TSTP Solution File: RNG069+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG069+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 : 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 13:59:08 EDT 2023
% Result : Theorem 3.88s 0.89s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG069+2 : 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
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:54:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.88/0.89 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 3.88/0.89
% 3.88/0.89 % SZS status Theorem
% 3.88/0.89
% 3.88/0.91 % SZS output start Proof
% 3.88/0.91 Take the following subset of the input axioms:
% 3.88/0.91 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))))).
% 3.88/0.91 fof(m__, conjecture, sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), sdtasdt0(sdtpldt0(xR, xS), sdtpldt0(xR, xS)))).
% 3.88/0.91 fof(m__1892, hypothesis, aScalar0(xR) & xR=sdtasdt0(xC, xG)).
% 3.88/0.91 fof(m__1911, hypothesis, aScalar0(xP) & xP=sdtasdt0(xE, xH)).
% 3.88/0.91 fof(m__1930, hypothesis, aScalar0(xS) & xS=sdtasdt0(xF, xD)).
% 3.88/0.91 fof(m__2580, hypothesis, sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP)), sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP))), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))).
% 3.88/0.91
% 3.88/0.91 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.88/0.91 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.88/0.91 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.88/0.91 fresh(y, y, x1...xn) = u
% 3.88/0.91 C => fresh(s, t, x1...xn) = v
% 3.88/0.91 where fresh is a fresh function symbol and x1..xn are the free
% 3.88/0.91 variables of u and v.
% 3.88/0.91 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.88/0.91 input problem has no model of domain size 1).
% 3.88/0.91
% 3.88/0.91 The encoding turns the above axioms into the following unit equations and goals:
% 3.88/0.91
% 3.88/0.91 Axiom 1 (m__1911_1): aScalar0(xP) = true2.
% 3.88/0.91 Axiom 2 (m__1892_1): aScalar0(xR) = true2.
% 3.88/0.91 Axiom 3 (m__1930_1): aScalar0(xS) = true2.
% 3.88/0.91 Axiom 4 (mDistr): fresh33(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 3.88/0.91 Axiom 5 (mDistr2): fresh86(X, X, Y, Z, W, V) = sdtasdt0(sdtpldt0(Y, Z), sdtpldt0(W, V)).
% 3.88/0.91 Axiom 6 (mDistr2): fresh85(X, X, Y, Z, W, V) = fresh86(aScalar0(Y), true2, Y, Z, W, V).
% 3.88/0.91 Axiom 7 (mDistr2): fresh84(X, X, Y, Z, W, V) = fresh85(aScalar0(Z), true2, Y, Z, W, V).
% 3.88/0.91 Axiom 8 (mDistr2): fresh83(X, X, Y, Z, W, V) = fresh84(aScalar0(W), true2, Y, Z, W, V).
% 3.88/0.91 Axiom 9 (mDistr2): fresh83(aScalar0(X), true2, Y, Z, W, X) = sdtpldt0(sdtpldt0(sdtasdt0(Y, W), sdtasdt0(Y, X)), sdtpldt0(sdtasdt0(Z, W), sdtasdt0(Z, X))).
% 3.88/0.91 Axiom 10 (m__2580): sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP)), sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP))), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS)))) = true2.
% 3.88/0.91
% 3.88/0.91 Lemma 11: sdtpldt0(fresh33(X, X, Y, Z, W), fresh33(V, V, U, Z, W)) = fresh83(aScalar0(W), true2, Y, U, Z, W).
% 3.88/0.91 Proof:
% 3.88/0.91 sdtpldt0(fresh33(X, X, Y, Z, W), fresh33(V, V, U, Z, W))
% 3.88/0.91 = { by axiom 4 (mDistr) }
% 3.88/0.91 sdtpldt0(fresh33(X, X, Y, Z, W), sdtpldt0(sdtasdt0(U, Z), sdtasdt0(U, W)))
% 3.88/0.91 = { by axiom 4 (mDistr) }
% 3.88/0.91 sdtpldt0(sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)), sdtpldt0(sdtasdt0(U, Z), sdtasdt0(U, W)))
% 3.88/0.91 = { by axiom 9 (mDistr2) R->L }
% 3.88/0.91 fresh83(aScalar0(W), true2, Y, U, Z, W)
% 3.88/0.91
% 3.88/0.91 Goal 1 (m__): sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), sdtasdt0(sdtpldt0(xR, xS), sdtpldt0(xR, xS))) = true2.
% 4.23/0.91 Proof:
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), sdtasdt0(sdtpldt0(xR, xS), sdtpldt0(xR, xS)))
% 4.23/0.91 = { by axiom 5 (mDistr2) R->L }
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), fresh86(true2, true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 2 (m__1892_1) R->L }
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), fresh86(aScalar0(xR), true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 6 (mDistr2) R->L }
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), fresh85(true2, true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 3 (m__1930_1) R->L }
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), fresh85(aScalar0(xS), true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 7 (mDistr2) R->L }
% 4.23/0.91 sdtlseqdt0(sdtasdt0(sdtpldt0(xP, xP), sdtpldt0(xP, xP)), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 5 (mDistr2) R->L }
% 4.23/0.91 sdtlseqdt0(fresh86(true2, true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 1 (m__1911_1) R->L }
% 4.23/0.91 sdtlseqdt0(fresh86(aScalar0(xP), true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.91 = { by axiom 6 (mDistr2) R->L }
% 4.23/0.91 sdtlseqdt0(fresh85(true2, true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 1 (m__1911_1) R->L }
% 4.23/0.92 sdtlseqdt0(fresh85(aScalar0(xP), true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 7 (mDistr2) R->L }
% 4.23/0.92 sdtlseqdt0(fresh84(true2, true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 1 (m__1911_1) R->L }
% 4.23/0.92 sdtlseqdt0(fresh84(aScalar0(xP), true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 8 (mDistr2) R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), fresh84(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 2 (m__1892_1) R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), fresh84(aScalar0(xR), true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 8 (mDistr2) R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), fresh83(true2, true2, xR, xS, xR, xS))
% 4.23/0.92 = { by axiom 3 (m__1930_1) R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), fresh83(aScalar0(xS), true2, xR, xS, xR, xS))
% 4.23/0.92 = { by lemma 11 R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), sdtpldt0(fresh33(X, X, xR, xR, xS), fresh33(Y, Y, xS, xR, xS)))
% 4.23/0.92 = { by axiom 4 (mDistr) }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), sdtpldt0(fresh33(X, X, xR, xR, xS), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by axiom 4 (mDistr) }
% 4.23/0.92 sdtlseqdt0(fresh83(true2, true2, xP, xP, xP, xP), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by axiom 1 (m__1911_1) R->L }
% 4.23/0.92 sdtlseqdt0(fresh83(aScalar0(xP), true2, xP, xP, xP, xP), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by lemma 11 R->L }
% 4.23/0.92 sdtlseqdt0(sdtpldt0(fresh33(Z, Z, xP, xP, xP), fresh33(W, W, xP, xP, xP)), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by axiom 4 (mDistr) }
% 4.23/0.92 sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP)), fresh33(W, W, xP, xP, xP)), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by axiom 4 (mDistr) }
% 4.23/0.92 sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP)), sdtpldt0(sdtasdt0(xP, xP), sdtasdt0(xP, xP))), sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), sdtasdt0(xR, xS)), sdtpldt0(sdtasdt0(xS, xR), sdtasdt0(xS, xS))))
% 4.23/0.92 = { by axiom 10 (m__2580) }
% 4.23/0.92 true2
% 4.23/0.92 % SZS output end Proof
% 4.23/0.92
% 4.23/0.92 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------