%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LAT385+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 0.78s 0.99s
% Output   : Proof 0.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LAT385+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n026.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   : Thu Aug 24 07:37:32 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.78/0.99  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.61xjZPlTDE/cvc5---1.0.5_3081.p...
% 0.78/0.99  ------- get file name : TPTP file name is LAT385+4
% 0.78/0.99  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3081.smt2...
% 0.78/0.99  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.78/0.99  % SZS status Theorem for LAT385+4
% 0.78/0.99  % SZS output start Proof for LAT385+4
% 0.78/0.99  (
% 0.78/0.99  (let ((_let_1 (not (exists ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 tptp.xU))) (or (and _let_1 (or (and _let_1 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xP) (tptp.sdtlseqdt0 W0 W1)))) (tptp.aLowerBoundOfIn0 W0 tptp.xP tptp.xU)) (forall ((W1 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.xU) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 tptp.xP) (tptp.sdtlseqdt0 W1 W2))) (tptp.aLowerBoundOfIn0 W1 tptp.xP tptp.xU)) (tptp.sdtlseqdt0 W1 W0)))) (tptp.aInfimumOfIn0 W0 tptp.xP tptp.xU))))))) (let ((_let_2 (tptp.aSet0 tptp.xP))) (let ((_let_3 (and _let_2 (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 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xT) (tptp.sdtlseqdt0 W1 W0))) _let_2)) _let_1))))))) (= tptp.xP (tptp.cS1241 tptp.xU tptp.xf tptp.xT))))) (let ((_let_4 (tptp.szRzazndt0 tptp.xf))) (let ((_let_5 (and (tptp.aSet0 tptp.xU) (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElementOf0 W4 W0) (tptp.sdtlseqdt0 W4 W3)))) (tptp.aUpperBoundOfIn0 W3 W0 tptp.xU)) (tptp.sdtlseqdt0 W2 W3))) (tptp.aSupremumOfIn0 W2 W0 tptp.xU))))))))) (tptp.aCompleteLattice0 tptp.xU) (tptp.aFunction0 tptp.xf) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 tptp.xf))) (=> (and (tptp.aElementOf0 W0 _let_1) (tptp.aElementOf0 W1 _let_1)) (=> (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf W0) (tptp.sdtlpdtrp0 tptp.xf W1)))))) (tptp.isMonotone0 tptp.xf) (= (tptp.szDzozmdt0 tptp.xf) _let_4) (= _let_4 tptp.xU) (tptp.isOn0 tptp.xf tptp.xU)))) (let ((_let_6 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.xP))) (let ((_let_7 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.xU))) (let ((_let_8 (and _let_7 (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (or (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xT)) (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.aUpperBoundOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.xT tptp.xU)))) (let ((_let_9 (not _let_6))) (let ((_let_10 (or _let_9 _let_8))) (let ((_let_11 (or _let_9 _let_7))) (let ((_let_12 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xP)) (tptp.aElementOf0 W1 tptp.xU))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (not _let_2))) (let ((_let_16 (or _let_15 _let_14))) (let ((_let_17 (and _let_16 (not (tptp.aSubsetOf0 tptp.xP tptp.xU))))) (let ((_let_18 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xU)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xP)) (tptp.sdtlseqdt0 W1 W2)))) (not (tptp.aLowerBoundOfIn0 W1 tptp.xP tptp.xU)) (not (forall ((W2 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W2 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 tptp.xP)) (tptp.sdtlseqdt0 W2 W3))))) (not (tptp.aLowerBoundOfIn0 W2 tptp.xP tptp.xU))) (tptp.sdtlseqdt0 W2 W1)))) (not (tptp.aInfimumOfIn0 W1 tptp.xP tptp.xU)))))) (let ((_let_19 (not _let_18))) (let ((_let_20 (and (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 tptp.xP)) (tptp.sdtlseqdt0 W3 W2)))) (not (tptp.aUpperBoundOfIn0 W2 tptp.xP tptp.xU)) (not (forall ((W3 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W3 tptp.xU)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xP)) (tptp.sdtlseqdt0 W4 W3))))) (not (tptp.aUpperBoundOfIn0 W3 tptp.xP tptp.xU))) (tptp.sdtlseqdt0 W2 W3)))) (not (tptp.aSupremumOfIn0 W2 tptp.xP tptp.xU))))) _let_19))) (let ((_let_21 (or _let_17 _let_20))) (let ((_let_22 (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 W3 W2)))) (not (tptp.aUpperBoundOfIn0 W2 W0 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W3 tptp.xU)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElementOf0 W4 W0)) (tptp.sdtlseqdt0 W4 W3))))) (not (tptp.aUpperBoundOfIn0 W3 W0 tptp.xU))) (tptp.sdtlseqdt0 W2 W3)))) (not (tptp.aSupremumOfIn0 W2 W0 tptp.xU))))) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xU)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 W0)) (tptp.sdtlseqdt0 W1 W2)))) (not (tptp.aLowerBoundOfIn0 W1 W0 tptp.xU)) (not (forall ((W2 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W2 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 W0)) (tptp.sdtlseqdt0 W2 W3))))) (not (tptp.aLowerBoundOfIn0 W2 W0 tptp.xU))) (tptp.sdtlseqdt0 W2 W1)))) (not (tptp.aInfimumOfIn0 W1 W0 tptp.xU)))))))))) (let ((_let_23 (1))) (let ((_let_24 (_let_22))) (let ((_let_25 (not _let_20))) (let ((_let_26 (tptp.aInfimumOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xP tptp.xU))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xU)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aElementOf0 W2 tptp.xP)) (tptp.sdtlseqdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 W2)))) (not (tptp.aLowerBoundOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xP tptp.xU)) (not (forall ((W2 $$unsorted)) (or (and (or (not (tptp.aElementOf0 W2 tptp.xU)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElementOf0 W3 tptp.xP)) (tptp.sdtlseqdt0 W2 W3))))) (not (tptp.aLowerBoundOfIn0 W2 tptp.xP tptp.xU))) (tptp.sdtlseqdt0 W2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) _let_27))) (let ((_let_29 (forall ((BOUND_VARIABLE_1907 $$unsorted)) (not (tptp.aInfimumOfIn0 BOUND_VARIABLE_1907 tptp.xP tptp.xU))))) (let ((_let_30 (_let_29))) (let ((_let_31 (or))) (let ((_let_32 (_let_19))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_14))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_12))) (REFL :args (_let_13)) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_14 (not _let_16)))) (AND_ELIM _let_33 :args (0)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 0)) :args ((or _let_16 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_17 _let_20 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_19 _let_25))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) (REFL :args ((not _let_28))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 4)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_31)) :args ((or _let_26 _let_28))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aInfimumOfIn0 BOUND_VARIABLE_1907 tptp.xP tptp.xU) false))))) :args _let_30)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args _let_23) :args (_let_27 false _let_29)) :args (_let_28 true _let_26)) :args (_let_18 false _let_28)) :args (_let_25 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (tptp.xP QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSet0 W0)))) :args _let_24)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args _let_23) :args (_let_21 false _let_22)) :args (_let_17 true _let_20 false _let_21)) :args (_let_16 false _let_17)) :args (_let_14 false _let_2 false _let_16)) :args (_let_13 true _let_12)))) (let ((_let_36 (not _let_8))) (let ((_let_37 (forall ((BOUND_VARIABLE_1803 $$unsorted) (BOUND_VARIABLE_1837 $$unsorted)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1803 tptp.xP)) (and (tptp.aElementOf0 BOUND_VARIABLE_1803 tptp.xU) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf BOUND_VARIABLE_1803) BOUND_VARIABLE_1803) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1837 tptp.xT)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1837 BOUND_VARIABLE_1803)) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1803 tptp.xT tptp.xU)))))) (let ((_let_38 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_8 (not _let_10)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sdtlseqdt0 BOUND_VARIABLE_1837 BOUND_VARIABLE_1803)))) :args _let_38)) (AND_ELIM _let_33 :args (2)) :args (_let_10 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_8 0)) :args ((or _let_7 _let_36))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 1)) _let_35 :args ((not _let_7) true _let_11)) :args (_let_36 true _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_6))) :args _let_31)) :args ((or _let_6 _let_11))) _let_35 :args (_let_6 true _let_11)) :args (false false _let_10 true _let_8 false _let_6)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (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 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (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)))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.szRzazndt0 W0)))))) (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 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 W2 _let_1)) (=> (tptp.sdtlseqdt0 W1 W2) (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlpdtrp0 W0 W2))))))))) _let_5 (and (tptp.aSet0 tptp.xS) (forall ((W0 $$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))))))) (= tptp.xS (tptp.cS1142 tptp.xf))) (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_3 _let_1 true)))))))))))))))))))))))))))))))))))))))))
% 0.78/1.00  )
% 0.78/1.00  % SZS output end Proof for LAT385+4
% 0.78/1.00  % cvc5---1.0.5 exiting
% 0.78/1.00  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------