TSTP Solution File: NUM432+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM432+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 : n007.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 11:56:16 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM432+3 : 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
% 0.15/0.34 % Computer : n007.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
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Aug 25 11:06:55 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.58 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.58
% 0.21/0.58 % SZS status Theorem
% 0.21/0.58
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 Take the following subset of the input axioms:
% 0.21/0.59 fof(mDivisor, definition, ![W0]: (aInteger0(W0) => ![W1]: (aDivisorOf0(W1, W0) <=> (aInteger0(W1) & (W1!=sz00 & ?[W2]: (aInteger0(W2) & sdtasdt0(W1, W2)=W0)))))).
% 0.21/0.59 fof(mIntPlus, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => aInteger0(sdtpldt0(W0_2, W1_2)))).
% 0.21/0.59 fof(m__, conjecture, ?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xa, smndt0(xc))) | (aDivisorOf0(xq, sdtpldt0(xa, smndt0(xc))) | sdteqdtlpzmzozddtrp0(xa, xc, xq))).
% 0.21/0.59 fof(m__876, hypothesis, aInteger0(xn) & sdtasdt0(xq, xn)=sdtpldt0(xa, smndt0(xb))).
% 0.21/0.59 fof(m__899, hypothesis, aInteger0(xm) & sdtasdt0(xq, xm)=sdtpldt0(xb, smndt0(xc))).
% 0.21/0.59 fof(m__924, hypothesis, sdtasdt0(xq, sdtpldt0(xn, xm))=sdtpldt0(xa, smndt0(xc))).
% 0.21/0.59
% 0.21/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.59 fresh(y, y, x1...xn) = u
% 0.21/0.59 C => fresh(s, t, x1...xn) = v
% 0.21/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.59 variables of u and v.
% 0.21/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.59 input problem has no model of domain size 1).
% 0.21/0.59
% 0.21/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.59
% 0.21/0.59 Axiom 1 (m__876_1): aInteger0(xn) = true2.
% 0.21/0.59 Axiom 2 (m__899_1): aInteger0(xm) = true2.
% 0.21/0.59 Axiom 3 (m__924): sdtasdt0(xq, sdtpldt0(xn, xm)) = sdtpldt0(xa, smndt0(xc)).
% 0.21/0.59 Axiom 4 (mIntPlus): fresh14(X, X, Y, Z) = aInteger0(sdtpldt0(Y, Z)).
% 0.21/0.59 Axiom 5 (mIntPlus): fresh13(X, X, Y, Z) = true2.
% 0.21/0.59 Axiom 6 (mIntPlus): fresh14(aInteger0(X), true2, Y, X) = fresh13(aInteger0(Y), true2, Y, X).
% 0.21/0.59
% 0.21/0.59 Goal 1 (m__): tuple2(sdtasdt0(xq, X), aInteger0(X)) = tuple2(sdtpldt0(xa, smndt0(xc)), true2).
% 0.21/0.59 The goal is true when:
% 0.21/0.59 X = sdtpldt0(xn, xm)
% 0.21/0.59
% 0.21/0.59 Proof:
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), aInteger0(sdtpldt0(xn, xm)))
% 0.21/0.59 = { by axiom 4 (mIntPlus) R->L }
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), fresh14(true2, true2, xn, xm))
% 0.21/0.59 = { by axiom 2 (m__899_1) R->L }
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), fresh14(aInteger0(xm), true2, xn, xm))
% 0.21/0.59 = { by axiom 6 (mIntPlus) }
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), fresh13(aInteger0(xn), true2, xn, xm))
% 0.21/0.59 = { by axiom 1 (m__876_1) }
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), fresh13(true2, true2, xn, xm))
% 0.21/0.59 = { by axiom 5 (mIntPlus) }
% 0.21/0.59 tuple2(sdtasdt0(xq, sdtpldt0(xn, xm)), true2)
% 0.21/0.59 = { by axiom 3 (m__924) }
% 0.21/0.59 tuple2(sdtpldt0(xa, smndt0(xc)), true2)
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59
% 0.21/0.59 RESULT: Theorem (the conjecture is true).
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