TSTP Solution File: NUM558+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM558+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 : n018.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 11:56:58 EDT 2023
% Result : Theorem 0.20s 0.79s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM558+3 : 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
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 18:01:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.79 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.79
% 0.20/0.79 % SZS status Theorem
% 0.20/0.79
% 0.20/0.80 % SZS output start Proof
% 0.20/0.80 Take the following subset of the input axioms:
% 0.20/0.80 fof(mEOfElem, axiom, ![W0]: (aSet0(W0) => ![W1]: (aElementOf0(W1, W0) => aElement0(W1)))).
% 0.20/0.80 fof(m__, conjecture, aElementOf0(xx, xT)).
% 0.20/0.80 fof(m__2202_02, hypothesis, aSet0(xS) & (aSet0(xT) & xk!=sz00)).
% 0.20/0.81 fof(m__2227, hypothesis, aSet0(slbdtsldtrb0(xS, xk)) & (![W0_2]: ((aElementOf0(W0_2, slbdtsldtrb0(xS, xk)) => (aSet0(W0_2) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS)) & (aSubsetOf0(W0_2, xS) & sbrdtbr0(W0_2)=xk)))) & ((((aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS))) | aSubsetOf0(W0_2, xS)) & sbrdtbr0(W0_2)=xk) => aElementOf0(W0_2, slbdtsldtrb0(xS, xk)))) & (aSet0(slbdtsldtrb0(xT, xk)) & (![W0_2]: ((aElementOf0(W0_2, slbdtsldtrb0(xT, xk)) => (aSet0(W0_2) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xT)) & (aSubsetOf0(W0_2, xT) & sbrdtbr0(W0_2)=xk)))) & ((((aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xT))) | aSubsetOf0(W0_2, xT)) & sbrdtbr0(W0_2)=xk) => aElementOf0(W0_2, slbdtsldtrb0(xT, xk)))) & (![W0_2]: (aElementOf0(W0_2, slbdtsldtrb0(xS, xk)) => aElementOf0(W0_2, slbdtsldtrb0(xT, xk))) & (aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) & ~(![W0_2]: ((aElementOf0(W0_2, slbdtsldtrb0(xS, xk)) => (aSet0(W0_2) & (![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS)) & (aSubsetOf0(W0_2, xS) & sbrdtbr0(W0_2)=xk)))) & ((((aSet0(W0_2) & ![W1_2]: (aElementOf0(W1_2, W0_2) => aElementOf0(W1_2, xS))) | aSubsetOf0(W0_2, xS)) & sbrdtbr0(W0_2)=xk) => aElementOf0(W0_2, slbdtsldtrb0(xS, xk)))) => (~?[W0_2]: aElementOf0(W0_2, slbdtsldtrb0(xS, xk)) | slbdtsldtrb0(xS, xk)=slcrc0)))))))).
% 0.20/0.81 fof(m__2256, hypothesis, aElementOf0(xx, xS)).
% 0.20/0.81 fof(m__2357, hypothesis, aSet0(sdtmndt0(xQ, xy)) & (![W0_2]: (aElementOf0(W0_2, sdtmndt0(xQ, xy)) <=> (aElement0(W0_2) & (aElementOf0(W0_2, xQ) & W0_2!=xy))) & (aSet0(xP) & (![W0_2]: (aElementOf0(W0_2, xP) <=> (aElement0(W0_2) & (aElementOf0(W0_2, sdtmndt0(xQ, xy)) | W0_2=xx))) & xP=sdtpldt0(sdtmndt0(xQ, xy), xx))))).
% 0.20/0.81 fof(m__2378, hypothesis, ![W0_2]: (aElementOf0(W0_2, xP) => aElementOf0(W0_2, xS)) & (aSubsetOf0(xP, xS) & (sbrdtbr0(xP)=xk & aElementOf0(xP, slbdtsldtrb0(xS, xk))))).
% 0.20/0.81
% 0.20/0.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.81 fresh(y, y, x1...xn) = u
% 0.20/0.81 C => fresh(s, t, x1...xn) = v
% 0.20/0.81 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.81 variables of u and v.
% 0.20/0.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.81 input problem has no model of domain size 1).
% 0.20/0.81
% 0.20/0.81 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.81
% 0.20/0.81 Axiom 1 (m__2256): aElementOf0(xx, xS) = true2.
% 0.20/0.81 Axiom 2 (m__2202_02): aSet0(xS) = true2.
% 0.20/0.81 Axiom 3 (m__2378_1): aElementOf0(xP, slbdtsldtrb0(xS, xk)) = true2.
% 0.20/0.81 Axiom 4 (mEOfElem): fresh62(X, X, Y) = true2.
% 0.20/0.81 Axiom 5 (m__2227_21): fresh25(X, X, Y) = true2.
% 0.20/0.81 Axiom 6 (m__2227_22): fresh24(X, X, Y) = true2.
% 0.20/0.81 Axiom 7 (m__2357_4): fresh12(X, X, Y) = aElementOf0(Y, xP).
% 0.20/0.81 Axiom 8 (m__2357_4): fresh11(X, X, Y) = true2.
% 0.20/0.82 Axiom 9 (mEOfElem): fresh63(X, X, Y, Z) = aElement0(Z).
% 0.20/0.82 Axiom 10 (m__2227_21): fresh26(X, X, Y, Z) = aElementOf0(Z, xT).
% 0.20/0.82 Axiom 11 (m__2357_4): fresh12(aElement0(X), true2, X) = fresh11(X, xx, X).
% 0.20/0.82 Axiom 12 (mEOfElem): fresh63(aElementOf0(X, Y), true2, Y, X) = fresh62(aSet0(Y), true2, X).
% 0.20/0.82 Axiom 13 (m__2227_21): fresh26(aElementOf0(X, Y), true2, Y, X) = fresh25(aElementOf0(Y, slbdtsldtrb0(xT, xk)), true2, X).
% 0.20/0.82 Axiom 14 (m__2227_22): fresh24(aElementOf0(X, slbdtsldtrb0(xS, xk)), true2, X) = aElementOf0(X, slbdtsldtrb0(xT, xk)).
% 0.20/0.82
% 0.20/0.82 Goal 1 (m__): aElementOf0(xx, xT) = true2.
% 0.20/0.82 Proof:
% 0.20/0.82 aElementOf0(xx, xT)
% 0.20/0.82 = { by axiom 10 (m__2227_21) R->L }
% 0.20/0.82 fresh26(true2, true2, xP, xx)
% 0.20/0.82 = { by axiom 8 (m__2357_4) R->L }
% 0.20/0.82 fresh26(fresh11(xx, xx, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 11 (m__2357_4) R->L }
% 0.20/0.82 fresh26(fresh12(aElement0(xx), true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 9 (mEOfElem) R->L }
% 0.20/0.82 fresh26(fresh12(fresh63(true2, true2, xS, xx), true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 1 (m__2256) R->L }
% 0.20/0.82 fresh26(fresh12(fresh63(aElementOf0(xx, xS), true2, xS, xx), true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 12 (mEOfElem) }
% 0.20/0.82 fresh26(fresh12(fresh62(aSet0(xS), true2, xx), true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 2 (m__2202_02) }
% 0.20/0.82 fresh26(fresh12(fresh62(true2, true2, xx), true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 4 (mEOfElem) }
% 0.20/0.82 fresh26(fresh12(true2, true2, xx), true2, xP, xx)
% 0.20/0.82 = { by axiom 7 (m__2357_4) }
% 0.20/0.82 fresh26(aElementOf0(xx, xP), true2, xP, xx)
% 0.20/0.82 = { by axiom 13 (m__2227_21) }
% 0.20/0.82 fresh25(aElementOf0(xP, slbdtsldtrb0(xT, xk)), true2, xx)
% 0.20/0.82 = { by axiom 14 (m__2227_22) R->L }
% 0.20/0.82 fresh25(fresh24(aElementOf0(xP, slbdtsldtrb0(xS, xk)), true2, xP), true2, xx)
% 0.20/0.82 = { by axiom 3 (m__2378_1) }
% 0.20/0.82 fresh25(fresh24(true2, true2, xP), true2, xx)
% 0.20/0.82 = { by axiom 6 (m__2227_22) }
% 0.20/0.82 fresh25(true2, true2, xx)
% 0.20/0.82 = { by axiom 5 (m__2227_21) }
% 0.20/0.82 true2
% 0.20/0.82 % SZS output end Proof
% 0.20/0.82
% 0.20/0.82 RESULT: Theorem (the conjecture is true).
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