TSTP Solution File: NUM561+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM561+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 : n031.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 11:56:59 EDT 2023
% Result : Theorem 3.97s 0.91s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % 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 : n031.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
% 0.13/0.35 % DateTime : Fri Aug 25 10:29:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.97/0.91 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 3.97/0.91
% 3.97/0.91 % SZS status Theorem
% 3.97/0.91
% 3.97/0.91 % SZS output start Proof
% 3.97/0.91 Take the following subset of the input axioms:
% 3.97/0.91 fof(mDefSImg, definition, ![W0]: (aFunction0(W0) => ![W1]: (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2]: (W2=sdtlcdtrc0(W0, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> ?[W4]: (aElementOf0(W4, W1) & sdtlpdtrp0(W0, W4)=W3))))))).
% 3.97/0.91 fof(mDomSet, axiom, ![W0_2]: (aFunction0(W0_2) => aSet0(szDzozmdt0(W0_2)))).
% 3.97/0.91 fof(mSubRefl, axiom, ![W0_2]: (aSet0(W0_2) => aSubsetOf0(W0_2, W0_2))).
% 3.97/0.91 fof(m__, conjecture, aElementOf0(sdtlpdtrp0(xF, xx), sdtlcdtrc0(xF, szDzozmdt0(xF)))).
% 3.97/0.91 fof(m__2911, hypothesis, aFunction0(xF)).
% 3.97/0.91 fof(m__2911_02, hypothesis, aElementOf0(xx, szDzozmdt0(xF))).
% 3.97/0.91
% 3.97/0.91 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.97/0.91 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.97/0.91 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.97/0.91 fresh(y, y, x1...xn) = u
% 3.97/0.91 C => fresh(s, t, x1...xn) = v
% 3.97/0.91 where fresh is a fresh function symbol and x1..xn are the free
% 3.97/0.91 variables of u and v.
% 3.97/0.91 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.97/0.91 input problem has no model of domain size 1).
% 3.97/0.91
% 3.97/0.91 The encoding turns the above axioms into the following unit equations and goals:
% 3.97/0.91
% 3.97/0.91 Axiom 1 (m__2911): aFunction0(xF) = true2.
% 3.97/0.91 Axiom 2 (m__2911_02): aElementOf0(xx, szDzozmdt0(xF)) = true2.
% 3.97/0.91 Axiom 3 (mDomSet): fresh38(X, X, Y) = true2.
% 3.97/0.91 Axiom 4 (mSubRefl): fresh12(X, X, Y) = true2.
% 3.97/0.91 Axiom 5 (mDefSImg_2): fresh97(X, X, Y, Z) = true2.
% 3.97/0.91 Axiom 6 (mDomSet): fresh38(aFunction0(X), true2, X) = aSet0(szDzozmdt0(X)).
% 3.97/0.91 Axiom 7 (mSubRefl): fresh12(aSet0(X), true2, X) = aSubsetOf0(X, X).
% 3.97/0.91 Axiom 8 (mDefSImg_3): fresh57(X, X, Y, Z, W) = true2.
% 3.97/0.91 Axiom 9 (mDefSImg_2): fresh96(X, X, Y, Z, W, V) = fresh97(W, sdtlcdtrc0(Y, Z), W, V).
% 3.97/0.91 Axiom 10 (mDefSImg_2): fresh59(X, X, Y, Z, W, V) = aElementOf0(V, W).
% 3.97/0.91 Axiom 11 (mDefSImg_3): fresh58(X, X, Y, Z, W, V) = equiv(Y, Z, W).
% 3.97/0.91 Axiom 12 (mDefSImg_2): fresh95(X, X, Y, Z, W, V) = fresh96(aFunction0(Y), true2, Y, Z, W, V).
% 3.97/0.91 Axiom 13 (mDefSImg_3): fresh58(aElementOf0(X, Y), true2, Z, Y, W, X) = fresh57(sdtlpdtrp0(Z, X), W, Z, Y, W).
% 3.97/0.91 Axiom 14 (mDefSImg_2): fresh95(equiv(X, Y, Z), true2, X, Y, W, Z) = fresh59(aSubsetOf0(Y, szDzozmdt0(X)), true2, X, Y, W, Z).
% 3.97/0.91
% 3.97/0.91 Goal 1 (m__): aElementOf0(sdtlpdtrp0(xF, xx), sdtlcdtrc0(xF, szDzozmdt0(xF))) = true2.
% 3.97/0.91 Proof:
% 3.97/0.91 aElementOf0(sdtlpdtrp0(xF, xx), sdtlcdtrc0(xF, szDzozmdt0(xF)))
% 3.97/0.91 = { by axiom 10 (mDefSImg_2) R->L }
% 3.97/0.91 fresh59(true2, true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 4 (mSubRefl) R->L }
% 3.97/0.91 fresh59(fresh12(true2, true2, szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 3 (mDomSet) R->L }
% 3.97/0.91 fresh59(fresh12(fresh38(true2, true2, xF), true2, szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 1 (m__2911) R->L }
% 3.97/0.91 fresh59(fresh12(fresh38(aFunction0(xF), true2, xF), true2, szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 6 (mDomSet) }
% 3.97/0.91 fresh59(fresh12(aSet0(szDzozmdt0(xF)), true2, szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 7 (mSubRefl) }
% 3.97/0.91 fresh59(aSubsetOf0(szDzozmdt0(xF), szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 14 (mDefSImg_2) R->L }
% 3.97/0.91 fresh95(equiv(xF, szDzozmdt0(xF), sdtlpdtrp0(xF, xx)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 11 (mDefSImg_3) R->L }
% 3.97/0.91 fresh95(fresh58(true2, true2, xF, szDzozmdt0(xF), sdtlpdtrp0(xF, xx), xx), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 2 (m__2911_02) R->L }
% 3.97/0.91 fresh95(fresh58(aElementOf0(xx, szDzozmdt0(xF)), true2, xF, szDzozmdt0(xF), sdtlpdtrp0(xF, xx), xx), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 13 (mDefSImg_3) }
% 3.97/0.91 fresh95(fresh57(sdtlpdtrp0(xF, xx), sdtlpdtrp0(xF, xx), xF, szDzozmdt0(xF), sdtlpdtrp0(xF, xx)), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 8 (mDefSImg_3) }
% 3.97/0.91 fresh95(true2, true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 12 (mDefSImg_2) }
% 3.97/0.91 fresh96(aFunction0(xF), true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 1 (m__2911) }
% 3.97/0.91 fresh96(true2, true2, xF, szDzozmdt0(xF), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 9 (mDefSImg_2) }
% 3.97/0.91 fresh97(sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlcdtrc0(xF, szDzozmdt0(xF)), sdtlpdtrp0(xF, xx))
% 3.97/0.91 = { by axiom 5 (mDefSImg_2) }
% 3.97/0.91 true2
% 3.97/0.91 % SZS output end Proof
% 3.97/0.91
% 3.97/0.91 RESULT: Theorem (the conjecture is true).
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