_63))) (let ((_let_400 (tptp.m1_subset_1 _let_42 _let_101))) (let ((_let_401 (not _let_400))) (let ((_let_402 (or _let_74 _let_73 _let_69 _let_152 _let_401 _let_152 _let_401 _let_129 _let_285 _let_115 _let_383 _let_399))) (let ((_let_403 (forall ((A $$unsorted) (BOUND_VARIABLE_4290 $$unsorted) (BOUND_VARIABLE_4288 $$unsorted) 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_let_171 (not _let_174)))) _let_96 _let_99 _let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_176)) :args ((or _let_74 _let_73 _let_69 _let_175 _let_137 _let_172 (not _let_176)))) _let_96 _let_99 _let_94 _let_194 _let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_178 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k19_filter_2 A B)))) :args (_let_177))) _let_178 :args (_let_176 false _let_177)) :args (_let_172 true _let_74 false _let_72 false _let_68 true _let_175 false _let_136 false _let_176)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_47 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_121)) _let_120 :args (_let_174 false _let_119)) :args (_let_171 true _let_74 false _let_72 false _let_68 false _let_172 false _let_174)) :args (_let_168 false _let_171)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_47 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_3403 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) true))))) :args _let_114)) _let_113 :args (_let_170 false _let_112)) :args (_let_150 true _let_74 false _let_72 false _let_68 false _let_168 false _let_170)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_163)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_164 _let_166) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_167) (REFL :args (_let_101)) :args _let_165) (TRUE_INTRO _let_164))) :args (_let_156 _let_41))) :args (_let_41 _let_156))) :args (true _let_163)) :args ((or _let_148 _let_162 (not _let_156)))) _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_157)) :args ((or _let_74 _let_73 _let_69 _let_105 _let_103 _let_115 _let_129 _let_156 (not _let_157)))) _let_96 _let_99 _let_94 _let_135 _let_125 _let_161 _let_160 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_159 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_158))) _let_159 :args (_let_157 false _let_158)) :args (_let_156 true _let_74 false _let_72 false _let_68 false _let_104 false _let_102 true _let_115 true _let_129 false _let_157)) :args (_let_148 false _let_41 false _let_156)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_155 :args (_let_42 _let_47 _let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.r1_filter_2 A B C)))) :args (_let_154))) _let_155 :args (_let_153 false _let_154)) :args (_let_146 true _let_152 false _let_150 false _let_148 false _let_153)) :args (_let_147 true _let_85 false _let_146)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_138)) :args ((or _let_74 _let_73 _let_69 _let_137 _let_46 (not _let_138)))) _let_96 _let_99 _let_94 _let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_43 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_3046 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args _let_141)) _let_140 :args (_let_138 false _let_139)) :args (_let_46 true _let_74 false _let_72 false _let_68 false _let_136 false _let_138)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_103 _let_44 (not _let_106)))) _let_135 _let_125 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k4_subset_1 A B C)))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_44 false _let_104 false _let_102 false _let_106)) _let_100 :args (false false _let_63 false _let_62 false _let_60 false _let_59 false _let_57 false _let_55 false _let_53 false _let_51 true _let_48 false _let_46 false _let_44 false _let_41)) :args (_let_38 _let_37 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v10_lattices A)) (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (not (tptp.v1_xboole_0 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (let ((_let_2 (tptp.v1_relat_1 A))) (=> (and _let_2 (tptp.v1_xboole_0 A) _let_1) (and _let_2 _let_1 (tptp.v2_funct_1 A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)) (and _let_1 (tptp.v10_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)) (and _let_1 (tptp.v15_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) _let_36 (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v11_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)) (and _let_1 (tptp.v17_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v11_lattices A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v12_lattices A))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_tarski A B) (tptp.k2_tarski B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A B) (tptp.k2_xboole_0 B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k3_lattices A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k4_lattices A C B))))) _let_35 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k20_filter_2 A B C) (tptp.a_3_0_filter_2 A B C)))))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k1_binop_1 A B C) (tptp.k1_funct_1 A (tptp.k4_tarski B C)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k1_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u2_lattices A) B C))))))))) _let_34 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) B C))))))))) _let_33 _let_32 _let_31 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (forall ((C $$unsorted)) (=> (and (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.k5_filter_0 A B C) (tptp.a_3_0_filter_0 A B C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_30 _let_29 true true _let_28 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k1_lattices A B C) _let_1)))) true true true _let_27 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A) (tptp.m2_filter_2 C A)) (tptp.m2_filter_2 (tptp.k21_filter_2 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (tptp.m1_subset_1 (tptp.k2_binop_1 A B C D E F) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k2_lattices A B C) _let_1)))) true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_filter_0 (tptp.k3_filter_0 A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_filter_2 (tptp.k3_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k3_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (tptp.m1_filter_2 (tptp.k4_filter_2 A B C) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_lattices A B C) _let_1)))) _let_26 true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k5_filter_0 A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (tptp.m1_filter_0 (tptp.k7_filter_0 A B C) A))) _let_25 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (tptp.m1_subset_1 (tptp.k8_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))) _let_24 true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_23 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) true true _let_22 _let_21 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_20 true _let_19 (exists ((A $$unsorted)) (tptp.l1_lattices A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$unsorted)) (tptp.l2_lattices A)) (exists ((A $$unsorted)) (tptp.l3_lattices A)) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_0 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_2 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_filter_2 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (not (tptp.v1_xboole_0 (tptp.k5_filter_0 A B C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v1_xboole_0 (tptp.k7_filter_2 A B))))) _let_18 _let_17 (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (not (tptp.v1_xboole_0 (tptp.k8_filter_2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_tarski A)))) _let_16 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B _let_1) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1)) (not (tptp.v1_xboole_0 (tptp.k20_filter_2 A B C)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finset_1 _let_1) (tptp.v1_realset1 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k2_tarski A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 (tptp.k2_xboole_0 B A))))) _let_15 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_0_filter_0 B C D)) (exists ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (and (tptp.m1_subset_1 E _let_1) (tptp.m1_subset_1 F _let_1) (= A (tptp.k4_lattices B E F)) (tptp.r2_hidden E C) (tptp.r2_hidden F D)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B)))) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (not (tptp.v1_xboole_0 C)) (tptp.m1_subset_1 C _let_1) (not (tptp.v1_xboole_0 D)) (tptp.m1_subset_1 D _let_1)) (= (tptp.r2_hidden A (tptp.a_3_0_filter_2 B C D)) (exists ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 B))) (and (tptp.m1_subset_1 E _let_1) (tptp.m1_subset_1 F _let_1) (= A (tptp.k3_lattices B E F)) (tptp.r2_hidden E C) (tptp.r2_hidden F D)))))))) _let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k2_xboole_0 A A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_subset_1 A B B) B)))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v12_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v17_lattices A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_lattice4 B A) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_realset1 A))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_realset1 A)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) _let_13 _let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (= (tptp.k2_binop_1 A B C D E F) (tptp.k1_binop_1 D E F))))) _let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k1_lattices A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A) (tptp.m1_filter_0 C A)) (= (tptp.k4_filter_2 A B C) (tptp.k5_filter_0 A B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k2_lattices A B C))))) _let_10 _let_9 _let_8 _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.r1_filter_2 A B B)))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (=> (tptp.r1_filter_2 A B C) (tptp.r1_filter_2 A C B))))) (forall ((A $$unsorted)) (= (tptp.k2_xboole_0 A tptp.k1_xboole_0) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.v1_xboole_0 B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 259.35/249.70 )
% 259.35/249.70 % SZS output end Proof for LAT320+1
% 259.35/249.70 % cvc5---1.0.5 exiting
% 259.35/249.70 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------