TSTP Solution File: COM018+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COM018+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 : n001.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 0.18s 0.53s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM018+1 : 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
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 13:36:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.53 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.53
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53
% 0.18/0.53 % SZS output start Proof
% 0.18/0.53 Take the following subset of the input axioms:
% 0.18/0.53 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)))))).
% 0.18/0.53 fof(mTermNF, axiom, ![W0_2]: ((aRewritingSystem0(W0_2) & isTerminating0(W0_2)) => ![W1_2]: (aElement0(W1_2) => ?[W2_2]: aNormalFormOfIn0(W2_2, W1_2, W0_2)))).
% 0.18/0.53 fof(m__, conjecture, ?[W0_2]: aNormalFormOfIn0(W0_2, xw, xR)).
% 0.18/0.53 fof(m__656, hypothesis, aRewritingSystem0(xR)).
% 0.18/0.53 fof(m__656_01, hypothesis, isLocallyConfluent0(xR) & isTerminating0(xR)).
% 0.18/0.53 fof(m__799, hypothesis, aElement0(xw) & (sdtmndtasgtdt0(xu, xR, xw) & sdtmndtasgtdt0(xv, xR, xw))).
% 0.18/0.53
% 0.18/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.53 fresh(y, y, x1...xn) = u
% 0.18/0.53 C => fresh(s, t, x1...xn) = v
% 0.18/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.53 variables of u and v.
% 0.18/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.53 input problem has no model of domain size 1).
% 0.18/0.53
% 0.18/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.53
% 0.18/0.53 Axiom 1 (m__799): aElement0(xw) = true2.
% 0.18/0.53 Axiom 2 (m__656): aRewritingSystem0(xR) = true2.
% 0.18/0.53 Axiom 3 (m__656_01_1): isTerminating0(xR) = true2.
% 0.18/0.53 Axiom 4 (mTermNF): fresh28(X, X, Y, Z) = true2.
% 0.18/0.53 Axiom 5 (mTermNF): fresh3(X, X, Y, Z) = aNormalFormOfIn0(w2(Y, Z), Z, Y).
% 0.18/0.53 Axiom 6 (mTermNF): fresh27(X, X, Y, Z) = fresh28(aElement0(Z), true2, Y, Z).
% 0.18/0.53 Axiom 7 (mTermNF): fresh27(isTerminating0(X), true2, X, Y) = fresh3(aRewritingSystem0(X), true2, X, Y).
% 0.18/0.53
% 0.18/0.53 Goal 1 (m__): aNormalFormOfIn0(X, xw, xR) = true2.
% 0.18/0.53 The goal is true when:
% 0.18/0.53 X = w2(xR, xw)
% 0.18/0.53
% 0.18/0.53 Proof:
% 0.18/0.53 aNormalFormOfIn0(w2(xR, xw), xw, xR)
% 0.18/0.53 = { by axiom 5 (mTermNF) R->L }
% 0.18/0.53 fresh3(true2, true2, xR, xw)
% 0.18/0.53 = { by axiom 2 (m__656) R->L }
% 0.18/0.53 fresh3(aRewritingSystem0(xR), true2, xR, xw)
% 0.18/0.53 = { by axiom 7 (mTermNF) R->L }
% 0.18/0.53 fresh27(isTerminating0(xR), true2, xR, xw)
% 0.18/0.53 = { by axiom 3 (m__656_01_1) }
% 0.18/0.53 fresh27(true2, true2, xR, xw)
% 0.18/0.53 = { by axiom 6 (mTermNF) }
% 0.18/0.53 fresh28(aElement0(xw), true2, xR, xw)
% 0.18/0.53 = { by axiom 1 (m__799) }
% 0.18/0.53 fresh28(true2, true2, xR, xw)
% 0.18/0.53 = { by axiom 4 (mTermNF) }
% 0.18/0.53 true2
% 0.18/0.53 % SZS output end Proof
% 0.18/0.53
% 0.18/0.53 RESULT: Theorem (the conjecture is true).
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