TSTP Solution File: RNG059+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG059+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 13:59:05 EDT 2023
% Result : Theorem 12.04s 1.92s
% Output : Proof 12.04s
% 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 : RNG059+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
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 02:26:53 EDT 2023
% 0.17/0.34 % CPUTime :
% 12.04/1.92 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 12.04/1.92
% 12.04/1.92 % SZS status Theorem
% 12.04/1.92
% 12.04/1.92 % SZS output start Proof
% 12.04/1.92 Take the following subset of the input axioms:
% 12.04/1.92 fof(mArith, axiom, ![W0, W1, W2]: ((aScalar0(W0) & (aScalar0(W1) & aScalar0(W2))) => (sdtpldt0(sdtpldt0(W0, W1), W2)=sdtpldt0(W0, sdtpldt0(W1, W2)) & (sdtpldt0(W0, W1)=sdtpldt0(W1, W0) & (sdtasdt0(sdtasdt0(W0, W1), W2)=sdtasdt0(W0, sdtasdt0(W1, W2)) & sdtasdt0(W0, W1)=sdtasdt0(W1, W0)))))).
% 12.04/1.92 fof(mMNeg, axiom, ![W0_2, W1_2]: ((aScalar0(W0_2) & aScalar0(W1_2)) => (sdtasdt0(W0_2, smndt0(W1_2))=smndt0(sdtasdt0(W0_2, W1_2)) & sdtasdt0(smndt0(W0_2), W1_2)=smndt0(sdtasdt0(W0_2, W1_2))))).
% 12.04/1.92 fof(mSZeroSc, axiom, aScalar0(sz0z00)).
% 12.04/1.92 fof(m__, conjecture, sdtasdt0(smndt0(xS), xR)=smndt0(xN)).
% 12.04/1.92 fof(m__1892, hypothesis, aScalar0(xR) & xR=sdtasdt0(xC, xG)).
% 12.04/1.92 fof(m__1930, hypothesis, aScalar0(xS) & xS=sdtasdt0(xF, xD)).
% 12.04/1.92 fof(m__1949, hypothesis, aScalar0(xN) & xN=sdtasdt0(xR, xS)).
% 12.04/1.92
% 12.04/1.92 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.04/1.92 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.04/1.92 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.04/1.92 fresh(y, y, x1...xn) = u
% 12.04/1.92 C => fresh(s, t, x1...xn) = v
% 12.04/1.92 where fresh is a fresh function symbol and x1..xn are the free
% 12.04/1.92 variables of u and v.
% 12.04/1.92 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.04/1.92 input problem has no model of domain size 1).
% 12.04/1.92
% 12.04/1.92 The encoding turns the above axioms into the following unit equations and goals:
% 12.04/1.92
% 12.04/1.92 Axiom 1 (mSZeroSc): aScalar0(sz0z00) = true2.
% 12.04/1.92 Axiom 2 (m__1930_1): aScalar0(xS) = true2.
% 12.04/1.92 Axiom 3 (m__1892_1): aScalar0(xR) = true2.
% 12.04/1.92 Axiom 4 (m__1949): xN = sdtasdt0(xR, xS).
% 12.04/1.92 Axiom 5 (mArith_2): fresh96(X, X, Y, Z) = sdtasdt0(Z, Y).
% 12.04/1.92 Axiom 6 (mArith_2): fresh37(X, X, Y, Z) = sdtasdt0(Y, Z).
% 12.04/1.92 Axiom 7 (mMNeg_1): fresh23(X, X, Y, Z) = sdtasdt0(smndt0(Y), Z).
% 12.04/1.92 Axiom 8 (mMNeg_1): fresh22(X, X, Y, Z) = smndt0(sdtasdt0(Y, Z)).
% 12.04/1.92 Axiom 9 (mArith_2): fresh95(X, X, Y, Z) = fresh96(aScalar0(Y), true2, Y, Z).
% 12.04/1.92 Axiom 10 (mArith_2): fresh95(aScalar0(X), true2, Y, Z) = fresh37(aScalar0(Z), true2, Y, Z).
% 12.04/1.92 Axiom 11 (mMNeg_1): fresh23(aScalar0(X), true2, Y, X) = fresh22(aScalar0(Y), true2, Y, X).
% 12.04/1.92
% 12.04/1.92 Goal 1 (m__): sdtasdt0(smndt0(xS), xR) = smndt0(xN).
% 12.04/1.92 Proof:
% 12.04/1.92 sdtasdt0(smndt0(xS), xR)
% 12.04/1.92 = { by axiom 7 (mMNeg_1) R->L }
% 12.04/1.92 fresh23(true2, true2, xS, xR)
% 12.04/1.92 = { by axiom 3 (m__1892_1) R->L }
% 12.04/1.92 fresh23(aScalar0(xR), true2, xS, xR)
% 12.04/1.92 = { by axiom 11 (mMNeg_1) }
% 12.04/1.93 fresh22(aScalar0(xS), true2, xS, xR)
% 12.04/1.93 = { by axiom 2 (m__1930_1) }
% 12.04/1.93 fresh22(true2, true2, xS, xR)
% 12.04/1.93 = { by axiom 8 (mMNeg_1) }
% 12.04/1.93 smndt0(sdtasdt0(xS, xR))
% 12.04/1.93 = { by axiom 5 (mArith_2) R->L }
% 12.04/1.93 smndt0(fresh96(true2, true2, xR, xS))
% 12.04/1.93 = { by axiom 3 (m__1892_1) R->L }
% 12.04/1.93 smndt0(fresh96(aScalar0(xR), true2, xR, xS))
% 12.04/1.93 = { by axiom 9 (mArith_2) R->L }
% 12.04/1.93 smndt0(fresh95(true2, true2, xR, xS))
% 12.04/1.93 = { by axiom 1 (mSZeroSc) R->L }
% 12.04/1.93 smndt0(fresh95(aScalar0(sz0z00), true2, xR, xS))
% 12.04/1.93 = { by axiom 10 (mArith_2) }
% 12.04/1.93 smndt0(fresh37(aScalar0(xS), true2, xR, xS))
% 12.04/1.93 = { by axiom 2 (m__1930_1) }
% 12.04/1.93 smndt0(fresh37(true2, true2, xR, xS))
% 12.04/1.93 = { by axiom 6 (mArith_2) }
% 12.04/1.93 smndt0(sdtasdt0(xR, xS))
% 12.04/1.93 = { by axiom 4 (m__1949) R->L }
% 12.04/1.93 smndt0(xN)
% 12.04/1.93 % SZS output end Proof
% 12.04/1.93
% 12.04/1.93 RESULT: Theorem (the conjecture is true).
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