TSTP Solution File: COM017+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM017+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 : n031.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 0.19s 0.64s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n031.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 29 13:29:11 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.64 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.64
% 0.19/0.64 % SZS status Theorem
% 0.19/0.64
% 0.19/0.66 % SZS output start Proof
% 0.19/0.66 Take the following subset of the input axioms:
% 0.19/0.67 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)))))).
% 0.19/0.67 fof(mWCRDef, definition, ![W0_2]: (aRewritingSystem0(W0_2) => (isLocallyConfluent0(W0_2) <=> ![W1_2, W2_2, W3_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))))))).
% 0.19/0.67 fof(m__, conjecture, ?[W0_2]: (aElement0(W0_2) & (sdtmndtasgtdt0(xu, xR, W0_2) & sdtmndtasgtdt0(xv, xR, W0_2)))).
% 0.19/0.67 fof(m__656, hypothesis, aRewritingSystem0(xR)).
% 0.19/0.67 fof(m__656_01, hypothesis, isLocallyConfluent0(xR) & isTerminating0(xR)).
% 0.19/0.67 fof(m__731, hypothesis, aElement0(xa) & (aElement0(xb) & aElement0(xc))).
% 0.19/0.67 fof(m__755, hypothesis, aElement0(xu) & (aReductOfIn0(xu, xa, xR) & sdtmndtasgtdt0(xu, xR, xb))).
% 0.19/0.67 fof(m__779, hypothesis, aElement0(xv) & (aReductOfIn0(xv, xa, xR) & sdtmndtasgtdt0(xv, xR, xc))).
% 0.19/0.67
% 0.19/0.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.67 fresh(y, y, x1...xn) = u
% 0.19/0.67 C => fresh(s, t, x1...xn) = v
% 0.19/0.67 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.67 variables of u and v.
% 0.19/0.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.67 input problem has no model of domain size 1).
% 0.19/0.67
% 0.19/0.67 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.67
% 0.19/0.67 Axiom 1 (m__656_01): isLocallyConfluent0(xR) = true2.
% 0.19/0.67 Axiom 2 (m__656): aRewritingSystem0(xR) = true2.
% 0.19/0.67 Axiom 3 (m__755): aElement0(xu) = true2.
% 0.19/0.67 Axiom 4 (m__779): aElement0(xv) = true2.
% 0.19/0.67 Axiom 5 (m__731): aElement0(xa) = true2.
% 0.19/0.67 Axiom 6 (m__755_1): aReductOfIn0(xu, xa, xR) = true2.
% 0.19/0.67 Axiom 7 (m__779_1): aReductOfIn0(xv, xa, xR) = true2.
% 0.19/0.67 Axiom 8 (mWCRDef_2): fresh58(X, X, Y, Z, W) = true2.
% 0.19/0.67 Axiom 9 (mWCRDef_1): fresh51(X, X, Y, Z, W) = true2.
% 0.19/0.67 Axiom 10 (mWCRDef): fresh44(X, X, Y, Z, W) = true2.
% 0.19/0.67 Axiom 11 (mWCRDef_2): fresh57(X, X, Y, Z, W, V) = fresh58(aElement0(Z), true2, Y, W, V).
% 0.19/0.67 Axiom 12 (mWCRDef_1): fresh50(X, X, Y, Z, W, V) = fresh51(aElement0(Z), true2, Y, W, V).
% 0.19/0.67 Axiom 13 (mWCRDef): fresh43(X, X, Y, Z, W, V) = fresh44(aElement0(Z), true2, Y, W, V).
% 0.19/0.67 Axiom 14 (mWCRDef): fresh42(X, X, Y, Z, W, V) = aElement0(w4(Y, W, V)).
% 0.19/0.67 Axiom 15 (mWCRDef_1): fresh49(X, X, Y, Z, W, V) = sdtmndtasgtdt0(W, Y, w4(Y, W, V)).
% 0.19/0.67 Axiom 16 (mWCRDef_2): fresh56(X, X, Y, Z, W, V) = sdtmndtasgtdt0(V, Y, w4(Y, W, V)).
% 0.19/0.67 Axiom 17 (mWCRDef_2): fresh54(X, X, Y, Z, W, V) = fresh57(aElement0(V), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 18 (mWCRDef_2): fresh55(X, X, Y, Z, W, V) = fresh56(aElement0(W), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 19 (mWCRDef_2): fresh53(X, X, Y, Z, W, V) = fresh55(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 20 (mWCRDef_1): fresh47(X, X, Y, Z, W, V) = fresh50(aElement0(V), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 21 (mWCRDef_1): fresh48(X, X, Y, Z, W, V) = fresh49(aElement0(W), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 22 (mWCRDef_1): fresh46(X, X, Y, Z, W, V) = fresh48(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 23 (mWCRDef): fresh40(X, X, Y, Z, W, V) = fresh43(aElement0(V), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 24 (mWCRDef): fresh41(X, X, Y, Z, W, V) = fresh42(aElement0(W), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 25 (mWCRDef): fresh39(X, X, Y, Z, W, V) = fresh41(aRewritingSystem0(Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 26 (mWCRDef_2): fresh52(X, X, Y, Z, W, V) = fresh54(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 27 (mWCRDef_2): fresh52(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh53(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 0.19/0.67 Axiom 28 (mWCRDef_1): fresh45(X, X, Y, Z, W, V) = fresh47(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 29 (mWCRDef_1): fresh45(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh46(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 0.19/0.67 Axiom 30 (mWCRDef): fresh38(X, X, Y, Z, W, V) = fresh40(aReductOfIn0(W, Z, Y), true2, Y, Z, W, V).
% 0.19/0.67 Axiom 31 (mWCRDef): fresh38(isLocallyConfluent0(X), true2, X, Y, Z, W) = fresh39(aReductOfIn0(W, Y, X), true2, X, Y, Z, W).
% 0.19/0.67
% 0.19/0.67 Goal 1 (m__): tuple2(aElement0(X), sdtmndtasgtdt0(xu, xR, X), sdtmndtasgtdt0(xv, xR, X)) = tuple2(true2, true2, true2).
% 0.19/0.67 The goal is true when:
% 0.19/0.67 X = w4(xR, xv, xu)
% 0.19/0.67
% 0.19/0.67 Proof:
% 0.19/0.67 tuple2(aElement0(w4(xR, xv, xu)), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 14 (mWCRDef) R->L }
% 0.19/0.67 tuple2(fresh42(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 4 (m__779) R->L }
% 0.19/0.67 tuple2(fresh42(aElement0(xv), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 24 (mWCRDef) R->L }
% 0.19/0.67 tuple2(fresh41(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 2 (m__656) R->L }
% 0.19/0.67 tuple2(fresh41(aRewritingSystem0(xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 25 (mWCRDef) R->L }
% 0.19/0.67 tuple2(fresh39(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 6 (m__755_1) R->L }
% 0.19/0.67 tuple2(fresh39(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 31 (mWCRDef) R->L }
% 0.19/0.67 tuple2(fresh38(isLocallyConfluent0(xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 1 (m__656_01) }
% 0.19/0.67 tuple2(fresh38(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 30 (mWCRDef) }
% 0.19/0.67 tuple2(fresh40(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 7 (m__779_1) }
% 0.19/0.67 tuple2(fresh40(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 23 (mWCRDef) }
% 0.19/0.67 tuple2(fresh43(aElement0(xu), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 3 (m__755) }
% 0.19/0.67 tuple2(fresh43(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 13 (mWCRDef) }
% 0.19/0.67 tuple2(fresh44(aElement0(xa), true2, xR, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 5 (m__731) }
% 0.19/0.67 tuple2(fresh44(true2, true2, xR, xv, xu), sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 10 (mWCRDef) }
% 0.19/0.67 tuple2(true2, sdtmndtasgtdt0(xu, xR, w4(xR, xv, xu)), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 16 (mWCRDef_2) R->L }
% 0.19/0.67 tuple2(true2, fresh56(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 4 (m__779) R->L }
% 0.19/0.67 tuple2(true2, fresh56(aElement0(xv), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 18 (mWCRDef_2) R->L }
% 0.19/0.67 tuple2(true2, fresh55(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 2 (m__656) R->L }
% 0.19/0.67 tuple2(true2, fresh55(aRewritingSystem0(xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 19 (mWCRDef_2) R->L }
% 0.19/0.67 tuple2(true2, fresh53(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 6 (m__755_1) R->L }
% 0.19/0.67 tuple2(true2, fresh53(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 27 (mWCRDef_2) R->L }
% 0.19/0.67 tuple2(true2, fresh52(isLocallyConfluent0(xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 1 (m__656_01) }
% 0.19/0.67 tuple2(true2, fresh52(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 26 (mWCRDef_2) }
% 0.19/0.67 tuple2(true2, fresh54(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 7 (m__779_1) }
% 0.19/0.67 tuple2(true2, fresh54(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 17 (mWCRDef_2) }
% 0.19/0.67 tuple2(true2, fresh57(aElement0(xu), true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 3 (m__755) }
% 0.19/0.67 tuple2(true2, fresh57(true2, true2, xR, xa, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 11 (mWCRDef_2) }
% 0.19/0.67 tuple2(true2, fresh58(aElement0(xa), true2, xR, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 5 (m__731) }
% 0.19/0.67 tuple2(true2, fresh58(true2, true2, xR, xv, xu), sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 8 (mWCRDef_2) }
% 0.19/0.67 tuple2(true2, true2, sdtmndtasgtdt0(xv, xR, w4(xR, xv, xu)))
% 0.19/0.67 = { by axiom 15 (mWCRDef_1) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh49(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 4 (m__779) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh49(aElement0(xv), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 21 (mWCRDef_1) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh48(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 2 (m__656) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh48(aRewritingSystem0(xR), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 22 (mWCRDef_1) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh46(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 6 (m__755_1) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh46(aReductOfIn0(xu, xa, xR), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 29 (mWCRDef_1) R->L }
% 0.19/0.67 tuple2(true2, true2, fresh45(isLocallyConfluent0(xR), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 1 (m__656_01) }
% 0.19/0.67 tuple2(true2, true2, fresh45(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 28 (mWCRDef_1) }
% 0.19/0.67 tuple2(true2, true2, fresh47(aReductOfIn0(xv, xa, xR), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 7 (m__779_1) }
% 0.19/0.67 tuple2(true2, true2, fresh47(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 20 (mWCRDef_1) }
% 0.19/0.67 tuple2(true2, true2, fresh50(aElement0(xu), true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 3 (m__755) }
% 0.19/0.67 tuple2(true2, true2, fresh50(true2, true2, xR, xa, xv, xu))
% 0.19/0.67 = { by axiom 12 (mWCRDef_1) }
% 0.19/0.67 tuple2(true2, true2, fresh51(aElement0(xa), true2, xR, xv, xu))
% 0.19/0.67 = { by axiom 5 (m__731) }
% 0.19/0.67 tuple2(true2, true2, fresh51(true2, true2, xR, xv, xu))
% 0.19/0.67 = { by axiom 9 (mWCRDef_1) }
% 0.19/0.67 tuple2(true2, true2, true2)
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67
% 0.19/0.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------