TSTP Solution File: RNG045+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG045+1 : 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 13:59:01 EDT 2023
% Result : Theorem 6.29s 1.16s
% Output : Proof 6.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:36:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.29/1.16 Command-line arguments: --no-flatten-goal
% 6.29/1.16
% 6.29/1.16 % SZS status Theorem
% 6.29/1.16
% 6.29/1.16 % SZS output start Proof
% 6.29/1.16 Take the following subset of the input axioms:
% 6.29/1.16 fof(mDistr, axiom, ![W0, W1, W2]: ((aScalar0(W0) & (aScalar0(W1) & aScalar0(W2))) => (sdtasdt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & sdtasdt0(sdtpldt0(W0, W1), W2)=sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))).
% 6.29/1.16 fof(m__, conjecture, sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv))=sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))).
% 6.29/1.16 fof(m__674, hypothesis, aScalar0(xx) & (aScalar0(xy) & (aScalar0(xu) & aScalar0(xv)))).
% 6.29/1.16 fof(m__733, hypothesis, sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv))=sdtpldt0(sdtasdt0(xx, sdtpldt0(xu, xv)), sdtasdt0(xy, sdtpldt0(xu, xv)))).
% 6.29/1.16
% 6.29/1.16 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.29/1.16 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.29/1.16 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.29/1.16 fresh(y, y, x1...xn) = u
% 6.29/1.16 C => fresh(s, t, x1...xn) = v
% 6.29/1.16 where fresh is a fresh function symbol and x1..xn are the free
% 6.29/1.16 variables of u and v.
% 6.29/1.16 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.29/1.16 input problem has no model of domain size 1).
% 6.29/1.16
% 6.29/1.16 The encoding turns the above axioms into the following unit equations and goals:
% 6.29/1.16
% 6.29/1.16 Axiom 1 (m__674): aScalar0(xx) = true2.
% 6.29/1.16 Axiom 2 (m__674_1): aScalar0(xy) = true2.
% 6.29/1.16 Axiom 3 (m__674_2): aScalar0(xu) = true2.
% 6.29/1.16 Axiom 4 (m__674_3): aScalar0(xv) = true2.
% 6.29/1.16 Axiom 5 (mDistr): fresh24(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 6.29/1.16 Axiom 6 (mDistr): fresh23(X, X, Y, Z, W) = fresh24(aScalar0(Y), true2, Y, Z, W).
% 6.29/1.16 Axiom 7 (mDistr): fresh23(aScalar0(X), true2, Y, Z, X) = fresh18(aScalar0(Z), true2, Y, Z, X).
% 6.29/1.16 Axiom 8 (mDistr): fresh18(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 6.29/1.16 Axiom 9 (m__733): sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv)) = sdtpldt0(sdtasdt0(xx, sdtpldt0(xu, xv)), sdtasdt0(xy, sdtpldt0(xu, xv))).
% 6.29/1.16
% 6.29/1.16 Lemma 10: fresh18(X, X, Y, xu, xv) = fresh23(Z, Z, Y, xu, xv).
% 6.29/1.16 Proof:
% 6.29/1.16 fresh18(X, X, Y, xu, xv)
% 6.29/1.16 = { by axiom 8 (mDistr) }
% 6.29/1.16 sdtpldt0(sdtasdt0(Y, xu), sdtasdt0(Y, xv))
% 6.29/1.16 = { by axiom 8 (mDistr) R->L }
% 6.29/1.16 fresh18(true2, true2, Y, xu, xv)
% 6.29/1.16 = { by axiom 3 (m__674_2) R->L }
% 6.29/1.16 fresh18(aScalar0(xu), true2, Y, xu, xv)
% 6.29/1.16 = { by axiom 7 (mDistr) R->L }
% 6.29/1.16 fresh23(aScalar0(xv), true2, Y, xu, xv)
% 6.29/1.16 = { by axiom 4 (m__674_3) }
% 6.29/1.16 fresh23(true2, true2, Y, xu, xv)
% 6.29/1.16 = { by axiom 6 (mDistr) }
% 6.29/1.16 fresh24(aScalar0(Y), true2, Y, xu, xv)
% 6.29/1.16 = { by axiom 6 (mDistr) R->L }
% 6.29/1.16 fresh23(Z, Z, Y, xu, xv)
% 6.29/1.16
% 6.29/1.16 Goal 1 (m__): sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv))).
% 6.29/1.16 Proof:
% 6.29/1.16 sdtasdt0(sdtpldt0(xx, xy), sdtpldt0(xu, xv))
% 6.29/1.16 = { by axiom 9 (m__733) }
% 6.29/1.16 sdtpldt0(sdtasdt0(xx, sdtpldt0(xu, xv)), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 6.29/1.16 = { by axiom 5 (mDistr) R->L }
% 6.29/1.16 sdtpldt0(fresh24(true2, true2, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 6.29/1.16 = { by axiom 1 (m__674) R->L }
% 6.29/1.16 sdtpldt0(fresh24(aScalar0(xx), true2, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 6.29/1.16 = { by axiom 6 (mDistr) R->L }
% 6.29/1.16 sdtpldt0(fresh23(X, X, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 6.29/1.16 = { by lemma 10 R->L }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), sdtasdt0(xy, sdtpldt0(xu, xv)))
% 6.29/1.16 = { by axiom 5 (mDistr) R->L }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), fresh24(true2, true2, xy, xu, xv))
% 6.29/1.16 = { by axiom 2 (m__674_1) R->L }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), fresh24(aScalar0(xy), true2, xy, xu, xv))
% 6.29/1.16 = { by axiom 6 (mDistr) R->L }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), fresh23(Z, Z, xy, xu, xv))
% 6.29/1.16 = { by lemma 10 R->L }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), fresh18(W, W, xy, xu, xv))
% 6.29/1.16 = { by axiom 8 (mDistr) }
% 6.29/1.16 sdtpldt0(fresh18(Y, Y, xx, xu, xv), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))
% 6.29/1.16 = { by axiom 8 (mDistr) }
% 6.29/1.16 sdtpldt0(sdtpldt0(sdtasdt0(xx, xu), sdtasdt0(xx, xv)), sdtpldt0(sdtasdt0(xy, xu), sdtasdt0(xy, xv)))
% 6.29/1.16 % SZS output end Proof
% 6.29/1.16
% 6.29/1.16 RESULT: Theorem (the conjecture is true).
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