TSTP Solution File: RNG095+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG095+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 13:59:15 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : Proof 0.20s
% 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 : RNG095+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 02:23:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.57
% 0.20/0.57 % SZS status Theorem
% 0.20/0.57
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Take the following subset of the input axioms:
% 0.20/0.57 fof(mSortsC_01, axiom, aElement0(sz10)).
% 0.20/0.57 fof(m__, conjecture, ?[W0, W1]: (aElementOf0(W0, xI) & (aElementOf0(W1, xJ) & sdtpldt0(W0, W1)=sz10))).
% 0.20/0.57 fof(m__1205_03, hypothesis, ![W0_2]: (aElement0(W0_2) => (?[W2, W1_2]: (aElementOf0(W1_2, xI) & (aElementOf0(W2, xJ) & sdtpldt0(W1_2, W2)=W0_2)) & aElementOf0(W0_2, sdtpldt1(xI, xJ))))).
% 0.20/0.57
% 0.20/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.58 fresh(y, y, x1...xn) = u
% 0.20/0.58 C => fresh(s, t, x1...xn) = v
% 0.20/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.58 variables of u and v.
% 0.20/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.58 input problem has no model of domain size 1).
% 0.20/0.58
% 0.20/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.58
% 0.20/0.58 Axiom 1 (mSortsC_01): aElement0(sz10) = true2.
% 0.20/0.58 Axiom 2 (m__1205_03): fresh(X, X, Y) = Y.
% 0.20/0.58 Axiom 3 (m__1205_03_2): fresh16(X, X, Y) = true2.
% 0.20/0.58 Axiom 4 (m__1205_03_3): fresh15(X, X, Y) = true2.
% 0.20/0.58 Axiom 5 (m__1205_03): fresh(aElement0(X), true2, X) = sdtpldt0(w1(X), w2(X)).
% 0.20/0.58 Axiom 6 (m__1205_03_2): fresh16(aElement0(X), true2, X) = aElementOf0(w2(X), xJ).
% 0.20/0.58 Axiom 7 (m__1205_03_3): fresh15(aElement0(X), true2, X) = aElementOf0(w1(X), xI).
% 0.20/0.58
% 0.20/0.58 Goal 1 (m__): tuple(sdtpldt0(X, Y), aElementOf0(X, xI), aElementOf0(Y, xJ)) = tuple(sz10, true2, true2).
% 0.20/0.58 The goal is true when:
% 0.20/0.58 X = w1(sz10)
% 0.20/0.58 Y = w2(sz10)
% 0.20/0.58
% 0.20/0.58 Proof:
% 0.20/0.58 tuple(sdtpldt0(w1(sz10), w2(sz10)), aElementOf0(w1(sz10), xI), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 5 (m__1205_03) R->L }
% 0.20/0.58 tuple(fresh(aElement0(sz10), true2, sz10), aElementOf0(w1(sz10), xI), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 1 (mSortsC_01) }
% 0.20/0.58 tuple(fresh(true2, true2, sz10), aElementOf0(w1(sz10), xI), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 2 (m__1205_03) }
% 0.20/0.58 tuple(sz10, aElementOf0(w1(sz10), xI), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 7 (m__1205_03_3) R->L }
% 0.20/0.58 tuple(sz10, fresh15(aElement0(sz10), true2, sz10), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 1 (mSortsC_01) }
% 0.20/0.58 tuple(sz10, fresh15(true2, true2, sz10), aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 4 (m__1205_03_3) }
% 0.20/0.58 tuple(sz10, true2, aElementOf0(w2(sz10), xJ))
% 0.20/0.58 = { by axiom 6 (m__1205_03_2) R->L }
% 0.20/0.58 tuple(sz10, true2, fresh16(aElement0(sz10), true2, sz10))
% 0.20/0.58 = { by axiom 1 (mSortsC_01) }
% 0.20/0.58 tuple(sz10, true2, fresh16(true2, true2, sz10))
% 0.20/0.58 = { by axiom 3 (m__1205_03_2) }
% 0.20/0.58 tuple(sz10, true2, true2)
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Theorem (the conjecture is true).
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