TSTP Solution File: NUM436+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM436+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 : n019.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 11:56:17 EDT 2023
% Result : Theorem 0.22s 0.60s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM436+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
% 0.18/0.36 % Computer : n019.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Fri Aug 25 08:42:28 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.22/0.60 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.60
% 0.22/0.60 % SZS status Theorem
% 0.22/0.60
% 0.22/0.60 % SZS output start Proof
% 0.22/0.60 Take the following subset of the input axioms:
% 0.22/0.60 fof(mDivisor, definition, ![W0]: (aInteger0(W0) => ![W1]: (aDivisorOf0(W1, W0) <=> (aInteger0(W1) & (W1!=sz00 & ?[W2]: (aInteger0(W2) & sdtasdt0(W1, W2)=W0)))))).
% 0.22/0.60 fof(mIntMult, axiom, ![W0_2, W1_2]: ((aInteger0(W0_2) & aInteger0(W1_2)) => aInteger0(sdtasdt0(W0_2, W1_2)))).
% 0.22/0.60 fof(m__, conjecture, (?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xp, W0_2)=sdtpldt0(xa, smndt0(xb))) | (aDivisorOf0(xp, sdtpldt0(xa, smndt0(xb))) | sdteqdtlpzmzozddtrp0(xa, xb, xp))) & (?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xa, smndt0(xb))) | (aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb))) | sdteqdtlpzmzozddtrp0(xa, xb, xq)))).
% 0.22/0.60 fof(m__1032, hypothesis, aInteger0(xm) & sdtasdt0(sdtasdt0(xp, xq), xm)=sdtpldt0(xa, smndt0(xb))).
% 0.22/0.60 fof(m__1071, hypothesis, sdtasdt0(xp, sdtasdt0(xq, xm))=sdtpldt0(xa, smndt0(xb)) & sdtpldt0(xa, smndt0(xb))=sdtasdt0(xq, sdtasdt0(xp, xm))).
% 0.22/0.60 fof(m__979, hypothesis, aInteger0(xa) & (aInteger0(xb) & (aInteger0(xp) & (xp!=sz00 & (aInteger0(xq) & xq!=sz00))))).
% 0.22/0.60
% 0.22/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.61 fresh(y, y, x1...xn) = u
% 0.22/0.61 C => fresh(s, t, x1...xn) = v
% 0.22/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.61 variables of u and v.
% 0.22/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.61 input problem has no model of domain size 1).
% 0.22/0.61
% 0.22/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.61
% 0.22/0.61 Axiom 1 (m__979_3): aInteger0(xq) = true2.
% 0.22/0.61 Axiom 2 (m__979_2): aInteger0(xp) = true2.
% 0.22/0.61 Axiom 3 (m__1032_1): aInteger0(xm) = true2.
% 0.22/0.61 Axiom 4 (m__): fresh8(X, X) = true2.
% 0.22/0.61 Axiom 5 (m__): fresh9(X, X, Y) = or.
% 0.22/0.61 Axiom 6 (m__1071_1): sdtpldt0(xa, smndt0(xb)) = sdtasdt0(xq, sdtasdt0(xp, xm)).
% 0.22/0.61 Axiom 7 (m__1071): sdtasdt0(xp, sdtasdt0(xq, xm)) = sdtpldt0(xa, smndt0(xb)).
% 0.22/0.61 Axiom 8 (mIntMult): fresh21(X, X, Y, Z) = aInteger0(sdtasdt0(Y, Z)).
% 0.22/0.61 Axiom 9 (mIntMult): fresh20(X, X, Y, Z) = true2.
% 0.22/0.61 Axiom 10 (mIntMult): fresh21(aInteger0(X), true2, Y, X) = fresh20(aInteger0(Y), true2, Y, X).
% 0.22/0.61 Axiom 11 (m__): fresh9(aInteger0(X), true2, X) = fresh8(sdtasdt0(xp, X), sdtpldt0(xa, smndt0(xb))).
% 0.22/0.61
% 0.22/0.61 Goal 1 (m___1): tuple2(sdtasdt0(xq, X), aInteger0(X), or) = tuple2(sdtpldt0(xa, smndt0(xb)), true2, true2).
% 0.22/0.61 The goal is true when:
% 0.22/0.61 X = sdtasdt0(xp, xm)
% 0.22/0.61
% 0.22/0.61 Proof:
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), aInteger0(sdtasdt0(xp, xm)), or)
% 0.22/0.61 = { by axiom 8 (mIntMult) R->L }
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), fresh21(true2, true2, xp, xm), or)
% 0.22/0.61 = { by axiom 3 (m__1032_1) R->L }
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), fresh21(aInteger0(xm), true2, xp, xm), or)
% 0.22/0.61 = { by axiom 10 (mIntMult) }
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), fresh20(aInteger0(xp), true2, xp, xm), or)
% 0.22/0.61 = { by axiom 2 (m__979_2) }
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), fresh20(true2, true2, xp, xm), or)
% 0.22/0.61 = { by axiom 9 (mIntMult) }
% 0.22/0.61 tuple2(sdtasdt0(xq, sdtasdt0(xp, xm)), true2, or)
% 0.22/0.61 = { by axiom 6 (m__1071_1) R->L }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, or)
% 0.22/0.61 = { by axiom 5 (m__) R->L }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(true2, true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 9 (mIntMult) R->L }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(fresh20(true2, true2, xq, xm), true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 1 (m__979_3) R->L }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(fresh20(aInteger0(xq), true2, xq, xm), true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 10 (mIntMult) R->L }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(fresh21(aInteger0(xm), true2, xq, xm), true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 3 (m__1032_1) }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(fresh21(true2, true2, xq, xm), true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 8 (mIntMult) }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh9(aInteger0(sdtasdt0(xq, xm)), true2, sdtasdt0(xq, xm)))
% 0.22/0.61 = { by axiom 11 (m__) }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh8(sdtasdt0(xp, sdtasdt0(xq, xm)), sdtpldt0(xa, smndt0(xb))))
% 0.22/0.61 = { by axiom 7 (m__1071) }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, fresh8(sdtpldt0(xa, smndt0(xb)), sdtpldt0(xa, smndt0(xb))))
% 0.22/0.61 = { by axiom 4 (m__) }
% 0.22/0.61 tuple2(sdtpldt0(xa, smndt0(xb)), true2, true2)
% 0.22/0.61 % SZS output end Proof
% 0.22/0.61
% 0.22/0.61 RESULT: Theorem (the conjecture is true).
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