TSTP Solution File: NUM552+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM552+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 : n025.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 11:56:56 EDT 2023
% Result : Theorem 77.77s 10.73s
% Output : Proof 77.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.34 % Computer : n025.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Fri Aug 25 16:08:22 EDT 2023
% 0.18/0.34 % CPUTime :
% 77.77/10.73 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 77.77/10.73
% 77.77/10.73 % SZS status Theorem
% 77.77/10.73
% 77.77/10.74 % SZS output start Proof
% 77.77/10.74 Take the following subset of the input axioms:
% 77.77/10.74 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)))))).
% 77.77/10.74 fof(mDefSub, definition, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) <=> (aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, W0_2)))))).
% 77.77/10.74 fof(m__, conjecture, aElementOf0(xx, xQ) => aElementOf0(xx, xT)).
% 77.77/10.74 fof(m__2202, hypothesis, aElementOf0(xk, szNzAzT0)).
% 77.77/10.74 fof(m__2202_02, hypothesis, aSet0(xS) & (aSet0(xT) & xk!=sz00)).
% 77.77/10.74 fof(m__2227, hypothesis, aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) & slbdtsldtrb0(xS, xk)!=slcrc0).
% 77.77/10.74 fof(m__2270, hypothesis, aElementOf0(xQ, slbdtsldtrb0(xS, xk))).
% 77.77/10.74
% 77.77/10.74 Now clausify the problem and encode Horn clauses using encoding 3 of
% 77.77/10.74 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 77.77/10.74 We repeatedly replace C & s=t => u=v by the two clauses:
% 77.77/10.74 fresh(y, y, x1...xn) = u
% 77.77/10.74 C => fresh(s, t, x1...xn) = v
% 77.77/10.74 where fresh is a fresh function symbol and x1..xn are the free
% 77.77/10.74 variables of u and v.
% 77.77/10.74 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 77.77/10.74 input problem has no model of domain size 1).
% 77.77/10.74
% 77.77/10.74 The encoding turns the above axioms into the following unit equations and goals:
% 77.77/10.74
% 77.77/10.74 Axiom 1 (m__2202): aElementOf0(xk, szNzAzT0) = true2.
% 77.77/10.74 Axiom 2 (m__): aElementOf0(xx, xQ) = true2.
% 77.77/10.74 Axiom 3 (m__2202_02_1): aSet0(xT) = true2.
% 77.77/10.74 Axiom 4 (m__2270): aElementOf0(xQ, slbdtsldtrb0(xS, xk)) = true2.
% 77.77/10.74 Axiom 5 (mDefSel_1): fresh75(X, X, Y) = true2.
% 77.77/10.74 Axiom 6 (m__2227): aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) = true2.
% 77.77/10.74 Axiom 7 (mDefSub_2): fresh180(X, X, Y, Z) = true2.
% 77.77/10.74 Axiom 8 (mDefSel_7): fresh34(X, X, Y, Z) = true2.
% 77.77/10.74 Axiom 9 (mDefSub_2): fresh32(X, X, Y, Z) = aElementOf0(Z, Y).
% 77.77/10.74 Axiom 10 (mDefSub_2): fresh179(X, X, Y, Z, W) = fresh180(aSet0(Y), true2, Y, W).
% 77.77/10.75 Axiom 11 (mDefSel_2): fresh79(X, X, Y, Z, W) = true2.
% 77.77/10.75 Axiom 12 (mDefSel_1): fresh74(X, X, Y, Z, W) = fresh75(W, slbdtsldtrb0(Y, Z), W).
% 77.77/10.75 Axiom 13 (mDefSel_1): fresh35(X, X, Y, Z, W) = aSet0(W).
% 77.77/10.75 Axiom 14 (mDefSub_2): fresh179(aSubsetOf0(X, Y), true2, Y, X, Z) = fresh32(aElementOf0(Z, X), true2, Y, Z).
% 77.77/10.75 Axiom 15 (mDefSel_2): fresh78(X, X, Y, Z, W, V) = fresh79(W, slbdtsldtrb0(Y, Z), Y, Z, V).
% 77.77/10.75 Axiom 16 (mDefSel_2): fresh77(X, X, Y, Z, W, V) = equiv(Y, Z, V).
% 77.77/10.75 Axiom 17 (mDefSel_1): fresh74(aElementOf0(X, szNzAzT0), true2, Y, X, Z) = fresh35(aSet0(Y), true2, Y, X, Z).
% 77.77/10.75 Axiom 18 (mDefSel_7): fresh34(equiv(X, Y, Z), true2, X, Z) = aSubsetOf0(Z, X).
% 77.77/10.75 Axiom 19 (mDefSel_2): fresh76(X, X, Y, Z, W, V) = fresh77(aSet0(Y), true2, Y, Z, W, V).
% 77.77/10.75 Axiom 20 (mDefSel_2): fresh76(aElementOf0(X, Y), true2, Z, W, Y, X) = fresh78(aElementOf0(W, szNzAzT0), true2, Z, W, Y, X).
% 77.77/10.75
% 77.77/10.75 Goal 1 (m___1): aElementOf0(xx, xT) = true2.
% 77.77/10.75 Proof:
% 77.77/10.75 aElementOf0(xx, xT)
% 77.77/10.75 = { by axiom 9 (mDefSub_2) R->L }
% 77.77/10.75 fresh32(true2, true2, xT, xx)
% 77.77/10.75 = { by axiom 2 (m__) R->L }
% 77.77/10.75 fresh32(aElementOf0(xx, xQ), true2, xT, xx)
% 77.77/10.75 = { by axiom 14 (mDefSub_2) R->L }
% 77.77/10.75 fresh179(aSubsetOf0(xQ, xT), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 18 (mDefSel_7) R->L }
% 77.77/10.75 fresh179(fresh34(equiv(xT, xk, xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 16 (mDefSel_2) R->L }
% 77.77/10.75 fresh179(fresh34(fresh77(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 3 (m__2202_02_1) R->L }
% 77.77/10.75 fresh179(fresh34(fresh77(aSet0(xT), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 19 (mDefSel_2) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 7 (mDefSub_2) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(true2, true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 5 (mDefSel_1) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(fresh75(slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 12 (mDefSel_1) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(fresh74(true2, true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 1 (m__2202) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(fresh74(aElementOf0(xk, szNzAzT0), true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 17 (mDefSel_1) }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(fresh35(aSet0(xT), true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 3 (m__2202_02_1) }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(fresh35(true2, true2, xT, xk, slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 13 (mDefSel_1) }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh180(aSet0(slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 10 (mDefSub_2) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh179(true2, true2, slbdtsldtrb0(xT, xk), slbdtsldtrb0(xS, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 6 (m__2227) R->L }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh179(aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)), true2, slbdtsldtrb0(xT, xk), slbdtsldtrb0(xS, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 14 (mDefSub_2) }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh32(aElementOf0(xQ, slbdtsldtrb0(xS, xk)), true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 4 (m__2270) }
% 77.77/10.75 fresh179(fresh34(fresh76(fresh32(true2, true2, slbdtsldtrb0(xT, xk), xQ), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 9 (mDefSub_2) }
% 77.77/10.75 fresh179(fresh34(fresh76(aElementOf0(xQ, slbdtsldtrb0(xT, xk)), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 20 (mDefSel_2) }
% 77.77/10.75 fresh179(fresh34(fresh78(aElementOf0(xk, szNzAzT0), true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 1 (m__2202) }
% 77.77/10.75 fresh179(fresh34(fresh78(true2, true2, xT, xk, slbdtsldtrb0(xT, xk), xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 15 (mDefSel_2) }
% 77.77/10.75 fresh179(fresh34(fresh79(slbdtsldtrb0(xT, xk), slbdtsldtrb0(xT, xk), xT, xk, xQ), true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 11 (mDefSel_2) }
% 77.77/10.75 fresh179(fresh34(true2, true2, xT, xQ), true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 8 (mDefSel_7) }
% 77.77/10.75 fresh179(true2, true2, xT, xQ, xx)
% 77.77/10.75 = { by axiom 10 (mDefSub_2) }
% 77.77/10.75 fresh180(aSet0(xT), true2, xT, xx)
% 77.77/10.75 = { by axiom 3 (m__2202_02_1) }
% 77.77/10.75 fresh180(true2, true2, xT, xx)
% 77.77/10.75 = { by axiom 7 (mDefSub_2) }
% 77.77/10.75 true2
% 77.77/10.75 % SZS output end Proof
% 77.77/10.75
% 77.77/10.75 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------