%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU346+1 : TPTP v8.1.2. Released v3.3.0.
% 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 16:31:04 EDT 2023

% Result   : Theorem 26.32s 26.53s
% Output   : Proof 26.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : SEU346+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n028.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Wed Aug 23 18:06:04 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.53  %----Proving TF0_NAR, FOF, or CNF
% 26.32/26.53  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.fSqJ1gkF4t/cvc5---1.0.5_13801.p...
% 26.32/26.53  ------- get file name : TPTP file name is SEU346+1
% 26.32/26.53  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13801.smt2...
% 26.32/26.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.32/26.53  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.32/26.53  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.32/26.53  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.32/26.53  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.32/26.53  % SZS status Theorem for SEU346+1
% 26.32/26.53  % SZS output start Proof for SEU346+1
% 26.32/26.53  (
% 26.32/26.53  (let ((_let_1 (not (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 $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below_refl A B C) (tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A B) (tptp.cast_to_el_of_LattPOSet A C)))))))))))) (let ((_let_2 (forall ((A $$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)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.in (tptp.ordered_pair_as_product_element _let_1 _let_1 B C) (tptp.relation_of_lattice A)) (tptp.below_refl A 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)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.k2_lattice3 A) (tptp.relation_of_lattice A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.element C A) (tptp.element D B)) (= (tptp.ordered_pair_as_product_element A B C D) (tptp.ordered_pair C D)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))))) (let ((_let_8 (forall ((A $$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_9 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A))) (tptp.element (tptp.cast_to_el_of_LattPOSet A B) (tptp.the_carrier (tptp.poset_of_lattice A))))))) (let ((_let_13 (forall ((A $$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_14 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.k2_lattice3 A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.relation_of2_as_subset _let_2 _let_1 _let_1)))))))) (let ((_let_15 (forall ((A $$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))))))))))) (let ((_let_16 (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_17 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.poset_of_lattice A) (tptp.rel_str_of (tptp.the_carrier A) (tptp.k2_lattice3 A))))))) (let ((_let_18 (forall ((A $$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_19 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_19))) (let ((_let_21 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_21))) (let ((_let_23 (tptp.relation_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_24 (tptp.k2_lattice3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_25 (= _let_24 _let_23))) (let ((_let_26 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_27 (tptp.ordered_pair_as_product_element _let_26 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_28 (= _let_27 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_29 (tptp.poset_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_30 (tptp.the_InternalRel _let_29))) (let ((_let_31 (= _let_24 _let_30))) (let ((_let_32 (tptp.in _let_27 _let_23))) (let ((_let_33 (tptp.in (tptp.ordered_pair _let_19 _let_21) _let_30))) (let ((_let_34 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_26))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.latt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_41 (or _let_40 _let_39 _let_37 _let_35 _let_20))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_1701 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_1701 (tptp.the_carrier A))) (= BOUND_VARIABLE_1701 (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_1701)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (_let_42))) (let ((_let_45 (tptp.related_reflexive _let_29 _let_19 _let_21))) (let ((_let_46 (tptp.below_refl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_26))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_40 _let_39 _let_37 _let_35 _let_49 _let_47))) (let ((_let_51 (forall ((A $$unsorted) (BOUND_VARIABLE_2327 $$unsorted) (BOUND_VARIABLE_2325 $$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_2325 _let_1)) (not (tptp.element BOUND_VARIABLE_2327 _let_1)) (= (tptp.below_refl A BOUND_VARIABLE_2325 BOUND_VARIABLE_2327) (tptp.related_reflexive (tptp.poset_of_lattice A) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_2325) (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_2327)))))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (REFL :args (_let_50)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 3)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_54)) :args ((or _let_34 _let_50))) _let_56 :args (_let_34 true _let_50)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_54)) :args ((or _let_36 _let_50))) _let_56 :args (_let_36 true _let_50)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_54)) :args ((or _let_38 _let_50))) _let_56 :args (_let_38 true _let_50)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 0)) _let_56 :args ((not _let_40) true _let_50)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_39 _let_37 _let_35 _let_20 (not _let_41)))) _let_61 _let_60 _let_59 _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_PROP)) :args _let_44)) _let_43 :args (_let_41 false _let_42)) :args (_let_20 true _let_40 false _let_38 false _let_36 false _let_34 false _let_41)))) (let ((_let_63 (or _let_40 _let_39 _let_37 _let_49 _let_22))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 4)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_54)) :args ((or _let_48 _let_50))) _let_56 :args (_let_48 true _let_50)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_40 _let_39 _let_37 _let_49 _let_22 (not _let_63)))) _let_61 _let_60 _let_59 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_CBQI_PROP)) :args _let_44)) _let_43 :args (_let_63 false _let_42)) :args (_let_22 true _let_40 false _let_38 false _let_36 false _let_48 false _let_63)))) (let ((_let_66 (or _let_40 _let_39 _let_37 _let_25))) (let ((_let_67 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (= (tptp.k2_lattice3 A) (tptp.relation_of_lattice A)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_40 _let_39 _let_37 _let_25 (not _let_66)))) _let_61 _let_60 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_25 true _let_40 false _let_38 false _let_36 false _let_66)))) (let ((_let_70 (tptp.empty _let_26))) (let ((_let_71 (or _let_70 _let_70 _let_35 _let_49 _let_28))) (let ((_let_72 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (tptp.empty A) (tptp.empty B) (not (tptp.element C A)) (not (tptp.element D B)) (= (tptp.ordered_pair_as_product_element A B C D) (tptp.ordered_pair C D)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (not _let_70))) (let ((_let_75 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_40 _let_76 _let_74))) (let ((_let_78 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (tptp.meet_semilatt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_75))) (let ((_let_83 (forall ((A $$unsorted)) (or (not (tptp.meet_semilatt_str A)) (tptp.one_sorted_str A))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (and _let_80 (tptp.join_semilatt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) (let ((_let_86 (or _let_37 _let_85))) (let ((_let_87 (forall ((A $$unsorted)) (or (not (tptp.latt_str A)) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_71))) :args ((or _let_35 _let_49 _let_70 _let_28 (not _let_71)))) _let_58 _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_40 _let_76 _let_74 (not _let_77)))) _let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_81 _let_75 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_85 0)) :args ((or _let_80 (not _let_85)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_37 _let_85 (not _let_86)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.latt_str A) false))))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_85 false _let_36 false _let_86)) :args (_let_80 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_75 false _let_80 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_74 true _let_40 false _let_75 false _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_26 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair_as_product_element A B C D)))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_28 false _let_34 false _let_48 true _let_70 false _let_71)))) (let ((_let_90 (tptp.the_carrier _let_29))) (let ((_let_91 (and (= _let_26 _let_90) _let_31))) (let ((_let_92 (tptp.rel_str_of _let_90 _let_30))) (let ((_let_93 (tptp.rel_str_of _let_26 _let_24))) (let ((_let_94 (= _let_93 _let_92))) (let ((_let_95 (not _let_94))) (let ((_let_96 (tptp.relation_of2 _let_24 _let_26 _let_26))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95 _let_91))) (let ((_let_99 (forall ((A $$unsorted) (B $$unsorted) 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false _let_38 false _let_36 false _let_34 false _let_48 false _let_137)))) (let ((_let_141 (tptp.related _let_29 _let_19 _let_21))) (let ((_let_142 (= _let_45 _let_141))) (let ((_let_143 (= _let_141 _let_33))) (let ((_let_144 (not _let_46))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 5)) _let_56 :args ((not _let_47) true _let_50)))) (let ((_let_146 (_let_47))) (let ((_let_147 (not _let_135))) (let ((_let_148 (_let_135))) (let ((_let_149 (tptp.element _let_21 _let_90))) (let ((_let_150 (not _let_149))) (let ((_let_151 (tptp.element _let_19 _let_90))) (let ((_let_152 (not _let_151))) (let ((_let_153 (not _let_112))) (let ((_let_154 (tptp.empty_carrier _let_29))) (let ((_let_155 (or _let_154 _let_153 _let_106 _let_152 _let_150 _let_142))) (let ((_let_156 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.reflexive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element B _let_1)) (not 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((_let_180 (not _let_33))) (let ((_let_181 (_let_143))) (let ((_let_182 (not _let_31))) (let ((_let_183 (not _let_28))) (let ((_let_184 (not _let_25))) (let ((_let_185 (not _let_22))) (let ((_let_186 (not _let_20))) (let ((_let_187 (and _let_20 _let_22 _let_25 _let_32 _let_28 _let_31))) (let ((_let_188 (ASSUME :args (_let_32)))) (let ((_let_189 (ASSUME :args (_let_25)))) (let ((_let_190 (ASSUME :args (_let_31)))) (let ((_let_191 (ASSUME :args (_let_28)))) (let ((_let_192 (APPLY_UF tptp.ordered_pair))) (let ((_let_193 (ASSUME :args (_let_20)))) (let ((_let_194 (ASSUME :args (_let_22)))) (let ((_let_195 (CONG (TRANS (CONG (REFL :args (_let_19)) (SYMM _let_194) :args _let_192) (CONG (SYMM _let_193) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) :args _let_192) (SYMM _let_191)) (TRANS (SYMM _let_190) (SYMM (SYMM _let_189))) :args (APPLY_UF tptp.in)))) (let ((_let_196 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_187)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_188 _let_191 _let_193 _let_194 _let_189 _let_190) (SCOPE (TRUE_ELIM (TRANS _let_195 (TRUE_INTRO _let_188))) :args (_let_32 _let_28 _let_20 _let_22 _let_25 _let_31))) :args (_let_20 _let_22 _let_25 _let_32 _let_28 _let_31))) :args (true _let_187)) :args ((or _let_186 _let_185 _let_184 _let_136 _let_33 _let_183 _let_182))) _let_134 _let_89 _let_69 _let_65 _let_62 (REORDERING (CNF_EQUIV_POS2 :args _let_181) :args ((or _let_141 _let_180 _let_179))) _let_178 (REORDERING (CNF_EQUIV_POS2 :args _let_174) :args ((or _let_45 _let_173 _let_172))) _let_171 (REORDERING (CNF_EQUIV_POS1 :args _let_148) :args ((or _let_144 _let_32 _let_147))) _let_140 (CNF_EQUIV_NEG2 :args _let_146) _let_145 :args (_let_144 false _let_31 false _let_28 false _let_25 false _let_22 false _let_20 true _let_33 false _let_143 true _let_141 false _let_142 false _let_32 false _let_135 true _let_45 true _let_47)))) (let ((_let_197 (and _let_20 _let_22 _let_25 _let_136 _let_28 _let_31))) (let ((_let_198 (ASSUME :args (_let_136)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_197)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_198 _let_191 _let_193 _let_194 _let_189 _let_190) (SCOPE (FALSE_ELIM (TRANS _let_195 (FALSE_INTRO _let_198))) :args (_let_136 _let_28 _let_20 _let_22 _let_25 _let_31))) :args (_let_20 _let_22 _let_25 _let_136 _let_28 _let_31))) :args (true _let_197)) (CONG (REFL :args (_let_186)) (REFL :args (_let_185)) (REFL :args (_let_184)) (MACRO_SR_PRED_INTRO :args ((= (not _let_136) _let_32))) (REFL :args (_let_183)) (REFL :args (_let_182)) (REFL :args (_let_180)) :args _let_54)) :args ((or _let_186 _let_185 _let_32 _let_184 _let_180 _let_183 _let_182))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_181) :args ((or _let_173 _let_33 _let_179))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_174) :args ((or (not _let_45) _let_141 _let_172))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_146) :args ((or _let_46 _let_45 _let_47))) _let_196 _let_145 :args (_let_45 true _let_46 true _let_47)) _let_171 :args (_let_141 false _let_45 false _let_142)) _let_178 :args (_let_33 false _let_141 false _let_143)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_148) :args ((or _let_46 _let_136 _let_147))) _let_196 _let_140 :args (_let_136 true _let_46 false _let_135)) _let_134 _let_89 _let_69 _let_65 _let_62 :args (false false _let_33 true _let_32 false _let_31 false _let_28 false _let_25 false _let_22 false _let_20)) :args (_let_18 (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 (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.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 $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_17 _let_16 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_15 (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 $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B) (tptp.element C (tptp.the_carrier A)) (tptp.element D (tptp.the_carrier B))) (tptp.element (tptp.k10_filter_1 A B C D) (tptp.the_carrier (tptp.k8_filter_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.element C A) (tptp.element D B)) (tptp.element (tptp.ordered_pair_as_product_element A B C D) (tptp.cartesian_product2 A B)))) true true true _let_14 true true _let_13 _let_12 true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_1 A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.latt_str B)) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (tptp.relation (tptp.relation_of_lattice A)))) _let_11 (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))) _let_10 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))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (forall ((A $$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 $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (not (tptp.empty A)) (tptp.relation_of2 B A A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1))))) _let_9 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (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.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_associative A) (tptp.join_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (not (tptp.empty A)) (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (forall ((A $$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.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_associative A) (tptp.meet_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) _let_7 (forall ((A $$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.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.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) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B) (tptp.element C (tptp.the_carrier A)) (tptp.element D (tptp.the_carrier B))) (= (tptp.k10_filter_1 A B C D) (tptp.ordered_pair C D)))) _let_6 _let_5 _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.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_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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.32/26.53  )
% 26.32/26.53  % SZS output end Proof for SEU346+1
% 26.32/26.53  % cvc5---1.0.5 exiting
% 26.32/26.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------