%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM549+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 10:44:58 EDT 2023

% Result   : Theorem 0.21s 0.75s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM549+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n002.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   : Fri Aug 25 11:05:17 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.75  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.hOfKfonL7z/cvc5---1.0.5_16255.p...
% 0.21/0.75  ------- get file name : TPTP file name is NUM549+3
% 0.21/0.75  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16255.smt2...
% 0.21/0.75  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.75  % SZS status Theorem for NUM549+3
% 0.21/0.75  % SZS output start Proof for NUM549+3
% 0.21/0.75  (
% 0.21/0.75  (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aElementOf0 W0 tptp.xQ)))))) (let ((_let_2 (tptp.sbrdtbr0 tptp.xQ))) (let ((_let_3 (= _let_2 tptp.xk))) (let ((_let_4 (tptp.aSet0 tptp.xQ))) (let ((_let_5 (tptp.slbdtsldtrb0 tptp.xS tptp.xk))) (let ((_let_6 (and _let_4 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xQ) (tptp.aElementOf0 W0 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) _let_3 (tptp.aElementOf0 tptp.xQ _let_5)))) (let ((_let_7 (tptp.slbdtsldtrb0 tptp.xT tptp.xk))) (let ((_let_8 (and (tptp.aSet0 tptp.xS) (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00))))) (let ((_let_9 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))))) (let ((_let_10 (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))) (let ((_let_11 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))) (let ((_let_12 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.xQ))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13))) (let ((_let_17 (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 tptp.xQ))))) (let ((_let_18 (and _let_4 _let_17))) (let ((_let_19 (not _let_17))) (let ((_let_20 (= tptp.slcrc0 tptp.xQ))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (not _let_18))) (let ((_let_23 (forall ((W0 $$unsorted)) (= (= tptp.slcrc0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (not (tptp.aElementOf0 W1 W0)))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (= tptp.sz00 _let_2))) (let ((_let_26 (= _let_20 _let_25))) (let ((_let_27 (not _let_20))) (let ((_let_28 (not _let_4))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (= (= tptp.sz00 (tptp.sbrdtbr0 W0)) (= tptp.slcrc0 W0)))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (AND_ELIM _let_32 :args (0)))) (let ((_let_34 (= tptp.xk _let_2))) (let ((_let_35 (= tptp.sz00 tptp.xk))) (let ((_let_36 (not _let_25))) (let ((_let_37 (or))) (let ((_let_38 (not _let_35))) (let ((_let_39 (and _let_38 _let_34))) (let ((_let_40 (_let_38 _let_34))) (let ((_let_41 (ASSUME :args (_let_38)))) (let ((_let_42 (ASSUME :args (_let_34)))) (let ((_let_43 (_let_19))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_43)) :args _let_43) (REWRITE :args ((=> _let_19 (not _let_13)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_17))) (REFL :args (_let_12)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_18)) :args ((or _let_28 _let_18 _let_19))) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_21)) :args ((or _let_20 _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_25 _let_27 (not _let_26)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_39)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_41 _let_42) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.sz00)) (SYMM _let_42) :args (=)) (FALSE_INTRO _let_41))) :args _let_40)) :args _let_40)) :args (true _let_39)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_35))) (REFL :args ((not _let_34))) (REFL :args (_let_36)) :args _let_37)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args (2)) (AND_ELIM _let_32 :args (3)) :args (_let_36 true _let_35 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_26 (not _let_29)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aSet0 W0) false))))) :args (_let_30)))) _let_31 :args (_let_29 false _let_30)) :args (_let_26 false _let_4 false _let_29)) :args (_let_27 true _let_25 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.xQ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aSet0 W0)))) :args (_let_23))) _let_24 :args (_let_21 false _let_23)) :args (_let_22 true _let_20 false _let_21)) :args (_let_19 false _let_4 true _let_18)) :args (_let_12 true _let_17)))) (let ((_let_45 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElementOf0 W0 tptp.xQ)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (or _let_28 _let_13 _let_14))) (let ((_let_48 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1480 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1480 W0)) (tptp.aElement0 BOUND_VARIABLE_1480))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_13 _let_15 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_28 _let_13 _let_14 (not _let_47)))) _let_33 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.xQ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 BOUND_VARIABLE_1480 W0) false))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_14 false _let_4 false _let_12 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.xQ) false))))) :args (_let_45))) _let_46 :args (_let_16 false _let_45)) _let_44 :args (false false _let_14 false _let_16 false _let_12)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_11 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) _let_10 (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) (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)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (= (tptp.sdtpldt0 (tptp.sdtmndt0 W0 W1) W1) W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aSet0 W1)) (=> (not (tptp.aElementOf0 W0 W1)) (= (tptp.sdtmndt0 (tptp.sdtpldt0 W1 W0) W0) W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtmndt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) _let_9 (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aSubsetOf0 W1 W0)) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.isFinite0 W0) (tptp.sdtlseqdt0 W1 (tptp.sbrdtbr0 W0))) (exists ((W2 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzizndt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzazxdt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 W1))) (or (tptp.aElementOf0 W0 (tptp.slbdtrb0 W1)) (= W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.aSubsetOf0 (tptp.slbdtrb0 W0) (tptp.slbdtrb0 W1))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0)) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aSubsetOf0 W0 (tptp.slbdtrb0 W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.slbdtsldtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtsldtrb0 W0 W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (not (tptp.isFinite0 W0))) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= (tptp.slbdtsldtrb0 W0 W1) tptp.slcrc0)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (forall ((W1 $$unsorted)) (=> (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W1 tptp.sz00))) (tptp.isCountable0 (tptp.slbdtsldtrb0 W0 W1)))))) (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) _let_8 (and (tptp.aSet0 _let_5) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (tptp.aSet0 _let_7) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xT))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xT)))) _let_3) _let_2) _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)))) (tptp.aSubsetOf0 _let_5 _let_7) (not (=> (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xk))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (or (not (exists ((W0 $$unsorted)) (tptp.aElementOf0 W0 (tptp.slbdtsldtrb0 tptp.xS tptp.xk)))) (= _let_5 tptp.slcrc0))))) (tptp.aElementOf0 tptp.xx tptp.xS) _let_6 (and _let_4 (tptp.isFinite0 tptp.xQ) _let_3) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.75  )
% 0.21/0.75  % SZS output end Proof for NUM549+3
% 0.21/0.75  % cvc5---1.0.5 exiting
% 0.21/0.76  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------