TSTP Solution File: NUM459+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM459+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 : n004.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 11:56:24 EDT 2023
% Result : Theorem 38.77s 5.39s
% Output : Proof 39.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM459+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
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 13:08:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 38.77/5.39 Command-line arguments: --flatten
% 38.77/5.39
% 38.77/5.39 % SZS status Theorem
% 38.77/5.39
% 39.41/5.46 % SZS output start Proof
% 39.41/5.46 Take the following subset of the input axioms:
% 39.41/5.47 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aNaturalNumber0(W0) & (aNaturalNumber0(W1) & aNaturalNumber0(W2))) => sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)))).
% 39.41/5.47 fof(mAddCanc, axiom, ![W0_2, W1_2, W2_2]: ((aNaturalNumber0(W0_2) & (aNaturalNumber0(W1_2) & aNaturalNumber0(W2_2))) => ((sdtpldt0(W0_2, W1_2)=sdtpldt0(W0_2, W2_2) | sdtpldt0(W1_2, W0_2)=sdtpldt0(W2_2, W0_2)) => W1_2=W2_2))).
% 39.41/5.47 fof(mAddComm, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => sdtpldt0(W0_2, W1_2)=sdtpldt0(W1_2, W0_2))).
% 39.41/5.47 fof(mSortsB, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => aNaturalNumber0(sdtpldt0(W0_2, W1_2)))).
% 39.41/5.47 fof(mSortsC, axiom, aNaturalNumber0(sz00)).
% 39.41/5.47 fof(mSortsC_01, axiom, aNaturalNumber0(sz10) & sz10!=sz00).
% 39.41/5.47 fof(mZeroAdd, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => (sdtpldt0(W0_2, W1_2)=sz00 => (W0_2=sz00 & W1_2=sz00)))).
% 39.41/5.47 fof(m_AddZero, axiom, ![W0_2]: (aNaturalNumber0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 39.41/5.47 fof(m__, conjecture, (?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xm, W0_2)=xn) & (sdtlseqdt0(xm, xn) & (?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xn, W0_2)=xm) & sdtlseqdt0(xn, xm)))) => xm=xn).
% 39.41/5.47 fof(m__745, hypothesis, aNaturalNumber0(xm) & aNaturalNumber0(xn)).
% 39.41/5.47
% 39.41/5.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.41/5.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.41/5.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.41/5.47 fresh(y, y, x1...xn) = u
% 39.41/5.47 C => fresh(s, t, x1...xn) = v
% 39.41/5.47 where fresh is a fresh function symbol and x1..xn are the free
% 39.41/5.47 variables of u and v.
% 39.41/5.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.41/5.47 input problem has no model of domain size 1).
% 39.41/5.47
% 39.41/5.47 The encoding turns the above axioms into the following unit equations and goals:
% 39.41/5.47
% 39.41/5.47 Axiom 1 (m___2): aNaturalNumber0(w0_2) = true.
% 39.41/5.47 Axiom 2 (m___3): aNaturalNumber0(w0) = true.
% 39.41/5.47 Axiom 3 (mSortsC_01): aNaturalNumber0(sz10) = true.
% 39.41/5.47 Axiom 4 (m__745): aNaturalNumber0(xm) = true.
% 39.41/5.47 Axiom 5 (m__745_1): aNaturalNumber0(xn) = true.
% 39.41/5.47 Axiom 6 (mSortsC): aNaturalNumber0(sz00) = true.
% 39.41/5.47 Axiom 7 (m__): sdtpldt0(xm, w0_2) = xn.
% 39.41/5.47 Axiom 8 (m___1): sdtpldt0(xn, w0) = xm.
% 39.41/5.47 Axiom 9 (mZeroAdd): fresh48(X, X, Y) = sz00.
% 39.41/5.47 Axiom 10 (m_AddZero_1): fresh10(X, X, Y) = Y.
% 39.41/5.47 Axiom 11 (mAddComm): fresh24(X, X, Y, Z) = sdtpldt0(Y, Z).
% 39.41/5.47 Axiom 12 (mAddComm): fresh23(X, X, Y, Z) = sdtpldt0(Z, Y).
% 39.41/5.47 Axiom 13 (mSortsB): fresh16(X, X, Y, Z) = aNaturalNumber0(sdtpldt0(Y, Z)).
% 39.41/5.47 Axiom 14 (mSortsB): fresh15(X, X, Y, Z) = true.
% 39.41/5.47 Axiom 15 (m_AddZero_1): fresh10(aNaturalNumber0(X), true, X) = sdtpldt0(sz00, X).
% 39.41/5.47 Axiom 16 (mAddCanc_1): fresh6(X, X, Y, Z) = Z.
% 39.41/5.47 Axiom 17 (mZeroAdd): fresh3(X, X, Y, Z) = Y.
% 39.41/5.47 Axiom 18 (mAddAsso): fresh64(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 39.41/5.47 Axiom 19 (mAddCanc_1): fresh56(X, X, Y, Z, W) = Z.
% 39.41/5.47 Axiom 20 (mZeroAdd): fresh47(X, X, Y, Z) = fresh48(sdtpldt0(Y, Z), sz00, Y).
% 39.41/5.47 Axiom 21 (mAddAsso): fresh25(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 39.41/5.47 Axiom 22 (mAddComm): fresh24(aNaturalNumber0(X), true, Y, X) = fresh23(aNaturalNumber0(Y), true, Y, X).
% 39.41/5.47 Axiom 23 (mSortsB): fresh16(aNaturalNumber0(X), true, Y, X) = fresh15(aNaturalNumber0(Y), true, Y, X).
% 39.41/5.47 Axiom 24 (mZeroAdd): fresh47(aNaturalNumber0(X), true, Y, X) = fresh3(aNaturalNumber0(Y), true, Y, X).
% 39.41/5.47 Axiom 25 (mAddAsso): fresh63(X, X, Y, Z, W) = fresh64(aNaturalNumber0(Y), true, Y, Z, W).
% 39.41/5.47 Axiom 26 (mAddCanc_1): fresh55(X, X, Y, Z, W) = fresh56(aNaturalNumber0(Y), true, Y, Z, W).
% 39.41/5.47 Axiom 27 (mAddCanc_1): fresh54(X, X, Y, Z, W) = fresh55(aNaturalNumber0(Z), true, Y, Z, W).
% 39.41/5.47 Axiom 28 (mAddAsso): fresh63(aNaturalNumber0(X), true, Y, Z, X) = fresh25(aNaturalNumber0(Z), true, Y, Z, X).
% 39.41/5.47 Axiom 29 (mAddCanc_1): fresh54(aNaturalNumber0(X), true, Y, Z, X) = fresh6(sdtpldt0(Z, Y), sdtpldt0(X, Y), Z, X).
% 39.41/5.47
% 39.41/5.47 Lemma 30: aNaturalNumber0(sz10) = aNaturalNumber0(w0_2).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(sz10)
% 39.41/5.47 = { by axiom 3 (mSortsC_01) }
% 39.41/5.47 true
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 aNaturalNumber0(w0_2)
% 39.41/5.47
% 39.41/5.47 Lemma 31: aNaturalNumber0(sz00) = aNaturalNumber0(sz10).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(sz00)
% 39.41/5.47 = { by axiom 6 (mSortsC) }
% 39.41/5.47 true
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 aNaturalNumber0(w0_2)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 aNaturalNumber0(sz10)
% 39.41/5.47
% 39.41/5.47 Lemma 32: aNaturalNumber0(xn) = aNaturalNumber0(sz10).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(xn)
% 39.41/5.47 = { by axiom 5 (m__745_1) }
% 39.41/5.47 true
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 aNaturalNumber0(w0_2)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 aNaturalNumber0(sz10)
% 39.41/5.47
% 39.41/5.47 Lemma 33: aNaturalNumber0(xm) = aNaturalNumber0(sz10).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(xm)
% 39.41/5.47 = { by axiom 4 (m__745) }
% 39.41/5.47 true
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 aNaturalNumber0(w0_2)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 aNaturalNumber0(sz10)
% 39.41/5.47
% 39.41/5.47 Lemma 34: aNaturalNumber0(w0) = aNaturalNumber0(w0_2).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(w0)
% 39.41/5.47 = { by axiom 2 (m___3) }
% 39.41/5.47 true
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 aNaturalNumber0(w0_2)
% 39.41/5.47
% 39.41/5.47 Lemma 35: aNaturalNumber0(sdtpldt0(xn, w0)) = aNaturalNumber0(sz00).
% 39.41/5.47 Proof:
% 39.41/5.47 aNaturalNumber0(sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 8 (m___1) }
% 39.41/5.47 aNaturalNumber0(xm)
% 39.41/5.47 = { by lemma 33 }
% 39.41/5.47 aNaturalNumber0(sz10)
% 39.41/5.47 = { by lemma 31 R->L }
% 39.41/5.47 aNaturalNumber0(sz00)
% 39.41/5.47
% 39.41/5.47 Lemma 36: fresh10(aNaturalNumber0(X), aNaturalNumber0(sz00), X) = sdtpldt0(sz00, X).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh10(aNaturalNumber0(X), aNaturalNumber0(sz00), X)
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh10(aNaturalNumber0(X), aNaturalNumber0(sz10), X)
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh10(aNaturalNumber0(X), aNaturalNumber0(w0_2), X)
% 39.41/5.47 = { by axiom 1 (m___2) }
% 39.41/5.47 fresh10(aNaturalNumber0(X), true, X)
% 39.41/5.47 = { by axiom 15 (m_AddZero_1) }
% 39.41/5.47 sdtpldt0(sz00, X)
% 39.41/5.47
% 39.41/5.47 Lemma 37: fresh23(aNaturalNumber0(Y), aNaturalNumber0(sz00), Y, X) = fresh24(aNaturalNumber0(X), aNaturalNumber0(sz00), Y, X).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh23(aNaturalNumber0(Y), aNaturalNumber0(sz00), Y, X)
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh23(aNaturalNumber0(Y), aNaturalNumber0(sz10), Y, X)
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh23(aNaturalNumber0(Y), aNaturalNumber0(w0_2), Y, X)
% 39.41/5.47 = { by axiom 1 (m___2) }
% 39.41/5.47 fresh23(aNaturalNumber0(Y), true, Y, X)
% 39.41/5.47 = { by axiom 22 (mAddComm) R->L }
% 39.41/5.47 fresh24(aNaturalNumber0(X), true, Y, X)
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 fresh24(aNaturalNumber0(X), aNaturalNumber0(w0_2), Y, X)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 fresh24(aNaturalNumber0(X), aNaturalNumber0(sz10), Y, X)
% 39.41/5.47 = { by lemma 31 R->L }
% 39.41/5.47 fresh24(aNaturalNumber0(X), aNaturalNumber0(sz00), Y, X)
% 39.41/5.47
% 39.41/5.47 Lemma 38: fresh24(aNaturalNumber0(X), aNaturalNumber0(sz00), w0_2, X) = sdtpldt0(X, w0_2).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh24(aNaturalNumber0(X), aNaturalNumber0(sz00), w0_2, X)
% 39.41/5.47 = { by lemma 37 R->L }
% 39.41/5.47 fresh23(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, X)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 fresh23(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, X)
% 39.41/5.47 = { by lemma 31 R->L }
% 39.41/5.47 fresh23(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, X)
% 39.41/5.47 = { by axiom 12 (mAddComm) }
% 39.41/5.47 sdtpldt0(X, w0_2)
% 39.41/5.47
% 39.41/5.47 Lemma 39: fresh56(aNaturalNumber0(X), aNaturalNumber0(sz00), X, Y, Z) = fresh55(W, W, X, Y, Z).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh56(aNaturalNumber0(X), aNaturalNumber0(sz00), X, Y, Z)
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh56(aNaturalNumber0(X), aNaturalNumber0(sz10), X, Y, Z)
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh56(aNaturalNumber0(X), aNaturalNumber0(w0_2), X, Y, Z)
% 39.41/5.47 = { by axiom 1 (m___2) }
% 39.41/5.47 fresh56(aNaturalNumber0(X), true, X, Y, Z)
% 39.41/5.47 = { by axiom 26 (mAddCanc_1) R->L }
% 39.41/5.47 fresh55(W, W, X, Y, Z)
% 39.41/5.47
% 39.41/5.47 Lemma 40: fresh55(aNaturalNumber0(X), aNaturalNumber0(sz00), Y, X, Z) = fresh54(W, W, Y, X, Z).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh55(aNaturalNumber0(X), aNaturalNumber0(sz00), Y, X, Z)
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh55(aNaturalNumber0(X), aNaturalNumber0(sz10), Y, X, Z)
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh55(aNaturalNumber0(X), aNaturalNumber0(w0_2), Y, X, Z)
% 39.41/5.47 = { by axiom 1 (m___2) }
% 39.41/5.47 fresh55(aNaturalNumber0(X), true, Y, X, Z)
% 39.41/5.47 = { by axiom 27 (mAddCanc_1) R->L }
% 39.41/5.47 fresh54(W, W, Y, X, Z)
% 39.41/5.47
% 39.41/5.47 Lemma 41: fresh6(sdtpldt0(X, Y), sdtpldt0(Z, Y), X, Z) = fresh54(aNaturalNumber0(Z), aNaturalNumber0(sz00), Y, X, Z).
% 39.41/5.47 Proof:
% 39.41/5.47 fresh6(sdtpldt0(X, Y), sdtpldt0(Z, Y), X, Z)
% 39.41/5.47 = { by axiom 29 (mAddCanc_1) R->L }
% 39.41/5.47 fresh54(aNaturalNumber0(Z), true, Y, X, Z)
% 39.41/5.47 = { by axiom 1 (m___2) R->L }
% 39.41/5.47 fresh54(aNaturalNumber0(Z), aNaturalNumber0(w0_2), Y, X, Z)
% 39.41/5.47 = { by lemma 30 R->L }
% 39.41/5.47 fresh54(aNaturalNumber0(Z), aNaturalNumber0(sz10), Y, X, Z)
% 39.41/5.47 = { by lemma 31 R->L }
% 39.41/5.47 fresh54(aNaturalNumber0(Z), aNaturalNumber0(sz00), Y, X, Z)
% 39.41/5.47
% 39.41/5.47 Goal 1 (m___6): xm = xn.
% 39.41/5.47 Proof:
% 39.41/5.47 xm
% 39.41/5.47 = { by axiom 8 (m___1) R->L }
% 39.41/5.47 sdtpldt0(xn, w0)
% 39.41/5.47 = { by axiom 16 (mAddCanc_1) R->L }
% 39.41/5.47 fresh6(sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 7 (m__) }
% 39.41/5.47 fresh6(xn, sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 10 (m_AddZero_1) R->L }
% 39.41/5.47 fresh6(fresh10(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh6(fresh10(aNaturalNumber0(sz10), aNaturalNumber0(sz00), xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 32 R->L }
% 39.41/5.47 fresh6(fresh10(aNaturalNumber0(xn), aNaturalNumber0(sz00), xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 36 }
% 39.41/5.47 fresh6(sdtpldt0(sz00, xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 7 (m__) R->L }
% 39.41/5.47 fresh6(sdtpldt0(sz00, sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 9 (mZeroAdd) R->L }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(sz00, sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 19 (mAddCanc_1) R->L }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh56(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xm, sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh56(aNaturalNumber0(sz10), aNaturalNumber0(sz00), xm, sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 33 R->L }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh56(aNaturalNumber0(xm), aNaturalNumber0(sz00), xm, sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 39 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh55(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xm, sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 8 (m___1) R->L }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh55(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 40 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(aNaturalNumber0(sz00), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(aNaturalNumber0(sz10), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 1 (m___2) }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(true, aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by axiom 14 (mSortsB) R->L }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 31 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.47 = { by lemma 30 }
% 39.41/5.47 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(w0_2), aNaturalNumber0(sz10), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(w0_2), aNaturalNumber0(w0_2), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 1 (m___2) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh15(aNaturalNumber0(w0_2), true, w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 23 (mSortsB) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(w0), true, w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 1 (m___2) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(w0), aNaturalNumber0(w0_2), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(w0), aNaturalNumber0(sz10), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(w0), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 34 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(fresh16(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, w0), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 13 (mSortsB) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh54(aNaturalNumber0(sdtpldt0(w0_2, w0)), aNaturalNumber0(sz00), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 41 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(sz00, sdtpldt0(xn, w0)), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 8 (m___1) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(sz00, xm), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 36 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(fresh10(aNaturalNumber0(xm), aNaturalNumber0(sz00), xm), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 33 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(fresh10(aNaturalNumber0(sz10), aNaturalNumber0(sz00), xm), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(fresh10(aNaturalNumber0(sz00), aNaturalNumber0(sz00), xm), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 10 (m_AddZero_1) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(xm, sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 8 (m___1) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(sdtpldt0(w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 11 (mAddComm) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(fresh24(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(fresh24(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 34 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(fresh24(aNaturalNumber0(w0), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 38 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(sdtpldt0(w0, w0_2), sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 21 (mAddAsso) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(w0_2), aNaturalNumber0(sz10), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(w0_2), aNaturalNumber0(w0_2), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 1 (m___2) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh25(aNaturalNumber0(w0_2), true, w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 28 (mAddAsso) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh63(aNaturalNumber0(sdtpldt0(xn, w0)), true, w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 1 (m___2) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh63(aNaturalNumber0(sdtpldt0(xn, w0)), aNaturalNumber0(w0_2), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh63(aNaturalNumber0(sdtpldt0(xn, w0)), aNaturalNumber0(sz10), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh63(aNaturalNumber0(sdtpldt0(xn, w0)), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 35 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh63(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 25 (mAddAsso) }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(w0), true, w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by axiom 1 (m___2) R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(w0), aNaturalNumber0(w0_2), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(w0), aNaturalNumber0(sz10), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 31 R->L }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(w0), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 34 }
% 39.41/5.48 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.48 = { by lemma 30 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh64(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0, w0_2, sdtpldt0(xn, w0)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 18 (mAddAsso) }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, sdtpldt0(w0_2, sdtpldt0(xn, w0))), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 8 (m___1) }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, sdtpldt0(w0_2, xm)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 11 (mAddComm) R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, xm)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, fresh24(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, xm)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 33 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, fresh24(aNaturalNumber0(xm), aNaturalNumber0(sz00), w0_2, xm)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 38 }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, sdtpldt0(xm, w0_2)), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 7 (m__) }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 11 (mAddComm) R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh24(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 32 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh24(aNaturalNumber0(xn), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 37 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh23(aNaturalNumber0(w0), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 34 }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh23(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 30 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh23(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), fresh23(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0, xn), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 12 (mAddComm) }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(fresh6(sdtpldt0(xn, w0), sdtpldt0(xn, w0), sz00, sdtpldt0(w0_2, w0)), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 16 (mAddCanc_1) }
% 39.41/5.49 fresh6(sdtpldt0(fresh48(sdtpldt0(w0_2, w0), sz00, w0_2), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 20 (mZeroAdd) R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 30 }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 34 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(w0), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(w0), aNaturalNumber0(sz10), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 30 }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(w0), aNaturalNumber0(w0_2), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 1 (m___2) }
% 39.41/5.49 fresh6(sdtpldt0(fresh47(aNaturalNumber0(w0), true, w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 24 (mZeroAdd) }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(w0_2), true, w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 1 (m___2) R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(w0_2), aNaturalNumber0(w0_2), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 30 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(w0_2), aNaturalNumber0(sz10), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 30 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by lemma 31 R->L }
% 39.41/5.49 fresh6(sdtpldt0(fresh3(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, w0), sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 17 (mZeroAdd) }
% 39.41/5.49 fresh6(sdtpldt0(w0_2, sdtpldt0(xm, w0_2)), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 7 (m__) }
% 39.41/5.49 fresh6(sdtpldt0(w0_2, xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.49 = { by axiom 11 (mAddComm) R->L }
% 39.41/5.49 fresh6(fresh24(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 31 }
% 39.41/5.50 fresh6(fresh24(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 32 R->L }
% 39.41/5.50 fresh6(fresh24(aNaturalNumber0(xn), aNaturalNumber0(sz00), w0_2, xn), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 38 }
% 39.41/5.50 fresh6(sdtpldt0(xn, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by axiom 7 (m__) R->L }
% 39.41/5.50 fresh6(sdtpldt0(sdtpldt0(xm, w0_2), w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by axiom 8 (m___1) R->L }
% 39.41/5.50 fresh6(sdtpldt0(sdtpldt0(xm, w0_2), w0_2), sdtpldt0(sdtpldt0(xn, w0), w0_2), sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 41 }
% 39.41/5.50 fresh54(aNaturalNumber0(sdtpldt0(xn, w0)), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 35 }
% 39.41/5.50 fresh54(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by axiom 7 (m__) }
% 39.41/5.50 fresh54(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, xn, sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 40 R->L }
% 39.41/5.50 fresh55(aNaturalNumber0(xn), aNaturalNumber0(sz00), w0_2, xn, sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 32 }
% 39.41/5.50 fresh55(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, xn, sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 31 R->L }
% 39.41/5.50 fresh55(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, xn, sdtpldt0(xn, w0))
% 39.41/5.50 = { by axiom 7 (m__) R->L }
% 39.41/5.50 fresh55(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 39 R->L }
% 39.41/5.50 fresh56(aNaturalNumber0(w0_2), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 30 R->L }
% 39.41/5.50 fresh56(aNaturalNumber0(sz10), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by lemma 31 R->L }
% 39.41/5.50 fresh56(aNaturalNumber0(sz00), aNaturalNumber0(sz00), w0_2, sdtpldt0(xm, w0_2), sdtpldt0(xn, w0))
% 39.41/5.50 = { by axiom 19 (mAddCanc_1) }
% 39.41/5.50 sdtpldt0(xm, w0_2)
% 39.41/5.50 = { by axiom 7 (m__) }
% 39.41/5.50 xn
% 39.41/5.50 % SZS output end Proof
% 39.41/5.50
% 39.41/5.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------