TSTP Solution File: RNG099+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG099+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 : n022.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 13:59:17 EDT 2023
% Result : Theorem 35.51s 5.01s
% Output : Proof 36.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG099+2 : 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
% 0.16/0.35 % Computer : n022.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 02:44:10 EDT 2023
% 0.16/0.35 % CPUTime :
% 35.51/5.01 Command-line arguments: --flatten
% 35.51/5.01
% 35.51/5.01 % SZS status Theorem
% 35.51/5.01
% 36.12/5.04 % SZS output start Proof
% 36.12/5.04 Take the following subset of the input axioms:
% 36.12/5.04 fof(mEOfElem, axiom, ![W0]: (aSet0(W0) => ![W1]: (aElementOf0(W1, W0) => aElement0(W1)))).
% 36.12/5.04 fof(mSortsB, axiom, ![W1_2, W0_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtpldt0(W0_2, W1_2)))).
% 36.12/5.04 fof(mSortsB_02, axiom, ![W1_2, W0_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtasdt0(W0_2, W1_2)))).
% 36.12/5.04 fof(mSortsC, axiom, aElement0(sz00)).
% 36.12/5.04 fof(mSortsC_01, axiom, aElement0(sz10)).
% 36.12/5.04 fof(m__, conjecture, ?[W0_2]: (aElement0(W0_2) & ((aElementOf0(sdtpldt0(W0_2, smndt0(xx)), xI) | sdteqdtlpzmzozddtrp0(W0_2, xx, xI)) & (aElementOf0(sdtpldt0(W0_2, smndt0(xy)), xJ) | sdteqdtlpzmzozddtrp0(W0_2, xy, xJ))))).
% 36.12/5.04 fof(m__1205, hypothesis, aSet0(xI) & (![W0_2]: (aElementOf0(W0_2, xI) => (![W1_2]: (aElementOf0(W1_2, xI) => aElementOf0(sdtpldt0(W0_2, W1_2), xI)) & ![W1_2]: (aElement0(W1_2) => aElementOf0(sdtasdt0(W1_2, W0_2), xI)))) & (aIdeal0(xI) & (aSet0(xJ) & (![W0_2]: (aElementOf0(W0_2, xJ) => (![W1_2]: (aElementOf0(W1_2, xJ) => aElementOf0(sdtpldt0(W0_2, W1_2), xJ)) & ![W1_2]: (aElement0(W1_2) => aElementOf0(sdtasdt0(W1_2, W0_2), xJ)))) & aIdeal0(xJ)))))).
% 36.12/5.04 fof(m__1217, hypothesis, aElement0(xx) & aElement0(xy)).
% 36.12/5.04 fof(m__1294, hypothesis, aElementOf0(xa, xI) & (aElementOf0(xb, xJ) & sdtpldt0(xa, xb)=sz10)).
% 36.12/5.04 fof(m__1319, hypothesis, xw=sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb))).
% 36.12/5.04 fof(m__1332, hypothesis, aElementOf0(sdtpldt0(xw, smndt0(xx)), xI)).
% 36.12/5.04 fof(m__1409, hypothesis, aElementOf0(sdtpldt0(xw, smndt0(xy)), xJ)).
% 36.12/5.04
% 36.12/5.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 36.12/5.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 36.12/5.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 36.12/5.04 fresh(y, y, x1...xn) = u
% 36.12/5.04 C => fresh(s, t, x1...xn) = v
% 36.12/5.04 where fresh is a fresh function symbol and x1..xn are the free
% 36.12/5.04 variables of u and v.
% 36.12/5.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 36.12/5.04 input problem has no model of domain size 1).
% 36.12/5.04
% 36.12/5.04 The encoding turns the above axioms into the following unit equations and goals:
% 36.12/5.04
% 36.12/5.04 Axiom 1 (m__1205_2): aIdeal0(xI) = true2.
% 36.12/5.04 Axiom 2 (m__1205): aSet0(xI) = true2.
% 36.12/5.04 Axiom 3 (m__1205_1): aSet0(xJ) = true2.
% 36.12/5.04 Axiom 4 (mSortsC_01): aElement0(sz10) = true2.
% 36.12/5.04 Axiom 5 (mSortsC): aElement0(sz00) = true2.
% 36.12/5.04 Axiom 6 (m__1217): aElement0(xx) = true2.
% 36.12/5.04 Axiom 7 (m__1217_1): aElement0(xy) = true2.
% 36.12/5.04 Axiom 8 (m__1294_1): aElementOf0(xa, xI) = true2.
% 36.12/5.04 Axiom 9 (m__1294_2): aElementOf0(xb, xJ) = true2.
% 36.12/5.04 Axiom 10 (mEOfElem): fresh34(X, X, Y) = true2.
% 36.12/5.04 Axiom 11 (mEOfElem): fresh35(X, X, Y, Z) = aElement0(Z).
% 36.12/5.04 Axiom 12 (mSortsB): fresh22(X, X, Y, Z) = aElement0(sdtpldt0(Y, Z)).
% 36.12/5.04 Axiom 13 (mSortsB): fresh21(X, X, Y, Z) = true2.
% 36.12/5.04 Axiom 14 (mSortsB_02): fresh20(X, X, Y, Z) = aElement0(sdtasdt0(Y, Z)).
% 36.12/5.04 Axiom 15 (mSortsB_02): fresh19(X, X, Y, Z) = true2.
% 36.12/5.04 Axiom 16 (mSortsB): fresh22(aElement0(X), true2, Y, X) = fresh21(aElement0(Y), true2, Y, X).
% 36.12/5.04 Axiom 17 (mSortsB_02): fresh20(aElement0(X), true2, Y, X) = fresh19(aElement0(Y), true2, Y, X).
% 36.12/5.04 Axiom 18 (mDefMod_1): fresh61(X, X, Y, Z, W) = aElementOf0(sdtpldt0(Y, smndt0(Z)), W).
% 36.12/5.04 Axiom 19 (m__1332): aElementOf0(sdtpldt0(xw, smndt0(xx)), xI) = true2.
% 36.12/5.04 Axiom 20 (m__1409): aElementOf0(sdtpldt0(xw, smndt0(xy)), xJ) = true2.
% 36.12/5.04 Axiom 21 (mEOfElem): fresh35(aElementOf0(X, Y), true2, Y, X) = fresh34(aSet0(Y), true2, X).
% 36.12/5.04 Axiom 22 (m__1319): xw = sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)).
% 36.12/5.04
% 36.12/5.04 Lemma 23: aSet0(xI) = aIdeal0(xI).
% 36.12/5.04 Proof:
% 36.12/5.04 aSet0(xI)
% 36.12/5.04 = { by axiom 2 (m__1205) }
% 36.12/5.04 true2
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 aIdeal0(xI)
% 36.12/5.04
% 36.12/5.04 Lemma 24: aElement0(sz10) = aSet0(xI).
% 36.12/5.04 Proof:
% 36.12/5.04 aElement0(sz10)
% 36.12/5.04 = { by axiom 4 (mSortsC_01) }
% 36.12/5.04 true2
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 aIdeal0(xI)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 aSet0(xI)
% 36.12/5.04
% 36.12/5.04 Lemma 25: aElement0(sz00) = aElement0(sz10).
% 36.12/5.04 Proof:
% 36.12/5.04 aElement0(sz00)
% 36.12/5.04 = { by axiom 5 (mSortsC) }
% 36.12/5.04 true2
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 aIdeal0(xI)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 aSet0(xI)
% 36.12/5.04 = { by lemma 24 R->L }
% 36.12/5.04 aElement0(sz10)
% 36.12/5.04
% 36.12/5.04 Lemma 26: fresh34(X, X, Y) = aElement0(sz00).
% 36.12/5.04 Proof:
% 36.12/5.04 fresh34(X, X, Y)
% 36.12/5.04 = { by axiom 10 (mEOfElem) }
% 36.12/5.04 true2
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 aIdeal0(xI)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 aSet0(xI)
% 36.12/5.04 = { by lemma 24 R->L }
% 36.12/5.04 aElement0(sz10)
% 36.12/5.04 = { by lemma 25 R->L }
% 36.12/5.04 aElement0(sz00)
% 36.12/5.04
% 36.12/5.04 Lemma 27: fresh19(X, X, Y, Z) = aElement0(sz00).
% 36.12/5.04 Proof:
% 36.12/5.04 fresh19(X, X, Y, Z)
% 36.12/5.04 = { by axiom 15 (mSortsB_02) }
% 36.12/5.04 true2
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 aIdeal0(xI)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 aSet0(xI)
% 36.12/5.04 = { by lemma 24 R->L }
% 36.12/5.04 aElement0(sz10)
% 36.12/5.04 = { by lemma 25 R->L }
% 36.12/5.04 aElement0(sz00)
% 36.12/5.04
% 36.12/5.04 Lemma 28: fresh19(aElement0(Y), aElement0(sz00), Y, X) = fresh20(aElement0(X), aElement0(sz00), Y, X).
% 36.12/5.04 Proof:
% 36.12/5.04 fresh19(aElement0(Y), aElement0(sz00), Y, X)
% 36.12/5.04 = { by lemma 25 }
% 36.12/5.04 fresh19(aElement0(Y), aElement0(sz10), Y, X)
% 36.12/5.04 = { by lemma 24 }
% 36.12/5.04 fresh19(aElement0(Y), aSet0(xI), Y, X)
% 36.12/5.04 = { by lemma 23 }
% 36.12/5.04 fresh19(aElement0(Y), aIdeal0(xI), Y, X)
% 36.12/5.04 = { by axiom 1 (m__1205_2) }
% 36.12/5.04 fresh19(aElement0(Y), true2, Y, X)
% 36.12/5.04 = { by axiom 17 (mSortsB_02) R->L }
% 36.12/5.04 fresh20(aElement0(X), true2, Y, X)
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 fresh20(aElement0(X), aIdeal0(xI), Y, X)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 fresh20(aElement0(X), aSet0(xI), Y, X)
% 36.12/5.04 = { by lemma 24 R->L }
% 36.12/5.04 fresh20(aElement0(X), aElement0(sz10), Y, X)
% 36.12/5.04 = { by lemma 25 R->L }
% 36.12/5.04 fresh20(aElement0(X), aElement0(sz00), Y, X)
% 36.12/5.04
% 36.12/5.04 Lemma 29: fresh35(aElementOf0(X, Y), aElement0(sz00), Y, X) = fresh34(aSet0(Y), aElement0(sz00), X).
% 36.12/5.04 Proof:
% 36.12/5.04 fresh35(aElementOf0(X, Y), aElement0(sz00), Y, X)
% 36.12/5.04 = { by lemma 25 }
% 36.12/5.04 fresh35(aElementOf0(X, Y), aElement0(sz10), Y, X)
% 36.12/5.04 = { by lemma 24 }
% 36.12/5.04 fresh35(aElementOf0(X, Y), aSet0(xI), Y, X)
% 36.12/5.04 = { by lemma 23 }
% 36.12/5.04 fresh35(aElementOf0(X, Y), aIdeal0(xI), Y, X)
% 36.12/5.04 = { by axiom 1 (m__1205_2) }
% 36.12/5.04 fresh35(aElementOf0(X, Y), true2, Y, X)
% 36.12/5.04 = { by axiom 21 (mEOfElem) }
% 36.12/5.04 fresh34(aSet0(Y), true2, X)
% 36.12/5.04 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.04 fresh34(aSet0(Y), aIdeal0(xI), X)
% 36.12/5.04 = { by lemma 23 R->L }
% 36.12/5.04 fresh34(aSet0(Y), aSet0(xI), X)
% 36.12/5.04 = { by lemma 24 R->L }
% 36.12/5.04 fresh34(aSet0(Y), aElement0(sz10), X)
% 36.12/5.04 = { by lemma 25 R->L }
% 36.12/5.04 fresh34(aSet0(Y), aElement0(sz00), X)
% 36.12/5.04
% 36.12/5.04 Goal 1 (m__): tuple(aElement0(X), aElementOf0(sdtpldt0(X, smndt0(xx)), xI), aElementOf0(sdtpldt0(X, smndt0(xy)), xJ)) = tuple(true2, true2, true2).
% 36.12/5.04 The goal is true when:
% 36.12/5.04 X = sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb))
% 36.12/5.04
% 36.12/5.04 Proof:
% 36.12/5.04 tuple(aElement0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb))), aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), smndt0(xx)), xI), aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), smndt0(xy)), xJ))
% 36.12/5.04 = { by axiom 18 (mDefMod_1) R->L }
% 36.12/5.04 tuple(aElement0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb))), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), smndt0(xy)), xJ))
% 36.12/5.04 = { by axiom 18 (mDefMod_1) R->L }
% 36.12/5.04 tuple(aElement0(sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb))), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.04 = { by axiom 12 (mSortsB) R->L }
% 36.12/5.04 tuple(fresh22(aElement0(sz00), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.04 = { by lemma 27 R->L }
% 36.12/5.04 tuple(fresh22(fresh19(aElement0(sz00), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(fresh22(fresh19(aElement0(sz10), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(fresh22(fresh19(aSet0(xI), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(fresh22(fresh19(aIdeal0(xI), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(fresh22(fresh19(true2, aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 6 (m__1217) R->L }
% 36.12/5.05 tuple(fresh22(fresh19(aElement0(xx), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 28 }
% 36.12/5.05 tuple(fresh22(fresh20(aElement0(xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 11 (mEOfElem) R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(aElement0(sz00), aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(aElement0(sz10), aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(aSet0(xI), aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(aIdeal0(xI), aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(true2, aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 9 (m__1294_2) R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh35(aElementOf0(xb, xJ), aElement0(sz00), xJ, xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 29 }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(aSet0(xJ), aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 3 (m__1205_1) }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(true2, aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(aIdeal0(xI), aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(aSet0(xI), aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(aElement0(sz10), aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(fresh22(fresh20(fresh34(aElement0(sz00), aElement0(sz00), xb), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 26 }
% 36.12/5.05 tuple(fresh22(fresh20(aElement0(sz00), aElement0(sz00), xx, xb), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 14 (mSortsB_02) }
% 36.12/5.05 tuple(fresh22(aElement0(sdtasdt0(xx, xb)), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(fresh22(aElement0(sdtasdt0(xx, xb)), aElement0(sz10), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(fresh22(aElement0(sdtasdt0(xx, xb)), aSet0(xI), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(fresh22(aElement0(sdtasdt0(xx, xb)), aIdeal0(xI), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(fresh22(aElement0(sdtasdt0(xx, xb)), true2, sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 16 (mSortsB) }
% 36.12/5.05 tuple(fresh21(aElement0(sdtasdt0(xy, xa)), true2, sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(fresh21(aElement0(sdtasdt0(xy, xa)), aIdeal0(xI), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(fresh21(aElement0(sdtasdt0(xy, xa)), aSet0(xI), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(fresh21(aElement0(sdtasdt0(xy, xa)), aElement0(sz10), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(fresh21(aElement0(sdtasdt0(xy, xa)), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 14 (mSortsB_02) R->L }
% 36.12/5.05 tuple(fresh21(fresh20(aElement0(sz00), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 26 R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh34(aElement0(sz00), aElement0(sz00), xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(fresh21(fresh20(fresh34(aElement0(sz10), aElement0(sz00), xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(fresh21(fresh20(fresh34(aSet0(xI), aElement0(sz00), xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 29 R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(aElementOf0(xa, xI), aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 8 (m__1294_1) }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(true2, aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(aIdeal0(xI), aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(aSet0(xI), aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(aElement0(sz10), aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(fresh21(fresh20(fresh35(aElement0(sz00), aElement0(sz00), xI, xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 11 (mEOfElem) }
% 36.12/5.05 tuple(fresh21(fresh20(aElement0(xa), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 28 R->L }
% 36.12/5.05 tuple(fresh21(fresh19(aElement0(xy), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 7 (m__1217_1) }
% 36.12/5.05 tuple(fresh21(fresh19(true2, aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(fresh21(fresh19(aIdeal0(xI), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(fresh21(fresh19(aSet0(xI), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(fresh21(fresh19(aElement0(sz10), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(fresh21(fresh19(aElement0(sz00), aElement0(sz00), xy, xa), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 27 }
% 36.12/5.05 tuple(fresh21(aElement0(sz00), aElement0(sz00), sdtasdt0(xy, xa), sdtasdt0(xx, xb)), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 13 (mSortsB) }
% 36.12/5.05 tuple(true2, fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(aIdeal0(xI), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(aSet0(xI), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(aElement0(sz10), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(aElement0(sz00), fresh61(Y, Y, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 22 (m__1319) R->L }
% 36.12/5.05 tuple(aElement0(sz00), fresh61(Y, Y, xw, xx, xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 18 (mDefMod_1) }
% 36.12/5.05 tuple(aElement0(sz00), aElementOf0(sdtpldt0(xw, smndt0(xx)), xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 19 (m__1332) }
% 36.12/5.05 tuple(aElement0(sz00), true2, fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(aElement0(sz00), aIdeal0(xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aSet0(xI), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz10), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), fresh61(X, X, sdtpldt0(sdtasdt0(xy, xa), sdtasdt0(xx, xb)), xy, xJ))
% 36.12/5.05 = { by axiom 22 (m__1319) R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), fresh61(X, X, xw, xy, xJ))
% 36.12/5.05 = { by axiom 18 (mDefMod_1) }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), aElementOf0(sdtpldt0(xw, smndt0(xy)), xJ))
% 36.12/5.05 = { by axiom 20 (m__1409) }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), true2)
% 36.12/5.05 = { by axiom 1 (m__1205_2) R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), aIdeal0(xI))
% 36.12/5.05 = { by lemma 23 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), aSet0(xI))
% 36.12/5.05 = { by lemma 24 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), aElement0(sz10))
% 36.12/5.05 = { by lemma 25 R->L }
% 36.12/5.05 tuple(aElement0(sz00), aElement0(sz00), aElement0(sz00))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(aElement0(sz10), aElement0(sz00), aElement0(sz00))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(aElement0(sz10), aElement0(sz10), aElement0(sz00))
% 36.12/5.05 = { by lemma 25 }
% 36.12/5.05 tuple(aElement0(sz10), aElement0(sz10), aElement0(sz10))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(aSet0(xI), aElement0(sz10), aElement0(sz10))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(aSet0(xI), aSet0(xI), aElement0(sz10))
% 36.12/5.05 = { by lemma 24 }
% 36.12/5.05 tuple(aSet0(xI), aSet0(xI), aSet0(xI))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(aIdeal0(xI), aSet0(xI), aSet0(xI))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(aIdeal0(xI), aIdeal0(xI), aSet0(xI))
% 36.12/5.05 = { by lemma 23 }
% 36.12/5.05 tuple(aIdeal0(xI), aIdeal0(xI), aIdeal0(xI))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(true2, aIdeal0(xI), aIdeal0(xI))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(true2, true2, aIdeal0(xI))
% 36.12/5.05 = { by axiom 1 (m__1205_2) }
% 36.12/5.05 tuple(true2, true2, true2)
% 36.12/5.05 % SZS output end Proof
% 36.12/5.05
% 36.12/5.05 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------