TSTP Solution File: NUM426+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM426+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 : n017.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 11:56:13 EDT 2023
% Result : Theorem 177.07s 22.95s
% Output : Proof 177.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM426+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % 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 : n017.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 08:55:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 177.07/22.95 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 177.07/22.95
% 177.07/22.95 % SZS status Theorem
% 177.07/22.95
% 177.07/22.97 % SZS output start Proof
% 177.07/22.97 Take the following subset of the input axioms:
% 177.07/22.97 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aInteger0(W0) & (aInteger0(W1) & aInteger0(W2))) => sdtpldt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtpldt0(W0, W1), W2))).
% 177.07/22.97 fof(mAddComm, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => sdtpldt0(W0_2, W1_2)=sdtpldt0(W1_2, W0_2))).
% 177.07/22.97 fof(mAddNeg, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtpldt0(W0_2, smndt0(W0_2))=sz00 & sz00=sdtpldt0(smndt0(W0_2), W0_2)))).
% 177.07/22.97 fof(mAddZero, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 177.07/22.97 fof(mDistrib, axiom, ![W0_2, W1_2, W2_2]: ((aInteger0(W0_2) & (aInteger0(W1_2) & aInteger0(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))))).
% 177.07/22.97 fof(mIntNeg, axiom, ![W0_2]: (aInteger0(W0_2) => aInteger0(smndt0(W0_2)))).
% 177.07/22.97 fof(mIntOne, axiom, aInteger0(sz10)).
% 177.07/22.97 fof(mIntPlus, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => aInteger0(sdtpldt0(W0_2, W1_2)))).
% 177.07/22.97 fof(mMulAsso, axiom, ![W0_2, W1_2, W2_2]: ((aInteger0(W0_2) & (aInteger0(W1_2) & aInteger0(W2_2))) => sdtasdt0(W0_2, sdtasdt0(W1_2, W2_2))=sdtasdt0(sdtasdt0(W0_2, W1_2), W2_2))).
% 177.07/22.97 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 177.07/22.97 fof(mMulMinOne, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtasdt0(smndt0(sz10), W0_2)=smndt0(W0_2) & smndt0(W0_2)=sdtasdt0(W0_2, smndt0(sz10))))).
% 177.07/22.97 fof(m__, conjecture, sdtasdt0(xq, smndt0(xn))=sdtpldt0(xb, smndt0(xa))).
% 177.07/22.97 fof(m__704, hypothesis, aInteger0(xa) & (aInteger0(xb) & (aInteger0(xq) & xq!=sz00))).
% 177.07/22.97 fof(m__747, hypothesis, aInteger0(xn) & sdtasdt0(xq, xn)=sdtpldt0(xa, smndt0(xb))).
% 177.07/22.97
% 177.07/22.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 177.07/22.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 177.07/22.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 177.07/22.97 fresh(y, y, x1...xn) = u
% 177.07/22.97 C => fresh(s, t, x1...xn) = v
% 177.07/22.97 where fresh is a fresh function symbol and x1..xn are the free
% 177.07/22.97 variables of u and v.
% 177.07/22.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 177.07/22.97 input problem has no model of domain size 1).
% 177.07/22.97
% 177.07/22.97 The encoding turns the above axioms into the following unit equations and goals:
% 177.07/22.97
% 177.07/22.97 Axiom 1 (m__704): aInteger0(xa) = true2.
% 177.07/22.97 Axiom 2 (m__704_2): aInteger0(xq) = true2.
% 177.07/22.97 Axiom 3 (mIntOne): aInteger0(sz10) = true2.
% 177.07/22.97 Axiom 4 (m__704_1): aInteger0(xb) = true2.
% 177.07/22.97 Axiom 5 (m__747_1): aInteger0(xn) = true2.
% 177.07/22.97 Axiom 6 (m__747): sdtasdt0(xq, xn) = sdtpldt0(xa, smndt0(xb)).
% 177.07/22.97 Axiom 7 (mAddNeg): fresh26(X, X, Y) = sz00.
% 177.07/22.97 Axiom 8 (mIntNeg): fresh15(X, X, Y) = true2.
% 177.07/22.97 Axiom 9 (mMulMinOne_1): fresh8(X, X, Y) = smndt0(Y).
% 177.07/22.97 Axiom 10 (mAddZero): fresh4(X, X, Y) = Y.
% 177.07/22.97 Axiom 11 (mAddComm): fresh28(X, X, Y, Z) = sdtpldt0(Y, Z).
% 177.07/22.97 Axiom 12 (mAddComm): fresh27(X, X, Y, Z) = sdtpldt0(Z, Y).
% 177.07/22.97 Axiom 13 (mAddNeg): fresh26(aInteger0(X), true2, X) = sdtpldt0(X, smndt0(X)).
% 177.07/22.97 Axiom 14 (mIntNeg): fresh15(aInteger0(X), true2, X) = aInteger0(smndt0(X)).
% 177.07/22.97 Axiom 15 (mIntPlus): fresh14(X, X, Y, Z) = aInteger0(sdtpldt0(Y, Z)).
% 177.07/22.97 Axiom 16 (mIntPlus): fresh13(X, X, Y, Z) = true2.
% 177.07/22.97 Axiom 17 (mMulComm): fresh11(X, X, Y, Z) = sdtasdt0(Y, Z).
% 177.07/22.97 Axiom 18 (mMulComm): fresh10(X, X, Y, Z) = sdtasdt0(Z, Y).
% 177.07/22.97 Axiom 19 (mMulMinOne_1): fresh8(aInteger0(X), true2, X) = sdtasdt0(smndt0(sz10), X).
% 177.07/22.97 Axiom 20 (mAddZero): fresh4(aInteger0(X), true2, X) = sdtpldt0(X, sz00).
% 177.07/22.97 Axiom 21 (mAddAsso): fresh37(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 177.07/22.97 Axiom 22 (mMulAsso): fresh35(X, X, Y, Z, W) = sdtasdt0(sdtasdt0(Y, Z), W).
% 177.07/22.97 Axiom 23 (mDistrib): fresh31(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 177.07/22.97 Axiom 24 (mAddAsso): fresh29(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 177.07/22.97 Axiom 25 (mAddComm): fresh28(aInteger0(X), true2, Y, X) = fresh27(aInteger0(Y), true2, Y, X).
% 177.07/22.97 Axiom 26 (mIntPlus): fresh14(aInteger0(X), true2, Y, X) = fresh13(aInteger0(Y), true2, Y, X).
% 177.07/22.97 Axiom 27 (mMulAsso): fresh12(X, X, Y, Z, W) = sdtasdt0(Y, sdtasdt0(Z, W)).
% 177.07/22.97 Axiom 28 (mMulComm): fresh11(aInteger0(X), true2, Y, X) = fresh10(aInteger0(Y), true2, Y, X).
% 177.07/22.97 Axiom 29 (mDistrib): fresh24(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 177.07/22.97 Axiom 30 (mAddAsso): fresh36(X, X, Y, Z, W) = fresh37(aInteger0(Y), true2, Y, Z, W).
% 177.07/22.97 Axiom 31 (mMulAsso): fresh34(X, X, Y, Z, W) = fresh35(aInteger0(Y), true2, Y, Z, W).
% 177.07/22.97 Axiom 32 (mDistrib): fresh30(X, X, Y, Z, W) = fresh31(aInteger0(Y), true2, Y, Z, W).
% 177.07/22.97 Axiom 33 (mAddAsso): fresh36(aInteger0(X), true2, Y, Z, X) = fresh29(aInteger0(Z), true2, Y, Z, X).
% 177.07/22.97 Axiom 34 (mDistrib): fresh30(aInteger0(X), true2, Y, Z, X) = fresh24(aInteger0(Z), true2, Y, Z, X).
% 177.07/22.97 Axiom 35 (mMulAsso): fresh34(aInteger0(X), true2, Y, Z, X) = fresh12(aInteger0(Z), true2, Y, Z, X).
% 177.07/22.97
% 177.07/22.97 Lemma 36: aInteger0(smndt0(sz10)) = true2.
% 177.07/22.97 Proof:
% 177.07/22.97 aInteger0(smndt0(sz10))
% 177.07/22.97 = { by axiom 14 (mIntNeg) R->L }
% 177.07/22.97 fresh15(aInteger0(sz10), true2, sz10)
% 177.07/22.97 = { by axiom 3 (mIntOne) }
% 177.07/22.97 fresh15(true2, true2, sz10)
% 177.07/22.97 = { by axiom 8 (mIntNeg) }
% 177.07/22.97 true2
% 177.07/22.97
% 177.07/22.97 Lemma 37: aInteger0(smndt0(xb)) = true2.
% 177.07/22.97 Proof:
% 177.07/22.97 aInteger0(smndt0(xb))
% 177.07/22.97 = { by axiom 14 (mIntNeg) R->L }
% 177.07/22.97 fresh15(aInteger0(xb), true2, xb)
% 177.07/22.97 = { by axiom 4 (m__704_1) }
% 177.07/22.97 fresh15(true2, true2, xb)
% 177.07/22.97 = { by axiom 8 (mIntNeg) }
% 177.07/22.97 true2
% 177.07/22.97
% 177.07/22.97 Lemma 38: aInteger0(smndt0(xa)) = true2.
% 177.07/22.97 Proof:
% 177.07/22.97 aInteger0(smndt0(xa))
% 177.07/22.97 = { by axiom 14 (mIntNeg) R->L }
% 177.07/22.97 fresh15(aInteger0(xa), true2, xa)
% 177.07/22.97 = { by axiom 1 (m__704) }
% 177.07/22.97 fresh15(true2, true2, xa)
% 177.07/22.97 = { by axiom 8 (mIntNeg) }
% 177.07/22.97 true2
% 177.07/22.97
% 177.07/22.97 Lemma 39: aInteger0(sdtpldt0(xb, smndt0(xa))) = true2.
% 177.07/22.97 Proof:
% 177.07/22.97 aInteger0(sdtpldt0(xb, smndt0(xa)))
% 177.07/22.97 = { by axiom 15 (mIntPlus) R->L }
% 177.07/22.97 fresh14(true2, true2, xb, smndt0(xa))
% 177.07/22.97 = { by lemma 38 R->L }
% 177.07/22.97 fresh14(aInteger0(smndt0(xa)), true2, xb, smndt0(xa))
% 177.07/22.97 = { by axiom 26 (mIntPlus) }
% 177.07/22.97 fresh13(aInteger0(xb), true2, xb, smndt0(xa))
% 177.07/22.97 = { by axiom 4 (m__704_1) }
% 177.07/22.97 fresh13(true2, true2, xb, smndt0(xa))
% 177.07/22.97 = { by axiom 16 (mIntPlus) }
% 177.07/22.97 true2
% 177.07/22.97
% 177.07/22.97 Lemma 40: fresh11(aInteger0(X), true2, xq, X) = sdtasdt0(X, xq).
% 177.07/22.97 Proof:
% 177.07/22.97 fresh11(aInteger0(X), true2, xq, X)
% 177.07/22.97 = { by axiom 28 (mMulComm) }
% 177.07/22.97 fresh10(aInteger0(xq), true2, xq, X)
% 177.07/22.97 = { by axiom 2 (m__704_2) }
% 177.07/22.97 fresh10(true2, true2, xq, X)
% 177.07/22.97 = { by axiom 18 (mMulComm) }
% 177.07/22.97 sdtasdt0(X, xq)
% 177.07/22.97
% 177.07/22.97 Goal 1 (m__): sdtasdt0(xq, smndt0(xn)) = sdtpldt0(xb, smndt0(xa)).
% 177.07/22.97 Proof:
% 177.07/22.97 sdtasdt0(xq, smndt0(xn))
% 177.07/22.97 = { by axiom 17 (mMulComm) R->L }
% 177.07/22.97 fresh11(true2, true2, xq, smndt0(xn))
% 177.07/22.97 = { by axiom 8 (mIntNeg) R->L }
% 177.07/22.97 fresh11(fresh15(true2, true2, xn), true2, xq, smndt0(xn))
% 177.07/22.97 = { by axiom 5 (m__747_1) R->L }
% 177.07/22.97 fresh11(fresh15(aInteger0(xn), true2, xn), true2, xq, smndt0(xn))
% 177.07/22.97 = { by axiom 14 (mIntNeg) }
% 177.07/22.97 fresh11(aInteger0(smndt0(xn)), true2, xq, smndt0(xn))
% 177.07/22.97 = { by lemma 40 }
% 177.07/22.97 sdtasdt0(smndt0(xn), xq)
% 177.07/22.97 = { by axiom 9 (mMulMinOne_1) R->L }
% 177.07/22.97 sdtasdt0(fresh8(true2, true2, xn), xq)
% 177.07/22.97 = { by axiom 5 (m__747_1) R->L }
% 177.07/22.97 sdtasdt0(fresh8(aInteger0(xn), true2, xn), xq)
% 177.07/22.97 = { by axiom 19 (mMulMinOne_1) }
% 177.07/22.97 sdtasdt0(sdtasdt0(smndt0(sz10), xn), xq)
% 177.07/22.97 = { by axiom 22 (mMulAsso) R->L }
% 177.07/22.97 fresh35(true2, true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by lemma 36 R->L }
% 177.07/22.97 fresh35(aInteger0(smndt0(sz10)), true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by axiom 31 (mMulAsso) R->L }
% 177.07/22.97 fresh34(true2, true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by axiom 2 (m__704_2) R->L }
% 177.07/22.97 fresh34(aInteger0(xq), true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by axiom 35 (mMulAsso) }
% 177.07/22.97 fresh12(aInteger0(xn), true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by axiom 5 (m__747_1) }
% 177.07/22.97 fresh12(true2, true2, smndt0(sz10), xn, xq)
% 177.07/22.97 = { by axiom 27 (mMulAsso) }
% 177.07/22.97 sdtasdt0(smndt0(sz10), sdtasdt0(xn, xq))
% 177.07/22.97 = { by lemma 40 R->L }
% 177.07/22.97 sdtasdt0(smndt0(sz10), fresh11(aInteger0(xn), true2, xq, xn))
% 177.07/22.97 = { by axiom 5 (m__747_1) }
% 177.07/22.97 sdtasdt0(smndt0(sz10), fresh11(true2, true2, xq, xn))
% 177.07/22.97 = { by axiom 17 (mMulComm) }
% 177.07/22.97 sdtasdt0(smndt0(sz10), sdtasdt0(xq, xn))
% 177.07/22.97 = { by axiom 6 (m__747) }
% 177.07/22.97 sdtasdt0(smndt0(sz10), sdtpldt0(xa, smndt0(xb)))
% 177.07/22.97 = { by axiom 23 (mDistrib) R->L }
% 177.07/22.97 fresh31(true2, true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by lemma 36 R->L }
% 177.07/22.97 fresh31(aInteger0(smndt0(sz10)), true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by axiom 32 (mDistrib) R->L }
% 177.07/22.97 fresh30(true2, true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by lemma 37 R->L }
% 177.07/22.97 fresh30(aInteger0(smndt0(xb)), true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by axiom 34 (mDistrib) }
% 177.07/22.97 fresh24(aInteger0(xa), true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by axiom 1 (m__704) }
% 177.07/22.97 fresh24(true2, true2, smndt0(sz10), xa, smndt0(xb))
% 177.07/22.97 = { by axiom 29 (mDistrib) }
% 177.07/22.97 sdtpldt0(sdtasdt0(smndt0(sz10), xa), sdtasdt0(smndt0(sz10), smndt0(xb)))
% 177.07/22.97 = { by axiom 19 (mMulMinOne_1) R->L }
% 177.07/22.97 sdtpldt0(fresh8(aInteger0(xa), true2, xa), sdtasdt0(smndt0(sz10), smndt0(xb)))
% 177.07/22.97 = { by axiom 1 (m__704) }
% 177.07/22.97 sdtpldt0(fresh8(true2, true2, xa), sdtasdt0(smndt0(sz10), smndt0(xb)))
% 177.07/22.97 = { by axiom 9 (mMulMinOne_1) }
% 177.07/22.97 sdtpldt0(smndt0(xa), sdtasdt0(smndt0(sz10), smndt0(xb)))
% 177.07/22.97 = { by axiom 19 (mMulMinOne_1) R->L }
% 177.07/22.97 sdtpldt0(smndt0(xa), fresh8(aInteger0(smndt0(xb)), true2, smndt0(xb)))
% 177.07/22.97 = { by lemma 37 }
% 177.07/22.97 sdtpldt0(smndt0(xa), fresh8(true2, true2, smndt0(xb)))
% 177.07/22.97 = { by axiom 9 (mMulMinOne_1) }
% 177.07/22.97 sdtpldt0(smndt0(xa), smndt0(smndt0(xb)))
% 177.07/22.97 = { by axiom 10 (mAddZero) R->L }
% 177.07/22.97 sdtpldt0(fresh4(true2, true2, smndt0(xa)), smndt0(smndt0(xb)))
% 177.07/22.97 = { by lemma 38 R->L }
% 177.07/22.97 sdtpldt0(fresh4(aInteger0(smndt0(xa)), true2, smndt0(xa)), smndt0(smndt0(xb)))
% 177.07/22.97 = { by axiom 20 (mAddZero) }
% 177.07/22.97 sdtpldt0(sdtpldt0(smndt0(xa), sz00), smndt0(smndt0(xb)))
% 177.07/22.97 = { by axiom 7 (mAddNeg) R->L }
% 177.07/22.97 sdtpldt0(sdtpldt0(smndt0(xa), fresh26(true2, true2, xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 4 (m__704_1) R->L }
% 177.07/22.98 sdtpldt0(sdtpldt0(smndt0(xa), fresh26(aInteger0(xb), true2, xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 13 (mAddNeg) }
% 177.07/22.98 sdtpldt0(sdtpldt0(smndt0(xa), sdtpldt0(xb, smndt0(xb))), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 24 (mAddAsso) R->L }
% 177.07/22.98 sdtpldt0(fresh29(true2, true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 4 (m__704_1) R->L }
% 177.07/22.98 sdtpldt0(fresh29(aInteger0(xb), true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 33 (mAddAsso) R->L }
% 177.07/22.98 sdtpldt0(fresh36(aInteger0(smndt0(xb)), true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 37 }
% 177.07/22.98 sdtpldt0(fresh36(true2, true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 30 (mAddAsso) }
% 177.07/22.98 sdtpldt0(fresh37(aInteger0(smndt0(xa)), true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 38 }
% 177.07/22.98 sdtpldt0(fresh37(true2, true2, smndt0(xa), xb, smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 21 (mAddAsso) }
% 177.07/22.98 sdtpldt0(sdtpldt0(sdtpldt0(smndt0(xa), xb), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 12 (mAddComm) R->L }
% 177.07/22.98 sdtpldt0(sdtpldt0(fresh27(true2, true2, xb, smndt0(xa)), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 4 (m__704_1) R->L }
% 177.07/22.98 sdtpldt0(sdtpldt0(fresh27(aInteger0(xb), true2, xb, smndt0(xa)), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 25 (mAddComm) R->L }
% 177.07/22.98 sdtpldt0(sdtpldt0(fresh28(aInteger0(smndt0(xa)), true2, xb, smndt0(xa)), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 38 }
% 177.07/22.98 sdtpldt0(sdtpldt0(fresh28(true2, true2, xb, smndt0(xa)), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 11 (mAddComm) }
% 177.07/22.98 sdtpldt0(sdtpldt0(sdtpldt0(xb, smndt0(xa)), smndt0(xb)), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 21 (mAddAsso) R->L }
% 177.07/22.98 fresh37(true2, true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 39 R->L }
% 177.07/22.98 fresh37(aInteger0(sdtpldt0(xb, smndt0(xa))), true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 30 (mAddAsso) R->L }
% 177.07/22.98 fresh36(true2, true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 8 (mIntNeg) R->L }
% 177.07/22.98 fresh36(fresh15(true2, true2, smndt0(xb)), true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 37 R->L }
% 177.07/22.98 fresh36(fresh15(aInteger0(smndt0(xb)), true2, smndt0(xb)), true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 14 (mIntNeg) }
% 177.07/22.98 fresh36(aInteger0(smndt0(smndt0(xb))), true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 33 (mAddAsso) }
% 177.07/22.98 fresh29(aInteger0(smndt0(xb)), true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by lemma 37 }
% 177.07/22.98 fresh29(true2, true2, sdtpldt0(xb, smndt0(xa)), smndt0(xb), smndt0(smndt0(xb)))
% 177.07/22.98 = { by axiom 24 (mAddAsso) }
% 177.07/22.98 sdtpldt0(sdtpldt0(xb, smndt0(xa)), sdtpldt0(smndt0(xb), smndt0(smndt0(xb))))
% 177.07/22.98 = { by axiom 13 (mAddNeg) R->L }
% 177.07/22.98 sdtpldt0(sdtpldt0(xb, smndt0(xa)), fresh26(aInteger0(smndt0(xb)), true2, smndt0(xb)))
% 177.07/22.98 = { by lemma 37 }
% 177.07/22.98 sdtpldt0(sdtpldt0(xb, smndt0(xa)), fresh26(true2, true2, smndt0(xb)))
% 177.07/22.98 = { by axiom 7 (mAddNeg) }
% 177.07/22.98 sdtpldt0(sdtpldt0(xb, smndt0(xa)), sz00)
% 177.07/22.98 = { by axiom 20 (mAddZero) R->L }
% 177.07/22.98 fresh4(aInteger0(sdtpldt0(xb, smndt0(xa))), true2, sdtpldt0(xb, smndt0(xa)))
% 177.07/22.98 = { by lemma 39 }
% 177.07/22.98 fresh4(true2, true2, sdtpldt0(xb, smndt0(xa)))
% 177.07/22.98 = { by axiom 10 (mAddZero) }
% 177.07/22.98 sdtpldt0(xb, smndt0(xa))
% 177.07/22.98 % SZS output end Proof
% 177.07/22.98
% 177.07/22.98 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------