%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 16:31:05 EDT 2023

% Result   : Theorem 26.05s 26.30s
% Output   : Proof 26.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n014.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   : Wed Aug 23 22:33:04 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.19/0.49  %----Proving TF0_NAR, FOF, or CNF
% 26.05/26.30  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MseAxtiqoo/cvc5---1.0.5_9968.p...
% 26.05/26.30  ------- get file name : TPTP file name is SEU349+1
% 26.05/26.30  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9968.smt2...
% 26.05/26.30  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.05/26.30  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.05/26.30  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.05/26.30  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.05/26.30  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.05/26.30  % SZS status Theorem for SEU349+1
% 26.05/26.30  % SZS output start Proof for SEU349+1
% 26.05/26.30  (
% 26.05/26.30  (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 $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (= (tptp.latt_element_smaller B C A) (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B C)))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.rel_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.related_reflexive A B C) (tptp.related A B C))))))) (let ((_let_4 (forall ((A $$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.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))))))) (let ((_let_8 (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))))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.rel_str _let_1))))))) (let ((_let_10 (forall ((A $$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)))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.relstr_set_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D B) (tptp.related A D C))))))))))) (let ((_let_12 (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_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)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (= (tptp.latt_element_smaller A B C) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.in D C) (tptp.below A D B)))))))))))) (let ((_let_15 (forall ((A $$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)))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))))) (let ((_let_17 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_17))) (let ((_let_19 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 _let_19))) (let ((_let_21 (tptp.poset_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_22 (tptp.related_reflexive _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_23 (tptp.related_reflexive _let_21 _let_19 _let_17))) (let ((_let_24 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_25 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_24))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.latt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_32 (or _let_31 _let_30 _let_28 _let_26 _let_18))) (let ((_let_33 (forall ((A $$unsorted) (BOUND_VARIABLE_1461 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_1461 (tptp.the_carrier A))) (= BOUND_VARIABLE_1461 (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_1461)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 (tptp.relstr_set_smaller _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_17))) (let ((_let_37 (tptp.latt_element_smaller SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_38 (= _let_37 _let_36))) (let ((_let_39 (or _let_31 _let_30 _let_28 _let_26 _let_38))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1847 $$unsorted)) (or (tptp.empty_carrier B) (not (tptp.lattice B)) (not (tptp.latt_str B)) (not (tptp.element BOUND_VARIABLE_1847 (tptp.the_carrier B))) (= (tptp.latt_element_smaller B BOUND_VARIABLE_1847 A) (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B BOUND_VARIABLE_1847))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_43)) :args ((or _let_25 _let_39))) _let_45 :args (_let_25 true _let_39)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_43)) :args ((or _let_27 _let_39))) _let_45 :args (_let_27 true _let_39)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_43)) :args ((or _let_29 _let_39))) _let_45 :args (_let_29 true _let_39)))) (let ((_let_50 (not _let_31))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 0)) _let_45 :args (_let_50 true _let_39)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_30 _let_28 _let_26 _let_18 (not _let_32)))) _let_51 _let_49 _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_PROP)) :args _let_35)) _let_34 :args (_let_32 false _let_33)) :args (_let_18 true _let_31 false _let_29 false _let_27 false _let_25 false _let_32)))) (let ((_let_53 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 _let_24))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_31 _let_30 _let_28 _let_54 _let_20))) (let ((_let_56 ((not (= (tptp.element BOUND_VARIABLE_1461 (tptp.the_carrier A)) false))))) (let ((_let_57 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_58 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_54 _let_59 _let_57))) (let ((_let_61 (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (= _let_37 _let_61))) (let ((_let_64 (not _let_61))) (let ((_let_65 (or _let_31 _let_28 _let_26 _let_63))) (let ((_let_66 (forall ((A $$unsorted) (BOUND_VARIABLE_1422 $$unsorted) (BOUND_VARIABLE_1420 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_1420 (tptp.the_carrier A))) (= (tptp.latt_element_smaller A BOUND_VARIABLE_1420 BOUND_VARIABLE_1422) (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier A))) (not (tptp.in D BOUND_VARIABLE_1422)) (tptp.below A D BOUND_VARIABLE_1420)))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_31 _let_28 _let_26 _let_63 (not _let_65)))) _let_51 _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_63 true _let_31 false _let_27 false _let_25 false _let_65)))) (let ((_let_69 (forall ((D $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (or (not (tptp.element D (tptp.the_carrier _let_1))) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (tptp.related _let_1 D (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))))) (let ((_let_70 (= _let_36 _let_69))) (let ((_let_71 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_72 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_24))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_73 _let_71))) (let ((_let_77 (tptp.related _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_17))) (let ((_let_78 (tptp.the_carrier _let_21))) (let ((_let_79 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_78))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_73 _let_77))) (let ((_let_82 (tptp.element _let_17 _let_78))) (let ((_let_83 (tptp.reflexive_relstr _let_21))) (let ((_let_84 (tptp.rel_str _let_21))) (let ((_let_85 (tptp.empty_carrier _let_21))) (let ((_let_86 (tptp.related_reflexive _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_17))) (let ((_let_87 (= _let_77 _let_86))) (let ((_let_88 (not _let_82))) (let ((_let_89 (not _let_84))) (let ((_let_90 (not _let_83))) (let ((_let_91 (or _let_85 _let_90 _let_89 _let_80 _let_88 _let_87))) (let ((_let_92 (= _let_24 _let_78))) (let ((_let_93 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_94 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_93))) (let ((_let_95 (or _let_31 _let_30 _let_28 _let_75 _let_94))) (let ((_let_96 (tptp.meet_commutative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_97 (tptp.meet_absorbing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_98 (tptp.join_absorbing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_99 (tptp.below_refl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_100 (= _let_71 _let_99))) (let ((_let_101 (not _let_98))) (let ((_let_102 (not _let_97))) (let ((_let_103 (not _let_96))) (let ((_let_104 (or _let_31 _let_103 _let_102 _let_101 _let_28 _let_75 _let_26 _let_100))) (let ((_let_105 (tptp.related_reflexive _let_21 _let_93 _let_17))) (let ((_let_106 (= _let_99 _let_105))) (let ((_let_107 (or _let_31 _let_30 _let_28 _let_75 _let_26 _let_106))) (let ((_let_108 (not _let_37))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 4)) _let_45 :args ((not _let_38) true _let_39)))) (let ((_let_110 (_let_38))) (let ((_let_111 (not _let_63))) (let ((_let_112 (_let_63))) (let ((_let_113 (or _let_89 _let_88 _let_70))) (let ((_let_114 (forall ((A $$unsorted) (BOUND_VARIABLE_1519 $$unsorted) (BOUND_VARIABLE_1517 $$unsorted)) (or (not (tptp.rel_str A)) (not (tptp.element BOUND_VARIABLE_1519 (tptp.the_carrier A))) (= (tptp.relstr_set_smaller A BOUND_VARIABLE_1517 BOUND_VARIABLE_1519) (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier A))) (not (tptp.in D BOUND_VARIABLE_1517)) (tptp.related A D BOUND_VARIABLE_1519)))))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (_let_114))) (let ((_let_117 (or _let_31 _let_30 _let_28 _let_26 _let_82))) (let ((_let_118 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (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))))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_31 _let_30 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_124 1)) :args ((or _let_83 _let_129))) _let_128 :args (_let_83 false _let_124)))) (let ((_let_136 (not _let_85))) (let ((_let_137 (and _let_136 _let_123 _let_83 _let_122 _let_121))) (let ((_let_138 (or _let_31 _let_30 _let_28 _let_137))) (let ((_let_139 (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (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))))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_137 0)) :args ((or _let_136 (not _let_137)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_138)) :args ((or _let_31 _let_30 _let_28 _let_137 (not _let_138)))) _let_51 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_let_230 _let_229))) (let ((_let_232 (or _let_89 _let_217 _let_231))) (let ((_let_233 (and _let_36 _let_18))) (let ((_let_234 (_let_36 _let_18))) (let ((_let_235 (ASSUME :args (_let_36)))) (let ((_let_236 (ASSUME :args (_let_18)))) (let ((_let_237 (SYMM _let_236))) (let ((_let_238 (_let_229))) (let ((_let_239 (tptp.below_refl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_240 (= _let_239 _let_23))) (let ((_let_241 (not _let_23))) (let ((_let_242 (or _let_31 _let_30 _let_28 _let_54 _let_26 _let_240))) (let ((_let_243 (= _let_57 _let_239))) (let ((_let_244 (not _let_239))) (let ((_let_245 (or _let_31 _let_103 _let_102 _let_101 _let_28 _let_54 _let_26 _let_243))) (let ((_let_246 (and _let_18 _let_20 _let_22))) (let ((_let_247 (ASSUME :args (_let_22)))) (let ((_let_248 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_246)) (IMPLIES_ELIM (SCOPE 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(SCOPE (TRUE_ELIM (TRANS (CONG _let_208 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (SYMM _let_237) :args (APPLY_UF tptp.relstr_set_smaller)) (TRUE_INTRO _let_235))) :args _let_234)) :args _let_234)) :args (true _let_233)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_110) :args ((or _let_37 _let_36 _let_38))) _let_209 _let_109 :args (_let_36 true _let_37 true _let_38)) _let_52 :args (_let_230 false _let_36 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_232)) :args ((or _let_89 _let_217 _let_231 (not _let_232)))) _let_130 _let_227 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (_let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_PROP)) :args _let_116)) _let_115 :args (_let_232 false _let_114)) :args (_let_231 false _let_84 false _let_216 false _let_232)) :args (_let_229 false _let_230 false _let_231)) :args (_let_228 false _let_229)) :args (_let_214 false _let_58 false _let_218 false _let_228)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_220)) :args ((or _let_89 _let_85 _let_90 _let_217 _let_219 _let_215 (not _let_220)))) _let_130 _let_141 _let_135 _let_227 _let_223 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_143 :args (_let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_145)) :args _let_144))) _let_143 :args (_let_220 false _let_142)) :args (_let_215 false _let_84 true _let_85 false _let_83 false _let_216 false _let_218 false _let_220)) :args (_let_22 false _let_214 false _let_215)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_31 _let_30 _let_28 _let_54 _let_20 (not _let_55)))) _let_51 _let_49 _let_48 _let_213 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_35)) _let_34 :args (_let_55 false _let_33)) :args (_let_20 true _let_31 false _let_29 false _let_27 false _let_53 false _let_55)) _let_52 :args (false true _let_23 false _let_22 false _let_20 false _let_18)) :args (_let_16 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) _let_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and _let_1 (tptp.lattice A)))))) _let_14 _let_13 _let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A))) (= (tptp.cast_to_el_of_lattice A B) B))))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) true true _let_10 true _let_9 _let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A)))) (tptp.element (tptp.cast_to_el_of_lattice A B) (tptp.the_carrier A)))) (forall ((A $$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))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (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 $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$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)) (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 $$unsorted) (B $$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))))) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) _let_6 (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 $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$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 _let_3 (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))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.05/26.31  )
% 26.05/26.31  % SZS output end Proof for SEU349+1
% 26.05/26.31  % cvc5---1.0.5 exiting
% 26.05/26.31  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------