TSTP Solution File: NUM597+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM597+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 : n032.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 11:57:11 EDT 2023
% Result : Theorem 9.63s 1.64s
% Output : Proof 10.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM597+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Fri Aug 25 14:55:43 EDT 2023
% 0.11/0.29 % CPUTime :
% 9.63/1.64 Command-line arguments: --flatten
% 9.63/1.64
% 9.63/1.64 % SZS status Theorem
% 9.63/1.64
% 9.63/1.65 % SZS output start Proof
% 9.63/1.65 Take the following subset of the input axioms:
% 9.63/1.66 fof(mEmpFin, axiom, isFinite0(slcrc0)).
% 9.63/1.66 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 9.63/1.66 fof(m__, conjecture, aElementOf0(szDzizrdt0(xd), xT)).
% 9.63/1.66 fof(m__3291, hypothesis, aSet0(xT) & isFinite0(xT)).
% 9.63/1.66 fof(m__3435, hypothesis, aSet0(xS) & (![W0]: (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0)) & (aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)))).
% 9.63/1.66 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]: (aElementOf0(W1, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W1, 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))))))))))))))).
% 10.34/1.66 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]: (aElementOf0(W2, W1_2) => aElementOf0(W2, 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)))))))))))))))))).
% 10.34/1.66 fof(m__4660, hypothesis, aFunction0(xe) & (szDzozmdt0(xe)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0_2), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(sdtlpdtrp0(xe, W0_2), W1_2)) & sdtlpdtrp0(xe, W0_2)=szmzizndt0(sdtlpdtrp0(xN, W0_2))))))).
% 10.34/1.66 fof(m__4730, hypothesis, aFunction0(xd) & (szDzozmdt0(xd)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((aSet0(W1_2) & (((![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2)))) | aSubsetOf0(W1_2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2)))) & sbrdtbr0(W1_2)=xk) | aElementOf0(W1_2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2)), xk)))) => sdtlpdtrp0(xd, W0_2)=sdtlpdtrp0(sdtlpdtrp0(xC, W0_2), W1_2))))).
% 10.34/1.66 fof(m__4758, hypothesis, aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & (![W0_2]: (aElementOf0(W0_2, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1_2]: (aElementOf0(W1_2, szDzozmdt0(xd)) & sdtlpdtrp0(xd, W1_2)=W0_2)) & (![W0_2]: (aElementOf0(W0_2, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0_2, xT)) & aSubsetOf0(sdtlcdtrc0(xd, szDzozmdt0(xd)), xT)))).
% 10.34/1.66 fof(m__4868, hypothesis, ~((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, sdtlbdtrb0(xd, szDzizrdt0(xd))))).
% 10.34/1.66
% 10.34/1.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.34/1.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.34/1.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.34/1.66 fresh(y, y, x1...xn) = u
% 10.34/1.66 C => fresh(s, t, x1...xn) = v
% 10.34/1.66 where fresh is a fresh function symbol and x1..xn are the free
% 10.34/1.66 variables of u and v.
% 10.34/1.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.34/1.66 input problem has no model of domain size 1).
% 10.34/1.66
% 10.34/1.66 The encoding turns the above axioms into the following unit equations and goals:
% 10.34/1.66
% 10.34/1.66 Axiom 1 (m__3435_1): isCountable0(xS) = true2.
% 10.34/1.66 Axiom 2 (mNATSet_1): isCountable0(szNzAzT0) = true2.
% 10.34/1.66 Axiom 3 (mEmpFin): isFinite0(slcrc0) = true2.
% 10.34/1.66 Axiom 4 (m__4660): szDzozmdt0(xe) = szNzAzT0.
% 10.34/1.66 Axiom 5 (m__4151): szDzozmdt0(xC) = szNzAzT0.
% 10.34/1.66 Axiom 6 (m__4730): szDzozmdt0(xd) = szNzAzT0.
% 10.34/1.66 Axiom 7 (m__3623): szDzozmdt0(xN) = szNzAzT0.
% 10.34/1.66 Axiom 8 (m__3435): aSet0(xS) = true2.
% 10.34/1.66 Axiom 9 (m__3291): aSet0(xT) = true2.
% 10.34/1.66 Axiom 10 (mNATSet): aSet0(szNzAzT0) = true2.
% 10.34/1.66 Axiom 11 (m__4758_2): fresh19(X, X, Y) = true2.
% 10.34/1.66 Axiom 12 (m__4758_5): fresh17(X, X, Y) = true2.
% 10.34/1.66 Axiom 13 (m__4868_3): fresh14(X, X, Y) = szDzizrdt0(xd).
% 10.34/1.66 Axiom 14 (m__4868_4): fresh13(X, X, Y) = true2.
% 10.34/1.66 Axiom 15 (m__4758_2): fresh20(X, X, Y, Z) = aElementOf0(Y, sdtlcdtrc0(xd, szDzozmdt0(xd))).
% 10.34/1.66 Axiom 16 (m__4868_1): aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))) = true2.
% 10.34/1.66 Axiom 17 (m__4758_2): fresh20(aElementOf0(X, szDzozmdt0(xd)), true2, Y, X) = fresh19(sdtlpdtrp0(xd, X), Y, Y).
% 10.34/1.66 Axiom 18 (m__4758_5): fresh17(aElementOf0(X, sdtlcdtrc0(xd, szDzozmdt0(xd))), true2, X) = aElementOf0(X, xT).
% 10.34/1.66 Axiom 19 (m__4868_3): fresh14(aElementOf0(X, sdtlbdtrb0(xd, szDzizrdt0(xd))), true2, X) = sdtlpdtrp0(xd, X).
% 10.34/1.66 Axiom 20 (m__4868_4): fresh13(aElementOf0(X, sdtlbdtrb0(xd, szDzizrdt0(xd))), true2, X) = aElementOf0(X, szDzozmdt0(xd)).
% 10.34/1.66
% 10.34/1.66 Lemma 21: isCountable0(szNzAzT0) = isCountable0(xS).
% 10.34/1.66 Proof:
% 10.34/1.66 isCountable0(szNzAzT0)
% 10.34/1.66 = { by axiom 2 (mNATSet_1) }
% 10.34/1.66 true2
% 10.34/1.66 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.66 isCountable0(xS)
% 10.34/1.66
% 10.34/1.66 Lemma 22: isFinite0(slcrc0) = isCountable0(szNzAzT0).
% 10.34/1.66 Proof:
% 10.34/1.66 isFinite0(slcrc0)
% 10.34/1.66 = { by axiom 3 (mEmpFin) }
% 10.34/1.66 true2
% 10.34/1.66 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.66 isCountable0(xS)
% 10.34/1.66 = { by lemma 21 R->L }
% 10.34/1.66 isCountable0(szNzAzT0)
% 10.34/1.66
% 10.34/1.66 Lemma 23: aSet0(xS) = isFinite0(slcrc0).
% 10.34/1.66 Proof:
% 10.34/1.66 aSet0(xS)
% 10.34/1.66 = { by axiom 8 (m__3435) }
% 10.34/1.66 true2
% 10.34/1.66 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.66 isCountable0(xS)
% 10.34/1.66 = { by lemma 21 R->L }
% 10.34/1.66 isCountable0(szNzAzT0)
% 10.34/1.66 = { by lemma 22 R->L }
% 10.34/1.66 isFinite0(slcrc0)
% 10.34/1.66
% 10.34/1.66 Lemma 24: aSet0(xT) = aSet0(xS).
% 10.34/1.66 Proof:
% 10.34/1.66 aSet0(xT)
% 10.34/1.66 = { by axiom 9 (m__3291) }
% 10.34/1.66 true2
% 10.34/1.66 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.66 isCountable0(xS)
% 10.34/1.66 = { by lemma 21 R->L }
% 10.34/1.66 isCountable0(szNzAzT0)
% 10.34/1.66 = { by lemma 22 R->L }
% 10.34/1.66 isFinite0(slcrc0)
% 10.34/1.66 = { by lemma 23 R->L }
% 10.34/1.66 aSet0(xS)
% 10.34/1.66
% 10.34/1.67 Lemma 25: aSet0(szNzAzT0) = aSet0(xT).
% 10.34/1.67 Proof:
% 10.34/1.67 aSet0(szNzAzT0)
% 10.34/1.67 = { by axiom 10 (mNATSet) }
% 10.34/1.67 true2
% 10.34/1.67 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.67 isCountable0(xS)
% 10.34/1.67 = { by lemma 21 R->L }
% 10.34/1.67 isCountable0(szNzAzT0)
% 10.34/1.67 = { by lemma 22 R->L }
% 10.34/1.67 isFinite0(slcrc0)
% 10.34/1.67 = { by lemma 23 R->L }
% 10.34/1.67 aSet0(xS)
% 10.34/1.67 = { by lemma 24 R->L }
% 10.34/1.67 aSet0(xT)
% 10.34/1.67
% 10.34/1.67 Lemma 26: szDzozmdt0(xC) = szDzozmdt0(xe).
% 10.34/1.67 Proof:
% 10.34/1.67 szDzozmdt0(xC)
% 10.34/1.67 = { by axiom 5 (m__4151) }
% 10.34/1.67 szNzAzT0
% 10.34/1.67 = { by axiom 4 (m__4660) R->L }
% 10.34/1.67 szDzozmdt0(xe)
% 10.34/1.67
% 10.34/1.67 Lemma 27: szDzozmdt0(xd) = szDzozmdt0(xC).
% 10.34/1.67 Proof:
% 10.34/1.67 szDzozmdt0(xd)
% 10.34/1.67 = { by axiom 6 (m__4730) }
% 10.34/1.67 szNzAzT0
% 10.34/1.67 = { by axiom 4 (m__4660) R->L }
% 10.34/1.67 szDzozmdt0(xe)
% 10.34/1.67 = { by lemma 26 R->L }
% 10.34/1.67 szDzozmdt0(xC)
% 10.34/1.67
% 10.34/1.67 Lemma 28: szDzozmdt0(xN) = szDzozmdt0(xC).
% 10.34/1.67 Proof:
% 10.34/1.67 szDzozmdt0(xN)
% 10.34/1.67 = { by axiom 7 (m__3623) }
% 10.34/1.67 szNzAzT0
% 10.34/1.67 = { by axiom 4 (m__4660) R->L }
% 10.34/1.67 szDzozmdt0(xe)
% 10.34/1.67 = { by lemma 26 R->L }
% 10.34/1.67 szDzozmdt0(xC)
% 10.34/1.67
% 10.34/1.67 Lemma 29: aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))) = aSet0(szNzAzT0).
% 10.34/1.67 Proof:
% 10.34/1.67 aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd)))
% 10.34/1.67 = { by axiom 16 (m__4868_1) }
% 10.34/1.67 true2
% 10.34/1.67 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.67 isCountable0(xS)
% 10.34/1.67 = { by lemma 21 R->L }
% 10.34/1.67 isCountable0(szNzAzT0)
% 10.34/1.67 = { by lemma 22 R->L }
% 10.34/1.67 isFinite0(slcrc0)
% 10.34/1.67 = { by lemma 23 R->L }
% 10.34/1.67 aSet0(xS)
% 10.34/1.67 = { by lemma 24 R->L }
% 10.34/1.67 aSet0(xT)
% 10.34/1.67 = { by lemma 25 R->L }
% 10.34/1.67 aSet0(szNzAzT0)
% 10.34/1.67
% 10.34/1.67 Goal 1 (m__): aElementOf0(szDzizrdt0(xd), xT) = true2.
% 10.34/1.67 Proof:
% 10.34/1.67 aElementOf0(szDzizrdt0(xd), xT)
% 10.34/1.67 = { by axiom 18 (m__4758_5) R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), true2, szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), isCountable0(xS), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), isCountable0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), isFinite0(slcrc0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), aSet0(xS), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), aSet0(xT), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 R->L }
% 10.34/1.67 fresh17(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 15 (m__4758_2) R->L }
% 10.34/1.67 fresh17(fresh20(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 }
% 10.34/1.67 fresh17(fresh20(aSet0(xT), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 }
% 10.34/1.67 fresh17(fresh20(aSet0(xS), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 }
% 10.34/1.67 fresh17(fresh20(isFinite0(slcrc0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 }
% 10.34/1.67 fresh17(fresh20(isCountable0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 }
% 10.34/1.67 fresh17(fresh20(isCountable0(xS), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) }
% 10.34/1.67 fresh17(fresh20(true2, aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 14 (m__4868_4) R->L }
% 10.34/1.67 fresh17(fresh20(fresh13(aSet0(szNzAzT0), aSet0(szNzAzT0), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 29 R->L }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(szNzAzT0), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(xT), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(xS), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isFinite0(slcrc0), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isCountable0(szNzAzT0), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isCountable0(xS), w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) }
% 10.34/1.67 fresh17(fresh20(fresh13(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), true2, w0), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 20 (m__4868_4) }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 27 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xC)), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 28 R->L }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), aSet0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), aSet0(xT), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), aSet0(xS), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), isFinite0(slcrc0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), isCountable0(szNzAzT0), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), isCountable0(xS), szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xN)), true2, szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 28 }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xC)), true2, szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 27 R->L }
% 10.34/1.67 fresh17(fresh20(aElementOf0(w0, szDzozmdt0(xd)), true2, szDzizrdt0(xd), w0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 17 (m__4758_2) }
% 10.34/1.67 fresh17(fresh19(sdtlpdtrp0(xd, w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 19 (m__4868_3) R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), true2, w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isCountable0(xS), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isCountable0(szNzAzT0), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), isFinite0(slcrc0), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(xS), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(xT), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 R->L }
% 10.34/1.67 fresh17(fresh19(fresh14(aElementOf0(w0, sdtlbdtrb0(xd, szDzizrdt0(xd))), aSet0(szNzAzT0), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 29 }
% 10.34/1.67 fresh17(fresh19(fresh14(aSet0(szNzAzT0), aSet0(szNzAzT0), w0), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 13 (m__4868_3) }
% 10.34/1.67 fresh17(fresh19(szDzizrdt0(xd), szDzizrdt0(xd), szDzizrdt0(xd)), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 11 (m__4758_2) }
% 10.34/1.67 fresh17(true2, aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 1 (m__3435_1) R->L }
% 10.34/1.67 fresh17(isCountable0(xS), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 21 R->L }
% 10.34/1.67 fresh17(isCountable0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 22 R->L }
% 10.34/1.67 fresh17(isFinite0(slcrc0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 23 R->L }
% 10.34/1.67 fresh17(aSet0(xS), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 24 R->L }
% 10.34/1.67 fresh17(aSet0(xT), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by lemma 25 R->L }
% 10.34/1.67 fresh17(aSet0(szNzAzT0), aSet0(szNzAzT0), szDzizrdt0(xd))
% 10.34/1.67 = { by axiom 12 (m__4758_5) }
% 10.34/1.67 true2
% 10.34/1.67 % SZS output end Proof
% 10.34/1.67
% 10.34/1.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------