TSTP Solution File: RNG109+4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG109+4 : 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 : n026.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 13:59:21 EDT 2023
% Result : Theorem 27.67s 3.94s
% Output : Proof 27.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG109+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 02:58:04 EDT 2023
% 0.12/0.34 % CPUTime :
% 27.67/3.94 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 27.67/3.94
% 27.67/3.94 % SZS status Theorem
% 27.67/3.94
% 27.67/3.95 % SZS output start Proof
% 27.67/3.95 Take the following subset of the input axioms:
% 27.67/3.95 fof(mAddZero, axiom, ![W0]: (aElement0(W0) => (sdtpldt0(W0, sz00)=W0 & W0=sdtpldt0(sz00, W0)))).
% 27.67/3.95 fof(m__, conjecture, ?[W0_2]: ((![W1]: (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2]: (aElement0(W2) & sdtasdt0(xa, W2)=W1)) => (![W1_2]: (aElementOf0(W1_2, slsdtgt0(xb)) <=> ?[W2_2]: (aElement0(W2_2) & sdtasdt0(xb, W2_2)=W1_2)) => (?[W1_2, W2_2]: (aElementOf0(W1_2, slsdtgt0(xa)) & (aElementOf0(W2_2, slsdtgt0(xb)) & sdtpldt0(W1_2, W2_2)=W0_2)) | aElementOf0(W0_2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) & W0_2!=sz00)).
% 27.67/3.95 fof(m__2091, hypothesis, aElement0(xa) & aElement0(xb)).
% 27.67/3.95 fof(m__2110, hypothesis, xa!=sz00 | xb!=sz00).
% 27.67/3.95 fof(m__2203, hypothesis, ?[W0_2]: (aElement0(W0_2) & sdtasdt0(xa, W0_2)=sz00) & (aElementOf0(sz00, slsdtgt0(xa)) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xa, W0_2)=xa) & (aElementOf0(xa, slsdtgt0(xa)) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xb, W0_2)=sz00) & (aElementOf0(sz00, slsdtgt0(xb)) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xb, W0_2)=xb) & aElementOf0(xb, slsdtgt0(xb))))))))).
% 27.67/3.95
% 27.67/3.95 Now clausify the problem and encode Horn clauses using encoding 3 of
% 27.67/3.95 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 27.67/3.95 We repeatedly replace C & s=t => u=v by the two clauses:
% 27.67/3.95 fresh(y, y, x1...xn) = u
% 27.67/3.95 C => fresh(s, t, x1...xn) = v
% 27.67/3.95 where fresh is a fresh function symbol and x1..xn are the free
% 27.67/3.95 variables of u and v.
% 27.67/3.95 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 27.67/3.95 input problem has no model of domain size 1).
% 27.67/3.95
% 27.67/3.95 The encoding turns the above axioms into the following unit equations and goals:
% 27.67/3.95
% 27.67/3.95 Axiom 1 (m__2091): aElement0(xa) = true2.
% 27.67/3.95 Axiom 2 (m__2091_1): aElement0(xb) = true2.
% 27.67/3.95 Axiom 3 (m__2203_10): aElementOf0(xa, slsdtgt0(xa)) = true2.
% 27.67/3.95 Axiom 4 (m__2203_11): aElementOf0(xb, slsdtgt0(xb)) = true2.
% 27.67/3.95 Axiom 5 (m__2203_8): aElementOf0(sz00, slsdtgt0(xa)) = true2.
% 27.67/3.95 Axiom 6 (m__2203_9): aElementOf0(sz00, slsdtgt0(xb)) = true2.
% 27.67/3.95 Axiom 7 (m__): fresh88(X, X, Y) = sz00.
% 27.67/3.95 Axiom 8 (mAddZero_1): fresh10(X, X, Y) = Y.
% 27.67/3.95 Axiom 9 (mAddZero): fresh9(X, X, Y) = Y.
% 27.67/3.95 Axiom 10 (mAddZero_1): fresh10(aElement0(X), true2, X) = sdtpldt0(sz00, X).
% 27.67/3.95 Axiom 11 (mAddZero): fresh9(aElement0(X), true2, X) = sdtpldt0(X, sz00).
% 27.67/3.95 Axiom 12 (m__): fresh(X, X, Y, Z, W) = Y.
% 27.67/3.95 Axiom 13 (m__): fresh87(X, X, Y, Z, W) = fresh88(sdtpldt0(Z, W), Y, Y).
% 27.67/3.95 Axiom 14 (m__): fresh87(aElementOf0(X, slsdtgt0(xb)), true2, Y, Z, X) = fresh(aElementOf0(Z, slsdtgt0(xa)), true2, Y, Z, X).
% 27.67/3.95
% 27.67/3.95 Lemma 15: fresh87(X, X, sdtpldt0(Y, Z), Y, Z) = sz00.
% 27.67/3.95 Proof:
% 27.67/3.95 fresh87(X, X, sdtpldt0(Y, Z), Y, Z)
% 27.67/3.95 = { by axiom 13 (m__) }
% 27.67/3.95 fresh88(sdtpldt0(Y, Z), sdtpldt0(Y, Z), sdtpldt0(Y, Z))
% 27.67/3.95 = { by axiom 7 (m__) }
% 27.67/3.95 sz00
% 27.67/3.95
% 27.67/3.95 Lemma 16: sz00 = xb.
% 27.67/3.95 Proof:
% 27.67/3.95 sz00
% 27.67/3.95 = { by lemma 15 R->L }
% 27.67/3.95 fresh87(true2, true2, sdtpldt0(sz00, xb), sz00, xb)
% 27.67/3.95 = { by axiom 10 (mAddZero_1) R->L }
% 27.67/3.95 fresh87(true2, true2, fresh10(aElement0(xb), true2, xb), sz00, xb)
% 27.67/3.95 = { by axiom 2 (m__2091_1) }
% 27.67/3.95 fresh87(true2, true2, fresh10(true2, true2, xb), sz00, xb)
% 27.67/3.95 = { by axiom 8 (mAddZero_1) }
% 27.67/3.95 fresh87(true2, true2, xb, sz00, xb)
% 27.67/3.95 = { by axiom 4 (m__2203_11) R->L }
% 27.67/3.95 fresh87(aElementOf0(xb, slsdtgt0(xb)), true2, xb, sz00, xb)
% 27.67/3.95 = { by axiom 14 (m__) }
% 27.67/3.95 fresh(aElementOf0(sz00, slsdtgt0(xa)), true2, xb, sz00, xb)
% 27.67/3.95 = { by axiom 5 (m__2203_8) }
% 27.67/3.95 fresh(true2, true2, xb, sz00, xb)
% 27.67/3.95 = { by axiom 12 (m__) }
% 27.67/3.95 xb
% 27.67/3.95
% 27.67/3.95 Lemma 17: xb = xa.
% 27.67/3.95 Proof:
% 27.67/3.95 xb
% 27.67/3.95 = { by lemma 16 R->L }
% 27.67/3.95 sz00
% 27.67/3.95 = { by lemma 15 R->L }
% 27.67/3.95 fresh87(true2, true2, sdtpldt0(xa, sz00), xa, sz00)
% 27.67/3.95 = { by axiom 11 (mAddZero) R->L }
% 27.67/3.95 fresh87(true2, true2, fresh9(aElement0(xa), true2, xa), xa, sz00)
% 27.67/3.95 = { by axiom 1 (m__2091) }
% 27.67/3.95 fresh87(true2, true2, fresh9(true2, true2, xa), xa, sz00)
% 27.67/3.95 = { by axiom 9 (mAddZero) }
% 27.67/3.96 fresh87(true2, true2, xa, xa, sz00)
% 27.67/3.96 = { by axiom 6 (m__2203_9) R->L }
% 27.67/3.96 fresh87(aElementOf0(sz00, slsdtgt0(xb)), true2, xa, xa, sz00)
% 27.67/3.96 = { by axiom 14 (m__) }
% 27.67/3.96 fresh(aElementOf0(xa, slsdtgt0(xa)), true2, xa, xa, sz00)
% 27.67/3.96 = { by axiom 3 (m__2203_10) }
% 27.67/3.96 fresh(true2, true2, xa, xa, sz00)
% 27.67/3.96 = { by axiom 12 (m__) }
% 27.67/3.96 xa
% 27.67/3.96
% 27.67/3.96 Goal 1 (m__2110): tuple4(xa, xb) = tuple4(sz00, sz00).
% 27.67/3.96 Proof:
% 27.67/3.96 tuple4(xa, xb)
% 27.67/3.96 = { by lemma 17 }
% 27.67/3.96 tuple4(xa, xa)
% 27.67/3.96 = { by lemma 17 R->L }
% 27.67/3.96 tuple4(xb, xa)
% 27.67/3.96 = { by lemma 17 R->L }
% 27.67/3.96 tuple4(xb, xb)
% 27.67/3.96 = { by lemma 16 R->L }
% 27.67/3.96 tuple4(sz00, xb)
% 27.67/3.96 = { by lemma 16 R->L }
% 27.67/3.96 tuple4(sz00, sz00)
% 27.67/3.96 % SZS output end Proof
% 27.67/3.96
% 27.67/3.96 RESULT: Theorem (the conjecture is true).
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