TSTP Solution File: NUM557+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM557+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 : n024.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 11:56:57 EDT 2023
% Result : Theorem 3.27s 0.80s
% Output : Proof 3.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM557+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 13:10:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.27/0.80 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 3.27/0.80
% 3.27/0.80 % SZS status Theorem
% 3.27/0.80
% 3.27/0.80 % SZS output start Proof
% 3.27/0.80 Take the following subset of the input axioms:
% 3.27/0.80 fof(mDefSel, definition, ![W0, W1]: ((aSet0(W0) & aElementOf0(W1, szNzAzT0)) => ![W2]: (W2=slbdtsldtrb0(W0, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & sbrdtbr0(W3)=W1)))))).
% 3.27/0.80 fof(m__, conjecture, aElementOf0(xP, slbdtsldtrb0(xS, xk))).
% 3.27/0.80 fof(m__2202, hypothesis, aElementOf0(xk, szNzAzT0)).
% 3.27/0.80 fof(m__2202_02, hypothesis, aSet0(xS) & (aSet0(xT) & xk!=sz00)).
% 3.27/0.80 fof(m__2431, hypothesis, aSubsetOf0(xP, xS) & sbrdtbr0(xP)=xk).
% 3.27/0.80
% 3.27/0.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.27/0.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.27/0.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.27/0.80 fresh(y, y, x1...xn) = u
% 3.27/0.80 C => fresh(s, t, x1...xn) = v
% 3.27/0.80 where fresh is a fresh function symbol and x1..xn are the free
% 3.27/0.80 variables of u and v.
% 3.27/0.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.27/0.80 input problem has no model of domain size 1).
% 3.27/0.80
% 3.27/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 3.27/0.81
% 3.27/0.81 Axiom 1 (m__2202): aElementOf0(xk, szNzAzT0) = true2.
% 3.27/0.81 Axiom 2 (m__2202_02): aSet0(xS) = true2.
% 3.27/0.81 Axiom 3 (m__2431_1): aSubsetOf0(xP, xS) = true2.
% 3.27/0.81 Axiom 4 (m__2431): sbrdtbr0(xP) = xk.
% 3.27/0.81 Axiom 5 (mDefSel_3): fresh83(X, X, Y, Z) = true2.
% 3.27/0.81 Axiom 6 (mDefSel): fresh37(X, X, Y, Z, W) = equiv(Y, Z, W).
% 3.27/0.81 Axiom 7 (mDefSel): fresh36(X, X, Y, Z, W) = true2.
% 3.27/0.81 Axiom 8 (mDefSel_3): fresh82(X, X, Y, Z, W, V) = fresh83(W, slbdtsldtrb0(Y, Z), W, V).
% 3.27/0.81 Axiom 9 (mDefSel_3): fresh81(X, X, Y, Z, W, V) = aElementOf0(V, W).
% 3.27/0.81 Axiom 10 (mDefSel): fresh37(aSubsetOf0(X, Y), true2, Y, Z, X) = fresh36(sbrdtbr0(X), Z, Y, Z, X).
% 3.27/0.81 Axiom 11 (mDefSel_3): fresh80(X, X, Y, Z, W, V) = fresh81(aSet0(Y), true2, Y, Z, W, V).
% 3.27/0.81 Axiom 12 (mDefSel_3): fresh80(equiv(X, Y, Z), true2, X, Y, W, Z) = fresh82(aElementOf0(Y, szNzAzT0), true2, X, Y, W, Z).
% 3.27/0.81
% 3.27/0.81 Goal 1 (m__): aElementOf0(xP, slbdtsldtrb0(xS, xk)) = true2.
% 3.27/0.81 Proof:
% 3.27/0.81 aElementOf0(xP, slbdtsldtrb0(xS, xk))
% 3.27/0.81 = { by axiom 9 (mDefSel_3) R->L }
% 3.27/0.81 fresh81(true2, true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 2 (m__2202_02) R->L }
% 3.27/0.81 fresh81(aSet0(xS), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 11 (mDefSel_3) R->L }
% 3.27/0.81 fresh80(true2, true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 7 (mDefSel) R->L }
% 3.27/0.81 fresh80(fresh36(xk, xk, xS, xk, xP), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 4 (m__2431) R->L }
% 3.27/0.81 fresh80(fresh36(sbrdtbr0(xP), xk, xS, xk, xP), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 10 (mDefSel) R->L }
% 3.27/0.81 fresh80(fresh37(aSubsetOf0(xP, xS), true2, xS, xk, xP), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 3 (m__2431_1) }
% 3.27/0.81 fresh80(fresh37(true2, true2, xS, xk, xP), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 6 (mDefSel) }
% 3.27/0.81 fresh80(equiv(xS, xk, xP), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 12 (mDefSel_3) }
% 3.27/0.81 fresh82(aElementOf0(xk, szNzAzT0), true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 1 (m__2202) }
% 3.27/0.81 fresh82(true2, true2, xS, xk, slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 8 (mDefSel_3) }
% 3.27/0.81 fresh83(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xS, xk), slbdtsldtrb0(xS, xk), xP)
% 3.27/0.81 = { by axiom 5 (mDefSel_3) }
% 3.27/0.81 true2
% 3.27/0.81 % SZS output end Proof
% 3.27/0.81
% 3.27/0.81 RESULT: Theorem (the conjecture is true).
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