%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU352+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 16:31:07 EDT 2023

% Result   : Theorem 27.73s 27.94s
% Output   : Proof 27.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU352+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Wed Aug 23 17:56:19 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 27.73/27.94  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XkkLuyuzpd/cvc5---1.0.5_5950.p...
% 27.73/27.94  ------- get file name : TPTP file name is SEU352+1
% 27.73/27.94  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5950.smt2...
% 27.73/27.94  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.73/27.94  --- Run --no-e-matching --full-saturate-quant at 5...
% 27.73/27.94  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.73/27.94  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.73/27.94  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.73/27.94  % SZS status Theorem for SEU352+1
% 27.73/27.94  % SZS output start Proof for SEU352+1
% 27.73/27.94  (
% 27.73/27.94  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))))) (let ((_let_2 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.latt_str A))) (let ((_let_2 (tptp.lattice A))) (let ((_let_3 (not (tptp.empty_carrier A)))) (=> (and _let_3 _let_2 (tptp.complete_latt_str A) _let_1) (and _let_3 _let_2 (tptp.lower_bounded_semilattstr A) _let_1 (= (tptp.bottom_of_semilattstr A) (tptp.join_of_latt_set A tptp.empty_set))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.below A B C) (tptp.below A C B)) (= B C)))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (tptp.below A (tptp.meet_commut A B C) B))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.meet_commut A B C) (tptp.meet A B C))))))) (let ((_let_6 (tptp.empty tptp.empty_set))) (let ((_let_7 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.meet A B C) _let_1)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.latt_str A)) (tptp.element (tptp.join_of_latt_set A B) (tptp.the_carrier A)))))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.latt_str A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (and _let_2 _let_1) (=> (and _let_2 (tptp.lattice A) (tptp.complete_latt_str A) _let_1) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (= C (tptp.join_of_latt_set A B)) (and (tptp.latt_element_smaller A C B) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (tptp.latt_element_smaller A D B) (tptp.below A C D))))))))))))))) (let ((_let_11 (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_12 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (=> (tptp.lower_bounded_semilattstr A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (= B (tptp.bottom_of_semilattstr A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B)))))))))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (= (tptp.lower_bounded_semilattstr A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B))))))))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.meet_commut A B C) (tptp.meet_commut A C B))))))) (let ((_let_15 (forall ((A $$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 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_18 (tptp.join_of_latt_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set))) (let ((_let_19 (tptp.element _let_18 _let_17))) (let ((_let_20 (tptp.meet_semilatt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_21 (tptp.lower_bounded_semilattstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_22 (forall ((C $$unsorted)) (let ((_let_1 (tptp.join_of_latt_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set))) (or (not (tptp.element C (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (and (= _let_1 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_1 C)) (= _let_1 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 C _let_1)))))))) (let ((_let_23 (= (tptp.bottom_of_semilattstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_18))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (not _let_19))) (let ((_let_26 (not _let_21))) (let ((_let_27 (not _let_20))) (let ((_let_28 (or _let_16 _let_27 _let_26 _let_25 _let_24))) (let ((_let_29 (tptp.latt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_30 (tptp.lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_31 (not _let_16))) (let ((_let_32 (and _let_31 _let_30 _let_21 _let_29 _let_23))) (let ((_let_33 (not _let_29))) (let ((_let_34 (tptp.complete_latt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_35 (not _let_34))) (let ((_let_36 (not _let_30))) (let ((_let_37 (or _let_16 _let_36 _let_35 _let_33 _let_32))) (let ((_let_38 (forall ((A $$unsorted)) (let ((_let_1 (tptp.latt_str A))) (let ((_let_2 (tptp.lattice A))) (let ((_let_3 (tptp.empty_carrier A))) (or _let_3 (not _let_2) (not (tptp.complete_latt_str A)) (not _let_1) (and (not _let_3) _let_2 (tptp.lower_bounded_semilattstr A) _let_1 (= (tptp.bottom_of_semilattstr A) (tptp.join_of_latt_set A tptp.empty_set)))))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_37 0)) :args ((or _let_31 _let_37))) _let_43 :args (_let_31 true _let_37)))) (let ((_let_45 (or _let_16 _let_33 _let_19))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.latt_str A)) (tptp.element (tptp.join_of_latt_set A B) (tptp.the_carrier A)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (REFL :args (_let_37)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 3)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) :args _let_41)) :args ((or _let_29 _let_37))) _let_43 :args (_let_29 true _let_37)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_16 _let_33 _let_19 (not _let_45)))) _let_44 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.join_of_latt_set A B)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_19 true _let_16 false _let_29 false _let_45)))) (let ((_let_51 (tptp.join_semilatt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_52 (and _let_20 _let_51))) (let ((_let_53 (or _let_33 _let_52))) (let ((_let_54 (forall ((A $$unsorted)) (or (not (tptp.latt_str A)) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_33 _let_52 (not _let_53)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.latt_str A) false))))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_52 false _let_29 false _let_53)))) (let ((_let_57 (not _let_52))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_20 _let_57))) _let_56 :args (_let_20 false _let_52)))) (let ((_let_59 (forall ((B $$unsorted)) (or (not (tptp.element B (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (not (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (and (= B (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 B C)) (= B (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 C B)))))))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (= _let_21 _let_60))) (let ((_let_62 (or _let_16 _let_27 _let_61))) (let ((_let_63 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.meet_semilatt_str A)) (= (tptp.lower_bounded_semilattstr A) (not (forall ((B $$unsorted)) (or (not (tptp.element B (tptp.the_carrier A))) (not (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.the_carrier A))) (and (= B (tptp.meet A B C)) (= B (tptp.meet A C B)))))))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (forall ((C $$unsorted)) (let ((_let_1 (tptp.join_of_latt_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set))) (or (not (tptp.element C (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (and (= _let_1 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_1 C)) (= _let_1 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 C _let_1)))))))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_25 _let_66))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_18))) (let ((_let_70 (= _let_18 _let_69))) (let ((_let_71 (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_72 (= _let_18 _let_71))) (let ((_let_73 (and _let_72 _let_70))) (let ((_let_74 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_17))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_73))) (let ((_let_77 (tptp.element _let_69 _let_17))) (let ((_let_78 (or _let_16 _let_27 _let_75 _let_25 _let_77))) (let ((_let_79 (tptp.meet_commutative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_80 (tptp.meet_commut SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_81 (= _let_71 _let_80))) (let ((_let_82 (not _let_79))) (let ((_let_83 (or _let_16 _let_82 _let_27 _let_25 _let_75 _let_81))) (let ((_let_84 (tptp.meet_commut SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_18))) (let ((_let_85 (= _let_69 _let_84))) (let ((_let_86 (or _let_16 _let_82 _let_27 _let_75 _let_25 _let_85))) (let ((_let_87 (tptp.meet_absorbing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_88 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_80 _let_18))) (let ((_let_89 (not _let_87))) (let ((_let_90 (or _let_16 _let_82 _let_89 _let_33 _let_25 _let_75 _let_88))) (let ((_let_91 (= _let_80 _let_84))) (let ((_let_92 (or _let_16 _let_82 _let_27 _let_25 _let_75 _let_91))) (let ((_let_93 (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (not (tptp.in D tptp.empty_set)) (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 D (tptp.meet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 (tptp.join_of_latt_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set))))))) (let ((_let_94 (tptp.latt_element_smaller SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_69 tptp.empty_set))) (let ((_let_95 (= _let_94 _let_93))) (let ((_let_96 (not _let_77))) (let ((_let_97 (or _let_16 _let_33 _let_96 _let_95))) (let ((_let_98 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_18 _let_69))) (let ((_let_99 (not _let_94))) (let ((_let_100 (or _let_96 _let_99 _let_98))) (let ((_let_101 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_69 _let_18))) (let ((_let_102 (tptp.join_commutative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_103 (not _let_101))) (let ((_let_104 (not _let_98))) (let ((_let_105 (not _let_51))) (let ((_let_106 (not _let_102))) (let ((_let_107 (or _let_16 _let_106 _let_105 _let_25 _let_96 _let_104 _let_103 _let_70))) (let ((_let_108 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.meet_semilatt_str A)) (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (tptp.element (tptp.meet A B C) _let_1)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (and _let_31 _let_102 (tptp.join_associative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_79 (tptp.meet_associative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_87 (tptp.join_absorbing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_111 (or _let_33 _let_16 _let_36 _let_110))) (let ((_let_112 (forall ((A $$unsorted)) (let ((_let_1 (tptp.empty_carrier A))) (or (not (tptp.latt_str A)) _let_1 (not (tptp.lattice A)) (and (not _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_113 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_30))) :args _let_41)) :args ((or _let_30 _let_37))) _let_43 :args (_let_30 true _let_37)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_16 _let_36 _let_33 _let_110 (not _let_111)))) _let_44 _let_114 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.latt_str A) false))))) :args (_let_112))) _let_113 :args (_let_111 false _let_112)) :args (_let_110 true _let_16 false _let_30 false _let_29 false _let_111)))) (let ((_let_116 (not _let_110))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_110 3)) :args ((or _let_79 _let_116))) _let_115 :args (_let_79 false 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BOUND_VARIABLE_1467 (tptp.the_carrier A))) (= (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.the_carrier A))) (and (= BOUND_VARIABLE_1467 (tptp.meet A BOUND_VARIABLE_1467 C)) (= BOUND_VARIABLE_1467 (tptp.meet A C BOUND_VARIABLE_1467))))) (= (tptp.bottom_of_semilattstr A) BOUND_VARIABLE_1467)))))) (let ((_let_160 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_161 (not _let_24))) (let ((_let_162 (not _let_23))) (let ((_let_163 (_let_32))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_16 _let_26 _let_27 _let_25 _let_24 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_24)) :args ((or _let_23 (not _let_22) _let_161))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_163) (CONG (REFL :args _let_163) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_16))) (REFL :args (_let_36)) (REFL :args (_let_26)) (REFL :args (_let_33)) (REFL :args (_let_162)) :args _let_41)) :args ((or _let_16 _let_36 _let_33 _let_32 _let_26 _let_162))) _let_44 _let_114 _let_49 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 4)) _let_43 :args ((not _let_32) true _let_37)) _let_158 :args (_let_162 true _let_16 false _let_30 false _let_29 true _let_32 false _let_21)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_65 (= C C)))) _let_155 :args (_let_22 false _let_65)) :args (_let_161 true _let_23 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_160 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1467 (tptp.the_carrier A)) false))))) :args (_let_159)))) _let_160 :args (_let_28 false _let_159)) _let_158 _let_58 _let_50 _let_44 :args (false true _let_24 false _let_28 false _let_21 false _let_20 false _let_19 true _let_16)) :args ((forall ((A $$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 $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and _let_1 (tptp.lattice A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_14 _let_13 _let_12 _let_11 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.apply_binary A B C) (tptp.apply A (tptp.ordered_pair B C)))))) _let_10 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.meet A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_meet A) B C))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_9 true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (tptp.element (tptp.apply_binary_as_element A B C D E F) C)))) _let_8 true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.meet_commut A B C) _let_1)))) true (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (tptp.element (tptp.bottom_of_semilattstr A) (tptp.the_carrier A)))) (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) _let_7 true true (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (tptp.meet_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) true (exists ((A $$unsorted)) (tptp.meet_semilatt_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)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_6 (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$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))))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$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) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F))))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.latt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.below_refl A B C) (tptp.below A B C))))) (forall ((A $$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)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) _let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.73/27.95  )
% 27.73/27.95  % SZS output end Proof for SEU352+1
% 27.73/27.95  % cvc5---1.0.5 exiting
% 27.73/27.95  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------