TSTP Solution File: NUM568+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM568+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 10:45:11 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM568+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n019.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 : Fri Aug 25 15:27:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UUjQGWWoLA/cvc5---1.0.5_2516.p...
% 0.20/0.62 ------- get file name : TPTP file name is NUM568+3
% 0.20/0.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2516.smt2...
% 0.20/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.62 % SZS status Theorem for NUM568+3
% 0.20/0.62 % SZS output start Proof for NUM568+3
% 0.20/0.62 (
% 0.20/0.62 (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.szszuzczcdt0 W0) tptp.xK)))))) (let ((_let_2 (not (= tptp.xK tptp.sz00)))) (let ((_let_3 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_4 (tptp.sdtlcdtrc0 tptp.xc _let_3))) (let ((_let_5 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0))) (let ((_let_6 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))))) (let ((_let_7 (= tptp.sz00 tptp.xK))) (let ((_let_8 (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= (tptp.szszuzczcdt0 W1) tptp.xK)))))) (let ((_let_9 (not _let_8))) (let ((_let_10 (not _let_5))) (let ((_let_11 (or _let_10 _let_7 _let_9))) (let ((_let_12 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (= tptp.xK (tptp.szszuzczcdt0 W0))))))) (let ((_let_13 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= tptp.sz00 W0) (not (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= W0 (tptp.szszuzczcdt0 W1)))))))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_7 _let_10 _let_9 (not _let_11)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_14 :args (tptp.xK QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.aElementOf0 W0 tptp.szNzAzT0) false))))) :args (_let_13)))) _let_14 :args (_let_11 false _let_13)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_12 (= W0 W1))) (MACRO_SR_PRED_INTRO :args ((= (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (= tptp.xK (tptp.szszuzczcdt0 W1))))) _let_8) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_8 false _let_12)) (SYMM (ASSUME :args (_let_2))) (ASSUME :args (_let_5)) :args (false false _let_11 false _let_8 true _let_7 false _let_5)) :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 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$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)))) _let_6 (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 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (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)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 W1) (tptp.aSet0 W2) (not (= W0 tptp.sz00))) (=> (and (tptp.aSubsetOf0 _let_1 (tptp.slbdtsldtrb0 W2 W0)) (not (= _let_1 tptp.slcrc0))) (tptp.aSubsetOf0 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (forall ((W2 $$unsorted)) (=> (and (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W0 W1)) (tptp.isFinite0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aSubsetOf0 W3 W0) (tptp.isFinite0 W3) (tptp.aSubsetOf0 W2 (tptp.slbdtsldtrb0 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (tptp.aSet0 (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.aElement0 (tptp.sdtlpdtrp0 W0 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlbdtrb0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W0)) (= (tptp.sdtlpdtrp0 W0 W3) W1))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aFunction0 W0) (tptp.aElement0 W1)) (tptp.aSubsetOf0 (tptp.sdtlbdtrb0 W0 W1) (tptp.szDzozmdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtlcdtrc0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 W1) (= (tptp.sdtlpdtrp0 W0 W4) W3)))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtlpdtrp0 W0 W1) (tptp.sdtlcdtrc0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtexdt0 W0 W1)) (and (tptp.aFunction0 W2) (= (tptp.szDzozmdt0 W2) W1) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (= (tptp.sdtlpdtrp0 W2 W3) (tptp.sdtlpdtrp0 W0 W3))))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aFunction0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 (tptp.szDzozmdt0 W0)) (tptp.isCountable0 W1)) (=> (forall ((W2 $$unsorted) (W3 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W0))) (=> (and (tptp.aElementOf0 W2 _let_1) (tptp.aElementOf0 W3 _let_1) (not (= W2 W3))) (not (= (tptp.sdtlpdtrp0 W0 W2) (tptp.sdtlpdtrp0 W0 W3)))))) (tptp.isCountable0 (tptp.sdtlcdtrc0 W0 W1))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) _let_5 (and (tptp.aSet0 tptp.xS) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xS) (tptp.aElementOf0 W0 tptp.szNzAzT0))) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xc)))) (let ((_let_2 (= (tptp.sbrdtbr0 W0) tptp.xK))) (let ((_let_3 (tptp.aSubsetOf0 W0 tptp.xS))) (let ((_let_4 (tptp.aSet0 W0))) (and (=> _let_1 (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS))) _let_3 _let_2)) (=> (and (or (and _let_4 (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElementOf0 W1 tptp.xS)))) _let_3) _let_2) _let_1))))))) (= _let_3 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 _let_4) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xc)) (= (tptp.sdtlpdtrp0 tptp.xc W1) W0))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtlcdtrc0 tptp.xc (tptp.szDzozmdt0 tptp.xc))) (tptp.aElementOf0 W0 tptp.xT))) (tptp.aSubsetOf0 _let_4 tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (or (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 tptp.szNzAzT0)))) (tptp.aSubsetOf0 W1 tptp.szNzAzT0)) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (let ((_let_2 (tptp.sdtlcdtrc0 W2 _let_1))) (=> (and (tptp.aFunction0 W2) (or (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.aElementOf0 W3 (tptp.szDzozmdt0 W2)))) (let ((_let_2 (= (tptp.sbrdtbr0 W3) W0))) (let ((_let_3 (tptp.aSubsetOf0 W3 W1))) (let ((_let_4 (tptp.aSet0 W3))) (and (=> _let_1 (and (or (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1)))) _let_3) _let_2)) (=> (and _let_4 (forall ((W4 $$unsorted)) (=> (tptp.aElementOf0 W4 W3) (tptp.aElementOf0 W4 W1))) _let_3 _let_2) _let_1))))))) (= _let_1 (tptp.slbdtsldtrb0 W1 W0))) (=> (and (tptp.aSet0 _let_2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (exists ((W4 $$unsorted)) (and (tptp.aElementOf0 W4 (tptp.szDzozmdt0 W2)) (= (tptp.sdtlpdtrp0 W2 W4) W3)))))) (or (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 (tptp.sdtlcdtrc0 W2 (tptp.szDzozmdt0 W2))) (tptp.aElementOf0 W3 tptp.xT))) (tptp.aSubsetOf0 _let_2 tptp.xT)))) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSet0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 W4) (tptp.aElementOf0 W5 W1))) (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (or (and (or (and (tptp.aSet0 W5) (forall ((W6 $$unsorted)) (=> (tptp.aElementOf0 W6 W5) (tptp.aElementOf0 W6 W4)))) (tptp.aSubsetOf0 W5 W4)) (= (tptp.sbrdtbr0 W5) W0)) (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0))) (= (tptp.sdtlpdtrp0 W2 W5) W3)))))))))))))))) _let_2 _let_2 _let_1 true)))))))))))))))))
% 0.20/0.63 )
% 0.20/0.63 % SZS output end Proof for NUM568+3
% 0.20/0.63 % cvc5---1.0.5 exiting
% 0.20/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------