TSTP Solution File: LAT381+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT381+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 06:28:58 EDT 2023
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT381+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
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 07:36:56 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.21/0.49
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 Take the following subset of the input axioms:
% 0.21/0.50 fof(mASymm, axiom, ![W0, W1]: ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => W0=W1))).
% 0.21/0.50 fof(mDefSup, definition, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) => ![W2]: (aSupremumOfIn0(W2, W1_2, W0_2) <=> (aElementOf0(W2, W0_2) & (aUpperBoundOfIn0(W2, W1_2, W0_2) & ![W3]: (aUpperBoundOfIn0(W3, W1_2, W0_2) => sdtlseqdt0(W2, W3)))))))).
% 0.21/0.50 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 0.21/0.50 fof(m__, conjecture, xu=xv).
% 0.21/0.50 fof(m__725, hypothesis, aSet0(xT)).
% 0.21/0.50 fof(m__725_01, hypothesis, aSubsetOf0(xS, xT)).
% 0.21/0.50 fof(m__744, hypothesis, aSupremumOfIn0(xu, xS, xT) & aSupremumOfIn0(xv, xS, xT)).
% 0.21/0.50
% 0.21/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.50 fresh(y, y, x1...xn) = u
% 0.21/0.50 C => fresh(s, t, x1...xn) = v
% 0.21/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.50 variables of u and v.
% 0.21/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.50 input problem has no model of domain size 1).
% 0.21/0.50
% 0.21/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.50
% 0.21/0.50 Axiom 1 (m__725): aSet0(xT) = true2.
% 0.21/0.50 Axiom 2 (m__725_01): aSubsetOf0(xS, xT) = true2.
% 0.21/0.50 Axiom 3 (m__744): aSupremumOfIn0(xu, xS, xT) = true2.
% 0.21/0.50 Axiom 4 (m__744_1): aSupremumOfIn0(xv, xS, xT) = true2.
% 0.21/0.50 Axiom 5 (mEOfElem): fresh(X, X, Y) = true2.
% 0.21/0.50 Axiom 6 (mASymm): fresh68(X, X, Y, Z) = Z.
% 0.21/0.50 Axiom 7 (mASymm): fresh66(X, X, Y, Z) = Y.
% 0.21/0.50 Axiom 8 (mDefSup_3): fresh24(X, X, Y, Z) = true2.
% 0.21/0.50 Axiom 9 (mDefSup_2): fresh22(X, X, Y, Z) = true2.
% 0.21/0.50 Axiom 10 (mDefSup_3): fresh5(X, X, Y, Z) = aElementOf0(Z, Y).
% 0.21/0.50 Axiom 11 (mEOfElem): fresh2(X, X, Y, Z) = aElement0(Z).
% 0.21/0.50 Axiom 12 (mASymm): fresh67(X, X, Y, Z) = fresh68(aElement0(Y), true2, Y, Z).
% 0.21/0.50 Axiom 13 (mASymm): fresh65(X, X, Y, Z) = fresh66(aElement0(Z), true2, Y, Z).
% 0.21/0.50 Axiom 14 (mDefSup_4): fresh26(X, X, Y, Z, W) = true2.
% 0.21/0.50 Axiom 15 (mDefSup_3): fresh23(X, X, Y, Z, W) = fresh24(aSet0(Y), true2, Y, W).
% 0.21/0.50 Axiom 16 (mDefSup_2): fresh20(X, X, Y, Z, W) = sdtlseqdt0(Z, W).
% 0.21/0.50 Axiom 17 (mDefSup_4): fresh4(X, X, Y, Z, W) = aUpperBoundOfIn0(W, Z, Y).
% 0.21/0.50 Axiom 18 (mASymm): fresh65(sdtlseqdt0(X, Y), true2, Y, X) = fresh67(sdtlseqdt0(Y, X), true2, Y, X).
% 0.21/0.50 Axiom 19 (mDefSup_4): fresh25(X, X, Y, Z, W) = fresh26(aSet0(Y), true2, Y, Z, W).
% 0.21/0.50 Axiom 20 (mDefSup_2): fresh21(X, X, Y, Z, W, V) = fresh22(aSet0(Y), true2, W, V).
% 0.21/0.50 Axiom 21 (mEOfElem): fresh2(aElementOf0(X, Y), true2, Y, X) = fresh(aSet0(Y), true2, X).
% 0.21/0.50 Axiom 22 (mDefSup_2): fresh19(X, X, Y, Z, W, V) = fresh20(aSubsetOf0(Z, Y), true2, Y, W, V).
% 0.21/0.50 Axiom 23 (mDefSup_4): fresh25(aSupremumOfIn0(X, Y, Z), true2, Z, Y, X) = fresh4(aSubsetOf0(Y, Z), true2, Z, Y, X).
% 0.21/0.50 Axiom 24 (mDefSup_3): fresh23(aSupremumOfIn0(X, Y, Z), true2, Z, Y, X) = fresh5(aSubsetOf0(Y, Z), true2, Z, X).
% 0.21/0.50 Axiom 25 (mDefSup_2): fresh19(aSupremumOfIn0(X, Y, Z), true2, Z, Y, X, W) = fresh21(aUpperBoundOfIn0(W, Y, Z), true2, Z, Y, X, W).
% 0.21/0.50
% 0.21/0.50 Lemma 26: fresh25(X, X, xT, Y, Z) = true2.
% 0.21/0.50 Proof:
% 0.21/0.50 fresh25(X, X, xT, Y, Z)
% 0.21/0.50 = { by axiom 19 (mDefSup_4) }
% 0.21/0.50 fresh26(aSet0(xT), true2, xT, Y, Z)
% 0.21/0.50 = { by axiom 1 (m__725) }
% 0.21/0.50 fresh26(true2, true2, xT, Y, Z)
% 0.21/0.50 = { by axiom 14 (mDefSup_4) }
% 0.21/0.50 true2
% 0.21/0.50
% 0.21/0.50 Lemma 27: fresh19(X, X, xT, xS, Y, Z) = sdtlseqdt0(Y, Z).
% 0.21/0.50 Proof:
% 0.21/0.50 fresh19(X, X, xT, xS, Y, Z)
% 0.21/0.50 = { by axiom 22 (mDefSup_2) }
% 0.21/0.50 fresh20(aSubsetOf0(xS, xT), true2, xT, Y, Z)
% 0.21/0.50 = { by axiom 2 (m__725_01) }
% 0.21/0.50 fresh20(true2, true2, xT, Y, Z)
% 0.21/0.50 = { by axiom 16 (mDefSup_2) }
% 0.21/0.50 sdtlseqdt0(Y, Z)
% 0.21/0.50
% 0.21/0.50 Goal 1 (m__): xu = xv.
% 0.21/0.50 Proof:
% 0.21/0.50 xu
% 0.21/0.50 = { by axiom 7 (mASymm) R->L }
% 0.21/0.50 fresh66(true2, true2, xu, xv)
% 0.21/0.50 = { by axiom 5 (mEOfElem) R->L }
% 0.21/0.50 fresh66(fresh(true2, true2, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) R->L }
% 0.21/0.50 fresh66(fresh(aSet0(xT), true2, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 21 (mEOfElem) R->L }
% 0.21/0.50 fresh66(fresh2(aElementOf0(xv, xT), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 10 (mDefSup_3) R->L }
% 0.21/0.50 fresh66(fresh2(fresh5(true2, true2, xT, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 2 (m__725_01) R->L }
% 0.21/0.50 fresh66(fresh2(fresh5(aSubsetOf0(xS, xT), true2, xT, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 24 (mDefSup_3) R->L }
% 0.21/0.50 fresh66(fresh2(fresh23(aSupremumOfIn0(xv, xS, xT), true2, xT, xS, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 4 (m__744_1) }
% 0.21/0.50 fresh66(fresh2(fresh23(true2, true2, xT, xS, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 15 (mDefSup_3) }
% 0.21/0.50 fresh66(fresh2(fresh24(aSet0(xT), true2, xT, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) }
% 0.21/0.50 fresh66(fresh2(fresh24(true2, true2, xT, xv), true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 8 (mDefSup_3) }
% 0.21/0.50 fresh66(fresh2(true2, true2, xT, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 11 (mEOfElem) }
% 0.21/0.50 fresh66(aElement0(xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 13 (mASymm) R->L }
% 0.21/0.50 fresh65(true2, true2, xu, xv)
% 0.21/0.50 = { by axiom 9 (mDefSup_2) R->L }
% 0.21/0.50 fresh65(fresh22(true2, true2, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) R->L }
% 0.21/0.50 fresh65(fresh22(aSet0(xT), true2, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 20 (mDefSup_2) R->L }
% 0.21/0.50 fresh65(fresh21(true2, true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by lemma 26 R->L }
% 0.21/0.50 fresh65(fresh21(fresh25(true2, true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 3 (m__744) R->L }
% 0.21/0.50 fresh65(fresh21(fresh25(aSupremumOfIn0(xu, xS, xT), true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 23 (mDefSup_4) }
% 0.21/0.50 fresh65(fresh21(fresh4(aSubsetOf0(xS, xT), true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 2 (m__725_01) }
% 0.21/0.50 fresh65(fresh21(fresh4(true2, true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 17 (mDefSup_4) }
% 0.21/0.50 fresh65(fresh21(aUpperBoundOfIn0(xu, xS, xT), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 25 (mDefSup_2) R->L }
% 0.21/0.50 fresh65(fresh19(aSupremumOfIn0(xv, xS, xT), true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 4 (m__744_1) }
% 0.21/0.50 fresh65(fresh19(true2, true2, xT, xS, xv, xu), true2, xu, xv)
% 0.21/0.50 = { by lemma 27 }
% 0.21/0.50 fresh65(sdtlseqdt0(xv, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 18 (mASymm) }
% 0.21/0.50 fresh67(sdtlseqdt0(xu, xv), true2, xu, xv)
% 0.21/0.50 = { by lemma 27 R->L }
% 0.21/0.50 fresh67(fresh19(true2, true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 3 (m__744) R->L }
% 0.21/0.50 fresh67(fresh19(aSupremumOfIn0(xu, xS, xT), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 25 (mDefSup_2) }
% 0.21/0.50 fresh67(fresh21(aUpperBoundOfIn0(xv, xS, xT), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 17 (mDefSup_4) R->L }
% 0.21/0.50 fresh67(fresh21(fresh4(true2, true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 2 (m__725_01) R->L }
% 0.21/0.50 fresh67(fresh21(fresh4(aSubsetOf0(xS, xT), true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 23 (mDefSup_4) R->L }
% 0.21/0.50 fresh67(fresh21(fresh25(aSupremumOfIn0(xv, xS, xT), true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 4 (m__744_1) }
% 0.21/0.50 fresh67(fresh21(fresh25(true2, true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by lemma 26 }
% 0.21/0.50 fresh67(fresh21(true2, true2, xT, xS, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 20 (mDefSup_2) }
% 0.21/0.50 fresh67(fresh22(aSet0(xT), true2, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) }
% 0.21/0.50 fresh67(fresh22(true2, true2, xu, xv), true2, xu, xv)
% 0.21/0.50 = { by axiom 9 (mDefSup_2) }
% 0.21/0.50 fresh67(true2, true2, xu, xv)
% 0.21/0.50 = { by axiom 12 (mASymm) }
% 0.21/0.50 fresh68(aElement0(xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 11 (mEOfElem) R->L }
% 0.21/0.50 fresh68(fresh2(true2, true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 8 (mDefSup_3) R->L }
% 0.21/0.50 fresh68(fresh2(fresh24(true2, true2, xT, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) R->L }
% 0.21/0.50 fresh68(fresh2(fresh24(aSet0(xT), true2, xT, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 15 (mDefSup_3) R->L }
% 0.21/0.50 fresh68(fresh2(fresh23(true2, true2, xT, xS, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 3 (m__744) R->L }
% 0.21/0.50 fresh68(fresh2(fresh23(aSupremumOfIn0(xu, xS, xT), true2, xT, xS, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 24 (mDefSup_3) }
% 0.21/0.50 fresh68(fresh2(fresh5(aSubsetOf0(xS, xT), true2, xT, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 2 (m__725_01) }
% 0.21/0.50 fresh68(fresh2(fresh5(true2, true2, xT, xu), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 10 (mDefSup_3) }
% 0.21/0.50 fresh68(fresh2(aElementOf0(xu, xT), true2, xT, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 21 (mEOfElem) }
% 0.21/0.50 fresh68(fresh(aSet0(xT), true2, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 1 (m__725) }
% 0.21/0.50 fresh68(fresh(true2, true2, xu), true2, xu, xv)
% 0.21/0.50 = { by axiom 5 (mEOfElem) }
% 0.21/0.50 fresh68(true2, true2, xu, xv)
% 0.21/0.50 = { by axiom 6 (mASymm) }
% 0.21/0.50 xv
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------