TSTP Solution File: COM020+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM020+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 : n006.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 : Wed Aug 30 18:45:23 EDT 2023
% Result : Theorem 4.22s 0.90s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM020+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
% 0.13/0.34 % Computer : n006.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 : Tue Aug 29 13:27:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.22/0.90 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 4.22/0.90
% 4.22/0.90 % SZS status Theorem
% 4.22/0.90
% 4.45/0.92 % SZS output start Proof
% 4.45/0.92 Take the following subset of the input axioms:
% 4.56/0.93 fof(mNFRDef, definition, ![W0, W1]: ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2]: (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & (sdtmndtasgtdt0(W0, W1, W2) & ~?[W3]: aReductOfIn0(W3, W2, W1)))))).
% 4.56/0.93 fof(mTCDef, definition, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aRewritingSystem0(W1_2) & aElement0(W2_2))) => (sdtmndtplgtdt0(W0_2, W1_2, W2_2) <=> (aReductOfIn0(W2_2, W0_2, W1_2) | ?[W3_2]: (aElement0(W3_2) & (aReductOfIn0(W3_2, W0_2, W1_2) & sdtmndtplgtdt0(W3_2, W1_2, W2_2))))))).
% 4.56/0.93 fof(mTCRTrans, axiom, ![W3_2, W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aRewritingSystem0(W1_2) & (aElement0(W2_2) & aElement0(W3_2)))) => ((sdtmndtasgtdt0(W0_2, W1_2, W2_2) & sdtmndtasgtdt0(W2_2, W1_2, W3_2)) => sdtmndtasgtdt0(W0_2, W1_2, W3_2)))).
% 4.56/0.93 fof(mTermin, definition, ![W0_2]: (aRewritingSystem0(W0_2) => (isTerminating0(W0_2) <=> ![W1_2, W2_2]: ((aElement0(W1_2) & aElement0(W2_2)) => (sdtmndtplgtdt0(W1_2, W0_2, W2_2) => iLess0(W2_2, W1_2)))))).
% 4.56/0.93 fof(m__, conjecture, ?[W0_2]: (aElement0(W0_2) & (sdtmndtasgtdt0(xb, xR, W0_2) & sdtmndtasgtdt0(xd, xR, W0_2)))).
% 4.56/0.93 fof(m__656, hypothesis, aRewritingSystem0(xR)).
% 4.56/0.93 fof(m__656_01, hypothesis, isLocallyConfluent0(xR) & isTerminating0(xR)).
% 4.56/0.93 fof(m__715, hypothesis, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aElement0(W1_2) & (aElement0(W2_2) & (sdtmndtasgtdt0(W0_2, xR, W1_2) & sdtmndtasgtdt0(W0_2, xR, W2_2))))) => (iLess0(W0_2, xa) => ?[W3_2]: (aElement0(W3_2) & (sdtmndtasgtdt0(W1_2, xR, W3_2) & sdtmndtasgtdt0(W2_2, xR, W3_2)))))).
% 4.56/0.93 fof(m__731, hypothesis, aElement0(xa) & (aElement0(xb) & aElement0(xc))).
% 4.56/0.93 fof(m__755, hypothesis, aElement0(xu) & (aReductOfIn0(xu, xa, xR) & sdtmndtasgtdt0(xu, xR, xb))).
% 4.56/0.93 fof(m__799, hypothesis, aElement0(xw) & (sdtmndtasgtdt0(xu, xR, xw) & sdtmndtasgtdt0(xv, xR, xw))).
% 4.56/0.93 fof(m__818, hypothesis, aNormalFormOfIn0(xd, xw, xR)).
% 4.56/0.93
% 4.56/0.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.56/0.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.56/0.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.56/0.93 fresh(y, y, x1...xn) = u
% 4.56/0.93 C => fresh(s, t, x1...xn) = v
% 4.56/0.93 where fresh is a fresh function symbol and x1..xn are the free
% 4.56/0.93 variables of u and v.
% 4.56/0.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.56/0.93 input problem has no model of domain size 1).
% 4.56/0.93
% 4.56/0.93 The encoding turns the above axioms into the following unit equations and goals:
% 4.56/0.93
% 4.56/0.93 Axiom 1 (m__656_01_1): isTerminating0(xR) = true2.
% 4.56/0.93 Axiom 2 (m__656): aRewritingSystem0(xR) = true2.
% 4.56/0.93 Axiom 3 (m__731_1): aElement0(xb) = true2.
% 4.56/0.93 Axiom 4 (m__755): aElement0(xu) = true2.
% 4.56/0.93 Axiom 5 (m__799): aElement0(xw) = true2.
% 4.56/0.93 Axiom 6 (m__731): aElement0(xa) = true2.
% 4.56/0.93 Axiom 7 (mNFRDef_2): fresh30(X, X, Y) = true2.
% 4.56/0.93 Axiom 8 (m__818): aNormalFormOfIn0(xd, xw, xR) = true2.
% 4.56/0.93 Axiom 9 (m__755_1): aReductOfIn0(xu, xa, xR) = true2.
% 4.56/0.93 Axiom 10 (m__755_2): sdtmndtasgtdt0(xu, xR, xb) = true2.
% 4.56/0.93 Axiom 11 (m__799_1): sdtmndtasgtdt0(xu, xR, xw) = true2.
% 4.56/0.93 Axiom 12 (mTermin): fresh37(X, X, Y, Z) = true2.
% 4.56/0.93 Axiom 13 (mTermin): fresh35(X, X, Y, Z) = iLess0(Z, Y).
% 4.56/0.93 Axiom 14 (m__715_2): fresh26(X, X, Y, Z) = true2.
% 4.56/0.93 Axiom 15 (m__715_1): fresh20(X, X, Y, Z) = true2.
% 4.56/0.93 Axiom 16 (m__715): fresh14(X, X, Y, Z) = true2.
% 4.56/0.93 Axiom 17 (mNFRDef_2): fresh8(X, X, Y, Z) = aElement0(Z).
% 4.56/0.93 Axiom 18 (mTCDef_1): fresh113(X, X, Y, Z, W) = true2.
% 4.56/0.93 Axiom 19 (mTCDef_1): fresh111(X, X, Y, Z, W) = sdtmndtplgtdt0(Y, Z, W).
% 4.56/0.93 Axiom 20 (mTCRTrans): fresh93(X, X, Y, Z, W) = true2.
% 4.56/0.93 Axiom 21 (mTCRTrans): fresh91(X, X, Y, Z, W) = sdtmndtasgtdt0(Y, Z, W).
% 4.56/0.93 Axiom 22 (mTermin): fresh36(X, X, Y, Z) = fresh37(aElement0(Y), true2, Y, Z).
% 4.56/0.93 Axiom 23 (mTermin): fresh34(X, X, Y, Z, W) = fresh35(aElement0(W), true2, Z, W).
% 4.56/0.93 Axiom 24 (mTermin): fresh33(X, X, Y, Z, W) = fresh36(aRewritingSystem0(Y), true2, Z, W).
% 4.56/0.93 Axiom 25 (mNFRDef_3): fresh32(X, X, Y, Z, W) = true2.
% 4.56/0.93 Axiom 26 (mNFRDef_2): fresh29(X, X, Y, Z, W) = fresh30(aElement0(Y), true2, W).
% 4.56/0.93 Axiom 27 (m__715_2): fresh25(X, X, Y, Z, W) = fresh26(aElement0(Y), true2, Z, W).
% 4.56/0.93 Axiom 28 (m__715_1): fresh19(X, X, Y, Z, W) = fresh20(aElement0(Y), true2, Z, W).
% 4.56/0.93 Axiom 29 (m__715): fresh13(X, X, Y, Z, W) = fresh14(aElement0(Y), true2, Z, W).
% 4.56/0.93 Axiom 30 (m__715): fresh12(X, X, Y, Z, W) = aElement0(w3(Z, W)).
% 4.56/0.93 Axiom 31 (mNFRDef_3): fresh7(X, X, Y, Z, W) = sdtmndtasgtdt0(Y, Z, W).
% 4.56/0.93 Axiom 32 (m__715_1): fresh18(X, X, Y, Z, W) = sdtmndtasgtdt0(Z, xR, w3(Z, W)).
% 4.56/0.93 Axiom 33 (m__715_2): fresh24(X, X, Y, Z, W) = sdtmndtasgtdt0(W, xR, w3(Z, W)).
% 4.56/0.93 Axiom 34 (mTCDef_1): fresh112(X, X, Y, Z, W) = fresh113(aElement0(Y), true2, Y, Z, W).
% 4.56/0.93 Axiom 35 (mTCDef_1): fresh110(X, X, Y, Z, W) = fresh111(aElement0(W), true2, Y, Z, W).
% 4.56/0.93 Axiom 36 (mTCRTrans): fresh92(X, X, Y, Z, W, V) = fresh93(aElement0(Y), true2, Y, Z, V).
% 4.56/0.93 Axiom 37 (mTCRTrans): fresh90(X, X, Y, Z, W, V) = fresh91(aElement0(W), true2, Y, Z, V).
% 4.56/0.93 Axiom 38 (mNFRDef_3): fresh31(X, X, Y, Z, W) = fresh32(aElement0(Y), true2, Y, Z, W).
% 4.56/0.93 Axiom 39 (m__715_2): fresh22(X, X, Y, Z, W) = fresh25(aElement0(W), true2, Y, Z, W).
% 4.56/0.93 Axiom 40 (m__715_2): fresh23(X, X, Y, Z, W) = fresh24(aElement0(Z), true2, Y, Z, W).
% 4.56/0.93 Axiom 41 (m__715_1): fresh16(X, X, Y, Z, W) = fresh19(aElement0(W), true2, Y, Z, W).
% 4.56/0.93 Axiom 42 (m__715_1): fresh17(X, X, Y, Z, W) = fresh18(aElement0(Z), true2, Y, Z, W).
% 4.56/0.93 Axiom 43 (m__715): fresh10(X, X, Y, Z, W) = fresh13(aElement0(W), true2, Y, Z, W).
% 4.56/0.93 Axiom 44 (m__715): fresh11(X, X, Y, Z, W) = fresh12(aElement0(Z), true2, Y, Z, W).
% 4.56/0.93 Axiom 45 (mTCRTrans): fresh89(X, X, Y, Z, W, V) = fresh92(aElement0(V), true2, Y, Z, W, V).
% 4.56/0.93 Axiom 46 (mTCRTrans): fresh88(X, X, Y, Z, W, V) = fresh90(aRewritingSystem0(Z), true2, Y, Z, W, V).
% 4.56/0.93 Axiom 47 (m__715_2): fresh21(X, X, Y, Z, W) = fresh23(iLess0(Y, xa), true2, Y, Z, W).
% 4.56/0.93 Axiom 48 (m__715_1): fresh15(X, X, Y, Z, W) = fresh17(iLess0(Y, xa), true2, Y, Z, W).
% 4.56/0.93 Axiom 49 (m__715): fresh9(X, X, Y, Z, W) = fresh11(iLess0(Y, xa), true2, Y, Z, W).
% 4.56/0.93 Axiom 50 (mTCDef_1): fresh110(aReductOfIn0(X, Y, Z), true2, Y, Z, X) = fresh112(aRewritingSystem0(Z), true2, Y, Z, X).
% 4.56/0.93 Axiom 51 (mTermin): fresh33(isTerminating0(X), true2, X, Y, Z) = fresh34(sdtmndtplgtdt0(Y, X, Z), true2, X, Y, Z).
% 4.56/0.93 Axiom 52 (mNFRDef_3): fresh31(aNormalFormOfIn0(X, Y, Z), true2, Y, Z, X) = fresh7(aRewritingSystem0(Z), true2, Y, Z, X).
% 4.56/0.93 Axiom 53 (mNFRDef_2): fresh29(aNormalFormOfIn0(X, Y, Z), true2, Y, Z, X) = fresh8(aRewritingSystem0(Z), true2, Y, X).
% 4.56/0.93 Axiom 54 (m__715_2): fresh21(sdtmndtasgtdt0(X, xR, Y), true2, X, Z, Y) = fresh22(sdtmndtasgtdt0(X, xR, Z), true2, X, Z, Y).
% 4.56/0.93 Axiom 55 (m__715_1): fresh15(sdtmndtasgtdt0(X, xR, Y), true2, X, Z, Y) = fresh16(sdtmndtasgtdt0(X, xR, Z), true2, X, Z, Y).
% 4.56/0.93 Axiom 56 (m__715): fresh9(sdtmndtasgtdt0(X, xR, Y), true2, X, Z, Y) = fresh10(sdtmndtasgtdt0(X, xR, Z), true2, X, Z, Y).
% 4.56/0.93 Axiom 57 (mTCRTrans): fresh88(sdtmndtasgtdt0(X, Y, Z), true2, W, Y, X, Z) = fresh89(sdtmndtasgtdt0(W, Y, X), true2, W, Y, X, Z).
% 4.56/0.93
% 4.56/0.93 Lemma 58: aElement0(xd) = true2.
% 4.56/0.93 Proof:
% 4.56/0.93 aElement0(xd)
% 4.56/0.93 = { by axiom 17 (mNFRDef_2) R->L }
% 4.56/0.93 fresh8(true2, true2, xw, xd)
% 4.56/0.93 = { by axiom 2 (m__656) R->L }
% 4.56/0.93 fresh8(aRewritingSystem0(xR), true2, xw, xd)
% 4.56/0.93 = { by axiom 53 (mNFRDef_2) R->L }
% 4.56/0.93 fresh29(aNormalFormOfIn0(xd, xw, xR), true2, xw, xR, xd)
% 4.56/0.93 = { by axiom 8 (m__818) }
% 4.56/0.93 fresh29(true2, true2, xw, xR, xd)
% 4.56/0.93 = { by axiom 26 (mNFRDef_2) }
% 4.56/0.93 fresh30(aElement0(xw), true2, xd)
% 4.56/0.93 = { by axiom 5 (m__799) }
% 4.56/0.93 fresh30(true2, true2, xd)
% 4.56/0.93 = { by axiom 7 (mNFRDef_2) }
% 4.56/0.93 true2
% 4.56/0.93
% 4.56/0.93 Lemma 59: iLess0(xu, xa) = true2.
% 4.56/0.93 Proof:
% 4.56/0.93 iLess0(xu, xa)
% 4.56/0.93 = { by axiom 13 (mTermin) R->L }
% 4.56/0.93 fresh35(true2, true2, xa, xu)
% 4.56/0.93 = { by axiom 4 (m__755) R->L }
% 4.56/0.93 fresh35(aElement0(xu), true2, xa, xu)
% 4.56/0.93 = { by axiom 23 (mTermin) R->L }
% 4.56/0.93 fresh34(true2, true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 18 (mTCDef_1) R->L }
% 4.56/0.93 fresh34(fresh113(true2, true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 6 (m__731) R->L }
% 4.56/0.93 fresh34(fresh113(aElement0(xa), true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 34 (mTCDef_1) R->L }
% 4.56/0.93 fresh34(fresh112(true2, true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 2 (m__656) R->L }
% 4.56/0.93 fresh34(fresh112(aRewritingSystem0(xR), true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 50 (mTCDef_1) R->L }
% 4.56/0.93 fresh34(fresh110(aReductOfIn0(xu, xa, xR), true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 9 (m__755_1) }
% 4.56/0.93 fresh34(fresh110(true2, true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 35 (mTCDef_1) }
% 4.56/0.93 fresh34(fresh111(aElement0(xu), true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 4 (m__755) }
% 4.56/0.93 fresh34(fresh111(true2, true2, xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 19 (mTCDef_1) }
% 4.56/0.93 fresh34(sdtmndtplgtdt0(xa, xR, xu), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 51 (mTermin) R->L }
% 4.56/0.93 fresh33(isTerminating0(xR), true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 1 (m__656_01_1) }
% 4.56/0.93 fresh33(true2, true2, xR, xa, xu)
% 4.56/0.93 = { by axiom 24 (mTermin) }
% 4.56/0.93 fresh36(aRewritingSystem0(xR), true2, xa, xu)
% 4.56/0.93 = { by axiom 2 (m__656) }
% 4.56/0.93 fresh36(true2, true2, xa, xu)
% 4.56/0.93 = { by axiom 22 (mTermin) }
% 4.56/0.93 fresh37(aElement0(xa), true2, xa, xu)
% 4.56/0.93 = { by axiom 6 (m__731) }
% 4.56/0.93 fresh37(true2, true2, xa, xu)
% 4.56/0.93 = { by axiom 12 (mTermin) }
% 4.56/0.93 true2
% 4.56/0.93
% 4.56/0.93 Lemma 60: sdtmndtasgtdt0(xu, xR, xd) = true2.
% 4.56/0.93 Proof:
% 4.56/0.93 sdtmndtasgtdt0(xu, xR, xd)
% 4.56/0.93 = { by axiom 21 (mTCRTrans) R->L }
% 4.56/0.93 fresh91(true2, true2, xu, xR, xd)
% 4.56/0.93 = { by axiom 5 (m__799) R->L }
% 4.56/0.93 fresh91(aElement0(xw), true2, xu, xR, xd)
% 4.56/0.93 = { by axiom 37 (mTCRTrans) R->L }
% 4.56/0.93 fresh90(true2, true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 2 (m__656) R->L }
% 4.56/0.93 fresh90(aRewritingSystem0(xR), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 46 (mTCRTrans) R->L }
% 4.56/0.93 fresh88(true2, true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 25 (mNFRDef_3) R->L }
% 4.56/0.93 fresh88(fresh32(true2, true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 5 (m__799) R->L }
% 4.56/0.93 fresh88(fresh32(aElement0(xw), true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 38 (mNFRDef_3) R->L }
% 4.56/0.93 fresh88(fresh31(true2, true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 8 (m__818) R->L }
% 4.56/0.93 fresh88(fresh31(aNormalFormOfIn0(xd, xw, xR), true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 52 (mNFRDef_3) }
% 4.56/0.93 fresh88(fresh7(aRewritingSystem0(xR), true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 2 (m__656) }
% 4.56/0.93 fresh88(fresh7(true2, true2, xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 31 (mNFRDef_3) }
% 4.56/0.93 fresh88(sdtmndtasgtdt0(xw, xR, xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 57 (mTCRTrans) }
% 4.56/0.93 fresh89(sdtmndtasgtdt0(xu, xR, xw), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 11 (m__799_1) }
% 4.56/0.93 fresh89(true2, true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 45 (mTCRTrans) }
% 4.56/0.93 fresh92(aElement0(xd), true2, xu, xR, xw, xd)
% 4.56/0.93 = { by lemma 58 }
% 4.56/0.93 fresh92(true2, true2, xu, xR, xw, xd)
% 4.56/0.93 = { by axiom 36 (mTCRTrans) }
% 4.56/0.93 fresh93(aElement0(xu), true2, xu, xR, xd)
% 4.56/0.93 = { by axiom 4 (m__755) }
% 4.56/0.93 fresh93(true2, true2, xu, xR, xd)
% 4.56/0.93 = { by axiom 20 (mTCRTrans) }
% 4.56/0.93 true2
% 4.56/0.93
% 4.56/0.93 Goal 1 (m__): tuple2(aElement0(X), sdtmndtasgtdt0(xb, xR, X), sdtmndtasgtdt0(xd, xR, X)) = tuple2(true2, true2, true2).
% 4.56/0.93 The goal is true when:
% 4.56/0.93 X = w3(xd, xb)
% 4.56/0.93
% 4.56/0.93 Proof:
% 4.56/0.93 tuple2(aElement0(w3(xd, xb)), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by axiom 30 (m__715) R->L }
% 4.56/0.93 tuple2(fresh12(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by lemma 58 R->L }
% 4.56/0.93 tuple2(fresh12(aElement0(xd), true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by axiom 44 (m__715) R->L }
% 4.56/0.93 tuple2(fresh11(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by lemma 59 R->L }
% 4.56/0.93 tuple2(fresh11(iLess0(xu, xa), true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by axiom 49 (m__715) R->L }
% 4.56/0.93 tuple2(fresh9(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.93 = { by axiom 10 (m__755_2) R->L }
% 4.56/0.94 tuple2(fresh9(sdtmndtasgtdt0(xu, xR, xb), true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 56 (m__715) }
% 4.56/0.94 tuple2(fresh10(sdtmndtasgtdt0(xu, xR, xd), true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by lemma 60 }
% 4.56/0.94 tuple2(fresh10(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 43 (m__715) }
% 4.56/0.94 tuple2(fresh13(aElement0(xb), true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 3 (m__731_1) }
% 4.56/0.94 tuple2(fresh13(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 29 (m__715) }
% 4.56/0.94 tuple2(fresh14(aElement0(xu), true2, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 4 (m__755) }
% 4.56/0.94 tuple2(fresh14(true2, true2, xd, xb), sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 16 (m__715) }
% 4.56/0.94 tuple2(true2, sdtmndtasgtdt0(xb, xR, w3(xd, xb)), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 33 (m__715_2) R->L }
% 4.56/0.94 tuple2(true2, fresh24(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by lemma 58 R->L }
% 4.56/0.94 tuple2(true2, fresh24(aElement0(xd), true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 40 (m__715_2) R->L }
% 4.56/0.94 tuple2(true2, fresh23(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by lemma 59 R->L }
% 4.56/0.94 tuple2(true2, fresh23(iLess0(xu, xa), true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 47 (m__715_2) R->L }
% 4.56/0.94 tuple2(true2, fresh21(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 10 (m__755_2) R->L }
% 4.56/0.94 tuple2(true2, fresh21(sdtmndtasgtdt0(xu, xR, xb), true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 54 (m__715_2) }
% 4.56/0.94 tuple2(true2, fresh22(sdtmndtasgtdt0(xu, xR, xd), true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by lemma 60 }
% 4.56/0.94 tuple2(true2, fresh22(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 39 (m__715_2) }
% 4.56/0.94 tuple2(true2, fresh25(aElement0(xb), true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 3 (m__731_1) }
% 4.56/0.94 tuple2(true2, fresh25(true2, true2, xu, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 27 (m__715_2) }
% 4.56/0.94 tuple2(true2, fresh26(aElement0(xu), true2, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 4 (m__755) }
% 4.56/0.94 tuple2(true2, fresh26(true2, true2, xd, xb), sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 14 (m__715_2) }
% 4.56/0.94 tuple2(true2, true2, sdtmndtasgtdt0(xd, xR, w3(xd, xb)))
% 4.56/0.94 = { by axiom 32 (m__715_1) R->L }
% 4.56/0.94 tuple2(true2, true2, fresh18(true2, true2, xu, xd, xb))
% 4.56/0.94 = { by lemma 58 R->L }
% 4.56/0.94 tuple2(true2, true2, fresh18(aElement0(xd), true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 42 (m__715_1) R->L }
% 4.56/0.94 tuple2(true2, true2, fresh17(true2, true2, xu, xd, xb))
% 4.56/0.94 = { by lemma 59 R->L }
% 4.56/0.94 tuple2(true2, true2, fresh17(iLess0(xu, xa), true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 48 (m__715_1) R->L }
% 4.56/0.94 tuple2(true2, true2, fresh15(true2, true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 10 (m__755_2) R->L }
% 4.56/0.94 tuple2(true2, true2, fresh15(sdtmndtasgtdt0(xu, xR, xb), true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 55 (m__715_1) }
% 4.56/0.94 tuple2(true2, true2, fresh16(sdtmndtasgtdt0(xu, xR, xd), true2, xu, xd, xb))
% 4.56/0.94 = { by lemma 60 }
% 4.56/0.94 tuple2(true2, true2, fresh16(true2, true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 41 (m__715_1) }
% 4.56/0.94 tuple2(true2, true2, fresh19(aElement0(xb), true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 3 (m__731_1) }
% 4.56/0.94 tuple2(true2, true2, fresh19(true2, true2, xu, xd, xb))
% 4.56/0.94 = { by axiom 28 (m__715_1) }
% 4.56/0.94 tuple2(true2, true2, fresh20(aElement0(xu), true2, xd, xb))
% 4.56/0.94 = { by axiom 4 (m__755) }
% 4.56/0.94 tuple2(true2, true2, fresh20(true2, true2, xd, xb))
% 4.56/0.94 = { by axiom 15 (m__715_1) }
% 4.56/0.94 tuple2(true2, true2, true2)
% 4.56/0.94 % SZS output end Proof
% 4.56/0.94
% 4.56/0.94 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------