TSTP Solution File: NUM605+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM605+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 : 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 11:57:14 EDT 2023
% Result : Theorem 165.08s 21.54s
% Output : Proof 165.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM605+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
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:31:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 165.08/21.54 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 165.08/21.54
% 165.08/21.54 % SZS status Theorem
% 165.08/21.54
% 165.08/21.55 % SZS output start Proof
% 165.08/21.55 Take the following subset of the input axioms:
% 165.08/21.55 fof(mCardSeg, axiom, ![W0]: (aElementOf0(W0, szNzAzT0) => sbrdtbr0(slbdtrb0(W0))=W0)).
% 165.08/21.55 fof(mDefSel, definition, ![W1, W0_2]: ((aSet0(W0_2) & aElementOf0(W1, szNzAzT0)) => ![W2]: (W2=slbdtsldtrb0(W0_2, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0_2) & sbrdtbr0(W3)=W1)))))).
% 165.08/21.55 fof(mSegZero, axiom, slbdtrb0(sz00)=slcrc0).
% 165.08/21.55 fof(mZeroNum, axiom, aElementOf0(sz00, szNzAzT0)).
% 165.08/21.55 fof(m__, conjecture, xQ!=slcrc0).
% 165.08/21.55 fof(m__3418, hypothesis, aElementOf0(xK, szNzAzT0)).
% 165.08/21.55 fof(m__3462, hypothesis, xK!=sz00).
% 165.08/21.55 fof(m__3520, hypothesis, xK!=sz00).
% 165.08/21.55 fof(m__4891, hypothesis, aSet0(xO) & xO=sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))).
% 165.08/21.55 fof(m__5078, hypothesis, aElementOf0(xQ, slbdtsldtrb0(xO, xK))).
% 165.08/21.55
% 165.08/21.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 165.08/21.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 165.08/21.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 165.08/21.55 fresh(y, y, x1...xn) = u
% 165.08/21.55 C => fresh(s, t, x1...xn) = v
% 165.08/21.55 where fresh is a fresh function symbol and x1..xn are the free
% 165.08/21.55 variables of u and v.
% 165.08/21.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 165.08/21.55 input problem has no model of domain size 1).
% 165.08/21.55
% 165.08/21.55 The encoding turns the above axioms into the following unit equations and goals:
% 165.08/21.55
% 165.08/21.55 Axiom 1 (m__): xQ = slcrc0.
% 165.08/21.55 Axiom 2 (m__4891_1): aSet0(xO) = true2.
% 165.08/21.55 Axiom 3 (mSegZero): slbdtrb0(sz00) = slcrc0.
% 165.08/21.55 Axiom 4 (mZeroNum): aElementOf0(sz00, szNzAzT0) = true2.
% 165.08/21.55 Axiom 5 (m__3418): aElementOf0(xK, szNzAzT0) = true2.
% 165.08/21.55 Axiom 6 (mCardSeg): fresh6(X, X, Y) = Y.
% 165.08/21.55 Axiom 7 (m__5078): aElementOf0(xQ, slbdtsldtrb0(xO, xK)) = true2.
% 165.08/21.55 Axiom 8 (mDefSel_6): fresh5(X, X, Y, Z) = Y.
% 165.08/21.55 Axiom 9 (mDefSel_2): fresh237(X, X, Y, Z, W) = true2.
% 165.08/21.55 Axiom 10 (mCardSeg): fresh6(aElementOf0(X, szNzAzT0), true2, X) = sbrdtbr0(slbdtrb0(X)).
% 165.08/21.55 Axiom 11 (mDefSel_2): fresh235(X, X, Y, Z, W, V) = equiv3(Y, Z, V).
% 165.08/21.55 Axiom 12 (mDefSel_2): fresh236(X, X, Y, Z, W, V) = fresh237(W, slbdtsldtrb0(Y, Z), Y, Z, V).
% 165.08/21.55 Axiom 13 (mDefSel_2): fresh234(X, X, Y, Z, W, V) = fresh235(aSet0(Y), true2, Y, Z, W, V).
% 165.08/21.55 Axiom 14 (mDefSel_6): fresh5(equiv3(X, Y, Z), true2, Y, Z) = sbrdtbr0(Z).
% 165.08/21.55 Axiom 15 (mDefSel_2): fresh234(aElementOf0(X, Y), true2, Z, W, Y, X) = fresh236(aElementOf0(W, szNzAzT0), true2, Z, W, Y, X).
% 165.08/21.55
% 165.08/21.55 Lemma 16: xK = sz00.
% 165.08/21.55 Proof:
% 165.08/21.55 xK
% 165.08/21.55 = { by axiom 8 (mDefSel_6) R->L }
% 165.08/21.55 fresh5(true2, true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 9 (mDefSel_2) R->L }
% 165.08/21.55 fresh5(fresh237(slbdtsldtrb0(xO, xK), slbdtsldtrb0(xO, xK), xO, xK, slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 12 (mDefSel_2) R->L }
% 165.08/21.55 fresh5(fresh236(true2, true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 5 (m__3418) R->L }
% 165.08/21.55 fresh5(fresh236(aElementOf0(xK, szNzAzT0), true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 15 (mDefSel_2) R->L }
% 165.08/21.55 fresh5(fresh234(aElementOf0(slcrc0, slbdtsldtrb0(xO, xK)), true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 1 (m__) R->L }
% 165.08/21.55 fresh5(fresh234(aElementOf0(xQ, slbdtsldtrb0(xO, xK)), true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 7 (m__5078) }
% 165.08/21.55 fresh5(fresh234(true2, true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 13 (mDefSel_2) }
% 165.08/21.55 fresh5(fresh235(aSet0(xO), true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 2 (m__4891_1) }
% 165.08/21.55 fresh5(fresh235(true2, true2, xO, xK, slbdtsldtrb0(xO, xK), slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 11 (mDefSel_2) }
% 165.08/21.55 fresh5(equiv3(xO, xK, slcrc0), true2, xK, slcrc0)
% 165.08/21.55 = { by axiom 14 (mDefSel_6) }
% 165.08/21.55 sbrdtbr0(slcrc0)
% 165.08/21.55 = { by axiom 3 (mSegZero) R->L }
% 165.08/21.55 sbrdtbr0(slbdtrb0(sz00))
% 165.08/21.55 = { by axiom 10 (mCardSeg) R->L }
% 165.08/21.55 fresh6(aElementOf0(sz00, szNzAzT0), true2, sz00)
% 165.08/21.55 = { by axiom 4 (mZeroNum) }
% 165.08/21.55 fresh6(true2, true2, sz00)
% 165.08/21.55 = { by axiom 6 (mCardSeg) }
% 165.08/21.55 sz00
% 165.08/21.55
% 165.08/21.55 Goal 1 (m__3520): xK = sz00.
% 165.08/21.55 Proof:
% 165.08/21.55 xK
% 165.08/21.55 = { by lemma 16 }
% 165.08/21.55 sz00
% 165.08/21.55
% 165.08/21.55 Goal 2 (m__3462): xK = sz00.
% 165.08/21.55 Proof:
% 165.08/21.55 xK
% 165.08/21.55 = { by lemma 16 }
% 165.08/21.55 sz00
% 165.08/21.55 % SZS output end Proof
% 165.08/21.55
% 165.08/21.55 RESULT: Theorem (the conjecture is true).
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