TSTP Solution File: NUM423+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM423+3 : 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 : n008.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 11:56:12 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 10:05:47 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.44
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 Take the following subset of the input axioms:
% 0.22/0.44 fof(mAddNeg, axiom, ![W0]: (aInteger0(W0) => (sdtpldt0(W0, smndt0(W0))=sz00 & sz00=sdtpldt0(smndt0(W0), W0)))).
% 0.22/0.44 fof(mDivisor, definition, ![W0_2]: (aInteger0(W0_2) => ![W1]: (aDivisorOf0(W1, W0_2) <=> (aInteger0(W1) & (W1!=sz00 & ?[W2]: (aInteger0(W2) & sdtasdt0(W1, W2)=W0_2)))))).
% 0.22/0.44 fof(mIntZero, axiom, aInteger0(sz00)).
% 0.22/0.44 fof(mMulZero, axiom, ![W0_2]: (aInteger0(W0_2) => (sdtasdt0(W0_2, sz00)=sz00 & sz00=sdtasdt0(sz00, W0_2)))).
% 0.22/0.44 fof(m__, conjecture, ?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xa, smndt0(xa))) | (aDivisorOf0(xq, sdtpldt0(xa, smndt0(xa))) | sdteqdtlpzmzozddtrp0(xa, xa, xq))).
% 0.22/0.44 fof(m__671, hypothesis, aInteger0(xa) & (aInteger0(xq) & xq!=sz00)).
% 0.22/0.44
% 0.22/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.44 fresh(y, y, x1...xn) = u
% 0.22/0.44 C => fresh(s, t, x1...xn) = v
% 0.22/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.44 variables of u and v.
% 0.22/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.44 input problem has no model of domain size 1).
% 0.22/0.44
% 0.22/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.44
% 0.22/0.44 Axiom 1 (m__671): aInteger0(xa) = true2.
% 0.22/0.44 Axiom 2 (mIntZero): aInteger0(sz00) = true2.
% 0.22/0.44 Axiom 3 (m__671_1): aInteger0(xq) = true2.
% 0.22/0.44 Axiom 4 (mAddNeg): fresh26(X, X, Y) = sz00.
% 0.22/0.44 Axiom 5 (mMulZero): fresh7(X, X, Y) = sz00.
% 0.22/0.44 Axiom 6 (mAddNeg): fresh26(aInteger0(X), true2, X) = sdtpldt0(X, smndt0(X)).
% 0.22/0.44 Axiom 7 (mMulZero): fresh7(aInteger0(X), true2, X) = sdtasdt0(X, sz00).
% 0.22/0.44
% 0.22/0.44 Goal 1 (m__): tuple2(sdtasdt0(xq, X), aInteger0(X)) = tuple2(sdtpldt0(xa, smndt0(xa)), true2).
% 0.22/0.44 The goal is true when:
% 0.22/0.44 X = sz00
% 0.22/0.44
% 0.22/0.44 Proof:
% 0.22/0.44 tuple2(sdtasdt0(xq, sz00), aInteger0(sz00))
% 0.22/0.44 = { by axiom 7 (mMulZero) R->L }
% 0.22/0.44 tuple2(fresh7(aInteger0(xq), true2, xq), aInteger0(sz00))
% 0.22/0.44 = { by axiom 3 (m__671_1) }
% 0.22/0.44 tuple2(fresh7(true2, true2, xq), aInteger0(sz00))
% 0.22/0.44 = { by axiom 5 (mMulZero) }
% 0.22/0.44 tuple2(sz00, aInteger0(sz00))
% 0.22/0.44 = { by axiom 2 (mIntZero) }
% 0.22/0.44 tuple2(sz00, true2)
% 0.22/0.44 = { by axiom 4 (mAddNeg) R->L }
% 0.22/0.44 tuple2(fresh26(true2, true2, xa), true2)
% 0.22/0.44 = { by axiom 1 (m__671) R->L }
% 0.22/0.44 tuple2(fresh26(aInteger0(xa), true2, xa), true2)
% 0.22/0.44 = { by axiom 6 (mAddNeg) }
% 0.22/0.44 tuple2(sdtpldt0(xa, smndt0(xa)), true2)
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44
% 0.22/0.44 RESULT: Theorem (the conjecture is true).
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