TSTP Solution File: NUM468+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM468+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 : n010.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 11:56:27 EDT 2023
% Result : Theorem 20.30s 3.04s
% Output : Proof 20.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM468+2 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % 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 : n010.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 : Fri Aug 25 11:46:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 20.30/3.04 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 20.30/3.04
% 20.30/3.04 % SZS status Theorem
% 20.30/3.04
% 20.30/3.04 % SZS output start Proof
% 20.30/3.04 Take the following subset of the input axioms:
% 20.30/3.04 fof(mAMDistr, axiom, ![W0, W1, W2]: ((aNaturalNumber0(W0) & (aNaturalNumber0(W1) & aNaturalNumber0(W2))) => (sdtasdt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & sdtasdt0(sdtpldt0(W1, W2), W0)=sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))).
% 20.30/3.04 fof(m__, conjecture, xl!=sz00 => ((aNaturalNumber0(sdtsldt0(xm, xl)) & xm=sdtasdt0(xl, sdtsldt0(xm, xl))) => ((aNaturalNumber0(sdtsldt0(xn, xl)) & xn=sdtasdt0(xl, sdtsldt0(xn, xl))) => sdtpldt0(xm, xn)=sdtasdt0(xl, sdtpldt0(sdtsldt0(xm, xl), sdtsldt0(xn, xl)))))).
% 20.30/3.04 fof(m__1240, hypothesis, aNaturalNumber0(xl) & (aNaturalNumber0(xm) & aNaturalNumber0(xn))).
% 20.30/3.04
% 20.30/3.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 20.30/3.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 20.30/3.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 20.30/3.04 fresh(y, y, x1...xn) = u
% 20.30/3.04 C => fresh(s, t, x1...xn) = v
% 20.30/3.04 where fresh is a fresh function symbol and x1..xn are the free
% 20.30/3.04 variables of u and v.
% 20.30/3.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 20.30/3.04 input problem has no model of domain size 1).
% 20.30/3.04
% 20.30/3.04 The encoding turns the above axioms into the following unit equations and goals:
% 20.30/3.04
% 20.30/3.04 Axiom 1 (m__1240): aNaturalNumber0(xl) = true.
% 20.30/3.04 Axiom 2 (m___2): aNaturalNumber0(sdtsldt0(xm, xl)) = true.
% 20.30/3.04 Axiom 3 (m___3): aNaturalNumber0(sdtsldt0(xn, xl)) = true.
% 20.30/3.04 Axiom 4 (m__): xm = sdtasdt0(xl, sdtsldt0(xm, xl)).
% 20.30/3.04 Axiom 5 (m___1): xn = sdtasdt0(xl, sdtsldt0(xn, xl)).
% 20.30/3.04 Axiom 6 (mAMDistr): fresh93(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 20.30/3.04 Axiom 7 (mAMDistr): fresh32(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 20.30/3.04 Axiom 8 (mAMDistr): fresh92(X, X, Y, Z, W) = fresh93(aNaturalNumber0(Y), true, Y, Z, W).
% 20.30/3.04 Axiom 9 (mAMDistr): fresh92(aNaturalNumber0(X), true, Y, Z, X) = fresh32(aNaturalNumber0(Z), true, Y, Z, X).
% 20.30/3.04
% 20.30/3.04 Goal 1 (m___5): sdtpldt0(xm, xn) = sdtasdt0(xl, sdtpldt0(sdtsldt0(xm, xl), sdtsldt0(xn, xl))).
% 20.30/3.04 Proof:
% 20.30/3.04 sdtpldt0(xm, xn)
% 20.30/3.04 = { by axiom 5 (m___1) }
% 20.30/3.04 sdtpldt0(xm, sdtasdt0(xl, sdtsldt0(xn, xl)))
% 20.30/3.04 = { by axiom 4 (m__) }
% 20.30/3.04 sdtpldt0(sdtasdt0(xl, sdtsldt0(xm, xl)), sdtasdt0(xl, sdtsldt0(xn, xl)))
% 20.30/3.04 = { by axiom 7 (mAMDistr) R->L }
% 20.30/3.04 fresh32(true, true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 2 (m___2) R->L }
% 20.30/3.04 fresh32(aNaturalNumber0(sdtsldt0(xm, xl)), true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 9 (mAMDistr) R->L }
% 20.30/3.04 fresh92(aNaturalNumber0(sdtsldt0(xn, xl)), true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 3 (m___3) }
% 20.30/3.04 fresh92(true, true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 8 (mAMDistr) }
% 20.30/3.04 fresh93(aNaturalNumber0(xl), true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 1 (m__1240) }
% 20.30/3.04 fresh93(true, true, xl, sdtsldt0(xm, xl), sdtsldt0(xn, xl))
% 20.30/3.04 = { by axiom 6 (mAMDistr) }
% 20.30/3.04 sdtasdt0(xl, sdtpldt0(sdtsldt0(xm, xl), sdtsldt0(xn, xl)))
% 20.30/3.04 % SZS output end Proof
% 20.30/3.04
% 20.30/3.04 RESULT: Theorem (the conjecture is true).
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