TSTP Solution File: NUM452+6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM452+6 : 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 : n002.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 11:56:22 EDT 2023
% Result : Theorem 9.53s 1.64s
% Output : Proof 10.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM452+6 : 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
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:33:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.53/1.64 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 9.53/1.64
% 9.53/1.64 % SZS status Theorem
% 9.53/1.64
% 10.20/1.66 % SZS output start Proof
% 10.20/1.66 Take the following subset of the input axioms:
% 10.20/1.67 fof(mAddAsso, axiom, ![W0, W1, W2]: ((aInteger0(W0) & (aInteger0(W1) & aInteger0(W2))) => sdtpldt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtpldt0(W0, W1), W2))).
% 10.20/1.67 fof(mAddComm, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => sdtpldt0(W0_2, W1_2)=sdtpldt0(W1_2, W0_2))).
% 10.20/1.67 fof(mAddNeg, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtpldt0(W0_2, smndt0(W0_2))=sz00 & sz00=sdtpldt0(smndt0(W0_2), W0_2)))).
% 10.20/1.67 fof(mAddZero, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 10.20/1.67 fof(mIntNeg, axiom, ![W0_2]: (aInteger0(W0_2) => aInteger0(smndt0(W0_2)))).
% 10.20/1.67 fof(mIntOne, axiom, aInteger0(sz10)).
% 10.20/1.67 fof(mIntPlus, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => aInteger0(sdtpldt0(W0_2, W1_2)))).
% 10.20/1.67 fof(mMulMinOne, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtasdt0(smndt0(sz10), W0_2)=smndt0(W0_2) & smndt0(W0_2)=sdtasdt0(W0_2, smndt0(sz10))))).
% 10.20/1.67 fof(mMulOne, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtasdt0(W0_2, sz10)=W0_2 & W0_2=sdtasdt0(sz10, W0_2)))).
% 10.20/1.67 fof(m__, conjecture, (?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xp, W0_2)=sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp) | aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & (?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xp, W0_2)=sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, smndt0(xp)), sz10, xp) | aElementOf0(sdtpldt0(sz10, smndt0(xp)), szAzrzSzezqlpdtcmdtrp0(sz10, xp)))))).
% 10.20/1.67 fof(m__2171, hypothesis, aInteger0(xp) & (xp!=sz00 & (aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (![W0_2]: ((aElementOf0(W0_2, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (aInteger0(W0_2) & (?[W1_2]: (aInteger0(W1_2) & sdtasdt0(xp, W1_2)=sdtpldt0(W0_2, smndt0(sz10))) & (aDivisorOf0(xp, sdtpldt0(W0_2, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0_2, sz10, xp))))) & ((aInteger0(W0_2) & (?[W1_2]: (aInteger0(W1_2) & sdtasdt0(xp, W1_2)=sdtpldt0(W0_2, smndt0(sz10))) | (aDivisorOf0(xp, sdtpldt0(W0_2, smndt0(sz10))) | sdteqdtlpzmzozddtrp0(W0_2, sz10, xp)))) => aElementOf0(W0_2, szAzrzSzezqlpdtcmdtrp0(sz10, xp)))) & (aSet0(sbsmnsldt0(xS)) & (![W0_2]: (aElementOf0(W0_2, sbsmnsldt0(xS)) <=> (aInteger0(W0_2) & ?[W1_2]: (aElementOf0(W1_2, xS) & aElementOf0(W0_2, W1_2)))) & (![W0_2]: (aElementOf0(W0_2, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0_2) & ~aElementOf0(W0_2, sbsmnsldt0(xS)))) & (![W0_2]: (aElementOf0(W0_2, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0_2, stldt0(sbsmnsldt0(xS)))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10, xp), stldt0(sbsmnsldt0(xS))))))))))).
% 10.20/1.67
% 10.20/1.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 10.20/1.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 10.20/1.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 10.20/1.67 fresh(y, y, x1...xn) = u
% 10.20/1.67 C => fresh(s, t, x1...xn) = v
% 10.20/1.67 where fresh is a fresh function symbol and x1..xn are the free
% 10.20/1.67 variables of u and v.
% 10.20/1.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 10.20/1.67 input problem has no model of domain size 1).
% 10.20/1.67
% 10.20/1.67 The encoding turns the above axioms into the following unit equations and goals:
% 10.20/1.67
% 10.20/1.67 Axiom 1 (mIntOne): aInteger0(sz10) = true2.
% 10.20/1.67 Axiom 2 (m__2171): aInteger0(xp) = true2.
% 10.20/1.67 Axiom 3 (m___1): fresh10(X, X) = true2.
% 10.20/1.67 Axiom 4 (mAddNeg): fresh159(X, X, Y) = sz00.
% 10.20/1.67 Axiom 5 (mAddNeg_1): fresh158(X, X, Y) = sz00.
% 10.20/1.67 Axiom 6 (mIntNeg): fresh134(X, X, Y) = true2.
% 10.20/1.67 Axiom 7 (mMulMinOne): fresh121(X, X, Y) = smndt0(Y).
% 10.20/1.67 Axiom 8 (m__2171_5): fresh17(X, X, Y) = true2.
% 10.20/1.67 Axiom 9 (m___1): fresh11(X, X, Y) = or.
% 10.20/1.67 Axiom 10 (mAddZero_1): fresh6(X, X, Y) = Y.
% 10.20/1.67 Axiom 11 (mAddZero): fresh5(X, X, Y) = Y.
% 10.20/1.67 Axiom 12 (mMulOne): fresh3(X, X, Y) = Y.
% 10.20/1.67 Axiom 13 (m__2171_5): fresh164(X, X, Y, Z) = aElementOf0(Z, szAzrzSzezqlpdtcmdtrp0(sz10, xp)).
% 10.20/1.67 Axiom 14 (mAddComm): fresh161(X, X, Y, Z) = sdtpldt0(Y, Z).
% 10.20/1.67 Axiom 15 (mAddComm): fresh160(X, X, Y, Z) = sdtpldt0(Z, Y).
% 10.20/1.67 Axiom 16 (mAddNeg): fresh159(aInteger0(X), true2, X) = sdtpldt0(X, smndt0(X)).
% 10.20/1.67 Axiom 17 (mAddNeg_1): fresh158(aInteger0(X), true2, X) = sdtpldt0(smndt0(X), X).
% 10.20/1.67 Axiom 18 (mIntNeg): fresh134(aInteger0(X), true2, X) = aInteger0(smndt0(X)).
% 10.20/1.67 Axiom 19 (mIntPlus): fresh133(X, X, Y, Z) = aInteger0(sdtpldt0(Y, Z)).
% 10.20/1.67 Axiom 20 (mIntPlus): fresh132(X, X, Y, Z) = true2.
% 10.20/1.67 Axiom 21 (mMulMinOne): fresh121(aInteger0(X), true2, X) = sdtasdt0(X, smndt0(sz10)).
% 10.20/1.67 Axiom 22 (mAddZero_1): fresh6(aInteger0(X), true2, X) = sdtpldt0(sz00, X).
% 10.20/1.67 Axiom 23 (mAddZero): fresh5(aInteger0(X), true2, X) = sdtpldt0(X, sz00).
% 10.20/1.67 Axiom 24 (mMulOne): fresh3(aInteger0(X), true2, X) = sdtasdt0(X, sz10).
% 10.20/1.67 Axiom 25 (mAddAsso): fresh274(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 10.20/1.67 Axiom 26 (m__2171_5): fresh163(X, X, Y, Z) = fresh164(aInteger0(Y), true2, Y, Z).
% 10.20/1.67 Axiom 27 (mAddAsso): fresh162(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 10.20/1.67 Axiom 28 (mAddComm): fresh161(aInteger0(X), true2, Y, X) = fresh160(aInteger0(Y), true2, Y, X).
% 10.20/1.67 Axiom 29 (mIntPlus): fresh133(aInteger0(X), true2, Y, X) = fresh132(aInteger0(Y), true2, Y, X).
% 10.20/1.67 Axiom 30 (mAddAsso): fresh273(X, X, Y, Z, W) = fresh274(aInteger0(Y), true2, Y, Z, W).
% 10.20/1.67 Axiom 31 (mAddAsso): fresh273(aInteger0(X), true2, Y, Z, X) = fresh162(aInteger0(Z), true2, Y, Z, X).
% 10.20/1.67 Axiom 32 (m__2171_5): fresh163(aInteger0(X), true2, Y, X) = fresh17(sdtasdt0(xp, Y), sdtpldt0(X, smndt0(sz10)), X).
% 10.20/1.67 Axiom 33 (m___1): fresh11(aInteger0(X), true2, X) = fresh10(sdtasdt0(xp, X), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))).
% 10.20/1.67
% 10.20/1.67 Lemma 34: aInteger0(smndt0(sz10)) = true2.
% 10.20/1.67 Proof:
% 10.20/1.67 aInteger0(smndt0(sz10))
% 10.20/1.67 = { by axiom 18 (mIntNeg) R->L }
% 10.20/1.67 fresh134(aInteger0(sz10), true2, sz10)
% 10.20/1.67 = { by axiom 1 (mIntOne) }
% 10.20/1.67 fresh134(true2, true2, sz10)
% 10.20/1.67 = { by axiom 6 (mIntNeg) }
% 10.20/1.67 true2
% 10.20/1.67
% 10.20/1.67 Lemma 35: aInteger0(smndt0(xp)) = true2.
% 10.20/1.67 Proof:
% 10.20/1.67 aInteger0(smndt0(xp))
% 10.20/1.67 = { by axiom 18 (mIntNeg) R->L }
% 10.20/1.67 fresh134(aInteger0(xp), true2, xp)
% 10.20/1.67 = { by axiom 2 (m__2171) }
% 10.20/1.67 fresh134(true2, true2, xp)
% 10.20/1.67 = { by axiom 6 (mIntNeg) }
% 10.20/1.67 true2
% 10.20/1.67
% 10.20/1.67 Lemma 36: aInteger0(sdtpldt0(sz10, smndt0(xp))) = true2.
% 10.20/1.67 Proof:
% 10.20/1.67 aInteger0(sdtpldt0(sz10, smndt0(xp)))
% 10.20/1.67 = { by axiom 19 (mIntPlus) R->L }
% 10.20/1.67 fresh133(true2, true2, sz10, smndt0(xp))
% 10.20/1.67 = { by lemma 35 R->L }
% 10.20/1.67 fresh133(aInteger0(smndt0(xp)), true2, sz10, smndt0(xp))
% 10.20/1.67 = { by axiom 29 (mIntPlus) }
% 10.20/1.67 fresh132(aInteger0(sz10), true2, sz10, smndt0(xp))
% 10.20/1.67 = { by axiom 1 (mIntOne) }
% 10.20/1.67 fresh132(true2, true2, sz10, smndt0(xp))
% 10.20/1.67 = { by axiom 20 (mIntPlus) }
% 10.20/1.67 true2
% 10.20/1.67
% 10.20/1.67 Lemma 37: fresh273(aInteger0(X), true2, Y, sz10, X) = sdtpldt0(Y, sdtpldt0(sz10, X)).
% 10.20/1.67 Proof:
% 10.20/1.67 fresh273(aInteger0(X), true2, Y, sz10, X)
% 10.20/1.67 = { by axiom 31 (mAddAsso) }
% 10.20/1.67 fresh162(aInteger0(sz10), true2, Y, sz10, X)
% 10.20/1.67 = { by axiom 1 (mIntOne) }
% 10.20/1.67 fresh162(true2, true2, Y, sz10, X)
% 10.20/1.67 = { by axiom 27 (mAddAsso) }
% 10.20/1.67 sdtpldt0(Y, sdtpldt0(sz10, X))
% 10.20/1.67
% 10.20/1.67 Goal 1 (m___6): tuple(aElementOf0(sdtpldt0(sz10, smndt0(xp)), szAzrzSzezqlpdtcmdtrp0(sz10, xp)), or) = tuple(true2, true2).
% 10.20/1.67 Proof:
% 10.20/1.67 tuple(aElementOf0(sdtpldt0(sz10, smndt0(xp)), szAzrzSzezqlpdtcmdtrp0(sz10, xp)), or)
% 10.20/1.67 = { by axiom 13 (m__2171_5) R->L }
% 10.20/1.67 tuple(fresh164(true2, true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 34 R->L }
% 10.20/1.67 tuple(fresh164(aInteger0(smndt0(sz10)), true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 26 (m__2171_5) R->L }
% 10.20/1.67 tuple(fresh163(true2, true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 36 R->L }
% 10.20/1.67 tuple(fresh163(aInteger0(sdtpldt0(sz10, smndt0(xp))), true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 32 (m__2171_5) }
% 10.20/1.67 tuple(fresh17(sdtasdt0(xp, smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 21 (mMulMinOne) R->L }
% 10.20/1.67 tuple(fresh17(fresh121(aInteger0(xp), true2, xp), sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 2 (m__2171) }
% 10.20/1.67 tuple(fresh17(fresh121(true2, true2, xp), sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 7 (mMulMinOne) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 15 (mAddComm) R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh160(true2, true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 34 R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh160(aInteger0(smndt0(sz10)), true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 28 (mAddComm) R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh161(aInteger0(sdtpldt0(sz10, smndt0(xp))), true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 36 }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh161(true2, true2, smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 14 (mAddComm) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 37 R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh273(aInteger0(smndt0(xp)), true2, smndt0(sz10), sz10, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 35 }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh273(true2, true2, smndt0(sz10), sz10, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 30 (mAddAsso) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh274(aInteger0(smndt0(sz10)), true2, smndt0(sz10), sz10, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 34 }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh274(true2, true2, smndt0(sz10), sz10, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 25 (mAddAsso) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 17 (mAddNeg_1) R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(fresh158(aInteger0(sz10), true2, sz10), smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 1 (mIntOne) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(fresh158(true2, true2, sz10), smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 5 (mAddNeg_1) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), sdtpldt0(sz00, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 22 (mAddZero_1) R->L }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh6(aInteger0(smndt0(xp)), true2, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by lemma 35 }
% 10.20/1.67 tuple(fresh17(smndt0(xp), fresh6(true2, true2, smndt0(xp)), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 10 (mAddZero_1) }
% 10.20/1.67 tuple(fresh17(smndt0(xp), smndt0(xp), sdtpldt0(sz10, smndt0(xp))), or)
% 10.20/1.67 = { by axiom 8 (m__2171_5) }
% 10.20/1.67 tuple(true2, or)
% 10.20/1.67 = { by axiom 9 (m___1) R->L }
% 10.20/1.67 tuple(true2, fresh11(true2, true2, sz10))
% 10.20/1.67 = { by axiom 1 (mIntOne) R->L }
% 10.20/1.67 tuple(true2, fresh11(aInteger0(sz10), true2, sz10))
% 10.20/1.67 = { by axiom 33 (m___1) }
% 10.20/1.68 tuple(true2, fresh10(sdtasdt0(xp, sz10), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 24 (mMulOne) R->L }
% 10.20/1.68 tuple(true2, fresh10(fresh3(aInteger0(xp), true2, xp), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 2 (m__2171) }
% 10.20/1.68 tuple(true2, fresh10(fresh3(true2, true2, xp), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 12 (mMulOne) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 14 (mAddComm) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(fresh161(true2, true2, sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 2 (m__2171) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(fresh161(aInteger0(xp), true2, sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 28 (mAddComm) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(fresh160(aInteger0(sz10), true2, sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 1 (mIntOne) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(fresh160(true2, true2, sz10, xp), smndt0(sz10))))
% 10.20/1.68 = { by axiom 15 (mAddComm) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(sdtpldt0(xp, sz10), smndt0(sz10))))
% 10.20/1.68 = { by axiom 25 (mAddAsso) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh274(true2, true2, xp, sz10, smndt0(sz10))))
% 10.20/1.68 = { by axiom 2 (m__2171) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh274(aInteger0(xp), true2, xp, sz10, smndt0(sz10))))
% 10.20/1.68 = { by axiom 30 (mAddAsso) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh273(true2, true2, xp, sz10, smndt0(sz10))))
% 10.20/1.68 = { by lemma 34 R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh273(aInteger0(smndt0(sz10)), true2, xp, sz10, smndt0(sz10))))
% 10.20/1.68 = { by lemma 37 }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(xp, sdtpldt0(sz10, smndt0(sz10)))))
% 10.20/1.68 = { by axiom 16 (mAddNeg) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(xp, fresh159(aInteger0(sz10), true2, sz10))))
% 10.20/1.68 = { by axiom 1 (mIntOne) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(xp, fresh159(true2, true2, sz10))))
% 10.20/1.68 = { by axiom 4 (mAddNeg) }
% 10.20/1.68 tuple(true2, fresh10(xp, sdtpldt0(xp, sz00)))
% 10.20/1.68 = { by axiom 23 (mAddZero) R->L }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh5(aInteger0(xp), true2, xp)))
% 10.20/1.68 = { by axiom 2 (m__2171) }
% 10.20/1.68 tuple(true2, fresh10(xp, fresh5(true2, true2, xp)))
% 10.20/1.68 = { by axiom 11 (mAddZero) }
% 10.20/1.68 tuple(true2, fresh10(xp, xp))
% 10.20/1.68 = { by axiom 3 (m___1) }
% 10.20/1.68 tuple(true2, true2)
% 10.20/1.68 % SZS output end Proof
% 10.20/1.68
% 10.20/1.68 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------