%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 16:31:13 EDT 2023

% Result   : Theorem 28.40s 28.61s
% Output   : Proof 28.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU369+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 17:49:23 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 28.40/28.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wqiwIc9SCq/cvc5---1.0.5_15955.p...
% 28.40/28.61  ------- get file name : TPTP file name is SEU369+1
% 28.40/28.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15955.smt2...
% 28.40/28.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.40/28.61  --- Run --no-e-matching --full-saturate-quant at 5...
% 28.40/28.61  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.40/28.61  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.40/28.61  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.40/28.61  % SZS status Theorem for SEU369+1
% 28.40/28.61  % SZS output start Proof for SEU369+1
% 28.40/28.61  (
% 28.40/28.61  (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below_refl A B C) (tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A B) (tptp.cast_to_el_of_LattPOSet A C))))))))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_POSet A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (=> (tptp.element C (tptp.the_carrier _let_1)) (= (tptp.related_reflexive _let_1 B C) (tptp.subset B C)))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (=> (tptp.element C (tptp.the_carrier _let_1)) (= (tptp.below _let_1 B C) (tptp.subset B C))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.latt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.below_refl A B C) (tptp.below A B C))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))))) (let ((_let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1) (tptp.join_commutative _let_1) (tptp.join_associative _let_1) (tptp.meet_commutative _let_1) (tptp.meet_associative _let_1) (tptp.meet_absorbing _let_1) (tptp.join_absorbing _let_1) (tptp.lattice _let_1) (tptp.distributive_lattstr _let_1) (tptp.modular_lattstr _let_1) (tptp.lower_bounded_semilattstr _let_1) (tptp.upper_bounded_semilattstr _let_1) (tptp.bounded_lattstr _let_1) (tptp.complemented_lattstr _let_1) (tptp.boolean_lattstr _let_1) (tptp.complete_latt_str _let_1)))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1)))))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (tptp.cast_to_el_of_LattPOSet A B) B))))))) (let ((_let_12 (forall ((A $$unsorted)) (= (tptp.boole_POSet A) (tptp.poset_of_lattice (tptp.boole_lattice A)))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.poset_of_lattice A) (tptp.rel_str_of (tptp.the_carrier A) (tptp.k2_lattice3 A))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))))) (let ((_let_15 (tptp.boole_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_16 (tptp.poset_of_lattice _let_15))) (let ((_let_17 (tptp.boole_POSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (tptp.cast_to_el_of_LattPOSet _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 _let_19))) (let ((_let_21 (tptp.cast_to_el_of_LattPOSet _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_21))) (let ((_let_23 (tptp.related_reflexive _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_24 (tptp.related_reflexive _let_16 _let_21 _let_19))) (let ((_let_25 (_let_12))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet A)))) :args _let_25)) _let_26 :args (_let_18 false _let_12)))) (let ((_let_28 (tptp.the_carrier _let_15))) (let ((_let_29 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 _let_28))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.latt_str _let_15))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.lattice _let_15))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.empty_carrier _let_15))) (let ((_let_36 (or _let_35 _let_34 _let_32 _let_30 _let_20))) (let ((_let_37 (forall ((A $$unsorted) (BOUND_VARIABLE_2189 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_2189 (tptp.the_carrier A))) (= BOUND_VARIABLE_2189 (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_2189)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((not (= (tptp.element BOUND_VARIABLE_2189 (tptp.the_carrier A)) false))))) (let ((_let_41 (tptp.the_carrier _let_17))) (let ((_let_42 (= _let_41 _let_28))) (let ((_let_43 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 _let_41))) (let ((_let_44 (tptp.k2_lattice3 _let_15))) (let ((_let_45 (tptp.the_InternalRel _let_17))) (let ((_let_46 (and _let_42 (= _let_45 _let_44)))) (let ((_let_47 (tptp.rel_str_of _let_28 _let_44))) (let ((_let_48 (tptp.rel_str_of _let_41 _let_45))) (let ((_let_49 (= _let_48 _let_47))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.relation_of2 _let_45 _let_41 _let_41))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50 _let_46))) (let ((_let_54 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2878 $$unsorted) (BOUND_VARIABLE_2876 $$unsorted)) (or (not (tptp.relation_of2 B A A)) (not (= (tptp.rel_str_of A B) (tptp.rel_str_of BOUND_VARIABLE_2876 BOUND_VARIABLE_2878))) (and (= A BOUND_VARIABLE_2876) (= B BOUND_VARIABLE_2878)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (= _let_16 _let_47))) (let ((_let_57 (= _let_17 _let_48))) (let ((_let_58 (or _let_35 _let_34 _let_32 _let_56))) (let ((_let_59 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (= (tptp.poset_of_lattice A) (tptp.rel_str_of (tptp.the_carrier A) (tptp.k2_lattice3 A))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (forall ((BOUND_VARIABLE_2269 $$unsorted)) (tptp.latt_str (tptp.boole_lattice BOUND_VARIABLE_2269))))) (let ((_let_62 (1))) (let ((_let_63 (_let_61))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2269)))) :args _let_63)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args _let_62) :args (_let_31 false _let_61)))) (let ((_let_65 (forall ((BOUND_VARIABLE_2442 $$unsorted)) (tptp.lattice (tptp.boole_lattice BOUND_VARIABLE_2442))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2442)))) :args _let_67)) (AND_ELIM _let_66 :args (8)) :args (_let_33 false _let_65)))) (let ((_let_69 (forall ((BOUND_VARIABLE_2387 $$unsorted)) (not (tptp.empty_carrier (tptp.boole_lattice BOUND_VARIABLE_2387)))))) (let ((_let_70 (0))) (let ((_let_71 (_let_69))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_71) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2387)))) :args _let_71)) (AND_ELIM _let_66 :args _let_70) :args ((not _let_35) false _let_69)))) (let ((_let_73 (tptp.strict_rel_str _let_17))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.rel_str _let_17))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_74 _let_57))) (let ((_let_78 (forall ((A $$unsorted)) (or (not (tptp.rel_str A)) (not (tptp.strict_rel_str A)) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (forall ((BOUND_VARIABLE_2291 $$unsorted)) (tptp.strict_rel_str (tptp.boole_POSet BOUND_VARIABLE_2291))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 (forall ((BOUND_VARIABLE_2297 $$unsorted)) (tptp.rel_str (tptp.boole_POSet BOUND_VARIABLE_2297))))) (let ((_let_84 (_let_83))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_2297)))) :args _let_84)) (AND_ELIM _let_81 :args _let_62) :args (_let_75 false _let_83)))) (let ((_let_86 (and _let_57 _let_18 _let_56))) (let ((_let_87 (ASSUME :args (_let_56)))) (let ((_let_88 (ASSUME :args (_let_18)))) (let ((_let_89 (SYMM _let_88))) (let ((_let_90 (ASSUME :args (_let_57)))) (let ((_let_91 (tptp.relation_of2_as_subset _let_45 _let_41 _let_41))) (let ((_let_92 (= _let_91 _let_51))) (let ((_let_93 (_let_5))) (let ((_let_94 (ASSUME :args _let_93))) (let ((_let_95 (or _let_76 _let_91))) (let ((_let_96 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.rel_str A)) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 0)) :args ((or _let_42 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_50 _let_46 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or (not _let_91) _let_51 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_76 _let_91 (not _let_95)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_carrier A)))) :args (_let_96))) _let_97 :args (_let_95 false _let_96)) :args (_let_91 false _let_75 false _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_41 _let_41 _let_45 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_of2_as_subset C A B)))) :args _let_93)) _let_94 :args (_let_92 false _let_5)) :args (_let_51 false _let_91 false _let_92)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_86)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_87 _let_88 _let_90) (SCOPE (TRANS (SYMM _let_90) (SYMM _let_89) (SYMM (SYMM _let_87))) :args (_let_56 _let_18 _let_57))) :args (_let_57 _let_18 _let_56))) :args (true _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_76 _let_74 _let_57 (not _let_77)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_2291)))) :args _let_82)) (AND_ELIM _let_81 :args _let_70) :args (_let_73 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_carrier A)))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_57 false _let_75 false _let_73 false _let_77)) _let_27 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_35 _let_34 _let_32 _let_56 (not _let_58)))) _let_72 _let_68 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.poset_of_lattice A)))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_56 true _let_35 false _let_33 false _let_31 false _let_58)) :args (_let_49 false _let_57 false _let_18 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_41 _let_45 _let_44 _let_28 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_46 false _let_51 false _let_49 false _let_53)) :args (_let_42 false _let_46)))) (let ((_let_99 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_100 (= _let_23 _let_99))) (let ((_let_101 (not _let_43))) (let ((_let_102 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_41))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101 _let_100))) (let ((_let_105 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_3276 $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (let ((_let_2 (tptp.the_carrier _let_1))) (or (not (tptp.element B _let_2)) (not (tptp.element BOUND_VARIABLE_3276 _let_2)) (= (tptp.related_reflexive _let_1 B BOUND_VARIABLE_3276) (tptp.subset B BOUND_VARIABLE_3276)))))))) (let ((_let_106 (not _let_104))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (or))) (let ((_let_109 (not _let_105))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_107) :args (_let_109))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_105))) (REFL :args (_let_106)) :args _let_108)) _let_107 :args (_let_106 true _let_105)))) (let ((_let_111 (REFL :args (_let_104)))) (let ((_let_112 (and _let_43 _let_42))) (let ((_let_113 (_let_43 _let_42))) (let ((_let_114 (ASSUME :args (_let_43)))) (let ((_let_115 (APPLY_UF tptp.element))) (let ((_let_116 (ASSUME :args (_let_42)))) (let ((_let_117 (SYMM _let_116))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_112)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_116) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) _let_117 :args _let_115) (TRUE_INTRO _let_114))) :args _let_113)) :args _let_113)) :args (true _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_104 1)) (CONG _let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_43))) :args _let_108)) :args ((or _let_43 _let_104))) _let_110 :args (_let_43 true _let_104)) _let_98 :args (_let_29 false _let_43 false _let_42)))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_34 _let_32 _let_30 _let_20 (not _let_36)))) _let_72 _let_68 _let_64 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING _let_40)) :args _let_39)) _let_38 :args (_let_36 false _let_37)) :args (_let_20 true _let_35 false _let_33 false _let_31 false _let_29 false _let_36)))) (let ((_let_120 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_28))) (let ((_let_121 (not _let_120))) (let ((_let_122 (or _let_35 _let_34 _let_32 _let_121 _let_22))) (let ((_let_123 (and _let_102 _let_42))) (let ((_let_124 (_let_102 _let_42))) (let ((_let_125 (ASSUME :args (_let_102)))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_123)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_116) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) _let_117 :args _let_115) (TRUE_INTRO _let_125))) :args _let_124)) :args _let_124)) :args (true _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_104 0)) (CONG _let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_102))) :args _let_108)) :args ((or _let_102 _let_104))) _let_110 :args (_let_102 true _let_104)) _let_98 :args (_let_120 false _let_102 false _let_42)))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_122)) :args ((or _let_35 _let_34 _let_32 _let_121 _let_22 (not _let_122)))) _let_72 _let_68 _let_64 _let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_15 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(not (tptp.element BOUND_VARIABLE_3250 _let_2)) (= (tptp.below _let_1 B BOUND_VARIABLE_3250) (tptp.subset B BOUND_VARIABLE_3250)))))))) (let ((_let_138 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_121 _let_30 _let_129 (not _let_136)))) _let_126 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_138 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING ((tptp.boole_lattice A) (tptp.subset B BOUND_VARIABLE_3250)))) :args (_let_137)))) _let_138 :args (_let_136 false _let_137)) :args (_let_129 false _let_120 false _let_29 false _let_136)))) (let ((_let_140 (not _let_129))) (let ((_let_141 (not _let_128))) (let ((_let_142 (_let_129))) (let ((_let_143 (tptp.join_absorbing _let_15))) (let ((_let_144 (not _let_143))) (let ((_let_145 (tptp.meet_absorbing _let_15))) (let ((_let_146 (not _let_145))) (let ((_let_147 (tptp.meet_commutative _let_15))) (let ((_let_148 (not _let_147))) (let ((_let_149 (or _let_35 _let_148 _let_146 _let_144 _let_32 _let_121 _let_30 _let_131))) (let ((_let_150 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.meet_commutative A)) (not (tptp.meet_absorbing A)) (not (tptp.join_absorbing A)) (not (tptp.latt_str A)) (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.below_refl A B C) (tptp.below A B C))))))) (let ((_let_151 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (tptp.the_carrier A))) (let ((_let_153 (forall ((BOUND_VARIABLE_2435 $$unsorted)) (tptp.join_absorbing (tptp.boole_lattice BOUND_VARIABLE_2435))))) (let ((_let_154 (_let_153))) (let ((_let_155 (forall ((BOUND_VARIABLE_2428 $$unsorted)) (tptp.meet_absorbing (tptp.boole_lattice BOUND_VARIABLE_2428))))) (let ((_let_156 (_let_155))) (let ((_let_157 (forall ((BOUND_VARIABLE_2414 $$unsorted)) (tptp.meet_commutative (tptp.boole_lattice BOUND_VARIABLE_2414))))) (let ((_let_158 (_let_157))) (let ((_let_159 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_35 _let_32 _let_148 _let_146 _let_144 _let_121 _let_30 _let_131 (not _let_149)))) _let_72 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_158) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2414)))) :args _let_158)) (AND_ELIM _let_66 :args (4)) :args (_let_147 false _let_157)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_156) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2428)))) :args _let_156)) (AND_ELIM _let_66 :args (6)) :args (_let_145 false _let_155)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_154) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_2435)))) :args _let_154)) (AND_ELIM _let_66 :args (7)) :args (_let_143 false _let_153)) _let_126 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_151 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B _let_152) false)) (not (= (tptp.element C _let_152) false))))) :args (_let_150))) _let_151 :args (_let_149 false _let_150)) :args (_let_131 true _let_35 false _let_31 false _let_147 false _let_145 false _let_143 false _let_120 false _let_29 false _let_149)))) (let ((_let_160 (not _let_131))) (let ((_let_161 (not _let_130))) (let ((_let_162 (_let_131))) (let ((_let_163 (or _let_35 _let_34 _let_32 _let_121 _let_30 _let_132))) (let ((_let_164 (forall ((A $$unsorted) (BOUND_VARIABLE_3348 $$unsorted) (BOUND_VARIABLE_3346 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_3346 _let_1)) (not (tptp.element BOUND_VARIABLE_3348 _let_1)) (= (tptp.below_refl A BOUND_VARIABLE_3346 BOUND_VARIABLE_3348) (tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_3346) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_3348)))))))) (let ((_let_165 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_166 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_163)) :args ((or _let_35 _let_34 _let_32 _let_121 _let_30 _let_132 (not _let_163)))) _let_72 _let_68 _let_64 _let_126 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_165 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING ((tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_3346) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_3348))))) :args (_let_164))) _let_165 :args (_let_163 false _let_164)) :args (_let_132 true _let_35 false _let_33 false _let_31 false _let_120 false _let_29 false _let_163)))) (let ((_let_167 (not _let_132))) (let ((_let_168 (not _let_24))) (let ((_let_169 (_let_132))) (let ((_let_170 (and _let_23 _let_18 _let_22 _let_20))) (let ((_let_171 (_let_23 _let_18 _let_22 _let_20))) (let ((_let_172 (ASSUME :args (_let_23)))) (let ((_let_173 (ASSUME :args (_let_20)))) (let ((_let_174 (ASSUME :args (_let_22)))) (let ((_let_175 (CONG _let_89 (SYMM _let_174) (SYMM _let_173) :args (APPLY_UF tptp.related_reflexive)))) (let ((_let_176 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_170)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_172 _let_88 _let_174 _let_173) (SCOPE (TRUE_ELIM (TRANS _let_175 (TRUE_INTRO _let_172))) :args _let_171)) :args _let_171)) :args (true _let_170)) _let_127 _let_119 _let_27 (REORDERING (CNF_EQUIV_POS2 :args _let_169) :args ((or _let_130 _let_168 _let_167))) _let_166 (REORDERING (CNF_EQUIV_POS1 :args _let_162) :args ((or _let_128 _let_161 _let_160))) _let_159 (REORDERING (CNF_EQUIV_POS2 :args _let_142) :args ((or _let_99 _let_141 _let_140))) _let_139 (CNF_EQUIV_NEG2 :args _let_135) _let_134 :args (_let_133 false _let_22 false _let_20 false _let_18 true _let_24 false _let_132 true _let_130 false _let_131 true _let_128 false _let_129 true _let_99 true _let_100)))) (let ((_let_177 (and _let_133 _let_18 _let_22 _let_20))) (let ((_let_178 (_let_133 _let_18 _let_22 _let_20))) (let ((_let_179 (ASSUME :args (_let_133)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_177)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_179 _let_88 _let_174 _let_173) (SCOPE (FALSE_ELIM (TRANS _let_175 (FALSE_INTRO _let_179))) :args _let_178)) :args _let_178)) :args (true _let_177)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_23))) (REFL :args ((not _let_18))) (REFL :args ((not _let_22))) (REFL :args ((not _let_20))) (REFL :args (_let_168)) :args _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_169) :args ((or _let_24 _let_161 _let_167))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_162) :args ((or _let_130 _let_141 _let_160))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_142) :args ((or (not _let_99) _let_128 _let_140))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_135) :args ((or _let_23 _let_99 _let_100))) _let_176 _let_134 :args (_let_99 true _let_23 true _let_100)) _let_139 :args (_let_128 false _let_99 false _let_129)) _let_159 :args (_let_130 false _let_128 false _let_131)) _let_166 :args (_let_24 false _let_130 false _let_132)) _let_176 _let_127 _let_119 _let_27 :args (false false _let_24 true _let_23 false _let_22 false _let_20 false _let_18)) :args (_let_14 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (tptp.strict_latt_str A) (= A (tptp.latt_str_of (tptp.the_carrier A) (tptp.the_L_join A) (tptp.the_L_meet A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.lattice A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_2 _let_1 (tptp.complete_latt_str A)) (and _let_2 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) _let_1 (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A) (tptp.bounded_lattstr A))))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_suprema_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.lattice A)) (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.with_infima_relstr A) (not (tptp.empty_carrier A))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and _let_1 (tptp.lattice A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A)) (and _let_1 (tptp.bounded_lattstr A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.bounded_relstr A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.bounded_lattstr A)) (and _let_1 (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.bounded_relstr A) (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.boolean_lattstr A)) (and _let_1 (tptp.distributive_lattstr A) (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A) (tptp.bounded_lattstr A) (tptp.complemented_lattstr A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A)) (tptp.bounded_relstr A)))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.distributive_lattstr A) (tptp.bounded_lattstr A) (tptp.complemented_lattstr A)) (and _let_1 (tptp.boolean_lattstr A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.lattice A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_2 _let_1 (tptp.distributive_lattstr A)) (and _let_2 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) _let_1 (tptp.modular_lattstr A))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_13 _let_12 _let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.related A B C) (tptp.in (tptp.ordered_pair B C) (tptp.the_InternalRel A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) _let_10 true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.k2_lattice3 A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.relation_of2_as_subset _let_2 _let_1 _let_1)))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.rel_str _let_1))))) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A))) (tptp.element (tptp.cast_to_el_of_LattPOSet A B) (tptp.the_carrier (tptp.poset_of_lattice A))))) true (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (tptp.relation (tptp.relation_of_lattice A)))) (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (tptp.meet_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) _let_8 true (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (tptp.join_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) (exists ((A $$unsorted)) (tptp.meet_semilatt_str A)) (exists ((A $$unsorted)) (tptp.rel_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (exists ((A $$unsorted)) (tptp.join_semilatt_str A)) (exists ((A $$unsorted)) (tptp.latt_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (not (tptp.empty A)) (tptp.relation_of2 B A A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton A))) (let ((_let_2 (tptp.rel_str_of _let_1 B))) (=> (tptp.relation_of2 B _let_1 _let_1) (and (not (tptp.empty_carrier _let_2)) (tptp.strict_rel_str _let_2) (tptp.trivial_carrier _let_2)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1) (tptp.join_commutative _let_1) (tptp.join_associative _let_1) (tptp.meet_commutative _let_1) (tptp.meet_associative _let_1) (tptp.meet_absorbing _let_1) (tptp.join_absorbing _let_1) (tptp.lattice _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_InternalRel A))) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (and (tptp.relation _let_2) (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.upper_bounded_semilattstr A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1) (tptp.join_commutative _let_1) (tptp.join_associative _let_1) (tptp.meet_commutative _let_1) (tptp.meet_associative _let_1) (tptp.meet_absorbing _let_1) (tptp.join_absorbing _let_1) (tptp.lattice _let_1) (tptp.distributive_lattstr _let_1) (tptp.modular_lattstr _let_1) (tptp.lower_bounded_semilattstr _let_1) (tptp.upper_bounded_semilattstr _let_1) (tptp.bounded_lattstr _let_1) (tptp.complemented_lattstr _let_1) (tptp.boolean_lattstr _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (not (tptp.empty A)) (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (tptp.reflexive B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A) (tptp.relation_of2 B A A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.lower_bounded_semilattstr A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.complete_latt_str A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) _let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_1 A) (tptp.relation_of2 B _let_1 A) (tptp.function C) (tptp.quasi_total C _let_1 A) (tptp.relation_of2 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.latt_str_of A B C) (tptp.latt_str_of D E F)) (and (= A D) (= B E) (= C F))))))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A) (tptp.distributive_lattstr A) (tptp.modular_lattstr A) (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A) (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A) (tptp.bounded_lattstr A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A) (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A) (tptp.bounded_lattstr A) (tptp.complemented_lattstr A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A) (tptp.distributive_lattstr A) (tptp.lower_bounded_semilattstr A) (tptp.upper_bounded_semilattstr A) (tptp.bounded_lattstr A) (tptp.complemented_lattstr A) (tptp.boolean_lattstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (tptp.strict_rel_str A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.trivial_carrier A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.with_suprema_relstr A) (tptp.with_infima_relstr A) (tptp.complete_relstr A) (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A) (tptp.bounded_relstr A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (tptp.strict_latt_str A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.k2_lattice3 A) (tptp.relation_of_lattice A)))) _let_5 _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.related_reflexive A B C) (tptp.related A B C))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.latt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.below_refl A B B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.related_reflexive A B B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.40/28.62  )
% 28.40/28.62  % SZS output end Proof for SEU369+1
% 28.40/28.62  % cvc5---1.0.5 exiting
% 28.40/28.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------