TSTP Solution File: NUM633+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM633+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 : n022.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 11:57:24 EDT 2023
% Result : Theorem 30.14s 4.26s
% Output : Proof 30.62s
% 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 : NUM633+1 : 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
% 0.14/0.35 % Computer : n022.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 11:46:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 30.14/4.26 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 30.14/4.26
% 30.14/4.26 % SZS status Theorem
% 30.14/4.26
% 30.14/4.26 % SZS output start Proof
% 30.14/4.26 Take the following subset of the input axioms:
% 30.14/4.27 fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 30.14/4.27 fof(mCountNFin_01, axiom, ![W0_2]: ((aSet0(W0_2) & isCountable0(W0_2)) => W0_2!=slcrc0)).
% 30.14/4.27 fof(mDefDiff, definition, ![W1, W0_2]: ((aSet0(W0_2) & aElement0(W1)) => ![W2]: (W2=sdtmndt0(W0_2, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0_2) & W3!=W1))))))).
% 30.14/4.27 fof(mDefEmp, definition, ![W0_2]: (W0_2=slcrc0 <=> (aSet0(W0_2) & ~?[W1_2]: aElementOf0(W1_2, W0_2)))).
% 30.14/4.27 fof(mNatNSucc, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => W0_2!=szszuzczcdt0(W0_2))).
% 30.14/4.27 fof(mNoScLessZr, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W0_2), sz00))).
% 30.14/4.27 fof(mSuccNum, axiom, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0_2), szNzAzT0) & szszuzczcdt0(W0_2)!=sz00))).
% 30.62/4.27 fof(m__, conjecture, ![W0_2]: (aElementOf0(W0_2, slbdtsldtrb0(xO, xK)) => (W0_2!=slcrc0 & (aSubsetOf0(W0_2, szNzAzT0) & (aElementOf0(W0_2, szDzozmdt0(xc)) & sdtlpdtrp0(xc, W0_2)=szDzizrdt0(xd))))) => ?[W0_2]: (aElementOf0(W0_2, xT) & ?[W1_2]: (aSubsetOf0(W1_2, xS) & (isCountable0(W1_2) & ![W2_2]: (aElementOf0(W2_2, slbdtsldtrb0(W1_2, xK)) => sdtlpdtrp0(xc, W2_2)=W0_2))))).
% 30.62/4.27 fof(m__4854, hypothesis, aElementOf0(szDzizrdt0(xd), xT) & isCountable0(sdtlbdtrb0(xd, szDzizrdt0(xd)))).
% 30.62/4.27 fof(m__4908, hypothesis, aSet0(xO) & isCountable0(xO)).
% 30.62/4.27 fof(m__4998, hypothesis, aSubsetOf0(xO, xS)).
% 30.62/4.27
% 30.62/4.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 30.62/4.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 30.62/4.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 30.62/4.27 fresh(y, y, x1...xn) = u
% 30.62/4.27 C => fresh(s, t, x1...xn) = v
% 30.62/4.27 where fresh is a fresh function symbol and x1..xn are the free
% 30.62/4.27 variables of u and v.
% 30.62/4.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 30.62/4.27 input problem has no model of domain size 1).
% 30.62/4.27
% 30.62/4.27 The encoding turns the above axioms into the following unit equations and goals:
% 30.62/4.27
% 30.62/4.27 Axiom 1 (m__4908_1): isCountable0(xO) = true2.
% 30.62/4.27 Axiom 2 (m__4998): aSubsetOf0(xO, xS) = true2.
% 30.62/4.27 Axiom 3 (m__4854): aElementOf0(szDzizrdt0(xd), xT) = true2.
% 30.62/4.27 Axiom 4 (m___2): fresh13(X, X, Y) = szDzizrdt0(xd).
% 30.62/4.27 Axiom 5 (m___5): fresh10(X, X, Y, Z) = true2.
% 30.62/4.27 Axiom 6 (m___5): fresh119(X, X, Y, Z) = fresh120(isCountable0(Z), true2, Y, Z).
% 30.62/4.27 Axiom 7 (m___5): fresh120(X, X, Y, Z) = aElementOf0(w2(Y, Z), slbdtsldtrb0(Z, xK)).
% 30.62/4.27 Axiom 8 (m___5): fresh119(aSubsetOf0(X, xS), true2, Y, X) = fresh10(aElementOf0(Y, xT), true2, Y, X).
% 30.62/4.27 Axiom 9 (m___2): fresh13(aElementOf0(X, slbdtsldtrb0(xO, xK)), true2, X) = sdtlpdtrp0(xc, X).
% 30.62/4.27
% 30.62/4.27 Goal 1 (m___1): tuple3(sdtlpdtrp0(xc, w2(X, Y)), aElementOf0(X, xT), isCountable0(Y), aSubsetOf0(Y, xS)) = tuple3(X, true2, true2, true2).
% 30.62/4.27 The goal is true when:
% 30.62/4.27 X = szDzizrdt0(xd)
% 30.62/4.27 Y = xO
% 30.62/4.27
% 30.62/4.27 Proof:
% 30.62/4.27 tuple3(sdtlpdtrp0(xc, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 9 (m___2) R->L }
% 30.62/4.27 tuple3(fresh13(aElementOf0(w2(szDzizrdt0(xd), xO), slbdtsldtrb0(xO, xK)), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 7 (m___5) R->L }
% 30.62/4.27 tuple3(fresh13(fresh120(true2, true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 1 (m__4908_1) R->L }
% 30.62/4.27 tuple3(fresh13(fresh120(isCountable0(xO), true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 6 (m___5) R->L }
% 30.62/4.27 tuple3(fresh13(fresh119(true2, true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 2 (m__4998) R->L }
% 30.62/4.27 tuple3(fresh13(fresh119(aSubsetOf0(xO, xS), true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 8 (m___5) }
% 30.62/4.27 tuple3(fresh13(fresh10(aElementOf0(szDzizrdt0(xd), xT), true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 3 (m__4854) }
% 30.62/4.27 tuple3(fresh13(fresh10(true2, true2, szDzizrdt0(xd), xO), true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 5 (m___5) }
% 30.62/4.27 tuple3(fresh13(true2, true2, w2(szDzizrdt0(xd), xO)), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 4 (m___2) }
% 30.62/4.27 tuple3(szDzizrdt0(xd), aElementOf0(szDzizrdt0(xd), xT), isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 3 (m__4854) }
% 30.62/4.27 tuple3(szDzizrdt0(xd), true2, isCountable0(xO), aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 1 (m__4908_1) }
% 30.62/4.27 tuple3(szDzizrdt0(xd), true2, true2, aSubsetOf0(xO, xS))
% 30.62/4.27 = { by axiom 2 (m__4998) }
% 30.62/4.27 tuple3(szDzizrdt0(xd), true2, true2, true2)
% 30.62/4.27 % SZS output end Proof
% 30.62/4.27
% 30.62/4.27 RESULT: Theorem (the conjecture is true).
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