TSTP Solution File: NUM459+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM459+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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:56:24 EDT 2023
% Result : Theorem 161.30s 21.01s
% Output : Proof 161.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM459+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:51:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 161.30/21.01 Command-line arguments: --no-flatten-goal
% 161.30/21.01
% 161.30/21.01 % SZS status Theorem
% 161.30/21.01
% 161.30/21.04 % SZS output start Proof
% 161.30/21.04 Take the following subset of the input axioms:
% 161.30/21.04 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aNaturalNumber0(W0) & (aNaturalNumber0(W1) & aNaturalNumber0(W2))) => sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)))).
% 161.30/21.04 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))).
% 161.30/21.04 fof(mAddComm, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => sdtpldt0(W0_2, W1_2)=sdtpldt0(W1_2, W0_2))).
% 161.30/21.04 fof(mDefLE, definition, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => (sdtlseqdt0(W0_2, W1_2) <=> ?[W2_2]: (aNaturalNumber0(W2_2) & sdtpldt0(W0_2, W2_2)=W1_2)))).
% 161.30/21.04 fof(mSortsB, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => aNaturalNumber0(sdtpldt0(W0_2, W1_2)))).
% 161.30/21.04 fof(mSortsC, axiom, aNaturalNumber0(sz00)).
% 161.30/21.04 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)))).
% 161.30/21.04 fof(m_AddZero, axiom, ![W0_2]: (aNaturalNumber0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 161.30/21.04 fof(m__, conjecture, (sdtlseqdt0(xm, xn) & sdtlseqdt0(xn, xm)) => xm=xn).
% 161.30/21.04 fof(m__745, hypothesis, aNaturalNumber0(xm) & aNaturalNumber0(xn)).
% 161.30/21.04
% 161.30/21.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 161.30/21.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 161.30/21.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 161.30/21.04 fresh(y, y, x1...xn) = u
% 161.30/21.04 C => fresh(s, t, x1...xn) = v
% 161.30/21.04 where fresh is a fresh function symbol and x1..xn are the free
% 161.30/21.04 variables of u and v.
% 161.30/21.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 161.30/21.04 input problem has no model of domain size 1).
% 161.30/21.04
% 161.30/21.04 The encoding turns the above axioms into the following unit equations and goals:
% 161.30/21.04
% 161.30/21.04 Axiom 1 (m__745): aNaturalNumber0(xm) = true.
% 161.30/21.04 Axiom 2 (m__745_1): aNaturalNumber0(xn) = true.
% 161.30/21.04 Axiom 3 (mSortsC): aNaturalNumber0(sz00) = true.
% 161.30/21.04 Axiom 4 (m__): sdtlseqdt0(xm, xn) = true.
% 161.30/21.04 Axiom 5 (m___1): sdtlseqdt0(xn, xm) = true.
% 161.30/21.04 Axiom 6 (mZeroAdd_1): fresh50(X, X, Y) = sz00.
% 161.30/21.04 Axiom 7 (m_AddZero_1): fresh10(X, X, Y) = Y.
% 161.30/21.04 Axiom 8 (m_AddZero): fresh9(X, X, Y) = Y.
% 161.30/21.04 Axiom 9 (mDefLE_2): fresh46(X, X, Y, Z) = true.
% 161.30/21.04 Axiom 10 (mDefLE_1): fresh44(X, X, Y, Z) = Z.
% 161.30/21.04 Axiom 11 (mAddComm): fresh24(X, X, Y, Z) = sdtpldt0(Y, Z).
% 161.30/21.04 Axiom 12 (mAddComm): fresh23(X, X, Y, Z) = sdtpldt0(Z, Y).
% 161.30/21.04 Axiom 13 (mDefLE_2): fresh21(X, X, Y, Z) = aNaturalNumber0(w2(Y, Z)).
% 161.30/21.04 Axiom 14 (mSortsB): fresh16(X, X, Y, Z) = aNaturalNumber0(sdtpldt0(Y, Z)).
% 161.30/21.04 Axiom 15 (mSortsB): fresh15(X, X, Y, Z) = true.
% 161.30/21.04 Axiom 16 (m_AddZero_1): fresh10(aNaturalNumber0(X), true, X) = sdtpldt0(sz00, X).
% 161.30/21.04 Axiom 17 (m_AddZero): fresh9(aNaturalNumber0(X), true, X) = sdtpldt0(X, sz00).
% 161.30/21.04 Axiom 18 (mAddCanc_1): fresh6(X, X, Y, Z) = Z.
% 161.30/21.04 Axiom 19 (mZeroAdd_1): fresh4(X, X, Y, Z) = Z.
% 161.30/21.04 Axiom 20 (mDefLE_1): fresh22(X, X, Y, Z) = sdtpldt0(Y, w2(Y, Z)).
% 161.30/21.04 Axiom 21 (mAddAsso): fresh64(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 161.30/21.04 Axiom 22 (mAddCanc_1): fresh56(X, X, Y, Z, W) = Z.
% 161.30/21.04 Axiom 23 (mZeroAdd_1): fresh49(X, X, Y, Z) = fresh50(sdtpldt0(Y, Z), sz00, Z).
% 161.30/21.04 Axiom 24 (mDefLE_2): fresh45(X, X, Y, Z) = fresh46(aNaturalNumber0(Y), true, Y, Z).
% 161.30/21.04 Axiom 25 (mDefLE_1): fresh43(X, X, Y, Z) = fresh44(aNaturalNumber0(Y), true, Y, Z).
% 161.30/21.04 Axiom 26 (mAddAsso): fresh25(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 161.30/21.04 Axiom 27 (mAddComm): fresh24(aNaturalNumber0(X), true, Y, X) = fresh23(aNaturalNumber0(Y), true, Y, X).
% 161.30/21.04 Axiom 28 (mSortsB): fresh16(aNaturalNumber0(X), true, Y, X) = fresh15(aNaturalNumber0(Y), true, Y, X).
% 161.30/21.04 Axiom 29 (mZeroAdd_1): fresh49(aNaturalNumber0(X), true, Y, X) = fresh4(aNaturalNumber0(Y), true, Y, X).
% 161.30/21.04 Axiom 30 (mAddAsso): fresh63(X, X, Y, Z, W) = fresh64(aNaturalNumber0(Y), true, Y, Z, W).
% 161.30/21.04 Axiom 31 (mAddCanc_1): fresh55(X, X, Y, Z, W) = fresh56(aNaturalNumber0(Y), true, Y, Z, W).
% 161.30/21.04 Axiom 32 (mAddCanc_1): fresh54(X, X, Y, Z, W) = fresh55(aNaturalNumber0(Z), true, Y, Z, W).
% 161.30/21.04 Axiom 33 (mDefLE_2): fresh45(sdtlseqdt0(X, Y), true, X, Y) = fresh21(aNaturalNumber0(Y), true, X, Y).
% 161.30/21.04 Axiom 34 (mDefLE_1): fresh43(sdtlseqdt0(X, Y), true, X, Y) = fresh22(aNaturalNumber0(Y), true, X, Y).
% 161.30/21.04 Axiom 35 (mAddAsso): fresh63(aNaturalNumber0(X), true, Y, Z, X) = fresh25(aNaturalNumber0(Z), true, Y, Z, X).
% 161.30/21.04 Axiom 36 (mAddCanc_1): fresh54(aNaturalNumber0(X), true, Y, Z, X) = fresh6(sdtpldt0(Z, Y), sdtpldt0(X, Y), Z, X).
% 161.30/21.04
% 161.30/21.04 Lemma 37: aNaturalNumber0(w2(xn, xm)) = true.
% 161.30/21.04 Proof:
% 161.30/21.04 aNaturalNumber0(w2(xn, xm))
% 161.30/21.04 = { by axiom 13 (mDefLE_2) R->L }
% 161.30/21.04 fresh21(true, true, xn, xm)
% 161.30/21.04 = { by axiom 1 (m__745) R->L }
% 161.30/21.04 fresh21(aNaturalNumber0(xm), true, xn, xm)
% 161.30/21.04 = { by axiom 33 (mDefLE_2) R->L }
% 161.30/21.04 fresh45(sdtlseqdt0(xn, xm), true, xn, xm)
% 161.30/21.04 = { by axiom 5 (m___1) }
% 161.30/21.04 fresh45(true, true, xn, xm)
% 161.30/21.04 = { by axiom 24 (mDefLE_2) }
% 161.30/21.04 fresh46(aNaturalNumber0(xn), true, xn, xm)
% 161.30/21.04 = { by axiom 2 (m__745_1) }
% 161.30/21.04 fresh46(true, true, xn, xm)
% 161.30/21.04 = { by axiom 9 (mDefLE_2) }
% 161.30/21.04 true
% 161.30/21.04
% 161.30/21.04 Lemma 38: aNaturalNumber0(w2(xm, xn)) = true.
% 161.30/21.04 Proof:
% 161.30/21.04 aNaturalNumber0(w2(xm, xn))
% 161.30/21.04 = { by axiom 13 (mDefLE_2) R->L }
% 161.30/21.04 fresh21(true, true, xm, xn)
% 161.30/21.04 = { by axiom 2 (m__745_1) R->L }
% 161.30/21.04 fresh21(aNaturalNumber0(xn), true, xm, xn)
% 161.30/21.04 = { by axiom 33 (mDefLE_2) R->L }
% 161.30/21.04 fresh45(sdtlseqdt0(xm, xn), true, xm, xn)
% 161.30/21.04 = { by axiom 4 (m__) }
% 161.30/21.04 fresh45(true, true, xm, xn)
% 161.30/21.04 = { by axiom 24 (mDefLE_2) }
% 161.30/21.04 fresh46(aNaturalNumber0(xm), true, xm, xn)
% 161.30/21.04 = { by axiom 1 (m__745) }
% 161.30/21.04 fresh46(true, true, xm, xn)
% 161.30/21.04 = { by axiom 9 (mDefLE_2) }
% 161.30/21.04 true
% 161.30/21.04
% 161.30/21.04 Lemma 39: fresh22(X, X, xn, xm) = xm.
% 161.30/21.04 Proof:
% 161.30/21.04 fresh22(X, X, xn, xm)
% 161.30/21.04 = { by axiom 20 (mDefLE_1) }
% 161.30/21.04 sdtpldt0(xn, w2(xn, xm))
% 161.30/21.04 = { by axiom 20 (mDefLE_1) R->L }
% 161.30/21.04 fresh22(true, true, xn, xm)
% 161.30/21.04 = { by axiom 1 (m__745) R->L }
% 161.30/21.04 fresh22(aNaturalNumber0(xm), true, xn, xm)
% 161.30/21.04 = { by axiom 34 (mDefLE_1) R->L }
% 161.30/21.04 fresh43(sdtlseqdt0(xn, xm), true, xn, xm)
% 161.30/21.04 = { by axiom 5 (m___1) }
% 161.30/21.04 fresh43(true, true, xn, xm)
% 161.30/21.04 = { by axiom 25 (mDefLE_1) }
% 161.30/21.04 fresh44(aNaturalNumber0(xn), true, xn, xm)
% 161.30/21.04 = { by axiom 2 (m__745_1) }
% 161.30/21.04 fresh44(true, true, xn, xm)
% 161.30/21.04 = { by axiom 10 (mDefLE_1) }
% 161.30/21.04 xm
% 161.30/21.04
% 161.30/21.04 Goal 1 (m___2): xm = xn.
% 161.30/21.04 Proof:
% 161.30/21.04 xm
% 161.30/21.04 = { by lemma 39 R->L }
% 161.30/21.04 fresh22(X, X, xn, xm)
% 161.30/21.04 = { by axiom 20 (mDefLE_1) }
% 161.30/21.04 sdtpldt0(xn, w2(xn, xm))
% 161.30/21.04 = { by axiom 19 (mZeroAdd_1) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh4(true, true, w2(xm, xn), w2(xn, xm)))
% 161.30/21.04 = { by lemma 38 R->L }
% 161.30/21.04 sdtpldt0(xn, fresh4(aNaturalNumber0(w2(xm, xn)), true, w2(xm, xn), w2(xn, xm)))
% 161.30/21.04 = { by axiom 29 (mZeroAdd_1) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh49(aNaturalNumber0(w2(xn, xm)), true, w2(xm, xn), w2(xn, xm)))
% 161.30/21.04 = { by lemma 37 }
% 161.30/21.04 sdtpldt0(xn, fresh49(true, true, w2(xm, xn), w2(xn, xm)))
% 161.30/21.04 = { by axiom 23 (mZeroAdd_1) }
% 161.30/21.04 sdtpldt0(xn, fresh50(sdtpldt0(w2(xm, xn), w2(xn, xm)), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 18 (mAddCanc_1) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by lemma 39 R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, fresh22(Y, Y, xn, xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 20 (mDefLE_1) }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(xn, w2(xn, xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 11 (mAddComm) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, fresh24(true, true, xn, w2(xn, xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by lemma 37 R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, fresh24(aNaturalNumber0(w2(xn, xm)), true, xn, w2(xn, xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 27 (mAddComm) }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, fresh23(aNaturalNumber0(xn), true, xn, w2(xn, xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 2 (m__745_1) }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, fresh23(true, true, xn, w2(xn, xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 12 (mAddComm) }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), xn), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 10 (mDefLE_1) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh44(true, true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 1 (m__745) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh44(aNaturalNumber0(xm), true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 25 (mDefLE_1) R->L }
% 161.30/21.04 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh43(true, true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.04 = { by axiom 4 (m__) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh43(sdtlseqdt0(xm, xn), true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 34 (mDefLE_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh22(aNaturalNumber0(xn), true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 2 (m__745_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh22(true, true, xm, xn)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 20 (mDefLE_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), sdtpldt0(xm, w2(xm, xn))), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 11 (mAddComm) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh24(true, true, xm, w2(xm, xn))), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 38 R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh24(aNaturalNumber0(w2(xm, xn)), true, xm, w2(xm, xn))), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 27 (mAddComm) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh23(aNaturalNumber0(xm), true, xm, w2(xm, xn))), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 1 (m__745) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), fresh23(true, true, xm, w2(xm, xn))), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 12 (mAddComm) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(w2(xn, xm), sdtpldt0(w2(xm, xn), xm)), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 21 (mAddAsso) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh64(true, true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 37 R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh64(aNaturalNumber0(w2(xn, xm)), true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 30 (mAddAsso) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh63(true, true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 1 (m__745) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh63(aNaturalNumber0(xm), true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 35 (mAddAsso) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh25(aNaturalNumber0(w2(xm, xn)), true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 38 }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, fresh25(true, true, w2(xn, xm), w2(xm, xn), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 26 (mAddAsso) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(sdtpldt0(w2(xn, xm), w2(xm, xn)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 11 (mAddComm) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(fresh24(true, true, w2(xn, xm), w2(xm, xn)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 38 R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(fresh24(aNaturalNumber0(w2(xm, xn)), true, w2(xn, xm), w2(xm, xn)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 27 (mAddComm) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(fresh23(aNaturalNumber0(w2(xn, xm)), true, w2(xn, xm), w2(xm, xn)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 37 }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(fresh23(true, true, w2(xn, xm), w2(xm, xn)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 12 (mAddComm) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(xm, sdtpldt0(sdtpldt0(w2(xm, xn), w2(xn, xm)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 7 (m_AddZero_1) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(fresh10(true, true, xm), sdtpldt0(sdtpldt0(w2(xm, xn), w2(xn, xm)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 1 (m__745) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(fresh10(aNaturalNumber0(xm), true, xm), sdtpldt0(sdtpldt0(w2(xm, xn), w2(xn, xm)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 16 (m_AddZero_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh6(sdtpldt0(sz00, xm), sdtpldt0(sdtpldt0(w2(xm, xn), w2(xn, xm)), xm), sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 36 (mAddCanc_1) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(aNaturalNumber0(sdtpldt0(w2(xm, xn), w2(xn, xm))), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 14 (mSortsB) R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(fresh16(true, true, w2(xm, xn), w2(xn, xm)), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 37 R->L }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(fresh16(aNaturalNumber0(w2(xn, xm)), true, w2(xm, xn), w2(xn, xm)), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 28 (mSortsB) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(fresh15(aNaturalNumber0(w2(xm, xn)), true, w2(xm, xn), w2(xn, xm)), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by lemma 38 }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(fresh15(true, true, w2(xm, xn), w2(xn, xm)), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 15 (mSortsB) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh54(true, true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 32 (mAddCanc_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh55(aNaturalNumber0(sz00), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 3 (mSortsC) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh55(true, true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 31 (mAddCanc_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh56(aNaturalNumber0(xm), true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 1 (m__745) }
% 161.30/21.05 sdtpldt0(xn, fresh50(fresh56(true, true, xm, sz00, sdtpldt0(w2(xm, xn), w2(xn, xm))), sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 22 (mAddCanc_1) }
% 161.30/21.05 sdtpldt0(xn, fresh50(sz00, sz00, w2(xn, xm)))
% 161.30/21.05 = { by axiom 6 (mZeroAdd_1) }
% 161.30/21.05 sdtpldt0(xn, sz00)
% 161.30/21.05 = { by axiom 17 (m_AddZero) R->L }
% 161.30/21.05 fresh9(aNaturalNumber0(xn), true, xn)
% 161.30/21.05 = { by axiom 2 (m__745_1) }
% 161.30/21.05 fresh9(true, true, xn)
% 161.30/21.05 = { by axiom 8 (m_AddZero) }
% 161.30/21.05 xn
% 161.30/21.05 % SZS output end Proof
% 161.30/21.05
% 161.30/21.05 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------