TSTP Solution File: NUM623+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM623+3 : 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 : n009.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 11:57:21 EDT 2023
% Result : Theorem 42.42s 5.80s
% Output : Proof 42.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM623+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 09:41:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 42.42/5.80 Command-line arguments: --no-flatten-goal
% 42.42/5.80
% 42.42/5.80 % SZS status Theorem
% 42.42/5.80
% 42.42/5.83 % SZS output start Proof
% 42.42/5.83 Take the following subset of the input axioms:
% 42.42/5.83 fof(mLessASymm, axiom, ![W0, W1]: ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => W0=W1))).
% 42.42/5.83 fof(m__, conjecture, xp=xx).
% 42.42/5.83 fof(m__5106, hypothesis, ![W0_2]: (aElementOf0(W0_2, xQ) => aElementOf0(W0_2, szNzAzT0)) & aSubsetOf0(xQ, szNzAzT0)).
% 42.42/5.83 fof(m__5147, hypothesis, aElementOf0(xp, xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(xp, W0_2)) & xp=szmzizndt0(xQ))).
% 42.42/5.83 fof(m__5348, hypothesis, aElement0(xx) & (aElementOf0(xx, xQ) & (xx!=szmzizndt0(xQ) & aElementOf0(xx, xP)))).
% 42.42/5.83 fof(m__5365, hypothesis, aElementOf0(xx, szNzAzT0) & ?[W0_2]: (aElementOf0(W0_2, sdtlbdtrb0(xd, szDzizrdt0(xd))) & sdtlpdtrp0(xe, W0_2)=xx)).
% 42.42/5.83 fof(m__5401, hypothesis, ![W0_2]: (aElementOf0(W0_2, sdtlpdtrp0(xN, xm)) => sdtlseqdt0(xx, W0_2))).
% 42.42/5.83 fof(m__5481, hypothesis, aElementOf0(xp, sdtlpdtrp0(xN, xm)) & aElementOf0(xx, xQ)).
% 42.42/5.83
% 42.42/5.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 42.42/5.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 42.42/5.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 42.42/5.83 fresh(y, y, x1...xn) = u
% 42.42/5.83 C => fresh(s, t, x1...xn) = v
% 42.42/5.83 where fresh is a fresh function symbol and x1..xn are the free
% 42.42/5.83 variables of u and v.
% 42.42/5.83 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 42.42/5.83 input problem has no model of domain size 1).
% 42.42/5.83
% 42.42/5.83 The encoding turns the above axioms into the following unit equations and goals:
% 42.42/5.83
% 42.42/5.83 Axiom 1 (m__5147): xp = szmzizndt0(xQ).
% 42.42/5.83 Axiom 2 (m__5147_1): aElementOf0(xp, xQ) = true2.
% 42.42/5.83 Axiom 3 (m__5348_1): aElementOf0(xx, xQ) = true2.
% 42.42/5.83 Axiom 4 (m__5365_1): aElementOf0(xx, szNzAzT0) = true2.
% 42.42/5.83 Axiom 5 (m__5106_1): fresh26(X, X, Y) = true2.
% 42.42/5.83 Axiom 6 (m__5147_2): fresh23(X, X, Y) = true2.
% 42.42/5.83 Axiom 7 (m__5401): fresh17(X, X, Y) = true2.
% 42.42/5.83 Axiom 8 (mLessASymm): fresh469(X, X, Y, Z) = Z.
% 42.42/5.83 Axiom 9 (mLessASymm): fresh467(X, X, Y, Z) = Y.
% 42.42/5.83 Axiom 10 (m__5481): aElementOf0(xp, sdtlpdtrp0(xN, xm)) = true2.
% 42.42/5.83 Axiom 11 (m__5106_1): fresh26(aElementOf0(X, xQ), true2, X) = aElementOf0(X, szNzAzT0).
% 42.42/5.83 Axiom 12 (m__5147_2): fresh23(aElementOf0(X, xQ), true2, X) = sdtlseqdt0(xp, X).
% 42.42/5.83 Axiom 13 (mLessASymm): fresh468(X, X, Y, Z) = fresh469(aElementOf0(Y, szNzAzT0), true2, Y, Z).
% 42.42/5.83 Axiom 14 (mLessASymm): fresh466(X, X, Y, Z) = fresh467(aElementOf0(Z, szNzAzT0), true2, Y, Z).
% 42.42/5.83 Axiom 15 (mLessASymm): fresh466(sdtlseqdt0(X, Y), true2, Y, X) = fresh468(sdtlseqdt0(Y, X), true2, Y, X).
% 42.42/5.83 Axiom 16 (m__5401): fresh17(aElementOf0(X, sdtlpdtrp0(xN, xm)), true2, X) = sdtlseqdt0(xx, X).
% 42.42/5.83
% 42.42/5.83 Lemma 17: xx = xp.
% 42.42/5.83 Proof:
% 42.42/5.83 xx
% 42.42/5.83 = { by axiom 8 (mLessASymm) R->L }
% 42.42/5.83 fresh469(true2, true2, xp, xx)
% 42.42/5.83 = { by axiom 5 (m__5106_1) R->L }
% 42.42/5.83 fresh469(fresh26(true2, true2, xp), true2, xp, xx)
% 42.42/5.83 = { by axiom 2 (m__5147_1) R->L }
% 42.42/5.83 fresh469(fresh26(aElementOf0(xp, xQ), true2, xp), true2, xp, xx)
% 42.42/5.83 = { by axiom 11 (m__5106_1) }
% 42.42/5.83 fresh469(aElementOf0(xp, szNzAzT0), true2, xp, xx)
% 42.42/5.83 = { by axiom 13 (mLessASymm) R->L }
% 42.42/5.83 fresh468(true2, true2, xp, xx)
% 42.42/5.83 = { by axiom 6 (m__5147_2) R->L }
% 42.42/5.83 fresh468(fresh23(true2, true2, xx), true2, xp, xx)
% 42.42/5.83 = { by axiom 3 (m__5348_1) R->L }
% 42.42/5.83 fresh468(fresh23(aElementOf0(xx, xQ), true2, xx), true2, xp, xx)
% 42.42/5.83 = { by axiom 12 (m__5147_2) }
% 42.42/5.83 fresh468(sdtlseqdt0(xp, xx), true2, xp, xx)
% 42.42/5.83 = { by axiom 15 (mLessASymm) R->L }
% 42.42/5.83 fresh466(sdtlseqdt0(xx, xp), true2, xp, xx)
% 42.42/5.83 = { by axiom 16 (m__5401) R->L }
% 42.42/5.83 fresh466(fresh17(aElementOf0(xp, sdtlpdtrp0(xN, xm)), true2, xp), true2, xp, xx)
% 42.42/5.83 = { by axiom 10 (m__5481) }
% 42.42/5.83 fresh466(fresh17(true2, true2, xp), true2, xp, xx)
% 42.42/5.83 = { by axiom 7 (m__5401) }
% 42.42/5.83 fresh466(true2, true2, xp, xx)
% 42.42/5.83 = { by axiom 14 (mLessASymm) }
% 42.42/5.83 fresh467(aElementOf0(xx, szNzAzT0), true2, xp, xx)
% 42.42/5.83 = { by axiom 4 (m__5365_1) }
% 42.42/5.83 fresh467(true2, true2, xp, xx)
% 42.42/5.83 = { by axiom 9 (mLessASymm) }
% 42.42/5.83 xp
% 42.42/5.83
% 42.42/5.83 Goal 1 (m__): xp = xx.
% 42.42/5.83 Proof:
% 42.42/5.83 xp
% 42.42/5.83 = { by lemma 17 R->L }
% 42.42/5.83 xx
% 42.42/5.83
% 42.42/5.83 Goal 2 (m__5348_3): xx = szmzizndt0(xQ).
% 42.42/5.83 Proof:
% 42.42/5.83 xx
% 42.42/5.83 = { by lemma 17 }
% 42.42/5.83 xp
% 42.42/5.83 = { by axiom 1 (m__5147) }
% 42.42/5.83 szmzizndt0(xQ)
% 42.42/5.83 % SZS output end Proof
% 42.42/5.83
% 42.42/5.83 RESULT: Theorem (the conjecture is true).
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