TSTP Solution File: NUM605+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 10:45:33 EDT 2023
% Result : Theorem 11.62s 11.78s
% Output : Proof 11.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri Aug 25 08:52:13 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 11.62/11.78 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MLWx7T42BK/cvc5---1.0.5_2385.p...
% 11.62/11.78 ------- get file name : TPTP file name is NUM605+1
% 11.62/11.78 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2385.smt2...
% 11.62/11.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.62/11.78 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.62/11.78 % SZS status Theorem for NUM605+1
% 11.62/11.78 % SZS output start Proof for NUM605+1
% 11.62/11.78 (
% 11.62/11.78 (let ((_let_1 (not (not (= tptp.xQ tptp.slcrc0))))) (let ((_let_2 (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK)))) (let ((_let_3 (tptp.aSet0 tptp.xO))) (let ((_let_4 (and _let_3 (tptp.isCountable0 tptp.xO)))) (let ((_let_5 (tptp.szDzizrdt0 tptp.xd))) (let ((_let_6 (tptp.sdtlbdtrb0 tptp.xd _let_5))) (let ((_let_7 (tptp.sdtlcdtrc0 tptp.xe _let_6))) (let ((_let_8 (and _let_3 (= tptp.xO _let_7)))) (let ((_let_9 (tptp.szDzozmdt0 tptp.xd))) (let ((_let_10 (tptp.szDzozmdt0 tptp.xN))) (let ((_let_11 (and (tptp.aFunction0 tptp.xN) (= _let_10 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (=> (and (tptp.aSubsetOf0 _let_2 tptp.szNzAzT0) (tptp.isCountable0 _let_2)) (and (tptp.aSubsetOf0 _let_1 (tptp.sdtmndt0 _let_2 (tptp.szmzizndt0 _let_2))) (tptp.isCountable0 _let_1)))))))))) (let ((_let_12 (tptp.szszuzczcdt0 tptp.xk))) (let ((_let_13 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= _let_12 tptp.xK)))) (let ((_let_14 (not (= tptp.xK tptp.sz00)))) (let ((_let_15 (tptp.szDzozmdt0 tptp.xc))) (let ((_let_16 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0))) (let ((_let_17 (forall ((W0 $$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 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aSubsetOf0 W3 W0) (= (tptp.sbrdtbr0 W3) W1))))))))))) (let ((_let_18 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sbrdtbr0 (tptp.slbdtrb0 W0)) W0))))) (let ((_let_19 (tptp.slbdtrb0 tptp.sz00))) (let ((_let_20 (= _let_19 tptp.slcrc0))) (let ((_let_21 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0))) (let ((_let_22 (= tptp.sz00 _let_12))) (let ((_let_23 (tptp.sbrdtbr0 _let_19))) (let ((_let_24 (= tptp.sz00 _let_23))) (let ((_let_25 (= _let_12 _let_23))) (let ((_let_26 (SYMM (ASSUME :args (_let_20))))) (let ((_let_27 (1))) (let ((_let_28 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) :args _let_27))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (AND_ELIM _let_29 :args _let_27))) (let ((_let_31 (AND_ELIM _let_29 :args (2)))) (let ((_let_32 (AND_ELIM (ASSUME :args (_let_8)) :args _let_27))) (let ((_let_33 (AND_INTRO (SYMM (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_32 _let_31 _let_30 _let_28 _let_26) :args ((= tptp.slcrc0 tptp.xQ) SB_DEFAULT SBA_FIXPOINT)))) _let_32 _let_31 _let_30 _let_28 _let_26))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_33 :args ((not (= tptp.sz00 tptp.xK)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_35 (tptp.aElementOf0 tptp.sz00 _let_10))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_24))) (let ((_let_38 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.szDzozmdt0 tptp.xN))) (= W0 (tptp.sbrdtbr0 (tptp.slbdtrb0 W0))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_33 :args ((forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= W0 (tptp.sbrdtbr0 (tptp.slbdtrb0 W0))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_40 (and (tptp.aSubsetOf0 _let_19 _let_7) _let_25))) (let ((_let_41 (tptp.slbdtsldtrb0 _let_7 _let_12))) (let ((_let_42 (tptp.aElementOf0 _let_19 _let_41))) (let ((_let_43 (= _let_42 _let_40))) (let ((_let_44 (forall ((W3 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 tptp.xk))) (let ((_let_2 (tptp.sdtlcdtrc0 tptp.xe (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))))) (= (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 _let_2 _let_1)) (and (tptp.aSubsetOf0 W3 _let_2) (= (tptp.sbrdtbr0 W3) _let_1)))))))) (let ((_let_45 (and (tptp.aSet0 _let_41) _let_44))) (let ((_let_46 (tptp.aElementOf0 _let_12 _let_10))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.aSet0 _let_7))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_45))) (let ((_let_51 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2668 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 W1 (tptp.szDzozmdt0 tptp.xN))) (= (= (tptp.slbdtsldtrb0 W0 W1) BOUND_VARIABLE_2668) (and (tptp.aSet0 BOUND_VARIABLE_2668) (forall ((W3 $$unsorted)) (= (and (tptp.aSubsetOf0 W3 W0) (= W1 (tptp.sbrdtbr0 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2668))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_33 :args ((forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_2668 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (= (tptp.slbdtsldtrb0 W0 W1) BOUND_VARIABLE_2668) (and (tptp.aSet0 BOUND_VARIABLE_2668) (forall ((W3 $$unsorted)) (= (and (tptp.aSubsetOf0 W3 W0) (= W1 (tptp.sbrdtbr0 W3))) (tptp.aElementOf0 W3 BOUND_VARIABLE_2668))))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_53 (_let_44))) (let ((_let_54 (not _let_22))) (let ((_let_55 (ASSUME :args (_let_25)))) (let ((_let_56 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_56 _let_55 _let_34) :args (_let_54 _let_24 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_34)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_56)) (SYMM _let_55))))) :args (_let_24 _let_25 _let_54)) :args ((not (and _let_54 _let_24 _let_25)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_22))) (REFL :args ((not _let_24))) (REFL :args ((not _let_25))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 1)) :args ((or _let_25 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or (not _let_42) _let_40 (not _let_43)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_33 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (_let_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_47 _let_49 _let_45 (not _let_50)))) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO _let_33 :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO _let_33 :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (_let_7 _let_12 _let_41 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_51)))) _let_52 :args (_let_50 false _let_51)) :args (_let_45 false _let_46 false _let_48 false _let_50)) :args (_let_44 false _let_45)) :args (_let_43 false _let_44)) :args (_let_40 false _let_42 false _let_43)) :args (_let_25 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_24 (not _let_37)))) (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO _let_33 :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.sz00 QUANTIFIERS_INST_ENUM)) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_24 false _let_35 false _let_37)) _let_34 :args (false false _let_25 false _let_24 true _let_22)) :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)) _let_21 (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)))) (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)))) _let_20 (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)))))) _let_18 _let_17 (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 $$unsorted)) (let ((_let_1 (tptp.szDzizrdt0 W0))) (let ((_let_2 (tptp.szDzozmdt0 W0))) (=> (tptp.aFunction0 W0) (=> (and (tptp.isCountable0 _let_2) (tptp.isFinite0 (tptp.sdtlcdtrc0 W0 _let_2))) (and (tptp.aElement0 _let_1) (tptp.isCountable0 (tptp.sdtlbdtrb0 W0 _let_1)))))))) (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT)) _let_16 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS)) (and (tptp.aFunction0 tptp.xc) (= _let_15 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc _let_15) tptp.xT)) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.szDzozmdt0 W2))) (=> (and (tptp.aFunction0 W2) (= _let_1 (tptp.slbdtsldtrb0 W1 W0)) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 W2 _let_1) tptp.xT)) (=> (tptp.iLess0 W0 tptp.xK) (exists ((W3 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xT) (exists ((W4 $$unsorted)) (and (tptp.aSubsetOf0 W4 W1) (tptp.isCountable0 W4) (forall ((W5 $$unsorted)) (=> (tptp.aElementOf0 W5 (tptp.slbdtsldtrb0 W4 W0)) (= (tptp.sdtlpdtrp0 W2 W5) W3))))))))))))))) _let_14 _let_14 _let_13 _let_11 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aSubsetOf0 _let_1 tptp.szNzAzT0) (tptp.isCountable0 _let_1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W1 W0) (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN W0) (tptp.sdtlpdtrp0 tptp.xN W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (not (= W0 W1))) (not (= (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (tptp.aElementOf0 (tptp.sdtpldt0 W1 _let_2) (tptp.slbdtsldtrb0 tptp.xS tptp.xK)))))))) (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aFunction0 _let_2) (= (tptp.szDzozmdt0 _let_2) (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (let ((_let_2 (tptp.szmzizndt0 _let_1))) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 _let_2) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 W1 _let_2))))))))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xC W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 _let_1 (tptp.szDzozmdt0 _let_1)) tptp.xT)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSubsetOf0 W1 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W1)) (forall ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 W1 tptp.xk))) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1)) tptp.xk)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (exists ((W2 $$unsorted)) (let ((_let_1 (tptp.sdtlpdtrp0 tptp.xN W0))) (and (tptp.aSubsetOf0 W2 (tptp.sdtmndt0 _let_1 (tptp.szmzizndt0 _let_1))) (tptp.isCountable0 W2) (forall ((W3 $$unsorted)) (=> (and (tptp.aSet0 W3) (tptp.aElementOf0 W3 (tptp.slbdtsldtrb0 W2 tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W3) W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xT) (forall ((W2 $$unsorted)) (=> (and (tptp.aSet0 W2) (tptp.aElementOf0 W2 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W2) W1))))))) (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe W0) (tptp.szmzizndt0 (tptp.sdtlpdtrp0 tptp.xN W0)))))) (and (tptp.aFunction0 tptp.xd) (= _let_9 tptp.szNzAzT0) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.aElementOf0 W1 (tptp.slbdtsldtrb0 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 W0)) tptp.xk))) (= (tptp.sdtlpdtrp0 tptp.xd W0) (tptp.sdtlpdtrp0 (tptp.sdtlpdtrp0 tptp.xC W0) W1))))))) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd _let_9) tptp.xT) (and (tptp.aElementOf0 _let_5 tptp.xT) (tptp.isCountable0 _let_6)) _let_8 _let_4 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xO) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W1 (tptp.sdtlbdtrb0 tptp.xd (tptp.szDzizrdt0 tptp.xd))) (= (tptp.sdtlpdtrp0 tptp.xe W1) W0))))) (tptp.aSubsetOf0 tptp.xO tptp.xS) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.62/11.79 )
% 11.62/11.79 % SZS output end Proof for NUM605+1
% 11.62/11.79 % cvc5---1.0.5 exiting
% 11.62/11.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------