%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 06:04:38 EDT 2023

% Result   : Theorem 11.14s 11.37s
% Output   : Proof 11.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LAT387+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n005.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Aug 24 06:27:38 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 11.14/11.37  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.fkk9texWmB/cvc5---1.0.5_11126.p...
% 11.14/11.37  ------- get file name : TPTP file name is LAT387+4
% 11.14/11.37  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11126.smt2...
% 11.14/11.37  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.14/11.37  --- Run --no-e-matching --full-saturate-quant at 5...
% 11.14/11.37  % SZS status Theorem for LAT387+4
% 11.14/11.37  % SZS output start Proof for LAT387+4
% 11.14/11.37  (
% 11.14/11.37  (let ((_let_1 (tptp.aSupremumOfIn0 tptp.xp tptp.xT tptp.xS))) (let ((_let_2 (tptp.aUpperBoundOfIn0 tptp.xp tptp.xT tptp.xS))) (let ((_let_3 (tptp.aFixedPointOf0 tptp.xp tptp.xf))) (let ((_let_4 (tptp.sdtlpdtrp0 tptp.xf tptp.xp))) (let ((_let_5 (tptp.szDzozmdt0 tptp.xf))) (let ((_let_6 (tptp.aElementOf0 tptp.xp _let_5))) (let ((_let_7 (not (and (or (and _let_6 (= _let_4 tptp.xp)) _let_3) (or (and (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xT) (tptp.sdtlseqdt0 W0 tptp.xp))) _let_2) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xS) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xT) (tptp.sdtlseqdt0 W1 W0))) (tptp.aUpperBoundOfIn0 W0 tptp.xT tptp.xS)) (tptp.sdtlseqdt0 tptp.xp W0)))) _let_1))))) (let ((_let_8 (tptp.aUpperBoundOfIn0 _let_4 tptp.xT tptp.xU))) (let ((_let_9 (tptp.aLowerBoundOfIn0 _let_4 tptp.xP tptp.xU))) (let ((_let_10 (and (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf tptp.xp) W0))) _let_9 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xT) (tptp.sdtlseqdt0 W0 (tptp.sdtlpdtrp0 tptp.xf tptp.xp)))) _let_8))) (let ((_let_11 (tptp.aInfimumOfIn0 tptp.xp tptp.xP tptp.xU))) (let ((_let_12 (tptp.aLowerBoundOfIn0 tptp.xp tptp.xP tptp.xU))) (let ((_let_13 (tptp.aElementOf0 tptp.xp tptp.xU))) (let ((_let_14 (and _let_13 _let_13 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xP) (tptp.sdtlseqdt0 tptp.xp W0))) _let_12 (forall ((W0 $$unsorted)) (=> (or (and (tptp.aElementOf0 W0 tptp.xU) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xP) (tptp.sdtlseqdt0 W0 W1)))) (tptp.aLowerBoundOfIn0 W0 tptp.xP tptp.xU)) (tptp.sdtlseqdt0 W0 tptp.xp))) _let_11))) (let ((_let_15 (= tptp.xP (tptp.cS1241 tptp.xU tptp.xf tptp.xT)))) (let ((_let_16 (tptp.aSet0 tptp.xP))) (let ((_let_17 (and _let_16 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xP))) (let ((_let_2 (tptp.aUpperBoundOfIn0 W0 tptp.xT tptp.xU))) (let ((_let_3 (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf W0) W0))) (let ((_let_4 (tptp.aElementOf0 W0 tptp.xU))) (and (=> _let_1 (and _let_4 _let_3 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xT) (tptp.sdtlseqdt0 W1 W0))) _let_2)) (=> (and _let_4 _let_3 (or (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xT) (tptp.sdtlseqdt0 W1 W0))) _let_2)) _let_1))))))) _let_15))) (let ((_let_18 (tptp.cS1142 tptp.xf))) (let ((_let_19 (= tptp.xS _let_18))) (let ((_let_20 (tptp.aSet0 tptp.xS))) (let ((_let_21 (and _let_20 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xS))) (let ((_let_2 (tptp.aFixedPointOf0 W0 tptp.xf))) (let ((_let_3 (= (tptp.sdtlpdtrp0 tptp.xf W0) W0))) (let ((_let_4 (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xf)))) (and (=> _let_1 (and _let_4 _let_3 _let_2)) (=> (or (and _let_4 _let_3) _let_2) _let_1))))))) _let_19))) (let ((_let_22 (tptp.isOn0 tptp.xf tptp.xU))) (let ((_let_23 (tptp.szRzazndt0 tptp.xf))) (let ((_let_24 (tptp.isMonotone0 tptp.xf))) (let ((_let_25 (tptp.aFunction0 tptp.xf))) (let ((_let_26 (tptp.aCompleteLattice0 tptp.xU))) (let ((_let_27 (tptp.aSet0 tptp.xU))) (let ((_let_28 (and _let_27 (forall ((W0 $$unsorted)) (=> (or (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xU)))) (tptp.aSubsetOf0 W0 tptp.xU)) (exists ((W1 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W1 tptp.xU))) (and _let_1 _let_1 (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2))) (tptp.aLowerBoundOfIn0 W1 W0 tptp.xU) (forall ((W2 $$unsorted)) (=> (or (and (tptp.aElementOf0 W2 tptp.xU) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W0) (tptp.sdtlseqdt0 W2 W3)))) (tptp.aLowerBoundOfIn0 W2 W0 tptp.xU)) (tptp.sdtlseqdt0 W2 W1))) (tptp.aInfimumOfIn0 W1 W0 tptp.xU) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W2 tptp.xU))) (and _let_1 _let_1 (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W0) (tptp.sdtlseqdt0 W3 W2))) (tptp.aUpperBoundOfIn0 W2 W0 tptp.xU) (forall ((W3 $$unsorted)) (=> (or (and (tptp.aElementOf0 W3 tptp.xU) (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W0) (tptp.sdtlseqdt0 W4 W3)))) (tptp.aUpperBoundOfIn0 W3 W0 tptp.xU)) (tptp.sdtlseqdt0 W2 W3))) (tptp.aSupremumOfIn0 W2 W0 tptp.xU))))))))) _let_26 _let_25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 tptp.xf))) (=> (and (tptp.aElementOf0 W0 _let_1) (tptp.aElementOf0 W1 _let_1)) (=> (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf W0) (tptp.sdtlpdtrp0 tptp.xf W1)))))) _let_24 (= _let_5 _let_23) (= _let_23 tptp.xU) _let_22))) (let ((_let_29 (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.szRzazndt0 W0)))))))) (let ((_let_30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_31 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_32 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_33 (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))) (let ((_let_34 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (tptp.sdtlpdtrp0 tptp.xf SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))) (let ((_let_38 (tptp.sdtlseqdt0 _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 _let_37))) (let ((_let_40 (not _let_33))) (let ((_let_41 (tptp.cS1241 _let_23 tptp.xf tptp.xT))) (let ((_let_42 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 _let_41))) (let ((_let_43 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (and _let_44 (not (tptp.aUpperBoundOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 tptp.xT _let_23))))) (let ((_let_46 (not _let_38))) (let ((_let_47 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 _let_23))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46 _let_45 _let_42))) (let ((_let_50 (forall ((BOUND_VARIABLE_1861 $$unsorted)) (let ((_let_1 (tptp.szRzazndt0 tptp.xf))) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1861 _let_1)) (not (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf BOUND_VARIABLE_1861) BOUND_VARIABLE_1861)) (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 BOUND_VARIABLE_1861)))) (not (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1861 tptp.xT _let_1))) (tptp.aElementOf0 BOUND_VARIABLE_1861 (tptp.cS1241 _let_1 tptp.xf tptp.xT))))))) (let ((_let_51 (2))) (let ((_let_52 (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_53 (ASSUME :args (_let_28)))) (let ((_let_54 (AND_ELIM (EQ_RESOLVE _let_53 _let_52) :args (7)))) (let ((_let_55 (1))) (let ((_let_56 (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_57 (ASSUME :args (_let_21)))) (let ((_let_58 (AND_ELIM (EQ_RESOLVE _let_57 _let_56) :args _let_55))) (let ((_let_59 (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_60 (ASSUME :args (_let_17)))) (let ((_let_61 (AND_INTRO (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE _let_60 _let_59) :args _let_55) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_54) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) _let_58 _let_54))) (let ((_let_62 (EQ_RESOLVE _let_60 (TRANS _let_59 (MACRO_SR_EQ_INTRO _let_61 :args ((and _let_16 _let_15 (forall ((BOUND_VARIABLE_1846 $$unsorted) (BOUND_VARIABLE_1880 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1846 tptp.xP)) (and (tptp.aElementOf0 BOUND_VARIABLE_1846 tptp.xU) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf BOUND_VARIABLE_1846) BOUND_VARIABLE_1846) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1880 tptp.xT)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1880 BOUND_VARIABLE_1846)) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1846 tptp.xT tptp.xU)))) (forall ((BOUND_VARIABLE_1861 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1861 tptp.xU)) (not (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf BOUND_VARIABLE_1861) BOUND_VARIABLE_1861)) (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 BOUND_VARIABLE_1861)))) (not (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1861 tptp.xT tptp.xU))) (tptp.aElementOf0 BOUND_VARIABLE_1861 tptp.xP)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_63 (AND_ELIM _let_62 :args _let_51))) (let ((_let_64 (_let_50))) (let ((_let_65 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 QUANTIFIERS_INST_ENUM))) (let ((_let_66 (ASSUME :args _let_64))) (let ((_let_67 (tptp.sdtlseqdt0 tptp.xp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))) (let ((_let_68 (not _let_42))) (let ((_let_69 (or _let_68 _let_67))) (let ((_let_70 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.cS1241 (tptp.szRzazndt0 tptp.xf) tptp.xf tptp.xT))) (tptp.sdtlseqdt0 tptp.xp W0))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((and _let_13 _let_13 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xP)) (tptp.sdtlseqdt0 tptp.xp W0))) _let_12 (forall ((W0 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W0 tptp.xU)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xP)) (tptp.sdtlseqdt0 W0 W1))))) (not (tptp.aLowerBoundOfIn0 W0 tptp.xP tptp.xU))) (tptp.sdtlseqdt0 W0 tptp.xp))) _let_11) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_72 (AND_ELIM _let_71 :args _let_51))) (let ((_let_73 (_let_70))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54))))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 _let_18))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_78 _let_76 (not (tptp.aUpperBoundOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 tptp.xT _let_18)) _let_67))) (let ((_let_80 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.cS1142 tptp.xf))) (or (not (tptp.aElementOf0 W0 _let_1)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 W0)))) (not (tptp.aUpperBoundOfIn0 W0 tptp.xT _let_1)) (tptp.sdtlseqdt0 tptp.xp W0)))))) (let ((_let_81 (not _let_79))) (let ((_let_82 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xT)) (tptp.sdtlseqdt0 W0 tptp.xp))))) (let ((_let_83 (or _let_82 (tptp.aUpperBoundOfIn0 tptp.xp tptp.xT _let_18)))) (let ((_let_84 (and _let_83 _let_80))) (let ((_let_85 (not _let_80))) (let ((_let_86 (or (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 tptp.xT)) (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 tptp.xp)))) (let ((_let_87 (tptp.sdtlseqdt0 _let_4 tptp.xp))) (let ((_let_88 (tptp.aElementOf0 tptp.xp _let_23))) (let ((_let_89 (and _let_88 _let_87 _let_86 (tptp.aUpperBoundOfIn0 tptp.xp tptp.xT _let_23)))) (let ((_let_90 (tptp.aElementOf0 tptp.xp _let_41))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_89))) (let ((_let_93 (forall ((BOUND_VARIABLE_1846 $$unsorted) (BOUND_VARIABLE_1880 $$unsorted)) (let ((_let_1 (tptp.szRzazndt0 tptp.xf))) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1846 (tptp.cS1241 _let_1 tptp.xf tptp.xT))) (and (tptp.aElementOf0 BOUND_VARIABLE_1846 _let_1) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf BOUND_VARIABLE_1846) BOUND_VARIABLE_1846) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1880 tptp.xT)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1880 BOUND_VARIABLE_1846)) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1846 tptp.xT _let_1))))))) (let ((_let_94 (_let_93))) (let ((_let_95 (tptp.aElementOf0 _let_4 _let_41))) (let ((_let_96 (= tptp.xp _let_4))) (let ((_let_97 (tptp.aUpperBoundOfIn0 _let_4 tptp.xT _let_23))) (let ((_let_98 (not _let_97))) (let ((_let_99 (and (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xT)) (tptp.sdtlseqdt0 W1 (tptp.sdtlpdtrp0 tptp.xf tptp.xp))))) _let_98))) (let ((_let_100 (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf _let_4) _let_4))) (let ((_let_101 (not _let_100))) (let ((_let_102 (tptp.aElementOf0 _let_4 _let_23))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101 _let_99 _let_95))) (let ((_let_105 (_let_4 QUANTIFIERS_INST_ENUM))) (let ((_let_106 (not _let_99))) (let ((_let_107 (3))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_61 :args ((and (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xP)) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf tptp.xp) W0))) _let_9 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xT)) (tptp.sdtlseqdt0 W0 (tptp.sdtlpdtrp0 tptp.xf tptp.xp)))) _let_8) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_109 (not _let_87))) (let ((_let_110 (not _let_6))) (let ((_let_111 (tptp.aElementOf0 _let_4 _let_5))) (let ((_let_112 (not _let_111))) (let ((_let_113 (or _let_112 _let_110 _let_109 _let_100))) (let ((_let_114 (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 tptp.xf))) (or (not (tptp.aElementOf0 W0 _let_1)) (not (tptp.aElementOf0 W1 _let_1)) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf W0) (tptp.sdtlpdtrp0 tptp.xf W1))))))) (let ((_let_115 (4))) (let ((_let_116 (= _let_23 _let_5))) (let ((_let_117 (EQ_RESOLVE _let_53 (TRANS _let_52 (MACRO_SR_EQ_INTRO _let_61 :args ((and _let_27 (forall ((W0 $$unsorted)) (or (and (or (not (tptp.aSet0 W0)) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElementOf0 W1 tptp.xU))))) (not (tptp.aSubsetOf0 W0 tptp.xU))) (and (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W0)) (tptp.sdtlseqdt0 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:args (_let_180 false _let_181)) :args (_let_47 false _let_116 false _let_180)))) (let ((_let_191 (and _let_39 _let_46))) (let ((_let_192 (ASSUME :args (_let_46)))) (let ((_let_193 (ASSUME :args (_let_39)))) (let ((_let_194 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.sdtlseqdt0 W0 W0))))) (let ((_let_195 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_196 (or _let_159 _let_48 _let_34))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_33 _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_196)) :args ((or _let_159 _let_48 _let_34 (not _let_196)))) _let_164 _let_190 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_162 :args (_let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 QUANTIFIERS_INST_ENUM)) :args _let_163)) _let_162 :args (_let_196 false _let_161)) :args (_let_34 false _let_158 false _let_47 false _let_196)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_195 :args _let_65) :args (_let_194))) _let_195 :args (_let_36 false _let_194)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_191)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_192 _let_193) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_193)) _let_189 :args (APPLY_UF tptp.sdtlseqdt0)) (FALSE_INTRO _let_192))) :args (_let_46 _let_39))) :args (_let_39 _let_46))) :args (true _let_191)) (CONG (REFL :args ((not _let_39))) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_38))) (REFL :args (_let_40)) :args _let_170)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_181 1)) :args ((or _let_39 _let_186))) _let_185 :args (_let_39 false _let_181)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_46 _let_45 _let_42 (not _let_49)))) _let_190 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_44 _let_178))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_75 (= W1 W1)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_79 1)) (CONG _let_179 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_170)) :args ((or _let_75 _let_79))) _let_177 :args (_let_75 true _let_79)) :args (_let_43 false _let_75)) :args (_let_178 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_67 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_79 3)) _let_177 :args ((not _let_67) true _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args _let_65) :args _let_73)) _let_72 :args (_let_69 false _let_70)) :args (_let_68 true _let_67 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args _let_65) :args _let_64)) _let_63 :args (_let_49 false _let_50)) :args (_let_46 false _let_47 true _let_45 true _let_42 false _let_49)) :args (_let_40 false _let_39 true _let_38)) :args (false false _let_34 false _let_36 true _let_33)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_32 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.isEmpty0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))) _let_31 _let_30 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aLowerBoundOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (tptp.sdtlseqdt0 W2 W3)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aUpperBoundOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (tptp.sdtlseqdt0 W3 W2)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aInfimumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aLowerBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aLowerBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W3 W2)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aSupremumOfIn0 W2 W1 W0) (tptp.aSupremumOfIn0 W3 W1 W0)) (= W2 W3))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aInfimumOfIn0 W2 W1 W0) (tptp.aInfimumOfIn0 W3 W1 W0)) (= W2 W3))))))) (forall ((W0 $$unsorted)) (= (tptp.aCompleteLattice0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (exists ((W2 $$unsorted)) (and (tptp.aInfimumOfIn0 W2 W1 W0) (exists ((W3 $$unsorted)) (tptp.aSupremumOfIn0 W3 W1 W0))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szRzazndt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szRzazndt0 W0))) (=> (and (tptp.aFunction0 W0) (tptp.aSet0 W1)) (= (tptp.isOn0 W0 W1) (and (= (tptp.szDzozmdt0 W0) _let_1) (= _let_1 W1)))))) _let_29 (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (= (tptp.aFixedPointOf0 W1 W0) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (= (tptp.sdtlpdtrp0 W0 W1) W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (= (tptp.isMonotone0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 W2 _let_1)) (=> (tptp.sdtlseqdt0 W1 W2) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlpdtrp0 W0 W2))))))))) _let_28 _let_21 (and (tptp.aSet0 tptp.xT) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xT) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xT tptp.xS)) _let_17 _let_14 _let_10 _let_7 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.14/11.38  )
% 11.14/11.38  % SZS output end Proof for LAT387+4
% 11.14/11.38  % cvc5---1.0.5 exiting
% 11.14/11.38  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------