TSTP Solution File: NUM539+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM539+2 : 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 : n032.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 11:56:51 EDT 2023
% Result : Theorem 0.14s 0.55s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM539+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Fri Aug 25 12:59:27 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.14/0.55 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.14/0.55
% 0.14/0.55 % SZS status Theorem
% 0.14/0.55
% 0.14/0.55 % SZS output start Proof
% 0.14/0.55 Take the following subset of the input axioms:
% 0.14/0.56 fof(mLessASymm, axiom, ![W0, W1]: ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => W0=W1))).
% 0.14/0.56 fof(m__, conjecture, (aElementOf0(szmzizndt0(xS), xS) & ![W0_2]: (aElementOf0(W0_2, xS) => sdtlseqdt0(szmzizndt0(xS), W0_2))) => (![W0_2]: (aElementOf0(W0_2, xT) => sdtlseqdt0(szmzizndt0(xS), W0_2)) | szmzizndt0(xS)=szmzizndt0(xT))).
% 0.14/0.56 fof(m__1779, hypothesis, aSet0(xS) & (![W0_2]: (aElementOf0(W0_2, xS) => aElementOf0(W0_2, szNzAzT0)) & (aSubsetOf0(xS, szNzAzT0) & (aSet0(xT) & (![W0_2]: (aElementOf0(W0_2, xT) => aElementOf0(W0_2, szNzAzT0)) & (aSubsetOf0(xT, szNzAzT0) & (~(~?[W0_2]: aElementOf0(W0_2, xS) | xS=slcrc0) & ~(~?[W0_2]: aElementOf0(W0_2, xT) | xT=slcrc0)))))))).
% 0.14/0.56 fof(m__1802, hypothesis, aElementOf0(szmzizndt0(xS), xS) & (![W0_2]: (aElementOf0(W0_2, xS) => sdtlseqdt0(szmzizndt0(xS), W0_2)) & (aElementOf0(szmzizndt0(xS), xT) & (aElementOf0(szmzizndt0(xT), xT) & (![W0_2]: (aElementOf0(W0_2, xT) => sdtlseqdt0(szmzizndt0(xT), W0_2)) & aElementOf0(szmzizndt0(xT), xS)))))).
% 0.14/0.56
% 0.14/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.56 fresh(y, y, x1...xn) = u
% 0.14/0.56 C => fresh(s, t, x1...xn) = v
% 0.14/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.56 variables of u and v.
% 0.14/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.56 input problem has no model of domain size 1).
% 0.14/0.56
% 0.14/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.56
% 0.14/0.56 Axiom 1 (m__1802): aElementOf0(szmzizndt0(xS), xS) = true2.
% 0.14/0.56 Axiom 2 (m__1802_1): aElementOf0(szmzizndt0(xS), xT) = true2.
% 0.14/0.56 Axiom 3 (m__1802_2): aElementOf0(szmzizndt0(xT), xS) = true2.
% 0.14/0.56 Axiom 4 (m__1779_8): fresh8(X, X, Y) = true2.
% 0.14/0.56 Axiom 5 (m__1802_4): fresh6(X, X, Y) = true2.
% 0.14/0.56 Axiom 6 (m__1802_5): fresh5(X, X, Y) = true2.
% 0.14/0.56 Axiom 7 (mLessASymm): fresh68(X, X, Y, Z) = Z.
% 0.14/0.56 Axiom 8 (mLessASymm): fresh66(X, X, Y, Z) = Y.
% 0.14/0.56 Axiom 9 (m__1779_8): fresh8(aElementOf0(X, xS), true2, X) = aElementOf0(X, szNzAzT0).
% 0.14/0.56 Axiom 10 (m__1802_4): fresh6(aElementOf0(X, xS), true2, X) = sdtlseqdt0(szmzizndt0(xS), X).
% 0.14/0.56 Axiom 11 (m__1802_5): fresh5(aElementOf0(X, xT), true2, X) = sdtlseqdt0(szmzizndt0(xT), X).
% 0.14/0.56 Axiom 12 (mLessASymm): fresh67(X, X, Y, Z) = fresh68(aElementOf0(Y, szNzAzT0), true2, Y, Z).
% 0.14/0.56 Axiom 13 (mLessASymm): fresh65(X, X, Y, Z) = fresh66(aElementOf0(Z, szNzAzT0), true2, Y, Z).
% 0.14/0.56 Axiom 14 (mLessASymm): fresh65(sdtlseqdt0(X, Y), true2, Y, X) = fresh67(sdtlseqdt0(Y, X), true2, Y, X).
% 0.14/0.56
% 0.14/0.56 Goal 1 (m___2): szmzizndt0(xS) = szmzizndt0(xT).
% 0.14/0.56 Proof:
% 0.14/0.56 szmzizndt0(xS)
% 0.14/0.56 = { by axiom 8 (mLessASymm) R->L }
% 0.14/0.56 fresh66(true2, true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 4 (m__1779_8) R->L }
% 0.14/0.56 fresh66(fresh8(true2, true2, szmzizndt0(xT)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 3 (m__1802_2) R->L }
% 0.14/0.56 fresh66(fresh8(aElementOf0(szmzizndt0(xT), xS), true2, szmzizndt0(xT)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 9 (m__1779_8) }
% 0.14/0.56 fresh66(aElementOf0(szmzizndt0(xT), szNzAzT0), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 13 (mLessASymm) R->L }
% 0.14/0.56 fresh65(true2, true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 6 (m__1802_5) R->L }
% 0.14/0.56 fresh65(fresh5(true2, true2, szmzizndt0(xS)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 2 (m__1802_1) R->L }
% 0.14/0.56 fresh65(fresh5(aElementOf0(szmzizndt0(xS), xT), true2, szmzizndt0(xS)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 11 (m__1802_5) }
% 0.14/0.56 fresh65(sdtlseqdt0(szmzizndt0(xT), szmzizndt0(xS)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 14 (mLessASymm) }
% 0.14/0.56 fresh67(sdtlseqdt0(szmzizndt0(xS), szmzizndt0(xT)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 10 (m__1802_4) R->L }
% 0.14/0.56 fresh67(fresh6(aElementOf0(szmzizndt0(xT), xS), true2, szmzizndt0(xT)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 3 (m__1802_2) }
% 0.14/0.56 fresh67(fresh6(true2, true2, szmzizndt0(xT)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 5 (m__1802_4) }
% 0.14/0.56 fresh67(true2, true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 12 (mLessASymm) }
% 0.14/0.56 fresh68(aElementOf0(szmzizndt0(xS), szNzAzT0), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 9 (m__1779_8) R->L }
% 0.14/0.56 fresh68(fresh8(aElementOf0(szmzizndt0(xS), xS), true2, szmzizndt0(xS)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 1 (m__1802) }
% 0.14/0.56 fresh68(fresh8(true2, true2, szmzizndt0(xS)), true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 4 (m__1779_8) }
% 0.14/0.56 fresh68(true2, true2, szmzizndt0(xS), szmzizndt0(xT))
% 0.14/0.56 = { by axiom 7 (mLessASymm) }
% 0.14/0.56 szmzizndt0(xT)
% 0.14/0.56 % SZS output end Proof
% 0.14/0.56
% 0.14/0.56 RESULT: Theorem (the conjecture is true).
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