%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP648+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 00:26:54 EDT 2023

% Result   : Theorem 9.82s 10.03s
% Output   : Proof 9.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : GRP648+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 01:01:40 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 9.82/10.03  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9Rl3v59IIL/cvc5---1.0.5_17620.p...
% 9.82/10.03  ------- get file name : TPTP file name is GRP648+1
% 9.82/10.03  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17620.smt2...
% 9.82/10.03  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 9.82/10.03  % SZS status Theorem for GRP648+1
% 9.82/10.03  % SZS output start Proof for GRP648+1
% 9.82/10.03  (
% 9.82/10.03  (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (forall ((C $$unsorted)) (=> (tptp.m1_group_2 C A) (=> (tptp.r1_tarski (tptp.u1_struct_0 B) (tptp.u1_struct_0 C)) (tptp.m1_group_2 B C)))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (forall ((C $$unsorted)) (=> (tptp.m1_group_2 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 (tptp.k11_group_4 A))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 _let_1)) (=> (and (= D B) (= E C)) (= (tptp.r3_lattices _let_1 D E) (tptp.r1_tarski (tptp.u1_struct_0 B) (tptp.u1_struct_0 C))))))))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 (tptp.k11_group_4 A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.m1_group_2 C A))) (=> _let_1 (=> (= B C) (and (tptp.v1_group_1 C) _let_1))))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.r1_lattices A B C) (= (tptp.k2_lattices A B C) B)))))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (forall ((C $$unsorted)) (=> (and (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (= (tptp.m1_group_2 C B) (tptp.r1_group_2 A (tptp.k9_group_2 A C B) C)))))))))) (let ((_let_6 (forall ((A $$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.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.r3_lattices A B C) (tptp.r1_lattices A B C))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (= (tptp.r1_group_2 A B C) (= B C)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A)) (forall ((C $$unsorted)) (= (tptp.m1_group_6 C A B) (tptp.m1_group_2 C B))))))) (let ((_let_10 (forall ((A $$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 ((_let_11 (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_12 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1))))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_14 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_group_3 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k9_group_4 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k9_group_2 A B C))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A) (tptp.m1_group_2 C A)) (and (tptp.v1_group_1 _let_1) (tptp.m1_group_2 _let_1 A))))))) (let ((_let_16 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_17 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_group_3 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k10_group_4 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 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_18 (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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) B C))))))))))) (let ((_let_19 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (= (tptp.k11_group_4 A) (tptp.g3_lattices (tptp.k1_group_3 A) (tptp.k9_group_4 A) (tptp.k10_group_4 A))))))) (let ((_let_20 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k1_group_3 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 _let_1) (tptp.m2_relset_1 B _let_2 _let_1)) (= (= B (tptp.k10_group_4 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_group_3 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_group_3 A)) (forall ((E $$unsorted)) (=> (tptp.m1_group_2 E A) (forall ((F $$unsorted)) (let ((_let_1 (tptp.k1_group_3 A))) (=> (tptp.m1_group_2 F A) (=> (and (= C E) (= D F)) (= (tptp.k2_binop_1 _let_1 _let_1 _let_1 B C D) (tptp.k9_group_2 A E F))))))))))))))))))))) (let ((_let_21 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A) (tptp.m1_group_2 C A)) (= (tptp.k9_group_2 A B C) (tptp.k9_group_2 A C B)))))) (let ((_let_22 (forall ((A $$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 ((_let_23 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))))) (let ((_let_24 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (forall ((C $$unsorted)) (=> (tptp.m1_group_2 C A) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 (tptp.k11_group_4 A))) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (=> (tptp.m1_subset_1 E (tptp.u1_struct_0 _let_1)) (=> (and (= D B) (= E C)) (= (tptp.r3_lattices _let_1 D E) (tptp.m1_group_6 B A C))))))))))))))))) (let ((_let_25 (tptp.k11_group_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (tptp.k2_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_26))) (let ((_let_28 (tptp.k4_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (= _let_26 _let_28))) (let ((_let_30 (tptp.k4_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (= _let_28 _let_30))) (let ((_let_32 (tptp.k9_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (tptp.k9_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_34 (= _let_33 _let_32))) (let ((_let_35 (tptp.u1_lattices _let_25))) (let ((_let_36 (tptp.u1_struct_0 _let_25))) (let ((_let_37 (tptp.k2_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (= _let_37 (tptp.k2_binop_1 _let_36 _let_36 _let_36 _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_39 (= _let_30 _let_37))) (let ((_let_40 (tptp.k1_group_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (= _let_36 _let_40))) (let ((_let_42 (tptp.k10_group_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (= _let_35 _let_42))) (let ((_let_44 (= _let_32 (tptp.k2_binop_1 _let_40 _let_40 _let_40 _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_33))) (let ((_let_46 (tptp.r1_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_47 (= _let_46 _let_27))) (let ((_let_48 (not _let_27))) (let ((_let_49 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_36))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_36))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.l3_lattices _let_25))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.v9_lattices _let_25))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.v8_lattices _let_25))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.v3_struct_0 _let_25))) (let ((_let_60 (or _let_59 _let_58 _let_56 _let_54 _let_52 _let_50 _let_47))) (let ((_let_61 (forall ((A $$unsorted) (BOUND_VARIABLE_2829 $$unsorted) (BOUND_VARIABLE_2827 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v8_lattices A)) (not (tptp.v9_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2827 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2829 _let_1)) (= (tptp.r1_lattices A BOUND_VARIABLE_2827 BOUND_VARIABLE_2829) (= BOUND_VARIABLE_2827 (tptp.k2_lattices A BOUND_VARIABLE_2827 BOUND_VARIABLE_2829)))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.v10_lattices _let_25))) (let ((_let_64 (tptp.v6_lattices _let_25))) (let ((_let_65 (tptp.v3_lattices _let_25))) (let ((_let_66 (not _let_59))) (let ((_let_67 (and _let_66 _let_65 (tptp.v4_lattices _let_25) (tptp.v5_lattices _let_25) _let_64 (tptp.v7_lattices _let_25) _let_57 _let_55 _let_63 (tptp.v13_lattices _let_25) (tptp.v14_lattices _let_25) (tptp.v15_lattices _let_25)))) (let ((_let_68 (tptp.l1_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.v4_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.v3_group_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_75 (or _let_74 _let_73 _let_71 _let_69 _let_67))) (let ((_let_76 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 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.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (tptp.r3_lattices _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_79 (tptp.m1_group_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_80 (= _let_79 _let_78))) (let ((_let_81 (tptp.m1_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.m1_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_74 _let_73 _let_71 _let_69 _let_84 _let_52 _let_82 _let_50 _let_80))) (let ((_let_86 (forall ((A $$unsorted) (BOUND_VARIABLE_1921 $$unsorted) (BOUND_VARIABLE_1919 $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (let ((_let_2 (tptp.u1_struct_0 _let_1))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_group_2 BOUND_VARIABLE_1919 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1919 _let_2)) (not (tptp.m1_group_2 BOUND_VARIABLE_1921 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1921 _let_2)) (= (tptp.m1_group_6 BOUND_VARIABLE_1919 A BOUND_VARIABLE_1921) (tptp.r3_lattices _let_1 BOUND_VARIABLE_1919 BOUND_VARIABLE_1921)))))))) (let ((_let_87 (not _let_85))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (or))) (let ((_let_90 (not _let_86))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_88) :args (_let_90))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_86))) (REFL :args (_let_87)) :args _let_89)) _let_88 :args (_let_87 true _let_86)))) (let ((_let_92 (REFL :args (_let_85)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 3)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_89)) :args ((or _let_68 _let_85))) _let_91 :args (_let_68 true _let_85)))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 2)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_89)) :args ((or _let_70 _let_85))) _let_91 :args (_let_70 true _let_85)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 1)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_72))) :args _let_89)) :args ((or _let_72 _let_85))) _let_91 :args (_let_72 true _let_85)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_85 0)) _let_91 :args ((not _let_74) true _let_85)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_67 (not _let_75)))) _let_96 _let_95 _let_94 _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l1_group_1 A) false))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_67 true _let_74 false _let_72 false _let_70 false _let_68 false _let_75)))) (let ((_let_98 (not _let_67))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 7)) :args ((or _let_55 _let_98))) _let_97 :args (_let_55 false _let_67)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 6)) :args ((or _let_57 _let_98))) _let_97 :args (_let_57 false _let_67)))) (let ((_let_101 (and _let_66 _let_65 _let_63 _let_53))) (let ((_let_102 (or _let_74 _let_73 _let_71 _let_69 _let_101))) (let ((_let_103 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_101 (not _let_102)))) _let_96 _let_95 _let_94 _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_group_1 A) false))))) :args (_let_103))) _let_104 :args (_let_102 false _let_103)) :args (_let_101 true _let_74 false _let_72 false _let_70 false _let_68 false _let_102)))) (let ((_let_106 (not _let_101))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_66 _let_106))) _let_105 :args (_let_66 false _let_101)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 3)) :args ((or _let_53 _let_106))) _let_105 :args (_let_53 false _let_101)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 7)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_89)) :args ((or _let_49 _let_85))) _let_91 :args (_let_49 true _let_85)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 5)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_89)) :args ((or _let_51 _let_85))) _let_91 :args (_let_51 true _let_85)))) (let ((_let_111 (= _let_78 _let_46))) (let ((_let_112 (not _let_46))) (let ((_let_113 (not _let_64))) (let ((_let_114 (or _let_59 _let_113 _let_58 _let_56 _let_54 _let_52 _let_50 _let_111))) (let ((_let_115 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v6_lattices A)) (not (tptp.v8_lattices A)) (not (tptp.v9_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.r3_lattices A B C) (tptp.r1_lattices A B C))))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 4)) :args ((or _let_64 _let_98))) _let_97 :args (_let_64 false _let_67)))) (let ((_let_118 (not _let_78))) (let ((_let_119 (tptp.m1_group_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_120 (= _let_79 _let_119))) (let ((_let_121 (tptp.r1_tarski (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_122 (= _let_78 _let_121))) (let ((_let_123 (not _let_121))) (let ((_let_124 (or _let_74 _let_73 _let_71 _let_69 _let_84 _let_82 _let_123 _let_119))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_85 8)) _let_91 :args ((not _let_80) true _let_85)))) (let ((_let_126 (_let_80))) (let ((_let_127 (or _let_74 _let_73 _let_71 _let_69 _let_82 _let_120))) (let ((_let_128 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2659 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_group_2 B A)) (= (tptp.m1_group_6 BOUND_VARIABLE_2659 A B) (tptp.m1_group_2 BOUND_VARIABLE_2659 B)))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 6)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_81))) :args _let_89)) :args ((or _let_81 _let_85))) _let_91 :args (_let_81 true _let_85)))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_127)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_82 _let_120 (not _let_127)))) _let_96 _let_95 _let_94 _let_93 _let_130 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_129 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.m1_group_6 BOUND_VARIABLE_2659 A B)))) :args (_let_128))) _let_129 :args (_let_127 false _let_128)) :args (_let_120 true _let_74 false _let_72 false _let_70 false _let_68 false _let_81 false _let_127)))) (let ((_let_132 (not _let_120))) (let ((_let_133 (not _let_119))) (let ((_let_134 (_let_120))) (let ((_let_135 (or _let_74 _let_73 _let_71 _let_69 _let_84 _let_52 _let_82 _let_50 _let_122))) (let ((_let_136 (forall ((A $$unsorted) (BOUND_VARIABLE_2981 $$unsorted) (BOUND_VARIABLE_2979 $$unsorted)) (let ((_let_1 (tptp.k11_group_4 A))) (let ((_let_2 (tptp.u1_struct_0 _let_1))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_group_2 BOUND_VARIABLE_2979 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2979 _let_2)) (not (tptp.m1_group_2 BOUND_VARIABLE_2981 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2981 _let_2)) (= (tptp.r1_tarski (tptp.u1_struct_0 BOUND_VARIABLE_2979) (tptp.u1_struct_0 BOUND_VARIABLE_2981)) (tptp.r3_lattices _let_1 BOUND_VARIABLE_2979 BOUND_VARIABLE_2981)))))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 4)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_83))) :args _let_89)) :args ((or _let_83 _let_85))) _let_91 :args (_let_83 true _let_85)))) (let ((_let_139 (forall ((A $$unsorted) (BOUND_VARIABLE_3051 $$unsorted) (BOUND_VARIABLE_3049 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_group_2 BOUND_VARIABLE_3049 A)) (not (tptp.m1_group_2 BOUND_VARIABLE_3051 A)) (not (tptp.r1_tarski (tptp.u1_struct_0 BOUND_VARIABLE_3049) (tptp.u1_struct_0 BOUND_VARIABLE_3051))) (tptp.m1_group_2 BOUND_VARIABLE_3049 BOUND_VARIABLE_3051))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_84 _let_82 _let_119 _let_123 (not _let_124)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_group_2 BOUND_VARIABLE_3049 A) false)) (not (= (tptp.m1_group_2 BOUND_VARIABLE_3051 A) false))))) :args (_let_139))) _let_140 :args (_let_124 false _let_139)) _let_130 _let_138 _let_93 _let_94 _let_95 _let_96 (REORDERING (CNF_EQUIV_POS1 :args (_let_122)) :args ((or _let_118 _let_121 (not _let_122)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_84 _let_52 _let_82 _let_50 _let_122 (not _let_135)))) _let_96 _let_95 _let_94 _let_93 _let_138 _let_110 _let_130 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_137 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.r3_lattices (tptp.k11_group_4 A) BOUND_VARIABLE_2979 BOUND_VARIABLE_2981)))) :args (_let_136)))) _let_137 :args (_let_135 false _let_136)) :args (_let_122 true _let_74 false _let_72 false _let_70 false _let_68 false _let_83 false _let_51 false _let_81 false _let_49 false _let_135)) (REORDERING (CNF_EQUIV_POS2 :args _let_134) :args ((or _let_79 _let_133 _let_132))) _let_131 (REORDERING (CNF_EQUIV_NEG1 :args _let_126) :args ((or _let_79 _let_78 _let_80))) _let_125 :args (_let_79 false _let_124 false _let_81 false _let_83 false _let_68 false _let_70 false _let_72 true _let_74 false _let_121 false _let_122 true _let_119 false _let_120 false _let_78 true _let_80)))) (let ((_let_142 (tptp.l1_lattices _let_25))) (let ((_let_143 (not _let_142))) (let ((_let_144 (or _let_59 _let_113 _let_143 _let_52 _let_50 _let_29))) (let ((_let_145 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v6_lattices A)) (not (tptp.l1_lattices A)) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k2_lattices A B C))))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (_let_145))) (let ((_let_148 (and _let_142 (tptp.l2_lattices _let_25)))) (let ((_let_149 (or _let_54 _let_148))) (let ((_let_150 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 0)) :args ((or _let_142 (not _let_148)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_54 _let_148 (not _let_149)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_151 :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_150))) _let_151 :args (_let_149 false _let_150)) :args (_let_148 false _let_53 false _let_149)) :args (_let_142 false _let_148)))) (let ((_let_153 (or _let_59 _let_113 _let_143 _let_52 _let_50 _let_31))) (let ((_let_154 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v6_lattices A)) (not (tptp.l1_lattices A)) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k4_lattices A C B))))))) (let ((_let_155 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_156 (or _let_74 _let_73 _let_71 _let_69 _let_84 _let_82 _let_34))) (let ((_let_157 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not (tptp.v4_group_1 A)) (not (tptp.l1_group_1 A)) (not (tptp.m1_group_2 B A)) (not (tptp.m1_group_2 C A)) (= (tptp.k9_group_2 A B C) (tptp.k9_group_2 A C B)))))) (let ((_let_158 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_159 (or _let_59 _let_143 _let_50 _let_52 _let_38))) (let ((_let_160 (forall ((A $$unsorted) (BOUND_VARIABLE_2205 $$unsorted) (BOUND_VARIABLE_2203 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.l1_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2203 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2205 _let_1)) (= (tptp.k2_lattices A BOUND_VARIABLE_2203 BOUND_VARIABLE_2205) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) BOUND_VARIABLE_2203 BOUND_VARIABLE_2205))))))) (let ((_let_161 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_162 (tptp.u1_struct_0 A))) (let ((_let_163 (or _let_59 _let_113 _let_143 _let_50 _let_52 _let_39))) (let ((_let_164 (tptp.u1_struct_0 A))) (let ((_let_165 (tptp.k9_group_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_166 (tptp.u2_lattices _let_25))) (let ((_let_167 (and _let_41 (= _let_166 _let_165) _let_43))) (let ((_let_168 (tptp.g3_lattices _let_40 _let_165 _let_42))) (let ((_let_169 (tptp.g3_lattices _let_36 _let_166 _let_35))) (let ((_let_170 (= _let_169 _let_168))) (let ((_let_171 (not _let_170))) (let ((_let_172 (tptp.k2_zfmisc_1 _let_40 _let_40))) (let ((_let_173 (tptp.m1_relset_1 _let_42 _let_172 _let_40))) (let ((_let_174 (not _let_173))) (let ((_let_175 (tptp.v1_funct_2 _let_42 _let_172 _let_40))) (let ((_let_176 (not _let_175))) (let ((_let_177 (tptp.v1_funct_1 _let_42))) (let ((_let_178 (not _let_177))) (let ((_let_179 (tptp.m1_relset_1 _let_165 _let_172 _let_40))) (let ((_let_180 (not _let_179))) (let ((_let_181 (tptp.v1_funct_2 _let_165 _let_172 _let_40))) (let ((_let_182 (not _let_181))) (let ((_let_183 (tptp.v1_funct_1 _let_165))) (let ((_let_184 (not _let_183))) (let ((_let_185 (or _let_184 _let_182 _let_180 _let_178 _let_176 _let_174 _let_171 _let_167))) (let ((_let_186 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2531 $$unsorted) (BOUND_VARIABLE_2529 $$unsorted) (BOUND_VARIABLE_2527 $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (or (not (tptp.v1_funct_1 B)) (not (tptp.v1_funct_2 B _let_1 A)) (not (tptp.m1_relset_1 B _let_1 A)) (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 A)) (not (tptp.m1_relset_1 C _let_1 A)) (not (= (tptp.g3_lattices A B C) (tptp.g3_lattices BOUND_VARIABLE_2527 BOUND_VARIABLE_2529 BOUND_VARIABLE_2531))) (and (= A BOUND_VARIABLE_2527) (= B BOUND_VARIABLE_2529) (= C BOUND_VARIABLE_2531))))))) (let ((_let_187 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (= _let_25 _let_168))) (let 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(MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_208 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_207))) _let_208 :args (_let_206 false _let_207)) :args (_let_205 true _let_74 false _let_72 false _let_70 false _let_68 false _let_206)))) (let ((_let_210 (not _let_205))) (let ((_let_211 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_205 2)) :args ((or _let_200 _let_210))) _let_209 :args (_let_200 false _let_205)))) (let ((_let_212 (not _let_200))) (let ((_let_213 (tptp.m2_relset_1 _let_165 _let_172 _let_40))) (let ((_let_214 (= _let_213 _let_179))) (let ((_let_215 (and _let_183 _let_181 _let_213))) (let ((_let_216 (or _let_74 _let_73 _let_71 _let_69 _let_215))) (let ((_let_217 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_group_3 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k9_group_4 A))) (or (tptp.v3_struct_0 A) (not (tptp.v3_group_1 A)) (not 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_let_165 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_204)) :args _let_202)) _let_203 :args (_let_214 false _let_8)) :args (_let_179 false _let_213 false _let_214)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_201)) :args ((or _let_212 _let_173 (not _let_201)))) _let_211 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_203 :args (_let_172 _let_40 _let_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_204)) :args _let_202)) _let_203 :args (_let_201 false _let_8)) :args (_let_173 false _let_200 false _let_201)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_197)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_198 _let_199) (SCOPE (TRANS (SYMM _let_199) (SYMM (SYMM _let_198))) :args (_let_188 _let_189))) :args (_let_189 _let_188))) :args (true _let_197)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_194)) :args ((or _let_54 _let_193 _let_189 (not _let_194)))) _let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 1)) :args ((or _let_65 _let_106))) _let_105 :args (_let_65 false _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_196 :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.u1_struct_0 A)))) :args (_let_195))) _let_196 :args (_let_194 false _let_195)) :args (_let_189 false _let_53 false _let_65 false _let_194)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_190)) :args ((or _let_74 _let_73 _let_71 _let_69 _let_188 (not _let_190)))) _let_96 _let_95 _let_94 _let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_192 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_191))) _let_192 :args (_let_190 false _let_191)) :args (_let_188 true _let_74 false _let_72 false _let_70 false _let_68 false _let_190)) :args (_let_170 false _let_189 false _let_188)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_187 :args (_let_40 _let_165 _let_42 _let_35 _let_166 _let_36 QUANTIFIERS_INST_E_MATCHING ((tptp.g3_lattices A B C) (tptp.g3_lattices BOUND_VARIABLE_2527 BOUND_VARIABLE_2529 BOUND_VARIABLE_2531)))) :args (_let_186)))) _let_187 :args (_let_185 false _let_186)) :args (_let_167 false _let_177 false _let_175 false _let_183 false _let_181 false _let_179 false _let_173 false _let_170 false _let_185)))) (let ((_let_224 (not _let_167))) (let ((_let_225 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_167 0)) :args ((or _let_41 _let_224))) _let_223 :args (_let_41 false _let_167)))) (let ((_let_226 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_40))) (let ((_let_227 (not _let_226))) (let ((_let_228 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_40))) (let ((_let_229 (not _let_228))) (let ((_let_230 (or _let_229 _let_82 _let_227 _let_84 _let_44))) (let ((_let_231 (forall ((C $$unsorted) (BOUND_VARIABLE_2106 $$unsorted)) (let ((_let_1 (tptp.k1_group_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or 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(IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.r1_lattices A BOUND_VARIABLE_2827 BOUND_VARIABLE_2829)))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_47 false _let_51 false _let_49 false _let_53 true _let_59 false _let_57 false _let_55 false _let_60)) :args (_let_48 true _let_46 false _let_47)) :args (false false _let_45 false _let_44 false _let_43 false _let_41 false _let_39 false _let_38 false _let_34 false _let_31 false _let_29 true _let_27)) :args (_let_24 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (=> (tptp.v1_group_1 A) (= A (tptp.g1_group_1 (tptp.u1_struct_0 A) (tptp.u1_group_1 A)))))) _let_23 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_1 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(tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A)) (and (tptp.v1_group_1 _let_1) (tptp.l1_group_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_17 _let_16 true true true true (forall ((A $$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 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k8_group_2 A B C))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A) (tptp.m1_group_2 C A)) (and (tptp.v1_group_1 _let_1) (tptp.m1_group_2 _let_1 A))))) _let_15 _let_14 (forall ((A $$unsorted)) (=> (tptp.l1_group_1 A) (tptp.l1_struct_0 A))) (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.l1_group_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_group_2 B A) (and (not (tptp.v3_struct_0 B)) (tptp.v3_group_1 B) (tptp.l1_group_1 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A)) (forall ((C $$unsorted)) (=> (tptp.m1_group_6 C A B) (tptp.m1_group_2 C A))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$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_group_1 A))) (=> (tptp.l1_group_1 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))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) true (forall ((A $$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))))))) (exists ((A $$unsorted)) (tptp.l1_group_1 A)) (exists ((A $$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.v3_group_1 A) (tptp.l1_group_1 A)) (exists ((B $$unsorted)) (tptp.m1_group_2 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A)) (exists ((C $$unsorted)) (tptp.m1_group_6 C A B)))) (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) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A)) (not (tptp.v1_xboole_0 (tptp.k1_group_3 A))))) _let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (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 $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g1_group_1 A B) (tptp.g1_group_1 C D)) (and (= A C) (= B D))))))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B)))) (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 $$unsorted)) (tptp.v1_xboole_0 A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (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.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)))))) (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_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.m1_group_2 B A) (tptp.m1_group_2 C A)) (= (tptp.k9_group_2 A B C) (tptp.k8_group_2 A B C)))) _let_9 _let_8 _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (tptp.r1_group_2 A B B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.r3_lattices A B B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v3_group_1 A) (tptp.v4_group_1 A) (tptp.l1_group_1 A) (tptp.v1_group_1 B) (tptp.m1_group_2 B A) (tptp.v1_group_1 C) (tptp.m1_group_2 C A)) (=> (tptp.r1_group_2 A B C) (tptp.r1_group_2 A C B)))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) (forall ((A $$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)))) _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 9.93/10.08  )
% 9.93/10.08  % SZS output end Proof for GRP648+1
% 9.93/10.08  % cvc5---1.0.5 exiting
% 9.93/10.08  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------