TSTP Solution File: NUM478+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM478+2 : 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 : n024.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 11:56:30 EDT 2023
% Result : Theorem 12.19s 1.94s
% Output : Proof 12.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUM478+2 : 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
% 0.11/0.34 % Computer : n024.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Aug 25 08:52:09 EDT 2023
% 0.11/0.34 % CPUTime :
% 12.19/1.94 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 12.19/1.94
% 12.19/1.94 % SZS status Theorem
% 12.19/1.94
% 12.19/1.94 % SZS output start Proof
% 12.19/1.94 Take the following subset of the input axioms:
% 12.19/1.94 fof(mMulAsso, axiom, ![W0, W1, W2]: ((aNaturalNumber0(W0) & (aNaturalNumber0(W1) & aNaturalNumber0(W2))) => sdtasdt0(sdtasdt0(W0, W1), W2)=sdtasdt0(W0, sdtasdt0(W1, W2)))).
% 12.19/1.94 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aNaturalNumber0(W0_2) & aNaturalNumber0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 12.19/1.94 fof(m__, conjecture, (aNaturalNumber0(sdtsldt0(xm, xl)) & xm=sdtasdt0(xl, sdtsldt0(xm, xl))) => (sdtasdt0(xn, xm)=sdtasdt0(xl, sdtasdt0(xn, sdtsldt0(xm, xl))) | sdtasdt0(xn, sdtsldt0(xm, xl))=sdtsldt0(sdtasdt0(xn, xm), xl))).
% 12.19/1.94 fof(m__1524, hypothesis, aNaturalNumber0(xl) & aNaturalNumber0(xm)).
% 12.19/1.94 fof(m__1553, hypothesis, aNaturalNumber0(xn)).
% 12.19/1.94
% 12.19/1.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.19/1.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.19/1.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.19/1.94 fresh(y, y, x1...xn) = u
% 12.19/1.94 C => fresh(s, t, x1...xn) = v
% 12.19/1.94 where fresh is a fresh function symbol and x1..xn are the free
% 12.19/1.94 variables of u and v.
% 12.19/1.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.19/1.94 input problem has no model of domain size 1).
% 12.19/1.94
% 12.19/1.95 The encoding turns the above axioms into the following unit equations and goals:
% 12.19/1.95
% 12.19/1.95 Axiom 1 (m__1524): aNaturalNumber0(xl) = true.
% 12.19/1.95 Axiom 2 (m__1524_1): aNaturalNumber0(xm) = true.
% 12.19/1.95 Axiom 3 (m__1553): aNaturalNumber0(xn) = true.
% 12.19/1.95 Axiom 4 (m___1): aNaturalNumber0(sdtsldt0(xm, xl)) = true.
% 12.19/1.95 Axiom 5 (m__): xm = sdtasdt0(xl, sdtsldt0(xm, xl)).
% 12.19/1.95 Axiom 6 (mMulComm): fresh20(X, X, Y, Z) = sdtasdt0(Y, Z).
% 12.19/1.95 Axiom 7 (mMulComm): fresh19(X, X, Y, Z) = sdtasdt0(Z, Y).
% 12.19/1.95 Axiom 8 (mMulAsso): fresh107(X, X, Y, Z, W) = sdtasdt0(Y, sdtasdt0(Z, W)).
% 12.19/1.95 Axiom 9 (mMulAsso): fresh21(X, X, Y, Z, W) = sdtasdt0(sdtasdt0(Y, Z), W).
% 12.19/1.95 Axiom 10 (mMulComm): fresh20(aNaturalNumber0(X), true, Y, X) = fresh19(aNaturalNumber0(Y), true, Y, X).
% 12.19/1.95 Axiom 11 (mMulAsso): fresh106(X, X, Y, Z, W) = fresh107(aNaturalNumber0(Y), true, Y, Z, W).
% 12.19/1.95 Axiom 12 (mMulAsso): fresh106(aNaturalNumber0(X), true, Y, Z, X) = fresh21(aNaturalNumber0(Z), true, Y, Z, X).
% 12.19/1.95
% 12.19/1.95 Goal 1 (m___2): sdtasdt0(xn, xm) = sdtasdt0(xl, sdtasdt0(xn, sdtsldt0(xm, xl))).
% 12.19/1.95 Proof:
% 12.19/1.95 sdtasdt0(xn, xm)
% 12.19/1.95 = { by axiom 7 (mMulComm) R->L }
% 12.19/1.95 fresh19(true, true, xm, xn)
% 12.19/1.95 = { by axiom 2 (m__1524_1) R->L }
% 12.19/1.95 fresh19(aNaturalNumber0(xm), true, xm, xn)
% 12.19/1.95 = { by axiom 10 (mMulComm) R->L }
% 12.19/1.95 fresh20(aNaturalNumber0(xn), true, xm, xn)
% 12.19/1.95 = { by axiom 3 (m__1553) }
% 12.19/1.95 fresh20(true, true, xm, xn)
% 12.19/1.95 = { by axiom 6 (mMulComm) }
% 12.19/1.95 sdtasdt0(xm, xn)
% 12.19/1.95 = { by axiom 5 (m__) }
% 12.19/1.95 sdtasdt0(sdtasdt0(xl, sdtsldt0(xm, xl)), xn)
% 12.19/1.95 = { by axiom 9 (mMulAsso) R->L }
% 12.19/1.95 fresh21(true, true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 4 (m___1) R->L }
% 12.19/1.95 fresh21(aNaturalNumber0(sdtsldt0(xm, xl)), true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 12 (mMulAsso) R->L }
% 12.19/1.95 fresh106(aNaturalNumber0(xn), true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 3 (m__1553) }
% 12.19/1.95 fresh106(true, true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 11 (mMulAsso) }
% 12.19/1.95 fresh107(aNaturalNumber0(xl), true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 1 (m__1524) }
% 12.19/1.95 fresh107(true, true, xl, sdtsldt0(xm, xl), xn)
% 12.19/1.95 = { by axiom 8 (mMulAsso) }
% 12.19/1.95 sdtasdt0(xl, sdtasdt0(sdtsldt0(xm, xl), xn))
% 12.19/1.95 = { by axiom 7 (mMulComm) R->L }
% 12.19/1.95 sdtasdt0(xl, fresh19(true, true, xn, sdtsldt0(xm, xl)))
% 12.19/1.95 = { by axiom 3 (m__1553) R->L }
% 12.19/1.95 sdtasdt0(xl, fresh19(aNaturalNumber0(xn), true, xn, sdtsldt0(xm, xl)))
% 12.19/1.95 = { by axiom 10 (mMulComm) R->L }
% 12.19/1.95 sdtasdt0(xl, fresh20(aNaturalNumber0(sdtsldt0(xm, xl)), true, xn, sdtsldt0(xm, xl)))
% 12.19/1.95 = { by axiom 4 (m___1) }
% 12.19/1.95 sdtasdt0(xl, fresh20(true, true, xn, sdtsldt0(xm, xl)))
% 12.19/1.95 = { by axiom 6 (mMulComm) }
% 12.19/1.95 sdtasdt0(xl, sdtasdt0(xn, sdtsldt0(xm, xl)))
% 12.19/1.95 % SZS output end Proof
% 12.19/1.95
% 12.19/1.95 RESULT: Theorem (the conjecture is true).
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