TSTP Solution File: NUM633+3 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM633+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.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 11:57:25 EDT 2023
% Result : Theorem 38.47s 5.42s
% Output : Proof 40.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM633+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n016.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 13:10:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 38.47/5.42 Command-line arguments: --flatten
% 38.47/5.42
% 38.47/5.42 % SZS status Theorem
% 38.47/5.42
% 39.55/5.45 % SZS output start Proof
% 39.55/5.45 Take the following subset of the input axioms:
% 39.55/5.51 fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 39.55/5.51 fof(mCountNFin_01, axiom, ![W0_2]: ((aSet0(W0_2) & isCountable0(W0_2)) => W0_2!=slcrc0)).
% 39.55/5.51 fof(mDefDiff, definition, ![W1, W0_2]: ((aSet0(W0_2) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0_2, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0_2) & W3!=W1))))))).
% 39.55/5.51 fof(mDefEmp, definition, ![W0_2]: (W0_2=slcrc0 <=> (aSet0(W0_2) & ~?[W1_2]: aElementOf0(W1_2, W0_2)))).
% 39.55/5.51 fof(mEmpFin, axiom, isFinite0(slcrc0)).
% 39.55/5.51 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 39.55/5.51 fof(mNatNSucc, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => W0_2!=szszuzczcdt0(W0_2))).
% 39.55/5.51 fof(mNoScLessZr, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W0_2), sz00))).
% 39.55/5.51 fof(mSuccNum, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0_2), szNzAzT0) & szszuzczcdt0(W0_2)!=sz00))).
% 39.55/5.51 fof(m__, conjecture, ![W0_2]: (((((aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xO))) | aSubsetOf0(W0_2, xO)) & sbrdtbr0(W0_2)=xK) | aElementOf0(W0_2, slbdtsldtrb0(xO, xK))) => (~(~?[W1_2]: aElementOf0(W1_2, W0_2) | W0_2=slcrc0) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, szNzAzT0)) & (aSubsetOf0(W0_2, szNzAzT0) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS)) & (aSubsetOf0(W0_2, xS) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS)) & (aSubsetOf0(W0_2, xS) & (aElementOf0(W0_2, szDzozmdt0(xc)) & sdtlpdtrp0(xc, W0_2)=szDzizrdt0(xd)))))))))) => ?[W0_2]: (aElementOf0(W0_2, xT) & ?[W1_2]: (((aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, xS))) | aSubsetOf0(W1_2, xS)) & (isCountable0(W1_2) & ![W2_2]: ((aSet0(W2_2) & (![W3_2]: (aElementOf0(W3_2, W2_2) => aElementOf0(W3_2, W1_2)) & (aSubsetOf0(W2_2, W1_2) & (sbrdtbr0(W2_2)=xK & aElementOf0(W2_2, slbdtsldtrb0(W1_2, xK)))))) => sdtlpdtrp0(xc, W2_2)=W0_2))))).
% 39.55/5.51 fof(m__3291, hypothesis, aSet0(xT) & isFinite0(xT)).
% 39.55/5.51 fof(m__3398, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((((aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, szNzAzT0))) | aSubsetOf0(W1_2, szNzAzT0)) & isCountable0(W1_2)) => ![W2_2]: ((aFunction0(W2_2) & ((![W3_2]: ((aElementOf0(W3_2, szDzozmdt0(W2_2)) => (((aSet0(W3_2) & ![W4]: (aElementOf0(W4, W3_2) => aElementOf0(W4, W1_2))) | aSubsetOf0(W3_2, W1_2)) & sbrdtbr0(W3_2)=W0_2)) & ((aSet0(W3_2) & (![W4_2]: (aElementOf0(W4_2, W3_2) => aElementOf0(W4_2, W1_2)) & (aSubsetOf0(W3_2, W1_2) & sbrdtbr0(W3_2)=W0_2))) => aElementOf0(W3_2, szDzozmdt0(W2_2)))) | szDzozmdt0(W2_2)=slbdtsldtrb0(W1_2, W0_2)) & ((aSet0(sdtlcdtrc0(W2_2, szDzozmdt0(W2_2))) & ![W3_2]: (aElementOf0(W3_2, sdtlcdtrc0(W2_2, szDzozmdt0(W2_2))) <=> ?[W4_2]: (aElementOf0(W4_2, szDzozmdt0(W2_2)) & sdtlpdtrp0(W2_2, W4_2)=W3_2))) => (![W3_2]: (aElementOf0(W3_2, sdtlcdtrc0(W2_2, szDzozmdt0(W2_2))) => aElementOf0(W3_2, xT)) | aSubsetOf0(sdtlcdtrc0(W2_2, szDzozmdt0(W2_2)), xT))))) => (iLess0(W0_2, xK) => ?[W3_2]: (aElementOf0(W3_2, xT) & ?[W4_2]: (aSet0(W4_2) & (![W5]: (aElementOf0(W5, W4_2) => aElementOf0(W5, W1_2)) & (aSubsetOf0(W4_2, W1_2) & (isCountable0(W4_2) & ![W5_2]: (((((aSet0(W5_2) & ![W6]: (aElementOf0(W6, W5_2) => aElementOf0(W6, W4_2))) | aSubsetOf0(W5_2, W4_2)) & sbrdtbr0(W5_2)=W0_2) | aElementOf0(W5_2, slbdtsldtrb0(W4_2, W0_2))) => sdtlpdtrp0(W2_2, W5_2)=W3_2))))))))))).
% 39.55/5.51 fof(m__3435, hypothesis, aSet0(xS) & (![W0_2]: (aElementOf0(W0_2, xS) => aElementOf0(W0_2, szNzAzT0)) & (aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)))).
% 39.55/5.51 fof(m__3533, hypothesis, aElementOf0(xk, szNzAzT0) & szszuzczcdt0(xk)=xK).
% 39.55/5.51 fof(m__3623, hypothesis, aFunction0(xN) & (szDzozmdt0(xN)=szNzAzT0 & (sdtlpdtrp0(xN, sz00)=xS & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ((((aSet0(sdtlpdtrp0(xN, W0_2)) & ![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W1_2, szNzAzT0))) | aSubsetOf0(sdtlpdtrp0(xN, W0_2), szNzAzT0)) & isCountable0(sdtlpdtrp0(xN, W0_2))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W1_2)) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W1_2]: (aElementOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W1_2) & (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) & W1_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSet0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2))) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2))) => aElementOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSubsetOf0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2)), sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & isCountable0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2))))))))))))))).
% 39.55/5.51 fof(m__3965, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((aSet0(W1_2) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & ![W2_2]: (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W2_2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & ![W2_2]: (aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W2_2) & (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) & W2_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2)))))) => (((![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) | aSubsetOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & sbrdtbr0(W1_2)=xk) | aElementOf0(W1_2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))), xk)))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W2_2]: (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W2_2)) & (aSet0(sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W2_2]: (aElementOf0(W2_2, sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W2_2) & (aElementOf0(W2_2, W1_2) | W2_2=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (![W2_2]: (aElementOf0(W2_2, sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2)))) => aElementOf0(W2_2, xS)) & (aSubsetOf0(sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2))), xS) & (sbrdtbr0(sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2))))=xK & aElementOf0(sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2))), slbdtsldtrb0(xS, xK)))))))))))).
% 39.55/5.51 fof(m__4151, hypothesis, aFunction0(xC) & (szDzozmdt0(xC)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0_2)) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W1_2)) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W1_2]: (aElementOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W1_2) & (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) & W1_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (![W1_2]: ((aElementOf0(W1_2, szDzozmdt0(sdtlpdtrp0(xC, W0_2))) => (aSet0(W1_2) & (![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSubsetOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & sbrdtbr0(W1_2)=xk)))) & ((((aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))))) | aSubsetOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & sbrdtbr0(W1_2)=xk) => aElementOf0(W1_2, szDzozmdt0(sdtlpdtrp0(xC, W0_2))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0_2))=slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))), xk) & ![W1_2]: ((aSet0(W1_2) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & ![W2_2]: (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W2_2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & ![W2_2]: (aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W2_2) & (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) & W2_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2)))))) => (((![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) | aSubsetOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & sbrdtbr0(W1_2)=xk) | aElementOf0(W1_2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))), xk)))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W2_2]: (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W2_2)) & (![W2_2]: (aElementOf0(W2_2, sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W2_2) & (aElementOf0(W2_2, W1_2) | W2_2=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & sdtlpdtrp0(sdtlpdtrp0(xC, W0_2), W1_2)=sdtlpdtrp0(xc, sdtpldt0(W1_2, szmzizndt0(sdtlpdtrp0(xN, W0_2)))))))))))))))))).
% 39.55/5.51 fof(m__4331, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & ![W2_2]: (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W2_2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & ![W2_2]: (aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W2_2) & (aElementOf0(W2_2, sdtlpdtrp0(xN, W0_2)) & W2_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2)))))) => ((aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))))) | aSubsetOf0(W1_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))))) & isCountable0(W1_2)) => ![W2_2]: ((aSet0(W2_2) & (((![W3_2]: (aElementOf0(W3_2, W2_2) => aElementOf0(W3_2, W1_2)) | aSubsetOf0(W2_2, W1_2)) & sbrdtbr0(W2_2)=xk) | aElementOf0(W2_2, slbdtsldtrb0(W1_2, xk)))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W3_2]: (aElementOf0(W3_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W3_2)) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W3_2]: (aElementOf0(W3_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W3_2) & (aElementOf0(W3_2, sdtlpdtrp0(xN, W0_2)) & W3_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (![W3_2]: (aElementOf0(W3_2, W2_2) => aElementOf0(W3_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSubsetOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & aElementOf0(W2_2, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))), xk)))))))))))).
% 39.55/5.51 fof(m__4411, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ?[W1_2]: (aElementOf0(W1_2, xT) & ?[W2_2]: (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), sdtlpdtrp0(xN, W0_2)) & (![W3_2]: (aElementOf0(W3_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0_2)), W3_2)) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (![W3_2]: (aElementOf0(W3_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) <=> (aElement0(W3_2) & (aElementOf0(W3_2, sdtlpdtrp0(xN, W0_2)) & W3_2!=szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSet0(W2_2) & (![W3_2]: (aElementOf0(W3_2, W2_2) => aElementOf0(W3_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2))))) & (aSubsetOf0(W2_2, sdtmndt0(sdtlpdtrp0(xN, W0_2), szmzizndt0(sdtlpdtrp0(xN, W0_2)))) & (isCountable0(W2_2) & ![W3_2]: ((aSet0(W3_2) & (((![W4_2]: (aElementOf0(W4_2, W3_2) => aElementOf0(W4_2, W2_2)) | aSubsetOf0(W3_2, W2_2)) & sbrdtbr0(W3_2)=xk) | aElementOf0(W3_2, slbdtsldtrb0(W2_2, xk)))) => sdtlpdtrp0(sdtlpdtrp0(xC, W0_2), W3_2)=W1_2)))))))))))).
% 39.55/5.51 fof(m__4854, hypothesis, aElementOf0(szDzizrdt0(xd), xT) & (aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0_2]: (aElementOf0(W0_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0_2, szDzozmdt0(xd)) & sdtlpdtrp0(xd, W0_2)=szDzizrdt0(xd))))).
% 39.55/5.51 fof(m__4891, hypothesis, aSet0(xO) & (aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & (![W0_2]: (aElementOf0(W0_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0_2, szDzozmdt0(xd)) & sdtlpdtrp0(xd, W0_2)=szDzizrdt0(xd))) & (![W0_2]: (aElementOf0(W0_2, xO) <=> ?[W1_2]: (aElementOf0(W1_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) & sdtlpdtrp0(xe, W1_2)=W0_2)) & xO=sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))).
% 39.55/5.51 fof(m__4908, hypothesis, aSet0(xO) & isCountable0(xO)).
% 39.55/5.51 fof(m__4998, hypothesis, ![W0_2]: (aElementOf0(W0_2, xO) => aElementOf0(W0_2, xS)) & aSubsetOf0(xO, xS)).
% 39.55/5.51
% 39.55/5.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.55/5.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.55/5.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.55/5.51 fresh(y, y, x1...xn) = u
% 39.55/5.51 C => fresh(s, t, x1...xn) = v
% 39.55/5.51 where fresh is a fresh function symbol and x1..xn are the free
% 39.55/5.51 variables of u and v.
% 39.55/5.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.55/5.51 input problem has no model of domain size 1).
% 39.55/5.51
% 39.55/5.51 The encoding turns the above axioms into the following unit equations and goals:
% 39.55/5.51
% 39.55/5.51 Axiom 1 (m__4908_1): isCountable0(xO) = true2.
% 39.55/5.51 Axiom 2 (m__3435_1): isCountable0(xS) = true2.
% 39.55/5.51 Axiom 3 (mNATSet_1): isCountable0(szNzAzT0) = true2.
% 39.55/5.51 Axiom 4 (mEmpFin): isFinite0(slcrc0) = true2.
% 39.55/5.51 Axiom 5 (m__3533): szszuzczcdt0(xk) = xK.
% 39.55/5.51 Axiom 6 (m__4891_2): aSet0(xO) = true2.
% 39.55/5.51 Axiom 7 (m__3291): aSet0(xT) = true2.
% 39.55/5.51 Axiom 8 (mNATSet): aSet0(szNzAzT0) = true2.
% 39.55/5.51 Axiom 9 (m__4998): aSubsetOf0(xO, xS) = true2.
% 39.55/5.51 Axiom 10 (m__3623_1): sdtlpdtrp0(xN, sz00) = xS.
% 39.55/5.51 Axiom 11 (m___13): fresh32(X, X, Y) = szDzizrdt0(xd).
% 39.55/5.51 Axiom 12 (m___4): fresh22(X, X, Y) = or2(Y).
% 39.55/5.51 Axiom 13 (m___4): fresh21(X, X, Y) = true2.
% 39.55/5.51 Axiom 14 (m__4854_1): aElementOf0(szDzizrdt0(xd), xT) = true2.
% 39.55/5.51 Axiom 15 (m___11): fresh284(X, X, Y, Z) = or(Y, Z).
% 39.55/5.51 Axiom 16 (m___11): fresh35(X, X, Y, Z) = true2.
% 39.55/5.51 Axiom 17 (m___13): fresh32(or2(X), true2, X) = sdtlpdtrp0(xc, X).
% 39.55/5.51 Axiom 18 (m___18): fresh27(X, X, Y, Z) = xK.
% 39.55/5.51 Axiom 19 (m___21): fresh24(X, X, Y, Z) = true2.
% 39.55/5.51 Axiom 20 (m___11): fresh283(X, X, Y, Z) = fresh284(isCountable0(Z), true2, Y, Z).
% 39.55/5.51 Axiom 21 (m___4): fresh22(aSubsetOf0(X, xO), true2, X) = fresh21(sbrdtbr0(X), xK, X).
% 39.55/5.51 Axiom 22 (m__4891): xO = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))).
% 39.55/5.51 Axiom 23 (m___11): fresh283(aSubsetOf0(X, xS), true2, Y, X) = fresh35(aElementOf0(Y, xT), true2, Y, X).
% 39.55/5.51 Axiom 24 (m___18): fresh27(or(X, Y), true2, X, Y) = sbrdtbr0(w2(X, Y)).
% 39.55/5.51 Axiom 25 (m___21): fresh24(or(X, Y), true2, X, Y) = aSubsetOf0(w2(X, Y), Y).
% 39.55/5.51
% 39.55/5.51 Lemma 26: isCountable0(xS) = isCountable0(xO).
% 39.55/5.51 Proof:
% 39.55/5.51 isCountable0(xS)
% 39.55/5.51 = { by axiom 2 (m__3435_1) }
% 39.55/5.51 true2
% 39.55/5.51 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.51 isCountable0(xO)
% 39.55/5.51
% 39.55/5.51 Lemma 27: isCountable0(szNzAzT0) = isCountable0(xS).
% 39.55/5.51 Proof:
% 39.55/5.51 isCountable0(szNzAzT0)
% 39.55/5.51 = { by axiom 3 (mNATSet_1) }
% 39.55/5.51 true2
% 39.55/5.51 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.51 isCountable0(xO)
% 39.55/5.51 = { by lemma 26 R->L }
% 39.55/5.51 isCountable0(xS)
% 39.55/5.51
% 39.55/5.51 Lemma 28: isFinite0(slcrc0) = isCountable0(szNzAzT0).
% 39.55/5.51 Proof:
% 39.55/5.51 isFinite0(slcrc0)
% 39.55/5.51 = { by axiom 4 (mEmpFin) }
% 39.55/5.51 true2
% 39.55/5.51 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.51 isCountable0(xO)
% 39.55/5.51 = { by lemma 26 R->L }
% 39.55/5.51 isCountable0(xS)
% 39.55/5.51 = { by lemma 27 R->L }
% 39.55/5.51 isCountable0(szNzAzT0)
% 39.55/5.51
% 39.55/5.51 Lemma 29: aSet0(xO) = isFinite0(slcrc0).
% 39.55/5.51 Proof:
% 39.55/5.51 aSet0(xO)
% 39.55/5.52 = { by axiom 6 (m__4891_2) }
% 39.55/5.52 true2
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 isCountable0(xO)
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 isCountable0(xS)
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 isCountable0(szNzAzT0)
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 isFinite0(slcrc0)
% 39.55/5.52
% 39.55/5.52 Lemma 30: aSet0(xT) = aSet0(xO).
% 39.55/5.52 Proof:
% 39.55/5.52 aSet0(xT)
% 39.55/5.52 = { by axiom 7 (m__3291) }
% 39.55/5.52 true2
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 isCountable0(xO)
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 isCountable0(xS)
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 isCountable0(szNzAzT0)
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 isFinite0(slcrc0)
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 aSet0(xO)
% 39.55/5.52
% 39.55/5.52 Lemma 31: aSet0(szNzAzT0) = aSet0(xT).
% 39.55/5.52 Proof:
% 39.55/5.52 aSet0(szNzAzT0)
% 39.55/5.52 = { by axiom 8 (mNATSet) }
% 39.55/5.52 true2
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 isCountable0(xO)
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 isCountable0(xS)
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 isCountable0(szNzAzT0)
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 isFinite0(slcrc0)
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 aSet0(xO)
% 39.55/5.52 = { by lemma 30 R->L }
% 39.55/5.52 aSet0(xT)
% 39.55/5.52
% 39.55/5.52 Lemma 32: or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) = aSet0(szNzAzT0).
% 39.55/5.52 Proof:
% 39.55/5.52 or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 15 (m___11) R->L }
% 39.55/5.52 fresh284(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 }
% 39.55/5.52 fresh284(aSet0(xT), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 }
% 39.55/5.52 fresh284(aSet0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 }
% 39.55/5.52 fresh284(isFinite0(slcrc0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 }
% 39.55/5.52 fresh284(isCountable0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 }
% 39.55/5.52 fresh284(isCountable0(xS), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 }
% 39.55/5.52 fresh284(isCountable0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 22 (m__4891) }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xT), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isFinite0(slcrc0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xS), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) }
% 39.55/5.52 fresh284(isCountable0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 20 (m___11) R->L }
% 39.55/5.52 fresh283(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 }
% 39.55/5.52 fresh283(aSet0(xT), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 }
% 39.55/5.52 fresh283(aSet0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 }
% 39.55/5.52 fresh283(isFinite0(slcrc0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 }
% 39.55/5.52 fresh283(isCountable0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 }
% 39.55/5.52 fresh283(isCountable0(xS), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 }
% 39.55/5.52 fresh283(isCountable0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) }
% 39.55/5.52 fresh283(true2, aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 9 (m__4998) R->L }
% 39.55/5.52 fresh283(aSubsetOf0(xO, xS), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 10 (m__3623_1) R->L }
% 39.55/5.52 fresh283(aSubsetOf0(xO, sdtlpdtrp0(xN, sz00)), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 22 (m__4891) }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), aSet0(xT), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), aSet0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), isFinite0(slcrc0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), isCountable0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), isCountable0(xS), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), isCountable0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlpdtrp0(xN, sz00)), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 10 (m__3623_1) }
% 39.55/5.52 fresh283(aSubsetOf0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), xS), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 23 (m___11) }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), isCountable0(xS), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), isCountable0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), isFinite0(slcrc0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), aSet0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), aSet0(xT), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 R->L }
% 39.55/5.52 fresh35(aElementOf0(szDzizrdt0(xd), xT), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 14 (m__4854_1) }
% 39.55/5.52 fresh35(true2, aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 fresh35(isCountable0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 fresh35(isCountable0(xS), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 fresh35(isCountable0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 fresh35(isFinite0(slcrc0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 fresh35(aSet0(xO), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 30 R->L }
% 39.55/5.52 fresh35(aSet0(xT), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by lemma 31 R->L }
% 39.55/5.52 fresh35(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))
% 39.55/5.52 = { by axiom 16 (m___11) }
% 39.55/5.52 true2
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 isCountable0(xO)
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 isCountable0(xS)
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 isCountable0(szNzAzT0)
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 isFinite0(slcrc0)
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 aSet0(xO)
% 39.55/5.52 = { by lemma 30 R->L }
% 39.55/5.52 aSet0(xT)
% 39.55/5.52 = { by lemma 31 R->L }
% 39.55/5.52 aSet0(szNzAzT0)
% 39.55/5.52
% 39.55/5.52 Goal 1 (m___1): tuple4(sdtlpdtrp0(xc, w2(X, Y)), or(X, Y)) = tuple4(X, true2).
% 39.55/5.52 The goal is true when:
% 39.55/5.52 X = szDzizrdt0(xd)
% 39.55/5.52 Y = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))
% 39.55/5.52
% 39.55/5.52 Proof:
% 39.55/5.52 tuple4(sdtlpdtrp0(xc, w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by axiom 17 (m___13) R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), true2, w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), isCountable0(xO), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 26 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), isCountable0(xS), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 27 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), isCountable0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 28 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), isFinite0(slcrc0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 29 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(xO), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 30 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(xT), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 31 R->L }
% 39.55/5.52 tuple4(fresh32(or2(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by axiom 12 (m___4) R->L }
% 39.55/5.52 tuple4(fresh32(fresh22(aSet0(szNzAzT0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 31 }
% 39.55/5.52 tuple4(fresh32(fresh22(aSet0(xT), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 30 }
% 39.55/5.52 tuple4(fresh32(fresh22(aSet0(xO), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 29 }
% 39.55/5.52 tuple4(fresh32(fresh22(isFinite0(slcrc0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 28 }
% 39.55/5.52 tuple4(fresh32(fresh22(isCountable0(szNzAzT0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 27 }
% 39.55/5.52 tuple4(fresh32(fresh22(isCountable0(xS), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by lemma 26 }
% 39.55/5.52 tuple4(fresh32(fresh22(isCountable0(xO), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by axiom 1 (m__4908_1) }
% 39.55/5.52 tuple4(fresh32(fresh22(true2, aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.52 = { by axiom 19 (m___21) R->L }
% 39.55/5.52 tuple4(fresh32(fresh22(fresh24(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 32 R->L }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 31 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xT), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 30 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 29 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isFinite0(slcrc0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 28 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 27 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xS), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 26 }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 1 (m__4908_1) }
% 39.55/5.53 tuple4(fresh32(fresh22(fresh24(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 25 (m___21) }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 22 (m__4891) R->L }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 31 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), aSet0(xT), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 30 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), aSet0(xO), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 29 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), isFinite0(slcrc0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 28 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), isCountable0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 27 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), isCountable0(xS), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 26 }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), isCountable0(xO), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 1 (m__4908_1) }
% 39.55/5.53 tuple4(fresh32(fresh22(aSubsetOf0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), xO), true2, w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 21 (m___4) }
% 39.55/5.53 tuple4(fresh32(fresh21(sbrdtbr0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), xK, w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 5 (m__3533) R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(sbrdtbr0(w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 24 (m___18) R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), true2, szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 26 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(xS), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 27 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isCountable0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 28 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), isFinite0(slcrc0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 29 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xO), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 30 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(xT), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 31 R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 32 }
% 39.55/5.53 tuple4(fresh32(fresh21(fresh27(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 18 (m___18) }
% 39.55/5.53 tuple4(fresh32(fresh21(xK, szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 5 (m__3533) R->L }
% 39.55/5.53 tuple4(fresh32(fresh21(szszuzczcdt0(xk), szszuzczcdt0(xk), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 13 (m___4) }
% 39.55/5.53 tuple4(fresh32(true2, aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by axiom 1 (m__4908_1) R->L }
% 39.55/5.53 tuple4(fresh32(isCountable0(xO), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 26 R->L }
% 39.55/5.53 tuple4(fresh32(isCountable0(xS), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 27 R->L }
% 39.55/5.53 tuple4(fresh32(isCountable0(szNzAzT0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 39.55/5.53 = { by lemma 28 R->L }
% 40.28/5.53 tuple4(fresh32(isFinite0(slcrc0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 40.28/5.53 = { by lemma 29 R->L }
% 40.28/5.53 tuple4(fresh32(aSet0(xO), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 40.28/5.53 = { by lemma 30 R->L }
% 40.28/5.53 tuple4(fresh32(aSet0(xT), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 40.28/5.53 = { by lemma 31 R->L }
% 40.28/5.53 tuple4(fresh32(aSet0(szNzAzT0), aSet0(szNzAzT0), w2(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 40.28/5.53 = { by axiom 11 (m___13) }
% 40.28/5.53 tuple4(szDzizrdt0(xd), or(szDzizrdt0(xd), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))
% 40.28/5.53 = { by lemma 32 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), aSet0(szNzAzT0))
% 40.28/5.53 = { by lemma 31 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), aSet0(xT))
% 40.28/5.53 = { by lemma 30 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), aSet0(xO))
% 40.28/5.53 = { by lemma 29 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), isFinite0(slcrc0))
% 40.28/5.53 = { by lemma 28 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), isCountable0(szNzAzT0))
% 40.28/5.53 = { by lemma 27 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), isCountable0(xS))
% 40.28/5.53 = { by lemma 26 }
% 40.28/5.53 tuple4(szDzizrdt0(xd), isCountable0(xO))
% 40.28/5.53 = { by axiom 1 (m__4908_1) }
% 40.28/5.53 tuple4(szDzizrdt0(xd), true2)
% 40.28/5.53 % SZS output end Proof
% 40.28/5.53
% 40.28/5.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------