TSTP Solution File: COM017+4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM017+4 : 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 : Wed Aug 30 18:45:22 EDT 2023
% Result : Theorem 2.94s 0.75s
% Output : Proof 3.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM017+4 : 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
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 13:32:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 2.94/0.75 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.94/0.75
% 2.94/0.75 % SZS status Theorem
% 2.94/0.75
% 3.30/0.78 % SZS output start Proof
% 3.30/0.78 Take the following subset of the input axioms:
% 3.30/0.79 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)))))).
% 3.30/0.79 fof(mWCRDef, definition, ![W0_2]: (aRewritingSystem0(W0_2) => (isLocallyConfluent0(W0_2) <=> ![W3_2, W1_2, W2_2]: ((aElement0(W1_2) & (aElement0(W2_2) & (aElement0(W3_2) & (aReductOfIn0(W2_2, W1_2, W0_2) & aReductOfIn0(W3_2, W1_2, W0_2))))) => ?[W4]: (aElement0(W4) & (sdtmndtasgtdt0(W2_2, W0_2, W4) & sdtmndtasgtdt0(W3_2, W0_2, W4))))))).
% 3.30/0.79 fof(m__, conjecture, ?[W0_2]: (aElement0(W0_2) & ((xu=W0_2 | (aReductOfIn0(W0_2, xu, xR) | (?[W1_2]: (aElement0(W1_2) & (aReductOfIn0(W1_2, xu, xR) & sdtmndtplgtdt0(W1_2, xR, W0_2))) | (sdtmndtplgtdt0(xu, xR, W0_2) | sdtmndtasgtdt0(xu, xR, W0_2))))) & (xv=W0_2 | (aReductOfIn0(W0_2, xv, xR) | (?[W1_2]: (aElement0(W1_2) & (aReductOfIn0(W1_2, xv, xR) & sdtmndtplgtdt0(W1_2, xR, W0_2))) | (sdtmndtplgtdt0(xv, xR, W0_2) | sdtmndtasgtdt0(xv, xR, W0_2)))))))).
% 3.30/0.79 fof(m__656, hypothesis, aRewritingSystem0(xR)).
% 3.30/0.80 fof(m__656_01, hypothesis, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aElement0(W1_2) & (aElement0(W2_2) & (aReductOfIn0(W1_2, W0_2, xR) & aReductOfIn0(W2_2, W0_2, xR))))) => ?[W3_2]: (aElement0(W3_2) & ((W1_2=W3_2 | ((aReductOfIn0(W3_2, W1_2, xR) | ?[W4_2]: (aElement0(W4_2) & (aReductOfIn0(W4_2, W1_2, xR) & sdtmndtplgtdt0(W4_2, xR, W3_2)))) & sdtmndtplgtdt0(W1_2, xR, W3_2))) & (sdtmndtasgtdt0(W1_2, xR, W3_2) & ((W2_2=W3_2 | ((aReductOfIn0(W3_2, W2_2, xR) | ?[W4_2]: (aElement0(W4_2) & (aReductOfIn0(W4_2, W2_2, xR) & sdtmndtplgtdt0(W4_2, xR, W3_2)))) & sdtmndtplgtdt0(W2_2, xR, W3_2))) & sdtmndtasgtdt0(W2_2, xR, W3_2)))))) & (isLocallyConfluent0(xR) & (![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => ((aReductOfIn0(W1_2, W0_2, xR) | (?[W2_2]: (aElement0(W2_2) & (aReductOfIn0(W2_2, W0_2, xR) & sdtmndtplgtdt0(W2_2, xR, W1_2))) | sdtmndtplgtdt0(W0_2, xR, W1_2))) => iLess0(W1_2, W0_2))) & isTerminating0(xR)))).
% 3.30/0.80 fof(m__715, hypothesis, ![W0_2, W1_2, W2_2]: ((aElement0(W0_2) & (aElement0(W1_2) & (aElement0(W2_2) & ((W0_2=W1_2 | (aReductOfIn0(W1_2, W0_2, xR) | (?[W3_2]: (aElement0(W3_2) & (aReductOfIn0(W3_2, W0_2, xR) & sdtmndtplgtdt0(W3_2, xR, W1_2))) | (sdtmndtplgtdt0(W0_2, xR, W1_2) | sdtmndtasgtdt0(W0_2, xR, W1_2))))) & (W0_2=W2_2 | (aReductOfIn0(W2_2, W0_2, xR) | (?[W3_2]: (aElement0(W3_2) & (aReductOfIn0(W3_2, W0_2, xR) & sdtmndtplgtdt0(W3_2, xR, W2_2))) | (sdtmndtplgtdt0(W0_2, xR, W2_2) | sdtmndtasgtdt0(W0_2, xR, W2_2))))))))) => (iLess0(W0_2, xa) => ?[W3_2]: (aElement0(W3_2) & ((W1_2=W3_2 | ((aReductOfIn0(W3_2, W1_2, xR) | ?[W4_2]: (aElement0(W4_2) & (aReductOfIn0(W4_2, W1_2, xR) & sdtmndtplgtdt0(W4_2, xR, W3_2)))) & sdtmndtplgtdt0(W1_2, xR, W3_2))) & (sdtmndtasgtdt0(W1_2, xR, W3_2) & ((W2_2=W3_2 | ((aReductOfIn0(W3_2, W2_2, xR) | ?[W4_2]: (aElement0(W4_2) & (aReductOfIn0(W4_2, W2_2, xR) & sdtmndtplgtdt0(W4_2, xR, W3_2)))) & sdtmndtplgtdt0(W2_2, xR, W3_2))) & sdtmndtasgtdt0(W2_2, xR, W3_2)))))))).
% 3.30/0.80 fof(m__731, hypothesis, aElement0(xa) & (aElement0(xb) & aElement0(xc))).
% 3.30/0.80 fof(m__755, hypothesis, aElement0(xu) & (aReductOfIn0(xu, xa, xR) & ((xu=xb | ((aReductOfIn0(xb, xu, xR) | ?[W0_2]: (aElement0(W0_2) & (aReductOfIn0(W0_2, xu, xR) & sdtmndtplgtdt0(W0_2, xR, xb)))) & sdtmndtplgtdt0(xu, xR, xb))) & sdtmndtasgtdt0(xu, xR, xb)))).
% 3.30/0.80 fof(m__779, hypothesis, aElement0(xv) & (aReductOfIn0(xv, xa, xR) & ((xv=xc | ((aReductOfIn0(xc, xv, xR) | ?[W0_2]: (aElement0(W0_2) & (aReductOfIn0(W0_2, xv, xR) & sdtmndtplgtdt0(W0_2, xR, xc)))) & sdtmndtplgtdt0(xv, xR, xc))) & sdtmndtasgtdt0(xv, xR, xc)))).
% 3.30/0.80
% 3.30/0.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.30/0.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.30/0.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.30/0.80 fresh(y, y, x1...xn) = u
% 3.30/0.80 C => fresh(s, t, x1...xn) = v
% 3.30/0.80 where fresh is a fresh function symbol and x1..xn are the free
% 3.30/0.80 variables of u and v.
% 3.30/0.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.30/0.80 input problem has no model of domain size 1).
% 3.30/0.80
% 3.30/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 3.30/0.80
% 3.30/0.80 Axiom 1 (m__755_4): aElement0(xu) = true2.
% 3.30/0.80 Axiom 2 (m__779_4): aElement0(xv) = true2.
% 3.30/0.80 Axiom 3 (m__731): aElement0(xa) = true2.
% 3.30/0.80 Axiom 4 (m__656): aRewritingSystem0(xR) = true2.
% 3.30/0.80 Axiom 5 (m__656_01): isLocallyConfluent0(xR) = true2.
% 3.30/0.80 Axiom 6 (m__755_5): aReductOfIn0(xu, xa, xR) = true2.
% 3.30/0.80 Axiom 7 (m__779_5): aReductOfIn0(xv, xa, xR) = true2.
% 3.30/0.80 Axiom 8 (m___5): fresh(X, X, Y) = true2.
% 3.30/0.80 Axiom 9 (m___5): fresh2(X, X, Y) = or(Y).
% 3.30/0.80 Axiom 10 (mWCRDef_2): fresh81(X, X, Y, Z, W) = true2.
% 3.30/0.80 Axiom 11 (mWCRDef_1): fresh74(X, X, Y, Z, W) = true2.
% 3.30/0.80 Axiom 12 (mWCRDef): fresh67(X, X, Y, Z, W) = true2.
% 3.30/0.80 Axiom 13 (mWCRDef_2): fresh80(X, X, Y, Z, W, V) = fresh81(aElement0(Z), true2, Y, W, V).
% 3.30/0.80 Axiom 14 (mWCRDef_2): fresh79(X, X, Y, Z, W, V) = sdtmndtasgtdt0(V, Y, w4_5(Y, W, V)).
% 3.30/0.80 Axiom 15 (mWCRDef_1): fresh73(X, X, Y, Z, W, V) = fresh74(aElement0(Z), true2, Y, W, V).
% 3.30/0.80 Axiom 16 (mWCRDef_1): fresh72(X, X, Y, Z, W, V) = sdtmndtasgtdt0(W, Y, w4_5(Y, W, V)).
% 3.30/0.80 Axiom 17 (mWCRDef): fresh66(X, X, Y, Z, W, V) = fresh67(aElement0(Z), true2, Y, W, V).
% 3.30/0.80 Axiom 18 (mWCRDef): fresh65(X, X, Y, Z, W, V) = aElement0(w4_5(Y, W, V)).
% 3.30/0.80 Axiom 19 (m___5): fresh2(sdtmndtasgtdt0(xu, xR, X), true2, X) = fresh(aElement0(X), true2, X).
% 3.30/0.80 Axiom 20 (mWCRDef_2): fresh77(X, X, Y, Z, W, V) = fresh80(aElement0(V), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 21 (mWCRDef_2): fresh78(X, X, Y, Z, W, V) = fresh79(aElement0(W), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 22 (mWCRDef_2): fresh76(X, X, Y, Z, W, V) = fresh78(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 23 (mWCRDef_1): fresh70(X, X, Y, Z, W, V) = fresh73(aElement0(V), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 24 (mWCRDef_1): fresh71(X, X, Y, Z, W, V) = fresh72(aElement0(W), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 25 (mWCRDef_1): fresh69(X, X, Y, Z, W, V) = fresh71(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 26 (mWCRDef): fresh63(X, X, Y, Z, W, V) = fresh66(aElement0(V), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 27 (mWCRDef): fresh64(X, X, Y, Z, W, V) = fresh65(aElement0(W), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 28 (mWCRDef): fresh62(X, X, Y, Z, W, V) = fresh64(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 29 (mWCRDef_2): fresh75(X, X, Y, Z, W, V) = fresh77(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 30 (mWCRDef_2): fresh75(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh76(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 3.30/0.80 Axiom 31 (mWCRDef_1): fresh68(X, X, Y, Z, W, V) = fresh70(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 32 (mWCRDef_1): fresh68(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh69(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 3.30/0.80 Axiom 33 (mWCRDef): fresh61(X, X, Y, Z, W, V) = fresh63(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 3.30/0.80 Axiom 34 (mWCRDef): fresh61(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh62(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 3.30/0.80
% 3.30/0.80 Goal 1 (m___9): tuple2(sdtmndtasgtdt0(xv, xR, X), or(X)) = tuple2(true2, true2).
% 3.30/0.80 The goal is true when:
% 3.30/0.80 X = w4_5(xR, xv, xu)
% 3.30/0.80
% 3.30/0.80 Proof:
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), or(w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 9 (m___5) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(true2, true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 10 (mWCRDef_2) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh81(true2, true2, xR, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 3 (m__731) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh81(aElement0(xa), true2, xR, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 13 (mWCRDef_2) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh80(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 1 (m__755_4) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh80(aElement0(xu), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 20 (mWCRDef_2) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh77(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 7 (m__779_5) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh77(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 29 (mWCRDef_2) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh75(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 5 (m__656_01) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh75(isLocallyConfluent0(xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 30 (mWCRDef_2) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh76(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 6 (m__755_5) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh76(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 22 (mWCRDef_2) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh78(aRewritingSystem0(xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 4 (m__656) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh78(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 21 (mWCRDef_2) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh79(aElement0(xv), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 2 (m__779_4) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(fresh79(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 14 (mWCRDef_2) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh2(sdtmndtasgtdt0(xu, xR, w4_5(xR, xv, xu)), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 19 (m___5) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(aElement0(w4_5(xR, xv, xu)), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 18 (mWCRDef) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh65(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 2 (m__779_4) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh65(aElement0(xv), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 27 (mWCRDef) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh64(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 4 (m__656) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh64(aRewritingSystem0(xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 28 (mWCRDef) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh62(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 6 (m__755_5) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh62(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 34 (mWCRDef) R->L }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh61(isLocallyConfluent0(xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 5 (m__656_01) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh61(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 33 (mWCRDef) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh63(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 7 (m__779_5) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh63(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 26 (mWCRDef) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh66(aElement0(xu), true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 1 (m__755_4) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh66(true2, true2, xR, xa, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 17 (mWCRDef) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh67(aElement0(xa), true2, xR, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 3 (m__731) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(fresh67(true2, true2, xR, xv, xu), true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 12 (mWCRDef) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), fresh(true2, true2, w4_5(xR, xv, xu)))
% 3.30/0.80 = { by axiom 8 (m___5) }
% 3.30/0.80 tuple2(sdtmndtasgtdt0(xv, xR, w4_5(xR, xv, xu)), true2)
% 3.30/0.80 = { by axiom 16 (mWCRDef_1) R->L }
% 3.30/0.80 tuple2(fresh72(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 2 (m__779_4) R->L }
% 3.30/0.80 tuple2(fresh72(aElement0(xv), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 24 (mWCRDef_1) R->L }
% 3.30/0.80 tuple2(fresh71(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 4 (m__656) R->L }
% 3.30/0.80 tuple2(fresh71(aRewritingSystem0(xR), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 25 (mWCRDef_1) R->L }
% 3.30/0.80 tuple2(fresh69(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 6 (m__755_5) R->L }
% 3.30/0.80 tuple2(fresh69(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 32 (mWCRDef_1) R->L }
% 3.30/0.80 tuple2(fresh68(isLocallyConfluent0(xR), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 5 (m__656_01) }
% 3.30/0.80 tuple2(fresh68(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 31 (mWCRDef_1) }
% 3.30/0.80 tuple2(fresh70(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 7 (m__779_5) }
% 3.30/0.80 tuple2(fresh70(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 23 (mWCRDef_1) }
% 3.30/0.80 tuple2(fresh73(aElement0(xu), true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 1 (m__755_4) }
% 3.30/0.80 tuple2(fresh73(true2, true2, xR, xa, xv, xu), true2)
% 3.30/0.80 = { by axiom 15 (mWCRDef_1) }
% 3.30/0.80 tuple2(fresh74(aElement0(xa), true2, xR, xv, xu), true2)
% 3.30/0.80 = { by axiom 3 (m__731) }
% 3.30/0.80 tuple2(fresh74(true2, true2, xR, xv, xu), true2)
% 3.30/0.80 = { by axiom 11 (mWCRDef_1) }
% 3.30/0.80 tuple2(true2, true2)
% 3.30/0.80 % SZS output end Proof
% 3.30/0.80
% 3.30/0.80 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------