TSTP Solution File: RNG097+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG097+1 : 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 : n023.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 13:59:16 EDT 2023
% Result : Theorem 204.59s 26.02s
% Output : Proof 204.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG097+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 03:01:41 EDT 2023
% 0.11/0.33 % CPUTime :
% 204.59/26.02 Command-line arguments: --no-flatten-goal
% 204.59/26.02
% 204.59/26.02 % SZS status Theorem
% 204.59/26.02
% 204.75/26.05 % SZS output start Proof
% 204.75/26.05 Take the following subset of the input axioms:
% 204.75/26.05 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aElement0(W0) & (aElement0(W1) & aElement0(W2))) => sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)))).
% 204.75/26.05 fof(mAddInvr, axiom, ![W0_2]: (aElement0(W0_2) => (sdtpldt0(W0_2, smndt0(W0_2))=sz00 & sz00=sdtpldt0(smndt0(W0_2), W0_2)))).
% 204.75/26.05 fof(mAddZero, axiom, ![W0_2]: (aElement0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 204.75/26.05 fof(mDefIdeal, definition, ![W0_2]: (aIdeal0(W0_2) <=> (aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => (![W2_2]: (aElementOf0(W2_2, W0_2) => aElementOf0(sdtpldt0(W1_2, W2_2), W0_2)) & ![W2_2]: (aElement0(W2_2) => aElementOf0(sdtasdt0(W2_2, W1_2), W0_2))))))).
% 204.75/26.05 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 204.75/26.05 fof(mMulAsso, axiom, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aElement0(W1_2) & aElement0(W2_2))) => sdtasdt0(sdtasdt0(W0_2, W1_2), W2_2)=sdtasdt0(W0_2, sdtasdt0(W1_2, W2_2)))).
% 204.75/26.05 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 204.75/26.05 fof(mMulMnOne, axiom, ![W0_2]: (aElement0(W0_2) => (sdtasdt0(smndt0(sz10), W0_2)=smndt0(W0_2) & smndt0(W0_2)=sdtasdt0(W0_2, smndt0(sz10))))).
% 204.75/26.05 fof(mSortsC_01, axiom, aElement0(sz10)).
% 204.75/26.05 fof(mSortsU, axiom, ![W0_2]: (aElement0(W0_2) => aElement0(smndt0(W0_2)))).
% 204.75/26.05 fof(m__, conjecture, aElementOf0(sdtasdt0(xx, sdtpldt0(xb, smndt0(sz10))), xI)).
% 204.75/26.05 fof(m__1205, hypothesis, aIdeal0(xI) & aIdeal0(xJ)).
% 204.75/26.05 fof(m__1217, hypothesis, aElement0(xx) & aElement0(xy)).
% 204.75/26.05 fof(m__1294, hypothesis, aElementOf0(xa, xI) & (aElementOf0(xb, xJ) & sdtpldt0(xa, xb)=sz10)).
% 204.75/26.05
% 204.75/26.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 204.75/26.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 204.75/26.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 204.75/26.05 fresh(y, y, x1...xn) = u
% 204.75/26.05 C => fresh(s, t, x1...xn) = v
% 204.75/26.05 where fresh is a fresh function symbol and x1..xn are the free
% 204.75/26.05 variables of u and v.
% 204.75/26.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 204.75/26.05 input problem has no model of domain size 1).
% 204.75/26.05
% 204.75/26.05 The encoding turns the above axioms into the following unit equations and goals:
% 204.75/26.05
% 204.75/26.05 Axiom 1 (m__1205_1): aIdeal0(xJ) = true.
% 204.75/26.05 Axiom 2 (m__1205): aIdeal0(xI) = true.
% 204.75/26.05 Axiom 3 (m__1217): aElement0(xx) = true.
% 204.75/26.05 Axiom 4 (mSortsC_01): aElement0(sz10) = true.
% 204.75/26.05 Axiom 5 (m__1294): sdtpldt0(xa, xb) = sz10.
% 204.75/26.05 Axiom 6 (m__1294_1): aElementOf0(xa, xI) = true.
% 204.75/26.05 Axiom 7 (m__1294_2): aElementOf0(xb, xJ) = true.
% 204.75/26.05 Axiom 8 (mAddInvr): fresh39(X, X, Y) = sz00.
% 204.75/26.05 Axiom 9 (mAddInvr_1): fresh38(X, X, Y) = sz00.
% 204.75/26.05 Axiom 10 (mDefIdeal_7): fresh34(X, X, Y) = true.
% 204.75/26.05 Axiom 11 (mEOfElem): fresh23(X, X, Y) = true.
% 204.75/26.05 Axiom 12 (mMulMnOne_1): fresh14(X, X, Y) = smndt0(Y).
% 204.75/26.05 Axiom 13 (mSortsU): fresh7(X, X, Y) = true.
% 204.75/26.05 Axiom 14 (mAddZero_1): fresh5(X, X, Y) = Y.
% 204.75/26.05 Axiom 15 (mAddZero): fresh4(X, X, Y) = Y.
% 204.75/26.05 Axiom 16 (mAddInvr): fresh39(aElement0(X), true, X) = sdtpldt0(X, smndt0(X)).
% 204.75/26.05 Axiom 17 (mAddInvr_1): fresh38(aElement0(X), true, X) = sdtpldt0(smndt0(X), X).
% 204.75/26.05 Axiom 18 (mDefIdeal_7): fresh34(aIdeal0(X), true, X) = aSet0(X).
% 204.75/26.05 Axiom 19 (mEOfElem): fresh24(X, X, Y, Z) = aElement0(Z).
% 204.75/26.05 Axiom 20 (mMulComm): fresh17(X, X, Y, Z) = sdtasdt0(Y, Z).
% 204.75/26.05 Axiom 21 (mMulComm): fresh16(X, X, Y, Z) = sdtasdt0(Z, Y).
% 204.75/26.05 Axiom 22 (mMulMnOne_1): fresh14(aElement0(X), true, X) = sdtasdt0(smndt0(sz10), X).
% 204.75/26.05 Axiom 23 (mSortsU): fresh7(aElement0(X), true, X) = aElement0(smndt0(X)).
% 204.75/26.05 Axiom 24 (mAddZero_1): fresh5(aElement0(X), true, X) = sdtpldt0(sz00, X).
% 204.75/26.05 Axiom 25 (mAddZero): fresh4(aElement0(X), true, X) = sdtpldt0(X, sz00).
% 204.75/26.05 Axiom 26 (mAddAsso): fresh102(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 204.75/26.05 Axiom 27 (mMulAsso): fresh100(X, X, Y, Z, W) = sdtasdt0(Y, sdtasdt0(Z, W)).
% 204.75/26.05 Axiom 28 (mDefIdeal): fresh54(X, X, Y, Z, W) = true.
% 204.75/26.05 Axiom 29 (mAddAsso): fresh42(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 204.75/26.05 Axiom 30 (mDefIdeal): fresh37(X, X, Y, Z, W) = aElementOf0(sdtasdt0(W, Z), Y).
% 204.75/26.05 Axiom 31 (mMulAsso): fresh18(X, X, Y, Z, W) = sdtasdt0(sdtasdt0(Y, Z), W).
% 204.75/26.05 Axiom 32 (mMulComm): fresh17(aElement0(X), true, Y, X) = fresh16(aElement0(Y), true, Y, X).
% 204.75/26.05 Axiom 33 (mAddAsso): fresh101(X, X, Y, Z, W) = fresh102(aElement0(Y), true, Y, Z, W).
% 204.75/26.05 Axiom 34 (mMulAsso): fresh99(X, X, Y, Z, W) = fresh100(aElement0(Y), true, Y, Z, W).
% 204.75/26.05 Axiom 35 (mDefIdeal): fresh53(X, X, Y, Z, W) = fresh54(aElement0(W), true, Y, Z, W).
% 204.75/26.05 Axiom 36 (mAddAsso): fresh101(aElement0(X), true, Y, Z, X) = fresh42(aElement0(Z), true, Y, Z, X).
% 204.75/26.05 Axiom 37 (mEOfElem): fresh24(aElementOf0(X, Y), true, Y, X) = fresh23(aSet0(Y), true, X).
% 204.75/26.05 Axiom 38 (mMulAsso): fresh99(aElement0(X), true, Y, Z, X) = fresh18(aElement0(Z), true, Y, Z, X).
% 204.75/26.05 Axiom 39 (mDefIdeal): fresh53(aIdeal0(X), true, X, Y, Z) = fresh37(aElementOf0(Y, X), true, X, Y, Z).
% 204.75/26.05
% 204.75/26.05 Lemma 40: aElement0(xb) = true.
% 204.75/26.05 Proof:
% 204.75/26.05 aElement0(xb)
% 204.75/26.05 = { by axiom 19 (mEOfElem) R->L }
% 204.75/26.05 fresh24(true, true, xJ, xb)
% 204.75/26.05 = { by axiom 7 (m__1294_2) R->L }
% 204.75/26.05 fresh24(aElementOf0(xb, xJ), true, xJ, xb)
% 204.75/26.05 = { by axiom 37 (mEOfElem) }
% 204.75/26.05 fresh23(aSet0(xJ), true, xb)
% 204.75/26.05 = { by axiom 18 (mDefIdeal_7) R->L }
% 204.75/26.05 fresh23(fresh34(aIdeal0(xJ), true, xJ), true, xb)
% 204.75/26.05 = { by axiom 1 (m__1205_1) }
% 204.75/26.05 fresh23(fresh34(true, true, xJ), true, xb)
% 204.75/26.05 = { by axiom 10 (mDefIdeal_7) }
% 204.75/26.05 fresh23(true, true, xb)
% 204.75/26.05 = { by axiom 11 (mEOfElem) }
% 204.75/26.05 true
% 204.75/26.05
% 204.75/26.05 Lemma 41: aElement0(xa) = true.
% 204.75/26.05 Proof:
% 204.75/26.05 aElement0(xa)
% 204.75/26.05 = { by axiom 19 (mEOfElem) R->L }
% 204.75/26.05 fresh24(true, true, xI, xa)
% 204.75/26.05 = { by axiom 6 (m__1294_1) R->L }
% 204.75/26.05 fresh24(aElementOf0(xa, xI), true, xI, xa)
% 204.75/26.05 = { by axiom 37 (mEOfElem) }
% 204.75/26.05 fresh23(aSet0(xI), true, xa)
% 204.75/26.05 = { by axiom 18 (mDefIdeal_7) R->L }
% 204.75/26.05 fresh23(fresh34(aIdeal0(xI), true, xI), true, xa)
% 204.75/26.05 = { by axiom 2 (m__1205) }
% 204.75/26.05 fresh23(fresh34(true, true, xI), true, xa)
% 204.75/26.05 = { by axiom 10 (mDefIdeal_7) }
% 204.75/26.05 fresh23(true, true, xa)
% 204.75/26.05 = { by axiom 11 (mEOfElem) }
% 204.75/26.05 true
% 204.75/26.05
% 204.75/26.05 Lemma 42: aElement0(smndt0(sz10)) = true.
% 204.75/26.05 Proof:
% 204.75/26.05 aElement0(smndt0(sz10))
% 204.75/26.05 = { by axiom 23 (mSortsU) R->L }
% 204.75/26.05 fresh7(aElement0(sz10), true, sz10)
% 204.75/26.05 = { by axiom 4 (mSortsC_01) }
% 204.75/26.05 fresh7(true, true, sz10)
% 204.75/26.05 = { by axiom 13 (mSortsU) }
% 204.75/26.05 true
% 204.75/26.05
% 204.75/26.05 Lemma 43: aElement0(smndt0(xa)) = true.
% 204.75/26.05 Proof:
% 204.75/26.05 aElement0(smndt0(xa))
% 204.75/26.05 = { by axiom 23 (mSortsU) R->L }
% 204.75/26.05 fresh7(aElement0(xa), true, xa)
% 204.75/26.05 = { by lemma 41 }
% 204.75/26.05 fresh7(true, true, xa)
% 204.75/26.05 = { by axiom 13 (mSortsU) }
% 204.75/26.05 true
% 204.75/26.05
% 204.75/26.05 Lemma 44: fresh17(aElement0(X), true, xx, X) = sdtasdt0(X, xx).
% 204.75/26.05 Proof:
% 204.75/26.05 fresh17(aElement0(X), true, xx, X)
% 204.75/26.05 = { by axiom 32 (mMulComm) }
% 204.75/26.05 fresh16(aElement0(xx), true, xx, X)
% 204.75/26.05 = { by axiom 3 (m__1217) }
% 204.75/26.05 fresh16(true, true, xx, X)
% 204.75/26.05 = { by axiom 21 (mMulComm) }
% 204.75/26.05 sdtasdt0(X, xx)
% 204.75/26.05
% 204.75/26.05 Lemma 45: fresh101(X, X, smndt0(xa), Y, Z) = sdtpldt0(smndt0(xa), sdtpldt0(Y, Z)).
% 204.75/26.05 Proof:
% 204.75/26.05 fresh101(X, X, smndt0(xa), Y, Z)
% 204.75/26.05 = { by axiom 33 (mAddAsso) }
% 204.75/26.05 fresh102(aElement0(smndt0(xa)), true, smndt0(xa), Y, Z)
% 204.75/26.05 = { by lemma 43 }
% 204.75/26.05 fresh102(true, true, smndt0(xa), Y, Z)
% 204.75/26.05 = { by axiom 26 (mAddAsso) }
% 204.75/26.05 sdtpldt0(smndt0(xa), sdtpldt0(Y, Z))
% 204.75/26.05
% 204.75/26.05 Lemma 46: fresh99(X, X, smndt0(sz10), Y, Z) = sdtasdt0(smndt0(sz10), sdtasdt0(Y, Z)).
% 204.75/26.05 Proof:
% 204.75/26.05 fresh99(X, X, smndt0(sz10), Y, Z)
% 204.75/26.05 = { by axiom 34 (mMulAsso) }
% 204.75/26.05 fresh100(aElement0(smndt0(sz10)), true, smndt0(sz10), Y, Z)
% 204.75/26.05 = { by lemma 42 }
% 204.75/26.05 fresh100(true, true, smndt0(sz10), Y, Z)
% 204.75/26.05 = { by axiom 27 (mMulAsso) }
% 204.75/26.06 sdtasdt0(smndt0(sz10), sdtasdt0(Y, Z))
% 204.75/26.06
% 204.75/26.06 Goal 1 (m__): aElementOf0(sdtasdt0(xx, sdtpldt0(xb, smndt0(sz10))), xI) = true.
% 204.75/26.06 Proof:
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(xb, smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 14 (mAddZero_1) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh5(true, true, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 40 R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh5(aElement0(xb), true, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 24 (mAddZero_1) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(sz00, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 9 (mAddInvr_1) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(fresh38(true, true, xa), xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 41 R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(fresh38(aElement0(xa), true, xa), xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 17 (mAddInvr_1) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(sdtpldt0(smndt0(xa), xa), xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 29 (mAddAsso) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh42(true, true, smndt0(xa), xa, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 41 R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh42(aElement0(xa), true, smndt0(xa), xa, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 36 (mAddAsso) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh101(aElement0(xb), true, smndt0(xa), xa, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 40 }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(fresh101(true, true, smndt0(xa), xa, xb), smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 45 }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(smndt0(xa), sdtpldt0(xa, xb)), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 5 (m__1294) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(sdtpldt0(smndt0(xa), sz10), smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 29 (mAddAsso) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh42(true, true, smndt0(xa), sz10, smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 4 (mSortsC_01) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh42(aElement0(sz10), true, smndt0(xa), sz10, smndt0(sz10))), xI)
% 204.75/26.06 = { by axiom 36 (mAddAsso) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh101(aElement0(smndt0(sz10)), true, smndt0(xa), sz10, smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 42 }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh101(true, true, smndt0(xa), sz10, smndt0(sz10))), xI)
% 204.75/26.06 = { by lemma 45 }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(smndt0(xa), sdtpldt0(sz10, smndt0(sz10)))), xI)
% 204.75/26.06 = { by axiom 16 (mAddInvr) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(smndt0(xa), fresh39(aElement0(sz10), true, sz10))), xI)
% 204.75/26.06 = { by axiom 4 (mSortsC_01) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(smndt0(xa), fresh39(true, true, sz10))), xI)
% 204.75/26.06 = { by axiom 8 (mAddInvr) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, sdtpldt0(smndt0(xa), sz00)), xI)
% 204.75/26.06 = { by axiom 25 (mAddZero) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh4(aElement0(smndt0(xa)), true, smndt0(xa))), xI)
% 204.75/26.06 = { by lemma 43 }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, fresh4(true, true, smndt0(xa))), xI)
% 204.75/26.06 = { by axiom 15 (mAddZero) }
% 204.75/26.06 aElementOf0(sdtasdt0(xx, smndt0(xa)), xI)
% 204.75/26.06 = { by axiom 20 (mMulComm) R->L }
% 204.75/26.06 aElementOf0(fresh17(true, true, xx, smndt0(xa)), xI)
% 204.75/26.06 = { by lemma 43 R->L }
% 204.75/26.06 aElementOf0(fresh17(aElement0(smndt0(xa)), true, xx, smndt0(xa)), xI)
% 204.75/26.06 = { by lemma 44 }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(xa), xx), xI)
% 204.75/26.06 = { by axiom 12 (mMulMnOne_1) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(fresh14(true, true, xa), xx), xI)
% 204.75/26.06 = { by lemma 41 R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(fresh14(aElement0(xa), true, xa), xx), xI)
% 204.75/26.06 = { by axiom 22 (mMulMnOne_1) }
% 204.75/26.06 aElementOf0(sdtasdt0(sdtasdt0(smndt0(sz10), xa), xx), xI)
% 204.75/26.06 = { by axiom 31 (mMulAsso) R->L }
% 204.75/26.06 aElementOf0(fresh18(true, true, smndt0(sz10), xa, xx), xI)
% 204.75/26.06 = { by lemma 41 R->L }
% 204.75/26.06 aElementOf0(fresh18(aElement0(xa), true, smndt0(sz10), xa, xx), xI)
% 204.75/26.06 = { by axiom 38 (mMulAsso) R->L }
% 204.75/26.06 aElementOf0(fresh99(aElement0(xx), true, smndt0(sz10), xa, xx), xI)
% 204.75/26.06 = { by axiom 3 (m__1217) }
% 204.75/26.06 aElementOf0(fresh99(true, true, smndt0(sz10), xa, xx), xI)
% 204.75/26.06 = { by lemma 46 }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(sz10), sdtasdt0(xa, xx)), xI)
% 204.75/26.06 = { by lemma 44 R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(sz10), fresh17(aElement0(xa), true, xx, xa)), xI)
% 204.75/26.06 = { by lemma 41 }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(sz10), fresh17(true, true, xx, xa)), xI)
% 204.75/26.06 = { by axiom 20 (mMulComm) }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(sz10), sdtasdt0(xx, xa)), xI)
% 204.75/26.06 = { by lemma 46 R->L }
% 204.75/26.06 aElementOf0(fresh99(true, true, smndt0(sz10), xx, xa), xI)
% 204.75/26.06 = { by lemma 41 R->L }
% 204.75/26.06 aElementOf0(fresh99(aElement0(xa), true, smndt0(sz10), xx, xa), xI)
% 204.75/26.06 = { by axiom 38 (mMulAsso) }
% 204.75/26.06 aElementOf0(fresh18(aElement0(xx), true, smndt0(sz10), xx, xa), xI)
% 204.75/26.06 = { by axiom 3 (m__1217) }
% 204.75/26.06 aElementOf0(fresh18(true, true, smndt0(sz10), xx, xa), xI)
% 204.75/26.06 = { by axiom 31 (mMulAsso) }
% 204.75/26.06 aElementOf0(sdtasdt0(sdtasdt0(smndt0(sz10), xx), xa), xI)
% 204.75/26.06 = { by axiom 22 (mMulMnOne_1) R->L }
% 204.75/26.06 aElementOf0(sdtasdt0(fresh14(aElement0(xx), true, xx), xa), xI)
% 204.75/26.06 = { by axiom 3 (m__1217) }
% 204.75/26.06 aElementOf0(sdtasdt0(fresh14(true, true, xx), xa), xI)
% 204.75/26.06 = { by axiom 12 (mMulMnOne_1) }
% 204.75/26.06 aElementOf0(sdtasdt0(smndt0(xx), xa), xI)
% 204.75/26.06 = { by axiom 30 (mDefIdeal) R->L }
% 204.75/26.06 fresh37(true, true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 6 (m__1294_1) R->L }
% 204.75/26.06 fresh37(aElementOf0(xa, xI), true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 39 (mDefIdeal) R->L }
% 204.75/26.06 fresh53(aIdeal0(xI), true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 2 (m__1205) }
% 204.75/26.06 fresh53(true, true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 35 (mDefIdeal) }
% 204.75/26.06 fresh54(aElement0(smndt0(xx)), true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 23 (mSortsU) R->L }
% 204.75/26.06 fresh54(fresh7(aElement0(xx), true, xx), true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 3 (m__1217) }
% 204.75/26.06 fresh54(fresh7(true, true, xx), true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 13 (mSortsU) }
% 204.75/26.06 fresh54(true, true, xI, xa, smndt0(xx))
% 204.75/26.06 = { by axiom 28 (mDefIdeal) }
% 204.75/26.06 true
% 204.75/26.06 % SZS output end Proof
% 204.75/26.06
% 204.75/26.06 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------