TSTP Solution File: NUM545+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM545+2 : 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 : n011.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 11:56:53 EDT 2023
% Result : Theorem 0.21s 0.70s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM545+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 17:47:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.70 Command-line arguments: --flatten
% 0.21/0.70
% 0.21/0.70 % SZS status Theorem
% 0.21/0.70
% 0.21/0.72 % SZS output start Proof
% 0.21/0.72 Take the following subset of the input axioms:
% 0.21/0.72 fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 0.21/0.72 fof(mCountNFin_01, axiom, ![W0_3]: ((aSet0(W0_3) & isCountable0(W0_3)) => W0_3!=slcrc0)).
% 0.21/0.72 fof(mDefDiff, definition, ![W1, W0_3]: ((aSet0(W0_3) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0_3, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0_3) & W3!=W1))))))).
% 0.21/0.72 fof(mDefEmp, definition, ![W0_3]: (W0_3=slcrc0 <=> (aSet0(W0_3) & ~?[W1_2]: aElementOf0(W1_2, W0_3)))).
% 0.21/0.72 fof(mEmpFin, axiom, isFinite0(slcrc0)).
% 0.21/0.72 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 0.21/0.72 fof(mNatNSucc, axiom, ![W0_3]: (aElementOf0(W0_3, szNzAzT0) => W0_3!=szszuzczcdt0(W0_3))).
% 0.21/0.72 fof(mNoScLessZr, axiom, ![W0_3]: (aElementOf0(W0_3, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W0_3), sz00))).
% 0.21/0.72 fof(mSuccNum, axiom, ![W0_3]: (aElementOf0(W0_3, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0_3), szNzAzT0) & szszuzczcdt0(W0_3)!=sz00))).
% 0.21/0.72 fof(mZeroNum, axiom, aElementOf0(sz00, szNzAzT0)).
% 0.21/0.72 fof(m__, conjecture, ?[W0_3]: (aElementOf0(W0_3, szNzAzT0) & ((aSet0(slbdtrb0(W0_3)) & ![W1_2]: (aElementOf0(W1_2, slbdtrb0(W0_3)) <=> (aElementOf0(W1_2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W1_2), W0_3)))) => (![W1_2]: (aElementOf0(W1_2, xS) => aElementOf0(W1_2, slbdtrb0(W0_3))) | aSubsetOf0(xS, slbdtrb0(W0_3)))))).
% 0.21/0.72 fof(m__1986, hypothesis, aSet0(xS) & (![W0_3]: (aElementOf0(W0_3, xS) => aElementOf0(W0_3, szNzAzT0)) & (aSubsetOf0(xS, szNzAzT0) & isFinite0(xS)))).
% 0.21/0.72 fof(m__2035, hypothesis, ~(~?[W0_2]: aElementOf0(W0_2, xS) & xS=slcrc0) => (aElementOf0(szmzazxdt0(xS), xS) & (![W0_2_2]: (aElementOf0(W0_2_2, xS) => sdtlseqdt0(W0_2_2, szmzazxdt0(xS))) & (aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) & (![W0_2_2]: (aElementOf0(W0_2_2, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) <=> (aElementOf0(W0_2_2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0_2_2), szszuzczcdt0(szmzazxdt0(xS))))) & (![W0_3]: (aElementOf0(W0_3, xS) => aElementOf0(W0_3, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) & aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))))))).
% 0.21/0.72
% 0.21/0.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.72 fresh(y, y, x1...xn) = u
% 0.21/0.72 C => fresh(s, t, x1...xn) = v
% 0.21/0.72 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.72 variables of u and v.
% 0.21/0.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.72 input problem has no model of domain size 1).
% 0.21/0.72
% 0.21/0.72 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.72
% 0.21/0.72 Axiom 1 (mNATSet_1): isCountable0(szNzAzT0) = true2.
% 0.21/0.72 Axiom 2 (mEmpFin): isFinite0(slcrc0) = true2.
% 0.21/0.72 Axiom 3 (m__1986): aSet0(xS) = true2.
% 0.21/0.72 Axiom 4 (mNATSet): aSet0(szNzAzT0) = true2.
% 0.21/0.72 Axiom 5 (m__2035_4): fresh18(X, X) = true2.
% 0.21/0.72 Axiom 6 (m__2035_5): fresh17(X, X) = true2.
% 0.21/0.72 Axiom 7 (mZeroNum): aElementOf0(sz00, szNzAzT0) = true2.
% 0.21/0.72 Axiom 8 (mSuccNum_1): fresh25(X, X, Y) = true2.
% 0.21/0.72 Axiom 9 (m__1986_3): fresh22(X, X, Y) = true2.
% 0.21/0.72 Axiom 10 (m___1): fresh9(X, X, Y) = true2.
% 0.21/0.72 Axiom 11 (m__2035_4): fresh18(aElementOf0(X, xS), true2) = aElementOf0(szmzazxdt0(xS), xS).
% 0.21/0.72 Axiom 12 (mSuccNum_1): fresh25(aElementOf0(X, szNzAzT0), true2, X) = aElementOf0(szszuzczcdt0(X), szNzAzT0).
% 0.21/0.72 Axiom 13 (m__1986_3): fresh22(aElementOf0(X, xS), true2, X) = aElementOf0(X, szNzAzT0).
% 0.21/0.72 Axiom 14 (m___1): fresh9(aElementOf0(X, szNzAzT0), true2, X) = aElementOf0(w1(X), xS).
% 0.21/0.72 Axiom 15 (m__2035_5): fresh17(aElementOf0(X, xS), true2) = aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))).
% 0.21/0.72
% 0.21/0.72 Lemma 16: isFinite0(slcrc0) = isCountable0(szNzAzT0).
% 0.21/0.72 Proof:
% 0.21/0.72 isFinite0(slcrc0)
% 0.21/0.72 = { by axiom 2 (mEmpFin) }
% 0.21/0.72 true2
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 isCountable0(szNzAzT0)
% 0.21/0.72
% 0.21/0.72 Lemma 17: aSet0(xS) = isFinite0(slcrc0).
% 0.21/0.72 Proof:
% 0.21/0.72 aSet0(xS)
% 0.21/0.72 = { by axiom 3 (m__1986) }
% 0.21/0.72 true2
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 isCountable0(szNzAzT0)
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 isFinite0(slcrc0)
% 0.21/0.72
% 0.21/0.72 Lemma 18: aSet0(szNzAzT0) = aSet0(xS).
% 0.21/0.72 Proof:
% 0.21/0.72 aSet0(szNzAzT0)
% 0.21/0.72 = { by axiom 4 (mNATSet) }
% 0.21/0.72 true2
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 isCountable0(szNzAzT0)
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 isFinite0(slcrc0)
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 aSet0(xS)
% 0.21/0.72
% 0.21/0.72 Lemma 19: aElementOf0(w1(sz00), xS) = aSet0(szNzAzT0).
% 0.21/0.72 Proof:
% 0.21/0.72 aElementOf0(w1(sz00), xS)
% 0.21/0.72 = { by axiom 14 (m___1) R->L }
% 0.21/0.72 fresh9(aElementOf0(sz00, szNzAzT0), true2, sz00)
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 fresh9(aElementOf0(sz00, szNzAzT0), isCountable0(szNzAzT0), sz00)
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 fresh9(aElementOf0(sz00, szNzAzT0), isFinite0(slcrc0), sz00)
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 fresh9(aElementOf0(sz00, szNzAzT0), aSet0(xS), sz00)
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 fresh9(aElementOf0(sz00, szNzAzT0), aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by axiom 7 (mZeroNum) }
% 0.21/0.72 fresh9(true2, aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 fresh9(isCountable0(szNzAzT0), aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 fresh9(isFinite0(slcrc0), aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 fresh9(aSet0(xS), aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 fresh9(aSet0(szNzAzT0), aSet0(szNzAzT0), sz00)
% 0.21/0.72 = { by axiom 10 (m___1) }
% 0.21/0.72 true2
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 isCountable0(szNzAzT0)
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 isFinite0(slcrc0)
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 aSet0(xS)
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 aSet0(szNzAzT0)
% 0.21/0.72
% 0.21/0.72 Goal 1 (m___6): tuple2(aElementOf0(X, szNzAzT0), aSubsetOf0(xS, slbdtrb0(X))) = tuple2(true2, true2).
% 0.21/0.72 The goal is true when:
% 0.21/0.72 X = szszuzczcdt0(szmzazxdt0(xS))
% 0.21/0.72
% 0.21/0.72 Proof:
% 0.21/0.72 tuple2(aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 12 (mSuccNum_1) R->L }
% 0.21/0.72 tuple2(fresh25(aElementOf0(szmzazxdt0(xS), szNzAzT0), true2, szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 tuple2(fresh25(aElementOf0(szmzazxdt0(xS), szNzAzT0), isCountable0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 tuple2(fresh25(aElementOf0(szmzazxdt0(xS), szNzAzT0), isFinite0(slcrc0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 tuple2(fresh25(aElementOf0(szmzazxdt0(xS), szNzAzT0), aSet0(xS), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 tuple2(fresh25(aElementOf0(szmzazxdt0(xS), szNzAzT0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 13 (m__1986_3) R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(aElementOf0(szmzazxdt0(xS), xS), true2, szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(aElementOf0(szmzazxdt0(xS), xS), isCountable0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(aElementOf0(szmzazxdt0(xS), xS), isFinite0(slcrc0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(aElementOf0(szmzazxdt0(xS), xS), aSet0(xS), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(aElementOf0(szmzazxdt0(xS), xS), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 11 (m__2035_4) R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aElementOf0(w1(sz00), xS), true2), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aElementOf0(w1(sz00), xS), isCountable0(szNzAzT0)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aElementOf0(w1(sz00), xS), isFinite0(slcrc0)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 17 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aElementOf0(w1(sz00), xS), aSet0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 18 R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aElementOf0(w1(sz00), xS), aSet0(szNzAzT0)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 19 }
% 0.21/0.72 tuple2(fresh25(fresh22(fresh18(aSet0(szNzAzT0), aSet0(szNzAzT0)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 5 (m__2035_4) }
% 0.21/0.72 tuple2(fresh25(fresh22(true2, aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.72 tuple2(fresh25(fresh22(isCountable0(szNzAzT0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.72 = { by lemma 16 R->L }
% 0.21/0.73 tuple2(fresh25(fresh22(isFinite0(slcrc0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 17 R->L }
% 0.21/0.73 tuple2(fresh25(fresh22(aSet0(xS), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 18 R->L }
% 0.21/0.73 tuple2(fresh25(fresh22(aSet0(szNzAzT0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by axiom 9 (m__1986_3) }
% 0.21/0.73 tuple2(fresh25(true2, aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.73 tuple2(fresh25(isCountable0(szNzAzT0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 16 R->L }
% 0.21/0.73 tuple2(fresh25(isFinite0(slcrc0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 17 R->L }
% 0.21/0.73 tuple2(fresh25(aSet0(xS), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 18 R->L }
% 0.21/0.73 tuple2(fresh25(aSet0(szNzAzT0), aSet0(szNzAzT0), szmzazxdt0(xS)), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by axiom 8 (mSuccNum_1) }
% 0.21/0.73 tuple2(true2, aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.73 tuple2(isCountable0(szNzAzT0), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 16 R->L }
% 0.21/0.73 tuple2(isFinite0(slcrc0), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 17 R->L }
% 0.21/0.73 tuple2(aSet0(xS), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by lemma 18 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))
% 0.21/0.73 = { by axiom 15 (m__2035_5) R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aElementOf0(w1(sz00), xS), true2))
% 0.21/0.73 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aElementOf0(w1(sz00), xS), isCountable0(szNzAzT0)))
% 0.21/0.73 = { by lemma 16 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aElementOf0(w1(sz00), xS), isFinite0(slcrc0)))
% 0.21/0.73 = { by lemma 17 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aElementOf0(w1(sz00), xS), aSet0(xS)))
% 0.21/0.73 = { by lemma 18 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aElementOf0(w1(sz00), xS), aSet0(szNzAzT0)))
% 0.21/0.73 = { by lemma 19 }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), fresh17(aSet0(szNzAzT0), aSet0(szNzAzT0)))
% 0.21/0.73 = { by axiom 6 (m__2035_5) }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), true2)
% 0.21/0.73 = { by axiom 1 (mNATSet_1) R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), isCountable0(szNzAzT0))
% 0.21/0.73 = { by lemma 16 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), isFinite0(slcrc0))
% 0.21/0.73 = { by lemma 17 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), aSet0(xS))
% 0.21/0.73 = { by lemma 18 R->L }
% 0.21/0.73 tuple2(aSet0(szNzAzT0), aSet0(szNzAzT0))
% 0.21/0.73 = { by lemma 18 }
% 0.21/0.73 tuple2(aSet0(xS), aSet0(szNzAzT0))
% 0.21/0.73 = { by lemma 18 }
% 0.21/0.73 tuple2(aSet0(xS), aSet0(xS))
% 0.21/0.73 = { by lemma 17 }
% 0.21/0.73 tuple2(isFinite0(slcrc0), aSet0(xS))
% 0.21/0.73 = { by lemma 17 }
% 0.21/0.73 tuple2(isFinite0(slcrc0), isFinite0(slcrc0))
% 0.21/0.73 = { by lemma 16 }
% 0.21/0.73 tuple2(isCountable0(szNzAzT0), isFinite0(slcrc0))
% 0.21/0.73 = { by lemma 16 }
% 0.21/0.73 tuple2(isCountable0(szNzAzT0), isCountable0(szNzAzT0))
% 0.21/0.73 = { by axiom 1 (mNATSet_1) }
% 0.21/0.73 tuple2(true2, isCountable0(szNzAzT0))
% 0.21/0.73 = { by axiom 1 (mNATSet_1) }
% 0.21/0.73 tuple2(true2, true2)
% 0.21/0.73 % SZS output end Proof
% 0.21/0.73
% 0.21/0.73 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------