TSTP Solution File: LAT381+3 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT381+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 : 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 06:28:59 EDT 2023
% Result : Theorem 0.15s 0.47s
% Output : Proof 0.15s
% 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 : LAT381+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu Aug 24 04:14:55 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.15/0.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.15/0.47
% 0.15/0.47 % SZS status Theorem
% 0.15/0.47
% 0.15/0.47 % SZS output start Proof
% 0.15/0.47 Take the following subset of the input axioms:
% 0.15/0.48 fof(mASymm, axiom, ![W0, W1]: ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => W0=W1))).
% 0.15/0.49 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 0.15/0.49 fof(m__, conjecture, xu=xv).
% 0.15/0.49 fof(m__725, hypothesis, aSet0(xT)).
% 0.15/0.49 fof(m__744, hypothesis, aElementOf0(xu, xT) & (aElementOf0(xu, xT) & (![W0_2]: (aElementOf0(W0_2, xS) => sdtlseqdt0(W0_2, xu)) & (aUpperBoundOfIn0(xu, xS, xT) & (![W0_2]: (((aElementOf0(W0_2, xT) & ![W1_2]: (aElementOf0(W1_2, xS) => sdtlseqdt0(W1_2, W0_2))) | aUpperBoundOfIn0(W0_2, xS, xT)) => sdtlseqdt0(xu, W0_2)) & (aSupremumOfIn0(xu, xS, xT) & (aElementOf0(xv, xT) & (aElementOf0(xv, xT) & (![W0_2]: (aElementOf0(W0_2, xS) => sdtlseqdt0(W0_2, xv)) & (aUpperBoundOfIn0(xv, xS, xT) & (![W0_2]: (((aElementOf0(W0_2, xT) & ![W1_2]: (aElementOf0(W1_2, xS) => sdtlseqdt0(W1_2, W0_2))) | aUpperBoundOfIn0(W0_2, xS, xT)) => sdtlseqdt0(xv, W0_2)) & aSupremumOfIn0(xv, xS, xT)))))))))))).
% 0.15/0.49
% 0.15/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.15/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.15/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.15/0.49 fresh(y, y, x1...xn) = u
% 0.15/0.49 C => fresh(s, t, x1...xn) = v
% 0.15/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.15/0.49 variables of u and v.
% 0.15/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.15/0.49 input problem has no model of domain size 1).
% 0.15/0.49
% 0.15/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.15/0.49
% 0.15/0.49 Axiom 1 (m__725): aSet0(xT) = true2.
% 0.15/0.49 Axiom 2 (m__744): aElementOf0(xu, xT) = true2.
% 0.15/0.49 Axiom 3 (m__744_1): aElementOf0(xv, xT) = true2.
% 0.15/0.49 Axiom 4 (m__744_2): aUpperBoundOfIn0(xu, xS, xT) = true2.
% 0.15/0.49 Axiom 5 (m__744_3): aUpperBoundOfIn0(xv, xS, xT) = true2.
% 0.15/0.49 Axiom 6 (mEOfElem): fresh10(X, X, Y) = true2.
% 0.15/0.49 Axiom 7 (m__744_12): fresh6(X, X, Y) = true2.
% 0.15/0.49 Axiom 8 (m__744_13): fresh5(X, X, Y) = true2.
% 0.15/0.49 Axiom 9 (mASymm): fresh77(X, X, Y, Z) = Z.
% 0.15/0.49 Axiom 10 (mASymm): fresh75(X, X, Y, Z) = Y.
% 0.15/0.49 Axiom 11 (mEOfElem): fresh11(X, X, Y, Z) = aElement0(Z).
% 0.15/0.49 Axiom 12 (mASymm): fresh76(X, X, Y, Z) = fresh77(aElement0(Y), true2, Y, Z).
% 0.15/0.49 Axiom 13 (mASymm): fresh74(X, X, Y, Z) = fresh75(aElement0(Z), true2, Y, Z).
% 0.15/0.49 Axiom 14 (mASymm): fresh74(sdtlseqdt0(X, Y), true2, Y, X) = fresh76(sdtlseqdt0(Y, X), true2, Y, X).
% 0.15/0.49 Axiom 15 (mEOfElem): fresh11(aElementOf0(X, Y), true2, Y, X) = fresh10(aSet0(Y), true2, X).
% 0.15/0.49 Axiom 16 (m__744_12): fresh6(aUpperBoundOfIn0(X, xS, xT), true2, X) = sdtlseqdt0(xu, X).
% 0.15/0.49 Axiom 17 (m__744_13): fresh5(aUpperBoundOfIn0(X, xS, xT), true2, X) = sdtlseqdt0(xv, X).
% 0.15/0.49
% 0.15/0.49 Goal 1 (m__): xu = xv.
% 0.15/0.49 Proof:
% 0.15/0.49 xu
% 0.15/0.49 = { by axiom 10 (mASymm) R->L }
% 0.15/0.49 fresh75(true2, true2, xu, xv)
% 0.15/0.49 = { by axiom 6 (mEOfElem) R->L }
% 0.15/0.49 fresh75(fresh10(true2, true2, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 1 (m__725) R->L }
% 0.15/0.49 fresh75(fresh10(aSet0(xT), true2, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 15 (mEOfElem) R->L }
% 0.15/0.49 fresh75(fresh11(aElementOf0(xv, xT), true2, xT, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 3 (m__744_1) }
% 0.15/0.49 fresh75(fresh11(true2, true2, xT, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 11 (mEOfElem) }
% 0.15/0.49 fresh75(aElement0(xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 13 (mASymm) R->L }
% 0.15/0.49 fresh74(true2, true2, xu, xv)
% 0.15/0.49 = { by axiom 8 (m__744_13) R->L }
% 0.15/0.49 fresh74(fresh5(true2, true2, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 4 (m__744_2) R->L }
% 0.15/0.49 fresh74(fresh5(aUpperBoundOfIn0(xu, xS, xT), true2, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 17 (m__744_13) }
% 0.15/0.49 fresh74(sdtlseqdt0(xv, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 14 (mASymm) }
% 0.15/0.49 fresh76(sdtlseqdt0(xu, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 16 (m__744_12) R->L }
% 0.15/0.49 fresh76(fresh6(aUpperBoundOfIn0(xv, xS, xT), true2, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 5 (m__744_3) }
% 0.15/0.49 fresh76(fresh6(true2, true2, xv), true2, xu, xv)
% 0.15/0.49 = { by axiom 7 (m__744_12) }
% 0.15/0.49 fresh76(true2, true2, xu, xv)
% 0.15/0.49 = { by axiom 12 (mASymm) }
% 0.15/0.49 fresh77(aElement0(xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 11 (mEOfElem) R->L }
% 0.15/0.49 fresh77(fresh11(true2, true2, xT, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 2 (m__744) R->L }
% 0.15/0.49 fresh77(fresh11(aElementOf0(xu, xT), true2, xT, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 15 (mEOfElem) }
% 0.15/0.49 fresh77(fresh10(aSet0(xT), true2, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 1 (m__725) }
% 0.15/0.49 fresh77(fresh10(true2, true2, xu), true2, xu, xv)
% 0.15/0.49 = { by axiom 6 (mEOfElem) }
% 0.15/0.49 fresh77(true2, true2, xu, xv)
% 0.15/0.49 = { by axiom 9 (mASymm) }
% 0.15/0.49 xv
% 0.15/0.49 % SZS output end Proof
% 0.15/0.49
% 0.15/0.49 RESULT: Theorem (the conjecture is true).
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