TSTP Solution File: RNG061+2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG061+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 : n028.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 126.24s 16.64s
% Output : Proof 126.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : RNG061+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 02:52:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 126.24/16.64 Command-line arguments: --ground-connectedness --complete-subsets
% 126.24/16.64
% 126.24/16.64 % SZS status Theorem
% 126.24/16.64
% 126.24/16.64 % SZS output start Proof
% 126.24/16.64 Take the following subset of the input axioms:
% 126.24/16.64 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)))))).
% 126.24/16.64 fof(mMulSc, axiom, ![W0_2, W1_2]: ((aScalar0(W0_2) & aScalar0(W1_2)) => aScalar0(sdtasdt0(W0_2, W1_2)))).
% 126.24/16.64 fof(mNegSc, axiom, ![W0_2]: (aScalar0(W0_2) => aScalar0(smndt0(W0_2)))).
% 126.24/16.64 fof(m__, conjecture, sdtasdt0(sdtpldt0(xR, smndt0(xS)), sdtpldt0(xR, smndt0(xS)))=sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(sdtasdt0(xS, xS), smndt0(xN)))).
% 126.24/16.64 fof(m__1837, hypothesis, aScalar0(xF) & xF=sdtasdt0(xA, xA)).
% 126.24/16.64 fof(m__1930, hypothesis, aScalar0(xS) & xS=sdtasdt0(xF, xD)).
% 126.24/16.64 fof(m__1949, hypothesis, aScalar0(xN) & xN=sdtasdt0(xR, xS)).
% 126.24/16.64 fof(m__2180, hypothesis, sdtasdt0(sdtpldt0(xR, smndt0(xS)), sdtpldt0(xR, smndt0(xS)))=sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(smndt0(xN), sdtasdt0(xS, xS)))).
% 126.24/16.64
% 126.24/16.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 126.24/16.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 126.24/16.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 126.24/16.64 fresh(y, y, x1...xn) = u
% 126.24/16.64 C => fresh(s, t, x1...xn) = v
% 126.24/16.64 where fresh is a fresh function symbol and x1..xn are the free
% 126.24/16.64 variables of u and v.
% 126.24/16.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 126.24/16.64 input problem has no model of domain size 1).
% 126.24/16.64
% 126.24/16.64 The encoding turns the above axioms into the following unit equations and goals:
% 126.24/16.64
% 126.24/16.64 Axiom 1 (m__1837_1): aScalar0(xF) = true2.
% 126.24/16.64 Axiom 2 (m__1949_1): aScalar0(xN) = true2.
% 126.24/16.64 Axiom 3 (m__1930_1): aScalar0(xS) = true2.
% 126.24/16.64 Axiom 4 (mNegSc): fresh19(X, X, Y) = true2.
% 126.24/16.64 Axiom 5 (mArith): fresh92(X, X, Y, Z) = sdtpldt0(Z, Y).
% 126.24/16.64 Axiom 6 (mArith): fresh39(X, X, Y, Z) = sdtpldt0(Y, Z).
% 126.24/16.64 Axiom 7 (mMulSc): fresh21(X, X, Y, Z) = aScalar0(sdtasdt0(Y, Z)).
% 126.24/16.64 Axiom 8 (mMulSc): fresh20(X, X, Y, Z) = true2.
% 126.24/16.64 Axiom 9 (mNegSc): fresh19(aScalar0(X), true2, X) = aScalar0(smndt0(X)).
% 126.24/16.64 Axiom 10 (mArith): fresh91(X, X, Y, Z) = fresh92(aScalar0(Y), true2, Y, Z).
% 126.24/16.64 Axiom 11 (mArith): fresh91(aScalar0(X), true2, Y, Z) = fresh39(aScalar0(Z), true2, Y, Z).
% 126.24/16.64 Axiom 12 (mMulSc): fresh21(aScalar0(X), true2, Y, X) = fresh20(aScalar0(Y), true2, Y, X).
% 126.24/16.64 Axiom 13 (m__2180): sdtasdt0(sdtpldt0(xR, smndt0(xS)), sdtpldt0(xR, smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(smndt0(xN), sdtasdt0(xS, xS))).
% 126.24/16.64
% 126.24/16.64 Goal 1 (m__): sdtasdt0(sdtpldt0(xR, smndt0(xS)), sdtpldt0(xR, smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(sdtasdt0(xS, xS), smndt0(xN))).
% 126.24/16.64 Proof:
% 126.24/16.64 sdtasdt0(sdtpldt0(xR, smndt0(xS)), sdtpldt0(xR, smndt0(xS)))
% 126.24/16.64 = { by axiom 13 (m__2180) }
% 126.24/16.64 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(smndt0(xN), sdtasdt0(xS, xS)))
% 126.24/16.64 = { by axiom 5 (mArith) R->L }
% 126.24/16.64 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(true2, true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.64 = { by axiom 8 (mMulSc) R->L }
% 126.24/16.64 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(fresh20(true2, true2, xS, xS), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 3 (m__1930_1) R->L }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(fresh20(aScalar0(xS), true2, xS, xS), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 12 (mMulSc) R->L }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(fresh21(aScalar0(xS), true2, xS, xS), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 3 (m__1930_1) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(fresh21(true2, true2, xS, xS), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 7 (mMulSc) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh92(aScalar0(sdtasdt0(xS, xS)), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 10 (mArith) R->L }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh91(true2, true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 1 (m__1837_1) R->L }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh91(aScalar0(xF), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 11 (mArith) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh39(aScalar0(smndt0(xN)), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 9 (mNegSc) R->L }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh39(fresh19(aScalar0(xN), true2, xN), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 2 (m__1949_1) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh39(fresh19(true2, true2, xN), true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 4 (mNegSc) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), fresh39(true2, true2, sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 = { by axiom 6 (mArith) }
% 126.24/16.65 sdtpldt0(sdtpldt0(sdtasdt0(xR, xR), smndt0(xN)), sdtpldt0(sdtasdt0(xS, xS), smndt0(xN)))
% 126.24/16.65 % SZS output end Proof
% 126.24/16.65
% 126.24/16.65 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------