TSTP Solution File: NUM590+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM590+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 : n008.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 11:57:08 EDT 2023
% Result : Theorem 14.63s 2.26s
% Output : Proof 14.63s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM590+3 : 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
% 0.13/0.34 % Computer : n008.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 : Fri Aug 25 12:51:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 14.63/2.26 Command-line arguments: --ground-connectedness --complete-subsets
% 14.63/2.26
% 14.63/2.26 % SZS status Theorem
% 14.63/2.26
% 14.63/2.26 % SZS output start Proof
% 14.63/2.26 Take the following subset of the input axioms:
% 14.63/2.26 fof(m__, conjecture, ![W0]: (aElementOf0(W0, xY) => aElementOf0(W0, szNzAzT0)) | aSubsetOf0(xY, szNzAzT0)).
% 14.63/2.26 fof(m__3671, hypothesis, ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aSet0(sdtlpdtrp0(xN, W0_2)) & (![W1]: (aElementOf0(W1, sdtlpdtrp0(xN, W0_2)) => aElementOf0(W1, szNzAzT0)) & (aSubsetOf0(sdtlpdtrp0(xN, W0_2), szNzAzT0) & isCountable0(sdtlpdtrp0(xN, W0_2))))))).
% 14.63/2.26 fof(m__4448, hypothesis, aElementOf0(xi, szNzAzT0)).
% 14.63/2.26 fof(m__4448_02, hypothesis, aElementOf0(szmzizndt0(sdtlpdtrp0(xN, xi)), sdtlpdtrp0(xN, xi)) & (![W0_2]: (aElementOf0(W0_2, sdtlpdtrp0(xN, xi)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xi)), W0_2)) & (aSet0(xY) & (![W0_2]: (aElementOf0(W0_2, xY) <=> (aElement0(W0_2) & (aElementOf0(W0_2, sdtlpdtrp0(xN, xi)) & W0_2!=szmzizndt0(sdtlpdtrp0(xN, xi))))) & (xY=sdtmndt0(sdtlpdtrp0(xN, xi), szmzizndt0(sdtlpdtrp0(xN, xi))) & xd=sdtlpdtrp0(xC, xi)))))).
% 14.63/2.26
% 14.63/2.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.63/2.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.63/2.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.63/2.26 fresh(y, y, x1...xn) = u
% 14.63/2.26 C => fresh(s, t, x1...xn) = v
% 14.63/2.26 where fresh is a fresh function symbol and x1..xn are the free
% 14.63/2.26 variables of u and v.
% 14.63/2.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.63/2.26 input problem has no model of domain size 1).
% 14.63/2.26
% 14.63/2.26 The encoding turns the above axioms into the following unit equations and goals:
% 14.63/2.26
% 14.63/2.26 Axiom 1 (m__): aElementOf0(w0, xY) = true2.
% 14.63/2.26 Axiom 2 (m__4448): aElementOf0(xi, szNzAzT0) = true2.
% 14.63/2.26 Axiom 3 (m__3671_3): fresh77(X, X, Y) = true2.
% 14.63/2.26 Axiom 4 (m__4448_02_8): fresh12(X, X, Y) = true2.
% 14.63/2.26 Axiom 5 (m__3671_3): fresh78(X, X, Y, Z) = aElementOf0(Z, szNzAzT0).
% 14.63/2.26 Axiom 6 (m__4448_02_8): fresh12(aElementOf0(X, xY), true2, X) = aElementOf0(X, sdtlpdtrp0(xN, xi)).
% 14.63/2.26 Axiom 7 (m__3671_3): fresh78(aElementOf0(X, sdtlpdtrp0(xN, Y)), true2, Y, X) = fresh77(aElementOf0(Y, szNzAzT0), true2, X).
% 14.63/2.26
% 14.63/2.26 Goal 1 (m___1): aElementOf0(w0, szNzAzT0) = true2.
% 14.63/2.26 Proof:
% 14.63/2.26 aElementOf0(w0, szNzAzT0)
% 14.63/2.26 = { by axiom 5 (m__3671_3) R->L }
% 14.63/2.26 fresh78(true2, true2, xi, w0)
% 14.63/2.26 = { by axiom 4 (m__4448_02_8) R->L }
% 14.63/2.26 fresh78(fresh12(true2, true2, w0), true2, xi, w0)
% 14.63/2.26 = { by axiom 1 (m__) R->L }
% 14.63/2.26 fresh78(fresh12(aElementOf0(w0, xY), true2, w0), true2, xi, w0)
% 14.63/2.27 = { by axiom 6 (m__4448_02_8) }
% 14.63/2.27 fresh78(aElementOf0(w0, sdtlpdtrp0(xN, xi)), true2, xi, w0)
% 14.63/2.27 = { by axiom 7 (m__3671_3) }
% 14.63/2.27 fresh77(aElementOf0(xi, szNzAzT0), true2, w0)
% 14.63/2.27 = { by axiom 2 (m__4448) }
% 14.63/2.27 fresh77(true2, true2, w0)
% 14.63/2.27 = { by axiom 3 (m__3671_3) }
% 14.63/2.27 true2
% 14.63/2.27 % SZS output end Proof
% 14.63/2.27
% 14.63/2.27 RESULT: Theorem (the conjecture is true).
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