TSTP Solution File: RNG079+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG079+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 : n025.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 13:59:11 EDT 2023
% Result : Theorem 4.42s 0.93s
% Output : Proof 4.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG079+2 : 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
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 : Sun Aug 27 03:14:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 4.42/0.93 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 4.42/0.93
% 4.42/0.93 % SZS status Theorem
% 4.42/0.93
% 4.42/0.94 % SZS output start Proof
% 4.42/0.94 Take the following subset of the input axioms:
% 4.42/0.94 fof(mDistr2, axiom, ![W0, W1, W2, W3]: ((aScalar0(W0) & (aScalar0(W1) & (aScalar0(W2) & aScalar0(W3)))) => sdtasdt0(sdtpldt0(W0, W1), sdtpldt0(W2, W3))=sdtpldt0(sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W0, W3)), sdtpldt0(sdtasdt0(W1, W2), sdtasdt0(W1, W3))))).
% 4.42/0.94 fof(m__, conjecture, sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), sdtasdt0(sdtpldt0(xC, xF), sdtpldt0(xD, xG)))).
% 4.42/0.94 fof(m__1783, hypothesis, aScalar0(xC) & xC=sdtasasdt0(xp, xp)).
% 4.42/0.94 fof(m__1800, hypothesis, aScalar0(xD) & xD=sdtasasdt0(xq, xq)).
% 4.42/0.94 fof(m__1820, hypothesis, aScalar0(xE) & xE=sdtasasdt0(xp, xq)).
% 4.42/0.94 fof(m__1837, hypothesis, aScalar0(xF) & xF=sdtasdt0(xA, xA)).
% 4.42/0.94 fof(m__1854, hypothesis, aScalar0(xG) & xG=sdtasdt0(xB, xB)).
% 4.42/0.94 fof(m__1873, hypothesis, aScalar0(xH) & xH=sdtasdt0(xA, xB)).
% 4.42/0.94 fof(m__2905, hypothesis, sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE, xE), sdtasdt0(xE, xH)), sdtpldt0(sdtasdt0(xH, xE), sdtasdt0(xH, xH))), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))).
% 4.42/0.94
% 4.42/0.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.42/0.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.42/0.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.42/0.94 fresh(y, y, x1...xn) = u
% 4.42/0.94 C => fresh(s, t, x1...xn) = v
% 4.42/0.94 where fresh is a fresh function symbol and x1..xn are the free
% 4.42/0.94 variables of u and v.
% 4.42/0.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.42/0.94 input problem has no model of domain size 1).
% 4.42/0.94
% 4.42/0.94 The encoding turns the above axioms into the following unit equations and goals:
% 4.42/0.94
% 4.42/0.94 Axiom 1 (m__1873_1): aScalar0(xH) = true2.
% 4.42/0.94 Axiom 2 (m__1820_1): aScalar0(xE) = true2.
% 4.42/0.94 Axiom 3 (m__1783_1): aScalar0(xC) = true2.
% 4.42/0.94 Axiom 4 (m__1800_1): aScalar0(xD) = true2.
% 4.42/0.94 Axiom 5 (m__1837_1): aScalar0(xF) = true2.
% 4.42/0.94 Axiom 6 (m__1854_1): aScalar0(xG) = true2.
% 4.42/0.94 Axiom 7 (mDistr): fresh33(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 4.42/0.94 Axiom 8 (mDistr2): fresh86(X, X, Y, Z, W, V) = sdtasdt0(sdtpldt0(Y, Z), sdtpldt0(W, V)).
% 4.42/0.94 Axiom 9 (mDistr2): fresh85(X, X, Y, Z, W, V) = fresh86(aScalar0(Y), true2, Y, Z, W, V).
% 4.42/0.94 Axiom 10 (mDistr2): fresh84(X, X, Y, Z, W, V) = fresh85(aScalar0(Z), true2, Y, Z, W, V).
% 4.42/0.94 Axiom 11 (mDistr2): fresh83(X, X, Y, Z, W, V) = fresh84(aScalar0(W), true2, Y, Z, W, V).
% 4.42/0.94 Axiom 12 (mDistr2): fresh83(aScalar0(X), true2, Y, Z, W, X) = sdtpldt0(sdtpldt0(sdtasdt0(Y, W), sdtasdt0(Y, X)), sdtpldt0(sdtasdt0(Z, W), sdtasdt0(Z, X))).
% 4.42/0.94 Axiom 13 (m__2905): sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE, xE), sdtasdt0(xE, xH)), sdtpldt0(sdtasdt0(xH, xE), sdtasdt0(xH, xH))), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG)))) = true2.
% 4.42/0.94
% 4.42/0.94 Lemma 14: sdtpldt0(fresh33(X, X, Y, Z, W), fresh33(V, V, U, Z, W)) = fresh83(aScalar0(W), true2, Y, U, Z, W).
% 4.42/0.94 Proof:
% 4.42/0.94 sdtpldt0(fresh33(X, X, Y, Z, W), fresh33(V, V, U, Z, W))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtpldt0(fresh33(X, X, Y, Z, W), sdtpldt0(sdtasdt0(U, Z), sdtasdt0(U, W)))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtpldt0(sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)), sdtpldt0(sdtasdt0(U, Z), sdtasdt0(U, W)))
% 4.42/0.94 = { by axiom 12 (mDistr2) R->L }
% 4.42/0.94 fresh83(aScalar0(W), true2, Y, U, Z, W)
% 4.42/0.94
% 4.42/0.94 Goal 1 (m__): sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), sdtasdt0(sdtpldt0(xC, xF), sdtpldt0(xD, xG))) = true2.
% 4.42/0.94 Proof:
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), sdtasdt0(sdtpldt0(xC, xF), sdtpldt0(xD, xG)))
% 4.42/0.94 = { by axiom 8 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), fresh86(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 3 (m__1783_1) R->L }
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), fresh86(aScalar0(xC), true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 9 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), fresh85(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 5 (m__1837_1) R->L }
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), fresh85(aScalar0(xF), true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 10 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(sdtasdt0(sdtpldt0(xE, xH), sdtpldt0(xE, xH)), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 8 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(fresh86(true2, true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 2 (m__1820_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh86(aScalar0(xE), true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 9 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(fresh85(true2, true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 1 (m__1873_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh85(aScalar0(xH), true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 10 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(fresh84(true2, true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 2 (m__1820_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh84(aScalar0(xE), true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 11 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), fresh84(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 4 (m__1800_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), fresh84(aScalar0(xD), true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 11 (mDistr2) R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), fresh83(true2, true2, xC, xF, xD, xG))
% 4.42/0.94 = { by axiom 6 (m__1854_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), fresh83(aScalar0(xG), true2, xC, xF, xD, xG))
% 4.42/0.94 = { by lemma 14 R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), sdtpldt0(fresh33(X, X, xC, xD, xG), fresh33(Y, Y, xF, xD, xG)))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), sdtpldt0(fresh33(X, X, xC, xD, xG), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtlseqdt0(fresh83(true2, true2, xE, xH, xE, xH), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by axiom 1 (m__1873_1) R->L }
% 4.42/0.94 sdtlseqdt0(fresh83(aScalar0(xH), true2, xE, xH, xE, xH), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by lemma 14 R->L }
% 4.42/0.94 sdtlseqdt0(sdtpldt0(fresh33(Z, Z, xE, xE, xH), fresh33(W, W, xH, xE, xH)), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtlseqdt0(sdtpldt0(fresh33(Z, Z, xE, xE, xH), sdtpldt0(sdtasdt0(xH, xE), sdtasdt0(xH, xH))), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by axiom 7 (mDistr) }
% 4.42/0.94 sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE, xE), sdtasdt0(xE, xH)), sdtpldt0(sdtasdt0(xH, xE), sdtasdt0(xH, xH))), sdtpldt0(sdtpldt0(sdtasdt0(xC, xD), sdtasdt0(xC, xG)), sdtpldt0(sdtasdt0(xF, xD), sdtasdt0(xF, xG))))
% 4.42/0.94 = { by axiom 13 (m__2905) }
% 4.42/0.94 true2
% 4.42/0.94 % SZS output end Proof
% 4.42/0.94
% 4.42/0.94 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------