TSTP Solution File: NUM435+3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM435+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 : n021.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 11:56:17 EDT 2023
% Result : Theorem 0.21s 0.83s
% 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
% 0.00/0.12 % Problem : NUM435+3 : 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 11:44:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.83 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.83
% 0.21/0.83 % SZS status Theorem
% 0.21/0.83
% 0.21/0.83 % SZS output start Proof
% 0.21/0.83 Take the following subset of the input axioms:
% 0.21/0.83 fof(mMulAsso, axiom, ![W0, W1, W2]: ((aInteger0(W0) & (aInteger0(W1) & aInteger0(W2))) => sdtasdt0(W0, sdtasdt0(W1, W2))=sdtasdt0(sdtasdt0(W0, W1), W2))).
% 0.21/0.83 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 0.21/0.83 fof(m__, conjecture, sdtpldt0(xa, smndt0(xb))=sdtasdt0(xq, sdtasdt0(xp, xm))).
% 0.21/0.83 fof(m__1032, hypothesis, aInteger0(xm) & sdtasdt0(sdtasdt0(xp, xq), xm)=sdtpldt0(xa, smndt0(xb))).
% 0.21/0.83 fof(m__979, hypothesis, aInteger0(xa) & (aInteger0(xb) & (aInteger0(xp) & (xp!=sz00 & (aInteger0(xq) & xq!=sz00))))).
% 0.21/0.83
% 0.21/0.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.83 fresh(y, y, x1...xn) = u
% 0.21/0.83 C => fresh(s, t, x1...xn) = v
% 0.21/0.83 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.83 variables of u and v.
% 0.21/0.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.83 input problem has no model of domain size 1).
% 0.21/0.83
% 0.21/0.83 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.83
% 0.21/0.83 Axiom 1 (m__979_2): aInteger0(xp) = true2.
% 0.21/0.83 Axiom 2 (m__979_3): aInteger0(xq) = true2.
% 0.21/0.83 Axiom 3 (m__1032_1): aInteger0(xm) = true2.
% 0.21/0.83 Axiom 4 (m__1032): sdtasdt0(sdtasdt0(xp, xq), xm) = sdtpldt0(xa, smndt0(xb)).
% 0.21/0.83 Axiom 5 (mMulComm): fresh11(X, X, Y, Z) = sdtasdt0(Y, Z).
% 0.21/0.83 Axiom 6 (mMulComm): fresh10(X, X, Y, Z) = sdtasdt0(Z, Y).
% 0.21/0.83 Axiom 7 (mMulAsso): fresh35(X, X, Y, Z, W) = sdtasdt0(sdtasdt0(Y, Z), W).
% 0.21/0.83 Axiom 8 (mMulAsso): fresh12(X, X, Y, Z, W) = sdtasdt0(Y, sdtasdt0(Z, W)).
% 0.21/0.83 Axiom 9 (mMulComm): fresh11(aInteger0(X), true2, Y, X) = fresh10(aInteger0(Y), true2, Y, X).
% 0.21/0.83 Axiom 10 (mMulAsso): fresh34(X, X, Y, Z, W) = fresh35(aInteger0(Y), true2, Y, Z, W).
% 0.21/0.83 Axiom 11 (mMulAsso): fresh34(aInteger0(X), true2, Y, Z, X) = fresh12(aInteger0(Z), true2, Y, Z, X).
% 0.21/0.83
% 0.21/0.83 Goal 1 (m__): sdtpldt0(xa, smndt0(xb)) = sdtasdt0(xq, sdtasdt0(xp, xm)).
% 0.21/0.83 Proof:
% 0.21/0.83 sdtpldt0(xa, smndt0(xb))
% 0.21/0.83 = { by axiom 4 (m__1032) R->L }
% 0.21/0.83 sdtasdt0(sdtasdt0(xp, xq), xm)
% 0.21/0.83 = { by axiom 5 (mMulComm) R->L }
% 0.21/0.83 sdtasdt0(fresh11(true2, true2, xp, xq), xm)
% 0.21/0.83 = { by axiom 2 (m__979_3) R->L }
% 0.21/0.83 sdtasdt0(fresh11(aInteger0(xq), true2, xp, xq), xm)
% 0.21/0.83 = { by axiom 9 (mMulComm) }
% 0.21/0.83 sdtasdt0(fresh10(aInteger0(xp), true2, xp, xq), xm)
% 0.21/0.83 = { by axiom 1 (m__979_2) }
% 0.21/0.83 sdtasdt0(fresh10(true2, true2, xp, xq), xm)
% 0.21/0.83 = { by axiom 6 (mMulComm) }
% 0.21/0.83 sdtasdt0(sdtasdt0(xq, xp), xm)
% 0.21/0.83 = { by axiom 7 (mMulAsso) R->L }
% 0.21/0.83 fresh35(true2, true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 2 (m__979_3) R->L }
% 0.21/0.83 fresh35(aInteger0(xq), true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 10 (mMulAsso) R->L }
% 0.21/0.83 fresh34(true2, true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 3 (m__1032_1) R->L }
% 0.21/0.83 fresh34(aInteger0(xm), true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 11 (mMulAsso) }
% 0.21/0.83 fresh12(aInteger0(xp), true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 1 (m__979_2) }
% 0.21/0.83 fresh12(true2, true2, xq, xp, xm)
% 0.21/0.83 = { by axiom 8 (mMulAsso) }
% 0.21/0.83 sdtasdt0(xq, sdtasdt0(xp, xm))
% 0.21/0.83 % SZS output end Proof
% 0.21/0.83
% 0.21/0.83 RESULT: Theorem (the conjecture is true).
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