TSTP Solution File: LAT382+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT382+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 : n011.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 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT382+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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 04:21:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.50 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Take the following subset of the input axioms:
% 0.20/0.51 fof(mASymm, axiom, ![W0, W1]: ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => W0=W1))).
% 0.20/0.51 fof(mDefInf, definition, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) => ![W2]: (aInfimumOfIn0(W2, W1_2, W0_2) <=> (aElementOf0(W2, W0_2) & (aLowerBoundOfIn0(W2, W1_2, W0_2) & ![W3]: (aLowerBoundOfIn0(W3, W1_2, W0_2) => sdtlseqdt0(W3, W2)))))))).
% 0.20/0.51 fof(mEOfElem, axiom, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aElementOf0(W1_2, W0_2) => aElement0(W1_2)))).
% 0.20/0.51 fof(m__, conjecture, xu=xv).
% 0.20/0.51 fof(m__773, hypothesis, aSet0(xT)).
% 0.20/0.51 fof(m__773_01, hypothesis, aSubsetOf0(xS, xT)).
% 0.20/0.51 fof(m__792, hypothesis, aInfimumOfIn0(xu, xS, xT) & aInfimumOfIn0(xv, xS, xT)).
% 0.20/0.51
% 0.20/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.51 fresh(y, y, x1...xn) = u
% 0.20/0.51 C => fresh(s, t, x1...xn) = v
% 0.20/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.51 variables of u and v.
% 0.20/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.51 input problem has no model of domain size 1).
% 0.20/0.51
% 0.20/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.51
% 0.20/0.51 Axiom 1 (m__773): aSet0(xT) = true2.
% 0.20/0.51 Axiom 2 (m__773_01): aSubsetOf0(xS, xT) = true2.
% 0.20/0.51 Axiom 3 (m__792): aInfimumOfIn0(xu, xS, xT) = true2.
% 0.20/0.51 Axiom 4 (m__792_1): aInfimumOfIn0(xv, xS, xT) = true2.
% 0.20/0.51 Axiom 5 (mEOfElem): fresh(X, X, Y) = true2.
% 0.20/0.51 Axiom 6 (mASymm): fresh72(X, X, Y, Z) = Z.
% 0.20/0.51 Axiom 7 (mASymm): fresh70(X, X, Y, Z) = Y.
% 0.20/0.51 Axiom 8 (mDefInf_3): fresh41(X, X, Y, Z) = true2.
% 0.20/0.51 Axiom 9 (mDefInf_2): fresh39(X, X, Y, Z) = true2.
% 0.20/0.51 Axiom 10 (mDefInf_3): fresh12(X, X, Y, Z) = aElementOf0(Z, Y).
% 0.20/0.51 Axiom 11 (mEOfElem): fresh2(X, X, Y, Z) = aElement0(Z).
% 0.20/0.51 Axiom 12 (mASymm): fresh71(X, X, Y, Z) = fresh72(aElement0(Y), true2, Y, Z).
% 0.20/0.51 Axiom 13 (mASymm): fresh69(X, X, Y, Z) = fresh70(aElement0(Z), true2, Y, Z).
% 0.20/0.51 Axiom 14 (mDefInf_4): fresh43(X, X, Y, Z, W) = true2.
% 0.20/0.51 Axiom 15 (mDefInf_3): fresh40(X, X, Y, Z, W) = fresh41(aSet0(Y), true2, Y, W).
% 0.20/0.51 Axiom 16 (mDefInf_2): fresh37(X, X, Y, Z, W) = sdtlseqdt0(W, Z).
% 0.20/0.51 Axiom 17 (mDefInf_4): fresh11(X, X, Y, Z, W) = aLowerBoundOfIn0(W, Z, Y).
% 0.20/0.51 Axiom 18 (mASymm): fresh69(sdtlseqdt0(X, Y), true2, Y, X) = fresh71(sdtlseqdt0(Y, X), true2, Y, X).
% 0.20/0.51 Axiom 19 (mDefInf_4): fresh42(X, X, Y, Z, W) = fresh43(aSet0(Y), true2, Y, Z, W).
% 0.20/0.51 Axiom 20 (mDefInf_2): fresh38(X, X, Y, Z, W, V) = fresh39(aSet0(Y), true2, W, V).
% 0.20/0.51 Axiom 21 (mEOfElem): fresh2(aElementOf0(X, Y), true2, Y, X) = fresh(aSet0(Y), true2, X).
% 0.20/0.51 Axiom 22 (mDefInf_2): fresh36(X, X, Y, Z, W, V) = fresh37(aSubsetOf0(Z, Y), true2, Y, W, V).
% 0.20/0.51 Axiom 23 (mDefInf_4): fresh42(aInfimumOfIn0(X, Y, Z), true2, Z, Y, X) = fresh11(aSubsetOf0(Y, Z), true2, Z, Y, X).
% 0.20/0.51 Axiom 24 (mDefInf_3): fresh40(aInfimumOfIn0(X, Y, Z), true2, Z, Y, X) = fresh12(aSubsetOf0(Y, Z), true2, Z, X).
% 0.20/0.51 Axiom 25 (mDefInf_2): fresh36(aInfimumOfIn0(X, Y, Z), true2, Z, Y, X, W) = fresh38(aLowerBoundOfIn0(W, Y, Z), true2, Z, Y, X, W).
% 0.20/0.51
% 0.20/0.51 Lemma 26: fresh42(X, X, xT, Y, Z) = true2.
% 0.20/0.51 Proof:
% 0.20/0.51 fresh42(X, X, xT, Y, Z)
% 0.20/0.51 = { by axiom 19 (mDefInf_4) }
% 0.20/0.51 fresh43(aSet0(xT), true2, xT, Y, Z)
% 0.20/0.51 = { by axiom 1 (m__773) }
% 0.20/0.51 fresh43(true2, true2, xT, Y, Z)
% 0.20/0.51 = { by axiom 14 (mDefInf_4) }
% 0.20/0.51 true2
% 0.20/0.51
% 0.20/0.51 Lemma 27: fresh36(X, X, xT, xS, Y, Z) = sdtlseqdt0(Z, Y).
% 0.20/0.51 Proof:
% 0.20/0.51 fresh36(X, X, xT, xS, Y, Z)
% 0.20/0.51 = { by axiom 22 (mDefInf_2) }
% 0.20/0.51 fresh37(aSubsetOf0(xS, xT), true2, xT, Y, Z)
% 0.20/0.51 = { by axiom 2 (m__773_01) }
% 0.20/0.51 fresh37(true2, true2, xT, Y, Z)
% 0.20/0.51 = { by axiom 16 (mDefInf_2) }
% 0.20/0.51 sdtlseqdt0(Z, Y)
% 0.20/0.51
% 0.20/0.51 Goal 1 (m__): xu = xv.
% 0.20/0.51 Proof:
% 0.20/0.51 xu
% 0.20/0.51 = { by axiom 6 (mASymm) R->L }
% 0.20/0.51 fresh72(true2, true2, xv, xu)
% 0.20/0.51 = { by axiom 5 (mEOfElem) R->L }
% 0.20/0.51 fresh72(fresh(true2, true2, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 1 (m__773) R->L }
% 0.20/0.51 fresh72(fresh(aSet0(xT), true2, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 21 (mEOfElem) R->L }
% 0.20/0.51 fresh72(fresh2(aElementOf0(xv, xT), true2, xT, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 10 (mDefInf_3) R->L }
% 0.20/0.51 fresh72(fresh2(fresh12(true2, true2, xT, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 2 (m__773_01) R->L }
% 0.20/0.51 fresh72(fresh2(fresh12(aSubsetOf0(xS, xT), true2, xT, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 24 (mDefInf_3) R->L }
% 0.20/0.51 fresh72(fresh2(fresh40(aInfimumOfIn0(xv, xS, xT), true2, xT, xS, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 4 (m__792_1) }
% 0.20/0.51 fresh72(fresh2(fresh40(true2, true2, xT, xS, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.51 = { by axiom 15 (mDefInf_3) }
% 0.20/0.52 fresh72(fresh2(fresh41(aSet0(xT), true2, xT, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 1 (m__773) }
% 0.20/0.52 fresh72(fresh2(fresh41(true2, true2, xT, xv), true2, xT, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 8 (mDefInf_3) }
% 0.20/0.52 fresh72(fresh2(true2, true2, xT, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 11 (mEOfElem) }
% 0.20/0.52 fresh72(aElement0(xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 12 (mASymm) R->L }
% 0.20/0.52 fresh71(true2, true2, xv, xu)
% 0.20/0.52 = { by axiom 9 (mDefInf_2) R->L }
% 0.20/0.52 fresh71(fresh39(true2, true2, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 1 (m__773) R->L }
% 0.20/0.52 fresh71(fresh39(aSet0(xT), true2, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 20 (mDefInf_2) R->L }
% 0.20/0.52 fresh71(fresh38(true2, true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by lemma 26 R->L }
% 0.20/0.52 fresh71(fresh38(fresh42(true2, true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 4 (m__792_1) R->L }
% 0.20/0.52 fresh71(fresh38(fresh42(aInfimumOfIn0(xv, xS, xT), true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 23 (mDefInf_4) }
% 0.20/0.52 fresh71(fresh38(fresh11(aSubsetOf0(xS, xT), true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 2 (m__773_01) }
% 0.20/0.52 fresh71(fresh38(fresh11(true2, true2, xT, xS, xv), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 17 (mDefInf_4) }
% 0.20/0.52 fresh71(fresh38(aLowerBoundOfIn0(xv, xS, xT), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 25 (mDefInf_2) R->L }
% 0.20/0.52 fresh71(fresh36(aInfimumOfIn0(xu, xS, xT), true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by axiom 3 (m__792) }
% 0.20/0.52 fresh71(fresh36(true2, true2, xT, xS, xu, xv), true2, xv, xu)
% 0.20/0.52 = { by lemma 27 }
% 0.20/0.52 fresh71(sdtlseqdt0(xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 18 (mASymm) R->L }
% 0.20/0.52 fresh69(sdtlseqdt0(xu, xv), true2, xv, xu)
% 0.20/0.52 = { by lemma 27 R->L }
% 0.20/0.52 fresh69(fresh36(true2, true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 4 (m__792_1) R->L }
% 0.20/0.52 fresh69(fresh36(aInfimumOfIn0(xv, xS, xT), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 25 (mDefInf_2) }
% 0.20/0.52 fresh69(fresh38(aLowerBoundOfIn0(xu, xS, xT), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 17 (mDefInf_4) R->L }
% 0.20/0.52 fresh69(fresh38(fresh11(true2, true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 2 (m__773_01) R->L }
% 0.20/0.52 fresh69(fresh38(fresh11(aSubsetOf0(xS, xT), true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 23 (mDefInf_4) R->L }
% 0.20/0.52 fresh69(fresh38(fresh42(aInfimumOfIn0(xu, xS, xT), true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 3 (m__792) }
% 0.20/0.52 fresh69(fresh38(fresh42(true2, true2, xT, xS, xu), true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by lemma 26 }
% 0.20/0.52 fresh69(fresh38(true2, true2, xT, xS, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 20 (mDefInf_2) }
% 0.20/0.52 fresh69(fresh39(aSet0(xT), true2, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 1 (m__773) }
% 0.20/0.52 fresh69(fresh39(true2, true2, xv, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 9 (mDefInf_2) }
% 0.20/0.52 fresh69(true2, true2, xv, xu)
% 0.20/0.52 = { by axiom 13 (mASymm) }
% 0.20/0.52 fresh70(aElement0(xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 11 (mEOfElem) R->L }
% 0.20/0.52 fresh70(fresh2(true2, true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 8 (mDefInf_3) R->L }
% 0.20/0.52 fresh70(fresh2(fresh41(true2, true2, xT, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 1 (m__773) R->L }
% 0.20/0.52 fresh70(fresh2(fresh41(aSet0(xT), true2, xT, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 15 (mDefInf_3) R->L }
% 0.20/0.52 fresh70(fresh2(fresh40(true2, true2, xT, xS, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 3 (m__792) R->L }
% 0.20/0.52 fresh70(fresh2(fresh40(aInfimumOfIn0(xu, xS, xT), true2, xT, xS, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 24 (mDefInf_3) }
% 0.20/0.52 fresh70(fresh2(fresh12(aSubsetOf0(xS, xT), true2, xT, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 2 (m__773_01) }
% 0.20/0.52 fresh70(fresh2(fresh12(true2, true2, xT, xu), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 10 (mDefInf_3) }
% 0.20/0.52 fresh70(fresh2(aElementOf0(xu, xT), true2, xT, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 21 (mEOfElem) }
% 0.20/0.52 fresh70(fresh(aSet0(xT), true2, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 1 (m__773) }
% 0.20/0.52 fresh70(fresh(true2, true2, xu), true2, xv, xu)
% 0.20/0.52 = { by axiom 5 (mEOfElem) }
% 0.20/0.52 fresh70(true2, true2, xv, xu)
% 0.20/0.52 = { by axiom 7 (mASymm) }
% 0.20/0.52 xv
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------