TSTP Solution File: RNG044+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG044+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 : n009.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 13:59:01 EDT 2023
% Result : Theorem 33.60s 4.64s
% Output : Proof 34.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG044+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 02:01:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 33.60/4.64 Command-line arguments: --flatten
% 33.60/4.64
% 33.60/4.64 % SZS status Theorem
% 33.60/4.64
% 34.19/4.65 % SZS output start Proof
% 34.19/4.65 Take the following subset of the input axioms:
% 34.19/4.66 fof(mArith, axiom, ![W0, W1, W2]: ((aScalar0(W0) & (aScalar0(W1) & aScalar0(W2))) => (sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)) & (sdtpldt0(W0, W1)=sdtpldt0(W1, W0) & (sdtasdt0(sdtasdt0(W0, W1), W2)=sdtasdt0(W0, sdtasdt0(W1, W2)) & sdtasdt0(W0, W1)=sdtasdt0(W1, W0)))))).
% 34.19/4.66 fof(mDistr, axiom, ![W0_2, W1_2, W2_2]: ((aScalar0(W0_2) & (aScalar0(W1_2) & aScalar0(W2_2))) => (sdtasdt0(W0_2, sdtpldt0(W1_2, W2_2))=sdtpldt0(sdtasdt0(W0_2, W1_2), sdtasdt0(W0_2, W2_2)) & sdtasdt0(sdtpldt0(W0_2, W1_2), W2_2)=sdtpldt0(sdtasdt0(W0_2, W2_2), sdtasdt0(W1_2, W2_2))))).
% 34.19/4.66 fof(mSZeroSc, axiom, aScalar0(sz0z00)).
% 34.19/4.66 fof(mSumSc, axiom, ![W0_2, W1_2]: ((aScalar0(W0_2) & aScalar0(W1_2)) => aScalar0(sdtpldt0(W0_2, W1_2)))).
% 34.19/4.66 fof(mZeroNat, axiom, aNaturalNumber0(sz00)).
% 34.19/4.66 fof(m__, conjecture, sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv))=sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))).
% 34.19/4.66 fof(m__674, hypothesis, aScalar0(xx) & (aScalar0(xy) & (aScalar0(xu) & aScalar0(xv)))).
% 34.19/4.66
% 34.19/4.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 34.19/4.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 34.19/4.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 34.19/4.66 fresh(y, y, x1...xn) = u
% 34.19/4.66 C => fresh(s, t, x1...xn) = v
% 34.19/4.66 where fresh is a fresh function symbol and x1..xn are the free
% 34.19/4.66 variables of u and v.
% 34.19/4.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 34.19/4.66 input problem has no model of domain size 1).
% 34.19/4.66
% 34.19/4.66 The encoding turns the above axioms into the following unit equations and goals:
% 34.19/4.66
% 34.19/4.66 Axiom 1 (mZeroNat): aNaturalNumber0(sz00) = true2.
% 34.19/4.66 Axiom 2 (mSZeroSc): aScalar0(sz0z00) = true2.
% 34.19/4.66 Axiom 3 (m__674): aScalar0(xx) = true2.
% 34.19/4.66 Axiom 4 (m__674_1): aScalar0(xy) = true2.
% 34.19/4.66 Axiom 5 (m__674_2): aScalar0(xu) = true2.
% 34.19/4.66 Axiom 6 (m__674_3): aScalar0(xv) = true2.
% 34.19/4.66 Axiom 7 (mArith_2): fresh32(X, X, Y, Z) = sdtasdt0(Z, Y).
% 34.19/4.66 Axiom 8 (mArith_2): fresh20(X, X, Y, Z) = sdtasdt0(Y, Z).
% 34.19/4.66 Axiom 9 (mSumSc): fresh6(X, X, Y, Z) = aScalar0(sdtpldt0(Y, Z)).
% 34.19/4.66 Axiom 10 (mSumSc): fresh5(X, X, Y, Z) = true2.
% 34.19/4.66 Axiom 11 (mArith_2): fresh31(X, X, Y, Z) = fresh32(aScalar0(Y), true2, Y, Z).
% 34.19/4.66 Axiom 12 (mDistr): fresh24(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 34.19/4.66 Axiom 13 (mArith_2): fresh31(aScalar0(X), true2, Y, Z) = fresh20(aScalar0(Z), true2, Y, Z).
% 34.19/4.66 Axiom 14 (mSumSc): fresh6(aScalar0(X), true2, Y, X) = fresh5(aScalar0(Y), true2, Y, X).
% 34.19/4.66 Axiom 15 (mDistr): fresh23(X, X, Y, Z, W) = fresh24(aScalar0(Y), true2, Y, Z, W).
% 34.19/4.66 Axiom 16 (mDistr): fresh23(aScalar0(X), true2, Y, Z, X) = fresh18(aScalar0(Z), true2, Y, Z, X).
% 34.19/4.66 Axiom 17 (mDistr): fresh18(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 34.19/4.66
% 34.19/4.66 Lemma 18: aScalar0(xv) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 aScalar0(xv)
% 34.19/4.66 = { by axiom 6 (m__674_3) }
% 34.19/4.66 true2
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 19: aScalar0(xu) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 aScalar0(xu)
% 34.19/4.66 = { by axiom 5 (m__674_2) }
% 34.19/4.66 true2
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 20: aScalar0(xy) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 aScalar0(xy)
% 34.19/4.66 = { by axiom 4 (m__674_1) }
% 34.19/4.66 true2
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 21: aScalar0(xx) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 aScalar0(xx)
% 34.19/4.66 = { by axiom 3 (m__674) }
% 34.19/4.66 true2
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 22: fresh5(aScalar0(Y), aNaturalNumber0(sz00), Y, X) = fresh6(aScalar0(X), aNaturalNumber0(sz00), Y, X).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh5(aScalar0(Y), aNaturalNumber0(sz00), Y, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh5(aScalar0(Y), true2, Y, X)
% 34.19/4.66 = { by axiom 14 (mSumSc) R->L }
% 34.19/4.66 fresh6(aScalar0(X), true2, Y, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh6(aScalar0(X), aNaturalNumber0(sz00), Y, X)
% 34.19/4.66
% 34.19/4.66 Lemma 23: fresh5(X, X, Y, Z) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh5(X, X, Y, Z)
% 34.19/4.66 = { by axiom 10 (mSumSc) }
% 34.19/4.66 true2
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 24: aScalar0(sdtpldt0(xu, xv)) = aNaturalNumber0(sz00).
% 34.19/4.66 Proof:
% 34.19/4.66 aScalar0(sdtpldt0(xu, xv))
% 34.19/4.66 = { by axiom 9 (mSumSc) R->L }
% 34.19/4.66 fresh6(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xu, xv)
% 34.19/4.66 = { by lemma 18 R->L }
% 34.19/4.66 fresh6(aScalar0(xv), aNaturalNumber0(sz00), xu, xv)
% 34.19/4.66 = { by lemma 22 R->L }
% 34.19/4.66 fresh5(aScalar0(xu), aNaturalNumber0(sz00), xu, xv)
% 34.19/4.66 = { by lemma 19 }
% 34.19/4.66 fresh5(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xu, xv)
% 34.19/4.66 = { by lemma 23 }
% 34.19/4.66 aNaturalNumber0(sz00)
% 34.19/4.66
% 34.19/4.66 Lemma 25: fresh18(aScalar0(Z), aNaturalNumber0(sz00), Y, Z, X) = fresh23(aScalar0(X), aNaturalNumber0(sz00), Y, Z, X).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh18(aScalar0(Z), aNaturalNumber0(sz00), Y, Z, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh18(aScalar0(Z), true2, Y, Z, X)
% 34.19/4.66 = { by axiom 16 (mDistr) R->L }
% 34.19/4.66 fresh23(aScalar0(X), true2, Y, Z, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh23(aScalar0(X), aNaturalNumber0(sz00), Y, Z, X)
% 34.19/4.66
% 34.19/4.66 Lemma 26: fresh18(X, X, Y, xu, xv) = fresh23(Z, Z, Y, xu, xv).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh18(X, X, Y, xu, xv)
% 34.19/4.66 = { by axiom 17 (mDistr) }
% 34.19/4.66 sdtpldt0(sdtasdt0(Y, xu), sdtasdt0(Y, xv))
% 34.19/4.66 = { by axiom 17 (mDistr) R->L }
% 34.19/4.66 fresh18(aNaturalNumber0(sz00), aNaturalNumber0(sz00), Y, xu, xv)
% 34.19/4.66 = { by lemma 19 R->L }
% 34.19/4.66 fresh18(aScalar0(xu), aNaturalNumber0(sz00), Y, xu, xv)
% 34.19/4.66 = { by lemma 25 }
% 34.19/4.66 fresh23(aScalar0(xv), aNaturalNumber0(sz00), Y, xu, xv)
% 34.19/4.66 = { by lemma 18 }
% 34.19/4.66 fresh23(aNaturalNumber0(sz00), aNaturalNumber0(sz00), Y, xu, xv)
% 34.19/4.66 = { by axiom 15 (mDistr) }
% 34.19/4.66 fresh24(aScalar0(Y), true2, Y, xu, xv)
% 34.19/4.66 = { by axiom 15 (mDistr) R->L }
% 34.19/4.66 fresh23(Z, Z, Y, xu, xv)
% 34.19/4.66
% 34.19/4.66 Lemma 27: fresh20(aScalar0(X), aNaturalNumber0(sz00), Y, X) = fresh31(aScalar0(Z), aNaturalNumber0(sz00), Y, X).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh20(aScalar0(X), aNaturalNumber0(sz00), Y, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh20(aScalar0(X), true2, Y, X)
% 34.19/4.66 = { by axiom 13 (mArith_2) R->L }
% 34.19/4.66 fresh31(aScalar0(Z), true2, Y, X)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh31(aScalar0(Z), aNaturalNumber0(sz00), Y, X)
% 34.19/4.66
% 34.19/4.66 Lemma 28: fresh31(X, X, sdtpldt0(xu, xv), Y) = sdtasdt0(Y, sdtpldt0(xu, xv)).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh31(X, X, sdtpldt0(xu, xv), Y)
% 34.19/4.66 = { by axiom 11 (mArith_2) }
% 34.19/4.66 fresh32(aScalar0(sdtpldt0(xu, xv)), true2, sdtpldt0(xu, xv), Y)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh32(aScalar0(sdtpldt0(xu, xv)), aNaturalNumber0(sz00), sdtpldt0(xu, xv), Y)
% 34.19/4.66 = { by lemma 24 }
% 34.19/4.66 fresh32(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), Y)
% 34.19/4.66 = { by axiom 7 (mArith_2) }
% 34.19/4.66 sdtasdt0(Y, sdtpldt0(xu, xv))
% 34.19/4.66
% 34.19/4.66 Lemma 29: fresh31(aScalar0(X), aNaturalNumber0(sz00), Y, Z) = fresh31(W, W, Y, Z).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh31(aScalar0(X), aNaturalNumber0(sz00), Y, Z)
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh31(aScalar0(X), true2, Y, Z)
% 34.19/4.66 = { by axiom 13 (mArith_2) }
% 34.19/4.66 fresh20(aScalar0(Z), true2, Y, Z)
% 34.19/4.66 = { by axiom 13 (mArith_2) R->L }
% 34.19/4.66 fresh31(aScalar0(sz0z00), true2, Y, Z)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh31(aScalar0(sz0z00), aNaturalNumber0(sz00), Y, Z)
% 34.19/4.66 = { by axiom 2 (mSZeroSc) }
% 34.19/4.66 fresh31(true2, aNaturalNumber0(sz00), Y, Z)
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh31(aNaturalNumber0(sz00), aNaturalNumber0(sz00), Y, Z)
% 34.19/4.66 = { by axiom 11 (mArith_2) }
% 34.19/4.66 fresh32(aScalar0(Y), true2, Y, Z)
% 34.19/4.66 = { by axiom 11 (mArith_2) R->L }
% 34.19/4.66 fresh31(W, W, Y, Z)
% 34.19/4.66
% 34.19/4.66 Lemma 30: fresh24(aScalar0(X), aNaturalNumber0(sz00), X, Y, Z) = fresh23(W, W, X, Y, Z).
% 34.19/4.66 Proof:
% 34.19/4.66 fresh24(aScalar0(X), aNaturalNumber0(sz00), X, Y, Z)
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh24(aScalar0(X), true2, X, Y, Z)
% 34.19/4.66 = { by axiom 15 (mDistr) R->L }
% 34.19/4.66 fresh23(W, W, X, Y, Z)
% 34.19/4.66
% 34.19/4.66 Goal 1 (m__): sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv))).
% 34.19/4.66 Proof:
% 34.19/4.66 sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv))
% 34.19/4.66 = { by lemma 28 R->L }
% 34.19/4.66 fresh31(X, X, sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by lemma 29 R->L }
% 34.19/4.66 fresh31(aScalar0(Y), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 1 (mZeroNat) }
% 34.19/4.66 fresh31(aScalar0(Y), true2, sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 13 (mArith_2) }
% 34.19/4.66 fresh20(aScalar0(sdtpldt0(xx, xy)), true2, sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 1 (mZeroNat) R->L }
% 34.19/4.66 fresh20(aScalar0(sdtpldt0(xx, xy)), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 9 (mSumSc) R->L }
% 34.19/4.66 fresh20(fresh6(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xx, xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by lemma 20 R->L }
% 34.19/4.66 fresh20(fresh6(aScalar0(xy), aNaturalNumber0(sz00), xx, xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by lemma 22 R->L }
% 34.19/4.66 fresh20(fresh5(aScalar0(xx), aNaturalNumber0(sz00), xx, xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by lemma 21 }
% 34.19/4.66 fresh20(fresh5(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xx, xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by lemma 23 }
% 34.19/4.66 fresh20(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 8 (mArith_2) }
% 34.19/4.66 sdtasdt0(sdtpldt0(xu, xv), sdtpldt0(xx, xy))
% 34.19/4.66 = { by axiom 12 (mDistr) R->L }
% 34.19/4.66 fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by lemma 24 R->L }
% 34.19/4.66 fresh24(aScalar0(sdtpldt0(xu, xv)), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by lemma 30 }
% 34.19/4.66 fresh23(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by lemma 20 R->L }
% 34.19/4.66 fresh23(aScalar0(xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by lemma 25 R->L }
% 34.19/4.66 fresh18(aScalar0(xx), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by lemma 21 }
% 34.19/4.66 fresh18(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx, xy)
% 34.19/4.66 = { by axiom 17 (mDistr) }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), sdtasdt0(sdtpldt0(xu, xv), xy))
% 34.19/4.66 = { by axiom 8 (mArith_2) R->L }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), fresh20(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xy))
% 34.19/4.66 = { by lemma 20 R->L }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), fresh20(aScalar0(xy), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xy))
% 34.19/4.66 = { by lemma 27 }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), fresh31(aScalar0(Z), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xy))
% 34.19/4.66 = { by lemma 29 }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), fresh31(W, W, sdtpldt0(xu, xv), xy))
% 34.19/4.66 = { by lemma 28 }
% 34.19/4.66 sdtpldt0(sdtasdt0(sdtpldt0(xu, xv), xx), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by axiom 8 (mArith_2) R->L }
% 34.19/4.66 sdtpldt0(fresh20(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 21 R->L }
% 34.19/4.66 sdtpldt0(fresh20(aScalar0(xx), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 27 }
% 34.19/4.66 sdtpldt0(fresh31(aScalar0(V), aNaturalNumber0(sz00), sdtpldt0(xu, xv), xx), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 29 }
% 34.19/4.66 sdtpldt0(fresh31(U, U, sdtpldt0(xu, xv), xx), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 28 }
% 34.19/4.66 sdtpldt0(sdtasdt0(xx, sdtpldt0(xu, xv)), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by axiom 12 (mDistr) R->L }
% 34.19/4.66 sdtpldt0(fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 21 R->L }
% 34.19/4.66 sdtpldt0(fresh24(aScalar0(xx), aNaturalNumber0(sz00), xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 30 }
% 34.19/4.66 sdtpldt0(fresh23(T, T, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by lemma 26 R->L }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 34.19/4.66 = { by axiom 12 (mDistr) R->L }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xy, xu, xv))
% 34.19/4.66 = { by lemma 20 R->L }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), fresh24(aScalar0(xy), aNaturalNumber0(sz00), xy, xu, xv))
% 34.19/4.66 = { by lemma 30 }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), fresh23(X2, X2, xy, xu, xv))
% 34.19/4.66 = { by lemma 26 R->L }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), fresh18(Y2, Y2, xy, xu, xv))
% 34.19/4.66 = { by axiom 17 (mDistr) }
% 34.19/4.66 sdtpldt0(fresh18(S, S, xx, xu, xv), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))
% 34.19/4.66 = { by axiom 17 (mDistr) }
% 34.19/4.66 sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))
% 34.19/4.66 % SZS output end Proof
% 34.19/4.66
% 34.19/4.66 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------