TSTP Solution File: RNG046+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG046+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 : n031.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 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : RNG046+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 03:11:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Take the following subset of the input axioms:
% 0.19/0.49 fof(mMNeg, axiom, ![W0, W1]: ((aScalar0(W0) & aScalar0(W1)) => (sdtasdt0(W0, smndt0(W1))=smndt0(sdtasdt0(W0, W1)) & sdtasdt0(smndt0(W0), W1)=smndt0(sdtasdt0(W0, W1))))).
% 0.19/0.49 fof(mMulSc, axiom, ![W0_2, W1_2]: ((aScalar0(W0_2) & aScalar0(W1_2)) => aScalar0(sdtasdt0(W0_2, W1_2)))).
% 0.19/0.49 fof(mNegSc, axiom, ![W0_2]: (aScalar0(W0_2) => aScalar0(smndt0(W0_2)))).
% 0.19/0.49 fof(mScZero, axiom, ![W0_2]: (aScalar0(W0_2) => (sdtpldt0(W0_2, sz0z00)=W0_2 & (sdtpldt0(sz0z00, W0_2)=W0_2 & (sdtasdt0(W0_2, sz0z00)=sz0z00 & (sdtasdt0(sz0z00, W0_2)=sz0z00 & (sdtpldt0(W0_2, smndt0(W0_2))=sz0z00 & (sdtpldt0(smndt0(W0_2), W0_2)=sz0z00 & (smndt0(smndt0(W0_2))=W0_2 & smndt0(sz0z00)=sz0z00))))))))).
% 0.19/0.49 fof(m__, conjecture, sdtasdt0(smndt0(xx), smndt0(xy))=sdtasdt0(xx, xy)).
% 0.19/0.49 fof(m__799, hypothesis, aScalar0(xx) & aScalar0(xy)).
% 0.19/0.49
% 0.19/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.49 fresh(y, y, x1...xn) = u
% 0.19/0.49 C => fresh(s, t, x1...xn) = v
% 0.19/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.49 variables of u and v.
% 0.19/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.49 input problem has no model of domain size 1).
% 0.19/0.49
% 0.19/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.49
% 0.19/0.49 Axiom 1 (m__799): aScalar0(xx) = true2.
% 0.19/0.49 Axiom 2 (m__799_1): aScalar0(xy) = true2.
% 0.19/0.49 Axiom 3 (mNegSc): fresh13(X, X, Y) = true2.
% 0.19/0.49 Axiom 4 (mScZero_2): fresh3(X, X, Y) = Y.
% 0.19/0.49 Axiom 5 (mMNeg): fresh19(X, X, Y, Z) = sdtasdt0(Y, smndt0(Z)).
% 0.19/0.49 Axiom 6 (mMNeg): fresh18(X, X, Y, Z) = smndt0(sdtasdt0(Y, Z)).
% 0.19/0.49 Axiom 7 (mMNeg_1): fresh17(X, X, Y, Z) = sdtasdt0(smndt0(Y), Z).
% 0.19/0.49 Axiom 8 (mMNeg_1): fresh16(X, X, Y, Z) = smndt0(sdtasdt0(Y, Z)).
% 0.19/0.49 Axiom 9 (mMulSc): fresh15(X, X, Y, Z) = aScalar0(sdtasdt0(Y, Z)).
% 0.19/0.49 Axiom 10 (mMulSc): fresh14(X, X, Y, Z) = true2.
% 0.19/0.49 Axiom 11 (mNegSc): fresh13(aScalar0(X), true2, X) = aScalar0(smndt0(X)).
% 0.19/0.49 Axiom 12 (mScZero_2): fresh3(aScalar0(X), true2, X) = smndt0(smndt0(X)).
% 0.19/0.49 Axiom 13 (mMNeg): fresh19(aScalar0(X), true2, Y, X) = fresh18(aScalar0(Y), true2, Y, X).
% 0.19/0.49 Axiom 14 (mMNeg_1): fresh17(aScalar0(X), true2, Y, X) = fresh16(aScalar0(Y), true2, Y, X).
% 0.19/0.49 Axiom 15 (mMulSc): fresh15(aScalar0(X), true2, Y, X) = fresh14(aScalar0(Y), true2, Y, X).
% 0.19/0.49
% 0.19/0.49 Goal 1 (m__): sdtasdt0(smndt0(xx), smndt0(xy)) = sdtasdt0(xx, xy).
% 0.19/0.49 Proof:
% 0.19/0.49 sdtasdt0(smndt0(xx), smndt0(xy))
% 0.19/0.49 = { by axiom 7 (mMNeg_1) R->L }
% 0.19/0.49 fresh17(true2, true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 3 (mNegSc) R->L }
% 0.19/0.49 fresh17(fresh13(true2, true2, xy), true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 2 (m__799_1) R->L }
% 0.19/0.49 fresh17(fresh13(aScalar0(xy), true2, xy), true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 11 (mNegSc) }
% 0.19/0.49 fresh17(aScalar0(smndt0(xy)), true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 14 (mMNeg_1) }
% 0.19/0.49 fresh16(aScalar0(xx), true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 1 (m__799) }
% 0.19/0.49 fresh16(true2, true2, xx, smndt0(xy))
% 0.19/0.49 = { by axiom 8 (mMNeg_1) }
% 0.19/0.49 smndt0(sdtasdt0(xx, smndt0(xy)))
% 0.19/0.49 = { by axiom 5 (mMNeg) R->L }
% 0.19/0.49 smndt0(fresh19(true2, true2, xx, xy))
% 0.19/0.49 = { by axiom 2 (m__799_1) R->L }
% 0.19/0.49 smndt0(fresh19(aScalar0(xy), true2, xx, xy))
% 0.19/0.49 = { by axiom 13 (mMNeg) }
% 0.19/0.49 smndt0(fresh18(aScalar0(xx), true2, xx, xy))
% 0.19/0.49 = { by axiom 1 (m__799) }
% 0.19/0.49 smndt0(fresh18(true2, true2, xx, xy))
% 0.19/0.49 = { by axiom 6 (mMNeg) }
% 0.19/0.49 smndt0(smndt0(sdtasdt0(xx, xy)))
% 0.19/0.49 = { by axiom 12 (mScZero_2) R->L }
% 0.19/0.49 fresh3(aScalar0(sdtasdt0(xx, xy)), true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 9 (mMulSc) R->L }
% 0.19/0.49 fresh3(fresh15(true2, true2, xx, xy), true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 2 (m__799_1) R->L }
% 0.19/0.49 fresh3(fresh15(aScalar0(xy), true2, xx, xy), true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 15 (mMulSc) }
% 0.19/0.49 fresh3(fresh14(aScalar0(xx), true2, xx, xy), true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 1 (m__799) }
% 0.19/0.49 fresh3(fresh14(true2, true2, xx, xy), true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 10 (mMulSc) }
% 0.19/0.49 fresh3(true2, true2, sdtasdt0(xx, xy))
% 0.19/0.49 = { by axiom 4 (mScZero_2) }
% 0.19/0.49 sdtasdt0(xx, xy)
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Theorem (the conjecture is true).
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