TSTP Solution File: RNG082+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG082+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:59:11 EDT 2023
% Result : Theorem 5.11s 1.01s
% Output : Proof 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG082+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 01:27:05 EDT 2023
% 0.14/0.34 % CPUTime :
% 5.11/1.01 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 5.11/1.01
% 5.11/1.01 % SZS status Theorem
% 5.11/1.01
% 5.11/1.03 % SZS output start Proof
% 5.11/1.03 Take the following subset of the input axioms:
% 5.11/1.04 fof(mAMDistr, axiom, ![W0, W1, W2]: ((aElement0(W0) & (aElement0(W1) & aElement0(W2))) => (sdtasdt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & sdtasdt0(sdtpldt0(W1, W2), W0)=sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))).
% 5.11/1.04 fof(mAddAsso, axiom, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aElement0(W1_2) & aElement0(W2_2))) => sdtpldt0(sdtpldt0(W0_2, W1_2), W2_2)=sdtpldt0(W0_2, sdtpldt0(W1_2, W2_2)))).
% 5.11/1.04 fof(mAddComm, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => sdtpldt0(W0_2, W1_2)=sdtpldt0(W1_2, W0_2))).
% 5.11/1.04 fof(mAddInvr, axiom, ![W0_2]: (aElement0(W0_2) => (sdtpldt0(W0_2, smndt0(W0_2))=sz00 & sz00=sdtpldt0(smndt0(W0_2), W0_2)))).
% 5.11/1.04 fof(mAddZero, axiom, ![W0_2]: (aElement0(W0_2) => (sdtpldt0(W0_2, sz00)=W0_2 & W0_2=sdtpldt0(sz00, W0_2)))).
% 5.11/1.04 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 5.11/1.04 fof(mMulUnit, axiom, ![W0_2]: (aElement0(W0_2) => (sdtasdt0(W0_2, sz10)=W0_2 & W0_2=sdtasdt0(sz10, W0_2)))).
% 5.11/1.04 fof(mSortsB_02, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtasdt0(W0_2, W1_2)))).
% 5.11/1.04 fof(mSortsC, axiom, aElement0(sz00)).
% 5.11/1.04 fof(mSortsC_01, axiom, aElement0(sz10)).
% 5.11/1.04 fof(mSortsU, axiom, ![W0_2]: (aElement0(W0_2) => aElement0(smndt0(W0_2)))).
% 5.11/1.04 fof(m__, conjecture, sdtasdt0(smndt0(sz10), xx)=smndt0(xx)).
% 5.11/1.04 fof(m__444, hypothesis, aElement0(xx)).
% 5.11/1.04
% 5.11/1.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.11/1.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.11/1.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.11/1.04 fresh(y, y, x1...xn) = u
% 5.11/1.04 C => fresh(s, t, x1...xn) = v
% 5.11/1.04 where fresh is a fresh function symbol and x1..xn are the free
% 5.11/1.04 variables of u and v.
% 5.11/1.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.11/1.04 input problem has no model of domain size 1).
% 5.11/1.04
% 5.11/1.04 The encoding turns the above axioms into the following unit equations and goals:
% 5.11/1.04
% 5.11/1.04 Axiom 1 (mSortsC_01): aElement0(sz10) = true.
% 5.11/1.04 Axiom 2 (mSortsC): aElement0(sz00) = true.
% 5.11/1.04 Axiom 3 (m__444): aElement0(xx) = true.
% 5.11/1.04 Axiom 4 (mMulUnit): fresh(X, X, Y) = Y.
% 5.11/1.04 Axiom 5 (mAddInvr): fresh14(X, X, Y) = sz00.
% 5.11/1.04 Axiom 6 (mSortsU): fresh5(X, X, Y) = true.
% 5.11/1.04 Axiom 7 (mAddZero_1): fresh4(X, X, Y) = Y.
% 5.11/1.04 Axiom 8 (mAddZero): fresh3(X, X, Y) = Y.
% 5.11/1.04 Axiom 9 (mMulUnit): fresh(aElement0(X), true, X) = sdtasdt0(X, sz10).
% 5.11/1.04 Axiom 10 (mAddComm): fresh16(X, X, Y, Z) = sdtpldt0(Y, Z).
% 5.11/1.04 Axiom 11 (mAddComm): fresh15(X, X, Y, Z) = sdtpldt0(Z, Y).
% 5.11/1.04 Axiom 12 (mAddInvr): fresh14(aElement0(X), true, X) = sdtpldt0(X, smndt0(X)).
% 5.11/1.04 Axiom 13 (mMulComm): fresh11(X, X, Y, Z) = sdtasdt0(Y, Z).
% 5.11/1.04 Axiom 14 (mMulComm): fresh10(X, X, Y, Z) = sdtasdt0(Z, Y).
% 5.11/1.04 Axiom 15 (mSortsB_02): fresh7(X, X, Y, Z) = aElement0(sdtasdt0(Y, Z)).
% 5.11/1.04 Axiom 16 (mSortsB_02): fresh6(X, X, Y, Z) = true.
% 5.11/1.04 Axiom 17 (mSortsU): fresh5(aElement0(X), true, X) = aElement0(smndt0(X)).
% 5.11/1.04 Axiom 18 (mAddZero_1): fresh4(aElement0(X), true, X) = sdtpldt0(sz00, X).
% 5.11/1.04 Axiom 19 (mAddZero): fresh3(aElement0(X), true, X) = sdtpldt0(X, sz00).
% 5.11/1.04 Axiom 20 (mAddAsso): fresh27(X, X, Y, Z, W) = sdtpldt0(Y, sdtpldt0(Z, W)).
% 5.11/1.04 Axiom 21 (mAMDistr): fresh21(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 5.11/1.04 Axiom 22 (mAddAsso): fresh17(X, X, Y, Z, W) = sdtpldt0(sdtpldt0(Y, Z), W).
% 5.11/1.04 Axiom 23 (mAddComm): fresh16(aElement0(X), true, Y, X) = fresh15(aElement0(Y), true, Y, X).
% 5.11/1.04 Axiom 24 (mMulComm): fresh11(aElement0(X), true, Y, X) = fresh10(aElement0(Y), true, Y, X).
% 5.11/1.04 Axiom 25 (mSortsB_02): fresh7(aElement0(X), true, Y, X) = fresh6(aElement0(Y), true, Y, X).
% 5.11/1.04 Axiom 26 (mAMDistr): fresh19(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 5.11/1.04 Axiom 27 (mAddAsso): fresh26(X, X, Y, Z, W) = fresh27(aElement0(Y), true, Y, Z, W).
% 5.11/1.04 Axiom 28 (mAMDistr): fresh20(X, X, Y, Z, W) = fresh21(aElement0(Y), true, Y, Z, W).
% 5.11/1.04 Axiom 29 (mAMDistr): fresh20(aElement0(X), true, Y, Z, X) = fresh19(aElement0(Z), true, Y, Z, X).
% 5.11/1.04 Axiom 30 (mAddAsso): fresh26(aElement0(X), true, Y, Z, X) = fresh17(aElement0(Z), true, Y, Z, X).
% 5.11/1.04
% 5.11/1.04 Lemma 31: sdtasdt0(xx, sz00) = sdtasdt0(sz00, xx).
% 5.11/1.04 Proof:
% 5.11/1.04 sdtasdt0(xx, sz00)
% 5.11/1.04 = { by axiom 14 (mMulComm) R->L }
% 5.11/1.04 fresh10(true, true, sz00, xx)
% 5.11/1.04 = { by axiom 2 (mSortsC) R->L }
% 5.11/1.04 fresh10(aElement0(sz00), true, sz00, xx)
% 5.11/1.04 = { by axiom 24 (mMulComm) R->L }
% 5.11/1.04 fresh11(aElement0(xx), true, sz00, xx)
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh11(true, true, sz00, xx)
% 5.11/1.04 = { by axiom 13 (mMulComm) }
% 5.11/1.04 sdtasdt0(sz00, xx)
% 5.11/1.04
% 5.11/1.04 Lemma 32: sdtasdt0(xx, sz10) = xx.
% 5.11/1.04 Proof:
% 5.11/1.04 sdtasdt0(xx, sz10)
% 5.11/1.04 = { by axiom 9 (mMulUnit) R->L }
% 5.11/1.04 fresh(aElement0(xx), true, xx)
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh(true, true, xx)
% 5.11/1.04 = { by axiom 4 (mMulUnit) }
% 5.11/1.04 xx
% 5.11/1.04
% 5.11/1.04 Lemma 33: aElement0(smndt0(sz10)) = true.
% 5.11/1.04 Proof:
% 5.11/1.04 aElement0(smndt0(sz10))
% 5.11/1.04 = { by axiom 17 (mSortsU) R->L }
% 5.11/1.04 fresh5(aElement0(sz10), true, sz10)
% 5.11/1.04 = { by axiom 1 (mSortsC_01) }
% 5.11/1.04 fresh5(true, true, sz10)
% 5.11/1.04 = { by axiom 6 (mSortsU) }
% 5.11/1.04 true
% 5.11/1.04
% 5.11/1.04 Lemma 34: aElement0(smndt0(xx)) = true.
% 5.11/1.04 Proof:
% 5.11/1.04 aElement0(smndt0(xx))
% 5.11/1.04 = { by axiom 17 (mSortsU) R->L }
% 5.11/1.04 fresh5(aElement0(xx), true, xx)
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh5(true, true, xx)
% 5.11/1.04 = { by axiom 6 (mSortsU) }
% 5.11/1.04 true
% 5.11/1.04
% 5.11/1.04 Lemma 35: sdtasdt0(smndt0(sz10), xx) = sdtasdt0(xx, smndt0(sz10)).
% 5.11/1.04 Proof:
% 5.11/1.04 sdtasdt0(smndt0(sz10), xx)
% 5.11/1.04 = { by axiom 14 (mMulComm) R->L }
% 5.11/1.04 fresh10(true, true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 3 (m__444) R->L }
% 5.11/1.04 fresh10(aElement0(xx), true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 24 (mMulComm) R->L }
% 5.11/1.04 fresh11(aElement0(smndt0(sz10)), true, xx, smndt0(sz10))
% 5.11/1.04 = { by lemma 33 }
% 5.11/1.04 fresh11(true, true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 13 (mMulComm) }
% 5.11/1.04 sdtasdt0(xx, smndt0(sz10))
% 5.11/1.04
% 5.11/1.04 Lemma 36: sdtpldt0(xx, smndt0(xx)) = sz00.
% 5.11/1.04 Proof:
% 5.11/1.04 sdtpldt0(xx, smndt0(xx))
% 5.11/1.04 = { by axiom 12 (mAddInvr) R->L }
% 5.11/1.04 fresh14(aElement0(xx), true, xx)
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh14(true, true, xx)
% 5.11/1.04 = { by axiom 5 (mAddInvr) }
% 5.11/1.04 sz00
% 5.11/1.04
% 5.11/1.04 Lemma 37: aElement0(sdtasdt0(sz00, xx)) = true.
% 5.11/1.04 Proof:
% 5.11/1.04 aElement0(sdtasdt0(sz00, xx))
% 5.11/1.04 = { by axiom 15 (mSortsB_02) R->L }
% 5.11/1.04 fresh7(true, true, sz00, xx)
% 5.11/1.04 = { by axiom 3 (m__444) R->L }
% 5.11/1.04 fresh7(aElement0(xx), true, sz00, xx)
% 5.11/1.04 = { by axiom 25 (mSortsB_02) }
% 5.11/1.04 fresh6(aElement0(sz00), true, sz00, xx)
% 5.11/1.04 = { by axiom 2 (mSortsC) }
% 5.11/1.04 fresh6(true, true, sz00, xx)
% 5.11/1.04 = { by axiom 16 (mSortsB_02) }
% 5.11/1.04 true
% 5.11/1.04
% 5.11/1.04 Lemma 38: aElement0(sdtasdt0(smndt0(sz10), xx)) = true.
% 5.11/1.04 Proof:
% 5.11/1.04 aElement0(sdtasdt0(smndt0(sz10), xx))
% 5.11/1.04 = { by lemma 35 }
% 5.11/1.04 aElement0(sdtasdt0(xx, smndt0(sz10)))
% 5.11/1.04 = { by axiom 15 (mSortsB_02) R->L }
% 5.11/1.04 fresh7(true, true, xx, smndt0(sz10))
% 5.11/1.04 = { by lemma 33 R->L }
% 5.11/1.04 fresh7(aElement0(smndt0(sz10)), true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 25 (mSortsB_02) }
% 5.11/1.04 fresh6(aElement0(xx), true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh6(true, true, xx, smndt0(sz10))
% 5.11/1.04 = { by axiom 16 (mSortsB_02) }
% 5.11/1.04 true
% 5.11/1.04
% 5.11/1.04 Lemma 39: fresh20(X, X, xx, Y, Z) = sdtasdt0(xx, sdtpldt0(Y, Z)).
% 5.11/1.04 Proof:
% 5.11/1.04 fresh20(X, X, xx, Y, Z)
% 5.11/1.04 = { by axiom 28 (mAMDistr) }
% 5.11/1.04 fresh21(aElement0(xx), true, xx, Y, Z)
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh21(true, true, xx, Y, Z)
% 5.11/1.04 = { by axiom 21 (mAMDistr) }
% 5.11/1.04 sdtasdt0(xx, sdtpldt0(Y, Z))
% 5.11/1.04
% 5.11/1.04 Lemma 40: fresh26(X, X, Y, xx, smndt0(xx)) = sdtpldt0(sdtpldt0(Y, xx), smndt0(xx)).
% 5.11/1.04 Proof:
% 5.11/1.04 fresh26(X, X, Y, xx, smndt0(xx))
% 5.11/1.04 = { by axiom 27 (mAddAsso) }
% 5.11/1.04 fresh27(aElement0(Y), true, Y, xx, smndt0(xx))
% 5.11/1.04 = { by axiom 27 (mAddAsso) R->L }
% 5.11/1.04 fresh26(true, true, Y, xx, smndt0(xx))
% 5.11/1.04 = { by lemma 34 R->L }
% 5.11/1.04 fresh26(aElement0(smndt0(xx)), true, Y, xx, smndt0(xx))
% 5.11/1.04 = { by axiom 30 (mAddAsso) }
% 5.11/1.04 fresh17(aElement0(xx), true, Y, xx, smndt0(xx))
% 5.11/1.04 = { by axiom 3 (m__444) }
% 5.11/1.04 fresh17(true, true, Y, xx, smndt0(xx))
% 5.11/1.04 = { by axiom 22 (mAddAsso) }
% 5.11/1.04 sdtpldt0(sdtpldt0(Y, xx), smndt0(xx))
% 5.11/1.04
% 5.11/1.04 Goal 1 (m__): sdtasdt0(smndt0(sz10), xx) = smndt0(xx).
% 5.11/1.04 Proof:
% 5.11/1.04 sdtasdt0(smndt0(sz10), xx)
% 5.11/1.04 = { by axiom 8 (mAddZero) R->L }
% 5.11/1.04 fresh3(true, true, sdtasdt0(smndt0(sz10), xx))
% 5.11/1.04 = { by lemma 38 R->L }
% 5.11/1.04 fresh3(aElement0(sdtasdt0(smndt0(sz10), xx)), true, sdtasdt0(smndt0(sz10), xx))
% 5.11/1.04 = { by axiom 19 (mAddZero) }
% 5.11/1.04 sdtpldt0(sdtasdt0(smndt0(sz10), xx), sz00)
% 5.11/1.04 = { by lemma 36 R->L }
% 5.11/1.04 sdtpldt0(sdtasdt0(smndt0(sz10), xx), sdtpldt0(xx, smndt0(xx)))
% 5.11/1.04 = { by axiom 20 (mAddAsso) R->L }
% 5.11/1.04 fresh27(true, true, sdtasdt0(smndt0(sz10), xx), xx, smndt0(xx))
% 5.11/1.04 = { by lemma 38 R->L }
% 5.11/1.04 fresh27(aElement0(sdtasdt0(smndt0(sz10), xx)), true, sdtasdt0(smndt0(sz10), xx), xx, smndt0(xx))
% 5.11/1.04 = { by axiom 27 (mAddAsso) R->L }
% 5.11/1.04 fresh26(X, X, sdtasdt0(smndt0(sz10), xx), xx, smndt0(xx))
% 5.11/1.04 = { by lemma 40 }
% 5.11/1.04 sdtpldt0(sdtpldt0(sdtasdt0(smndt0(sz10), xx), xx), smndt0(xx))
% 5.11/1.04 = { by axiom 11 (mAddComm) R->L }
% 5.11/1.04 sdtpldt0(fresh15(true, true, xx, sdtasdt0(smndt0(sz10), xx)), smndt0(xx))
% 5.11/1.04 = { by axiom 3 (m__444) R->L }
% 5.11/1.04 sdtpldt0(fresh15(aElement0(xx), true, xx, sdtasdt0(smndt0(sz10), xx)), smndt0(xx))
% 5.11/1.04 = { by axiom 23 (mAddComm) R->L }
% 5.11/1.04 sdtpldt0(fresh16(aElement0(sdtasdt0(smndt0(sz10), xx)), true, xx, sdtasdt0(smndt0(sz10), xx)), smndt0(xx))
% 5.11/1.04 = { by lemma 38 }
% 5.11/1.04 sdtpldt0(fresh16(true, true, xx, sdtasdt0(smndt0(sz10), xx)), smndt0(xx))
% 5.11/1.04 = { by axiom 10 (mAddComm) }
% 5.11/1.04 sdtpldt0(sdtpldt0(xx, sdtasdt0(smndt0(sz10), xx)), smndt0(xx))
% 5.11/1.04 = { by lemma 35 }
% 5.11/1.04 sdtpldt0(sdtpldt0(xx, sdtasdt0(xx, smndt0(sz10))), smndt0(xx))
% 5.11/1.04 = { by lemma 32 R->L }
% 5.11/1.04 sdtpldt0(sdtpldt0(sdtasdt0(xx, sz10), sdtasdt0(xx, smndt0(sz10))), smndt0(xx))
% 5.11/1.04 = { by axiom 26 (mAMDistr) R->L }
% 5.11/1.04 sdtpldt0(fresh19(true, true, xx, sz10, smndt0(sz10)), smndt0(xx))
% 5.11/1.04 = { by axiom 1 (mSortsC_01) R->L }
% 5.11/1.04 sdtpldt0(fresh19(aElement0(sz10), true, xx, sz10, smndt0(sz10)), smndt0(xx))
% 5.11/1.04 = { by axiom 29 (mAMDistr) R->L }
% 5.11/1.04 sdtpldt0(fresh20(aElement0(smndt0(sz10)), true, xx, sz10, smndt0(sz10)), smndt0(xx))
% 5.11/1.04 = { by lemma 33 }
% 5.11/1.04 sdtpldt0(fresh20(true, true, xx, sz10, smndt0(sz10)), smndt0(xx))
% 5.11/1.04 = { by lemma 39 }
% 5.11/1.04 sdtpldt0(sdtasdt0(xx, sdtpldt0(sz10, smndt0(sz10))), smndt0(xx))
% 5.11/1.04 = { by axiom 12 (mAddInvr) R->L }
% 5.11/1.04 sdtpldt0(sdtasdt0(xx, fresh14(aElement0(sz10), true, sz10)), smndt0(xx))
% 5.11/1.04 = { by axiom 1 (mSortsC_01) }
% 5.11/1.04 sdtpldt0(sdtasdt0(xx, fresh14(true, true, sz10)), smndt0(xx))
% 5.11/1.04 = { by axiom 5 (mAddInvr) }
% 5.11/1.04 sdtpldt0(sdtasdt0(xx, sz00), smndt0(xx))
% 5.11/1.04 = { by lemma 31 }
% 5.11/1.04 sdtpldt0(sdtasdt0(sz00, xx), smndt0(xx))
% 5.11/1.04 = { by axiom 11 (mAddComm) R->L }
% 5.11/1.04 fresh15(true, true, smndt0(xx), sdtasdt0(sz00, xx))
% 5.11/1.04 = { by lemma 34 R->L }
% 5.11/1.04 fresh15(aElement0(smndt0(xx)), true, smndt0(xx), sdtasdt0(sz00, xx))
% 5.11/1.04 = { by axiom 23 (mAddComm) R->L }
% 5.11/1.04 fresh16(aElement0(sdtasdt0(sz00, xx)), true, smndt0(xx), sdtasdt0(sz00, xx))
% 5.11/1.04 = { by lemma 37 }
% 5.11/1.04 fresh16(true, true, smndt0(xx), sdtasdt0(sz00, xx))
% 5.11/1.04 = { by axiom 10 (mAddComm) }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtasdt0(sz00, xx))
% 5.11/1.04 = { by axiom 8 (mAddZero) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), fresh3(true, true, sdtasdt0(sz00, xx)))
% 5.11/1.04 = { by lemma 37 R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), fresh3(aElement0(sdtasdt0(sz00, xx)), true, sdtasdt0(sz00, xx)))
% 5.11/1.04 = { by axiom 19 (mAddZero) }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(sz00, xx), sz00))
% 5.11/1.04 = { by lemma 36 R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(sz00, xx), sdtpldt0(xx, smndt0(xx))))
% 5.11/1.04 = { by axiom 20 (mAddAsso) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), fresh27(true, true, sdtasdt0(sz00, xx), xx, smndt0(xx)))
% 5.11/1.04 = { by lemma 37 R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), fresh27(aElement0(sdtasdt0(sz00, xx)), true, sdtasdt0(sz00, xx), xx, smndt0(xx)))
% 5.11/1.04 = { by axiom 27 (mAddAsso) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), fresh26(Y, Y, sdtasdt0(sz00, xx), xx, smndt0(xx)))
% 5.11/1.04 = { by lemma 40 }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtpldt0(sdtasdt0(sz00, xx), xx), smndt0(xx)))
% 5.11/1.04 = { by lemma 31 R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtpldt0(sdtasdt0(xx, sz00), xx), smndt0(xx)))
% 5.11/1.04 = { by lemma 32 R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtpldt0(sdtasdt0(xx, sz00), sdtasdt0(xx, sz10)), smndt0(xx)))
% 5.11/1.04 = { by axiom 26 (mAMDistr) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(fresh19(true, true, xx, sz00, sz10), smndt0(xx)))
% 5.11/1.04 = { by axiom 2 (mSortsC) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(fresh19(aElement0(sz00), true, xx, sz00, sz10), smndt0(xx)))
% 5.11/1.04 = { by axiom 29 (mAMDistr) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(fresh20(aElement0(sz10), true, xx, sz00, sz10), smndt0(xx)))
% 5.11/1.04 = { by axiom 1 (mSortsC_01) }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(fresh20(true, true, xx, sz00, sz10), smndt0(xx)))
% 5.11/1.04 = { by lemma 39 }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(xx, sdtpldt0(sz00, sz10)), smndt0(xx)))
% 5.11/1.04 = { by axiom 18 (mAddZero_1) R->L }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(xx, fresh4(aElement0(sz10), true, sz10)), smndt0(xx)))
% 5.11/1.04 = { by axiom 1 (mSortsC_01) }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(xx, fresh4(true, true, sz10)), smndt0(xx)))
% 5.11/1.04 = { by axiom 7 (mAddZero_1) }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(sdtasdt0(xx, sz10), smndt0(xx)))
% 5.11/1.04 = { by lemma 32 }
% 5.11/1.04 sdtpldt0(smndt0(xx), sdtpldt0(xx, smndt0(xx)))
% 5.11/1.04 = { by lemma 36 }
% 5.11/1.04 sdtpldt0(smndt0(xx), sz00)
% 5.11/1.04 = { by axiom 19 (mAddZero) R->L }
% 5.11/1.04 fresh3(aElement0(smndt0(xx)), true, smndt0(xx))
% 5.11/1.04 = { by lemma 34 }
% 5.11/1.04 fresh3(true, true, smndt0(xx))
% 5.11/1.04 = { by axiom 8 (mAddZero) }
% 5.11/1.04 smndt0(xx)
% 5.11/1.04 % SZS output end Proof
% 5.11/1.04
% 5.11/1.04 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------