0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn 0.03/0.26 % Computer : n145.star.cs.uiowa.edu 0.03/0.26 % Model : x86_64 x86_64 0.03/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.26 % Memory : 32218.625MB 0.03/0.26 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.26 % CPULimit : 300 0.03/0.26 % DateTime : Fri Jul 13 14:53:42 CDT 2018 0.03/0.26 % CPUTime : 0.03/0.28 % SZS status Theorem 0.03/0.28 0.06/0.36 % SZS output start Proof 0.06/0.36 Take the following subset of the input axioms: 0.06/0.40 fof(background, axiom, 0.06/0.40 ?[A, B, D, E, C]: 0.06/0.40 (relation(A, of, 'Oedipus') 0.06/0.40 & ('Iokaste'=A 0.06/0.40 & (relation(B, of, 'Polyneikes') 0.06/0.40 & (parent(C) 0.06/0.40 & ('Oedipus'=C 0.06/0.40 & ('Polyneikes'=D 0.06/0.40 & (patricide(E) 0.06/0.40 & (~?[F]: ('Thersandros'=F & patricide(F)) 0.06/0.40 & ('Oedipus'=E 0.06/0.40 & (relation(D, of, 'Thersandros') 0.06/0.40 & (parent(D) 0.06/0.40 & (relation(C, of, 'Polyneikes') 0.06/0.40 & (B='Iokaste' 0.06/0.40 & (parent(B) 0.06/0.40 & parent(A)))))))))))))))). 0.06/0.40 fof(prove, conjecture, 0.06/0.40 ?[A, B, D, C]: 0.06/0.40 (patricide(B) 0.06/0.40 & (parent(C) 0.06/0.40 & ($true 0.06/0.40 & (~?[E]: (E=D & patricide(E)) 0.06/0.40 & ('Iokaste'=A 0.06/0.40 & (relation(A, of, B) 0.06/0.40 & (C=B & (relation(C, of, D) & parent(A)))))))))). 0.06/0.40 0.06/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of 0.06/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 0.06/0.40 We repeatedly replace C & s=t => u=v by the two clauses: 0.06/0.40 $$fresh(y, y, x1...xn) = u 0.06/0.40 C => $$fresh(s, t, x1...xn) = v 0.06/0.40 where $$fresh is a fresh function symbol and x1..xn are the free 0.06/0.40 variables of u and v. 0.06/0.40 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 0.06/0.40 input problem has no model of domain size 1). 0.06/0.40 0.06/0.40 The encoding turns the above axioms into the following unit equations and goals: 0.06/0.40 0.06/0.40 Axiom 1 (prove): $$fresh11(X, X, Y) = Y. 0.06/0.40 Axiom 2 (prove): $$fresh9(X, X, Y, Z) = sK1_prove_E(Z). 0.06/0.40 Axiom 3 (prove): $$fresh12(X, X, Y, Z, W) = $$fresh11(Iokaste, Y, W). 0.06/0.40 Axiom 4 (prove): $$fresh10(X, X, Y, Z, W) = $$fresh9(relation(Y, of, Z), $$true2, Y, W). 0.06/0.40 Axiom 5 (prove): $$fresh8(X, X, Y, Z, W) = $$fresh10(parent(Y), $$true2, Y, Z, W). 0.06/0.40 Axiom 6 (prove): $$fresh7(X, X, Y, Z, W) = $$fresh8(parent(Z), $$true2, Y, Z, W). 0.06/0.40 Axiom 7 (prove_1): $$fresh3(X, X, Y, Z) = patricide(sK1_prove_E(Z)). 0.06/0.40 Axiom 8 (prove_1): $$fresh5(X, X, Y) = $$true2. 0.06/0.40 Axiom 9 (prove_1): $$fresh6(X, X, Y, Z, W) = $$fresh5(Iokaste, Y, W). 0.06/0.40 Axiom 10 (prove_1): $$fresh4(X, X, Y, Z, W) = $$fresh3(relation(Y, of, Z), $$true2, Y, W). 0.06/0.40 Axiom 11 (prove_1): $$fresh2(X, X, Y, Z, W) = $$fresh4(parent(Y), $$true2, Y, Z, W). 0.06/0.40 Axiom 12 (prove_1): $$fresh(X, X, Y, Z, W) = $$fresh2(parent(Z), $$true2, Y, Z, W). 0.06/0.40 Axiom 13 (background_13): patricide(sK2_background_E) = $$true2. 0.06/0.40 Axiom 14 (background_12): parent(sK3_background_D) = $$true2. 0.06/0.40 Axiom 15 (background_11): parent(sK4_background_C) = $$true2. 0.06/0.40 Axiom 16 (background_10): parent(sK5_background_B) = $$true2. 0.06/0.40 Axiom 18 (background_8): relation(sK3_background_D, of, Thersandros) = $$true2. 0.06/0.40 Axiom 19 (background_7): relation(sK4_background_C, of, Polyneikes) = $$true2. 0.06/0.40 Axiom 20 (background_6): relation(sK5_background_B, of, Polyneikes) = $$true2. 0.06/0.40 Axiom 21 (background_5): relation(sK6_background_A, of, Oedipus) = $$true2. 0.06/0.40 Axiom 22 (background_4): Polyneikes = sK3_background_D. 0.06/0.40 Axiom 23 (background_3): sK5_background_B = Iokaste. 0.06/0.40 Axiom 24 (background_2): Iokaste = sK6_background_A. 0.06/0.40 Axiom 25 (background_1): Oedipus = sK2_background_E. 0.06/0.40 Axiom 26 (background): Oedipus = sK4_background_C. 0.06/0.40 Axiom 27 (prove): $$fresh7(patricide(X), $$true2, Y, X, Z) = $$fresh12(relation(X, of, Z), $$true2, Y, X, Z). 0.06/0.40 Axiom 28 (prove_1): $$fresh(patricide(X), $$true2, Y, X, Z) = $$fresh6(relation(X, of, Z), $$true2, Y, X, Z). 0.06/0.40 0.06/0.40 Lemma 29: $$fresh8(X, X, Y, Z, W) = $$fresh8(?, ?, Y, Z, W). 0.06/0.40 Proof: 0.06/0.40 $$fresh8(X, X, Y, Z, W) 0.06/0.40 = { by axiom 5 (prove) } 0.06/0.40 $$fresh10(parent(Y), $$true2, Y, Z, W) 0.06/0.40 = { by axiom 5 (prove) } 0.06/0.40 $$fresh8(?, ?, Y, Z, W) 0.06/0.40 0.06/0.40 Lemma 30: $$fresh7(X, X, Y, Z, W) = $$fresh7(?, ?, Y, Z, W). 0.06/0.40 Proof: 0.06/0.40 $$fresh7(X, X, Y, Z, W) 0.06/0.40 = { by axiom 6 (prove) } 0.06/0.40 $$fresh8(parent(Z), $$true2, Y, Z, W) 0.06/0.40 = { by axiom 6 (prove) } 0.06/0.40 $$fresh7(?, ?, Y, Z, W) 0.06/0.40 0.06/0.40 Lemma 31: $$fresh2(X, X, Y, Z, W) = $$fresh2(?, ?, Y, Z, W). 0.06/0.40 Proof: 0.06/0.40 $$fresh2(X, X, Y, Z, W) 0.06/0.40 = { by axiom 11 (prove_1) } 0.06/0.40 $$fresh4(parent(Y), $$true2, Y, Z, W) 0.06/0.40 = { by axiom 11 (prove_1) } 0.06/0.40 $$fresh2(?, ?, Y, Z, W) 0.06/0.40 0.06/0.40 Lemma 32: $$fresh(X, X, Y, Z, W) = $$fresh(?, ?, Y, Z, W). 0.06/0.40 Proof: 0.06/0.40 $$fresh(X, X, Y, Z, W) 0.06/0.40 = { by axiom 12 (prove_1) } 0.06/0.40 $$fresh2(parent(Z), $$true2, Y, Z, W) 0.06/0.40 = { by axiom 12 (prove_1) } 0.06/0.40 $$fresh(?, ?, Y, Z, W) 0.06/0.40 0.06/0.40 Lemma 33: patricide(Oedipus) = $$true2. 0.06/0.40 Proof: 0.06/0.40 patricide(Oedipus) 0.06/0.40 = { by axiom 25 (background_1) } 0.06/0.40 patricide(sK2_background_E) 0.06/0.40 = { by axiom 13 (background_13) } 0.06/0.40 $$true2 0.06/0.40 0.06/0.40 Lemma 34: relation(Oedipus, of, Polyneikes) = $$true2. 0.06/0.40 Proof: 0.06/0.40 relation(Oedipus, of, Polyneikes) 0.06/0.41 = { by axiom 26 (background) } 0.06/0.41 relation(sK4_background_C, of, Polyneikes) 0.06/0.41 = { by axiom 19 (background_7) } 0.06/0.41 $$true2 0.06/0.41 0.06/0.41 Lemma 35: $$fresh8(?, ?, Iokaste, X, Y) = $$fresh10(?, ?, Iokaste, X, Y). 0.06/0.41 Proof: 0.06/0.41 $$fresh8(?, ?, Iokaste, X, Y) 0.06/0.41 = { by axiom 23 (background_3) } 0.06/0.41 $$fresh8(?, ?, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 5 (prove) } 0.06/0.41 $$fresh10(parent(sK5_background_B), $$true2, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 16 (background_10) } 0.06/0.41 $$fresh10($$true2, $$true2, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 4 (prove) } 0.06/0.41 $$fresh9(relation(sK5_background_B, of, X), $$true2, sK5_background_B, Y) 0.06/0.41 = { by axiom 4 (prove) } 0.06/0.41 $$fresh10(?, ?, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 23 (background_3) } 0.06/0.41 $$fresh10(?, ?, Iokaste, X, Y) 0.06/0.41 0.06/0.41 Lemma 36: $$fresh2(?, ?, Iokaste, X, Y) = $$fresh4(?, ?, Iokaste, X, Y). 0.06/0.41 Proof: 0.06/0.41 $$fresh2(?, ?, Iokaste, X, Y) 0.06/0.41 = { by axiom 23 (background_3) } 0.06/0.41 $$fresh2(?, ?, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 11 (prove_1) } 0.06/0.41 $$fresh4(parent(sK5_background_B), $$true2, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 16 (background_10) } 0.06/0.41 $$fresh4($$true2, $$true2, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 10 (prove_1) } 0.06/0.41 $$fresh3(relation(sK5_background_B, of, X), $$true2, sK5_background_B, Y) 0.06/0.41 = { by axiom 10 (prove_1) } 0.06/0.41 $$fresh4(?, ?, sK5_background_B, X, Y) 0.06/0.41 = { by axiom 23 (background_3) } 0.06/0.41 $$fresh4(?, ?, Iokaste, X, Y) 0.06/0.41 0.06/0.41 Lemma 37: patricide(Polyneikes) = $$true2. 0.06/0.41 Proof: 0.06/0.41 patricide(Polyneikes) 0.06/0.41 = { by axiom 1 (prove) } 0.06/0.41 patricide($$fresh11(Iokaste, Iokaste, Polyneikes)) 0.06/0.41 = { by axiom 3 (prove) } 0.06/0.41 patricide($$fresh12($$true2, $$true2, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by lemma 34 } 0.06/0.41 patricide($$fresh12(relation(Oedipus, of, Polyneikes), $$true2, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by axiom 27 (prove) } 0.06/0.41 patricide($$fresh7(patricide(Oedipus), $$true2, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by lemma 33 } 0.06/0.41 patricide($$fresh7($$true2, $$true2, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by lemma 30 } 0.06/0.41 patricide($$fresh7(?, ?, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by axiom 26 (background) } 0.06/0.41 patricide($$fresh7(?, ?, Iokaste, sK4_background_C, Polyneikes)) 0.06/0.41 = { by axiom 6 (prove) } 0.06/0.41 patricide($$fresh8(parent(sK4_background_C), $$true2, Iokaste, sK4_background_C, Polyneikes)) 0.06/0.41 = { by axiom 15 (background_11) } 0.06/0.41 patricide($$fresh8($$true2, $$true2, Iokaste, sK4_background_C, Polyneikes)) 0.06/0.41 = { by lemma 29 } 0.06/0.41 patricide($$fresh8(?, ?, Iokaste, sK4_background_C, Polyneikes)) 0.06/0.41 = { by axiom 26 (background) } 0.06/0.41 patricide($$fresh8(?, ?, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by lemma 35 } 0.06/0.41 patricide($$fresh10(?, ?, Iokaste, Oedipus, Polyneikes)) 0.06/0.41 = { by axiom 24 (background_2) } 0.06/0.41 patricide($$fresh10(?, ?, sK6_background_A, Oedipus, Polyneikes)) 0.06/0.41 = { by axiom 4 (prove) } 0.06/0.41 patricide($$fresh9(relation(sK6_background_A, of, Oedipus), $$true2, sK6_background_A, Polyneikes)) 0.06/0.41 = { by axiom 21 (background_5) } 0.06/0.41 patricide($$fresh9($$true2, $$true2, sK6_background_A, Polyneikes)) 0.06/0.41 = { by axiom 2 (prove) } 0.06/0.41 patricide(sK1_prove_E(Polyneikes)) 0.06/0.41 = { by axiom 7 (prove_1) } 0.06/0.41 $$fresh3($$true2, $$true2, sK6_background_A, Polyneikes) 0.06/0.41 = { by axiom 21 (background_5) } 0.06/0.41 $$fresh3(relation(sK6_background_A, of, Oedipus), $$true2, sK6_background_A, Polyneikes) 0.06/0.41 = { by axiom 10 (prove_1) } 0.06/0.41 $$fresh4(?, ?, sK6_background_A, Oedipus, Polyneikes) 0.06/0.41 = { by axiom 24 (background_2) } 0.06/0.42 $$fresh4(?, ?, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by lemma 36 } 0.06/0.42 $$fresh2(?, ?, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by axiom 26 (background) } 0.06/0.42 $$fresh2(?, ?, Iokaste, sK4_background_C, Polyneikes) 0.06/0.42 = { by lemma 31 } 0.06/0.42 $$fresh2($$true2, $$true2, Iokaste, sK4_background_C, Polyneikes) 0.06/0.42 = { by axiom 15 (background_11) } 0.06/0.42 $$fresh2(parent(sK4_background_C), $$true2, Iokaste, sK4_background_C, Polyneikes) 0.06/0.42 = { by axiom 12 (prove_1) } 0.06/0.42 $$fresh(?, ?, Iokaste, sK4_background_C, Polyneikes) 0.06/0.42 = { by axiom 26 (background) } 0.06/0.42 $$fresh(?, ?, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by lemma 32 } 0.06/0.42 $$fresh($$true2, $$true2, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by lemma 33 } 0.06/0.42 $$fresh(patricide(Oedipus), $$true2, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by axiom 28 (prove_1) } 0.06/0.42 $$fresh6(relation(Oedipus, of, Polyneikes), $$true2, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by lemma 34 } 0.06/0.42 $$fresh6($$true2, $$true2, Iokaste, Oedipus, Polyneikes) 0.06/0.42 = { by axiom 9 (prove_1) } 0.06/0.42 $$fresh5(Iokaste, Iokaste, Polyneikes) 0.06/0.42 = { by axiom 8 (prove_1) } 0.06/0.44 $$true2 0.06/0.44 0.06/0.44 Goal 1 (background_14): tuple(Thersandros, patricide(X)) = tuple(X, $$true2). 0.06/0.44 The goal is true when: 0.06/0.44 X = Thersandros 0.06/0.44 0.06/0.44 Proof: 0.06/0.44 tuple(Thersandros, patricide(Thersandros)) 0.06/0.44 = { by axiom 1 (prove) } 0.06/0.44 tuple(Thersandros, patricide($$fresh11(Iokaste, Iokaste, Thersandros))) 0.06/0.44 = { by axiom 3 (prove) } 0.06/0.44 tuple(Thersandros, patricide($$fresh12($$true2, $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 18 (background_8) } 0.06/0.44 tuple(Thersandros, patricide($$fresh12(relation(sK3_background_D, of, Thersandros), $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 27 (prove) } 0.06/0.44 tuple(Thersandros, patricide($$fresh7(patricide(sK3_background_D), $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, patricide($$fresh7(patricide(Polyneikes), $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by lemma 37 } 0.06/0.44 tuple(Thersandros, patricide($$fresh7($$true2, $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, patricide($$fresh7($$true2, $$true2, Iokaste, Polyneikes, Thersandros))) 0.06/0.44 = { by lemma 30 } 0.06/0.44 tuple(Thersandros, patricide($$fresh7(?, ?, Iokaste, Polyneikes, Thersandros))) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, patricide($$fresh7(?, ?, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 6 (prove) } 0.06/0.44 tuple(Thersandros, patricide($$fresh8(parent(sK3_background_D), $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 14 (background_12) } 0.06/0.44 tuple(Thersandros, patricide($$fresh8($$true2, $$true2, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by lemma 29 } 0.06/0.44 tuple(Thersandros, patricide($$fresh8(?, ?, Iokaste, sK3_background_D, Thersandros))) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, patricide($$fresh8(?, ?, Iokaste, Polyneikes, Thersandros))) 0.06/0.44 = { by lemma 35 } 0.06/0.44 tuple(Thersandros, patricide($$fresh10(?, ?, Iokaste, Polyneikes, Thersandros))) 0.06/0.44 = { by axiom 23 (background_3) } 0.06/0.44 tuple(Thersandros, patricide($$fresh10(?, ?, sK5_background_B, Polyneikes, Thersandros))) 0.06/0.44 = { by axiom 4 (prove) } 0.06/0.44 tuple(Thersandros, patricide($$fresh9(relation(sK5_background_B, of, Polyneikes), $$true2, sK5_background_B, Thersandros))) 0.06/0.44 = { by axiom 20 (background_6) } 0.06/0.44 tuple(Thersandros, patricide($$fresh9($$true2, $$true2, sK5_background_B, Thersandros))) 0.06/0.44 = { by axiom 2 (prove) } 0.06/0.44 tuple(Thersandros, patricide(sK1_prove_E(Thersandros))) 0.06/0.44 = { by axiom 7 (prove_1) } 0.06/0.44 tuple(Thersandros, $$fresh3($$true2, $$true2, sK5_background_B, Thersandros)) 0.06/0.44 = { by axiom 20 (background_6) } 0.06/0.44 tuple(Thersandros, $$fresh3(relation(sK5_background_B, of, Polyneikes), $$true2, sK5_background_B, Thersandros)) 0.06/0.44 = { by axiom 10 (prove_1) } 0.06/0.44 tuple(Thersandros, $$fresh4(?, ?, sK5_background_B, Polyneikes, Thersandros)) 0.06/0.44 = { by axiom 23 (background_3) } 0.06/0.44 tuple(Thersandros, $$fresh4(?, ?, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by lemma 36 } 0.06/0.44 tuple(Thersandros, $$fresh2(?, ?, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, $$fresh2(?, ?, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by lemma 31 } 0.06/0.44 tuple(Thersandros, $$fresh2($$true2, $$true2, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 14 (background_12) } 0.06/0.44 tuple(Thersandros, $$fresh2(parent(sK3_background_D), $$true2, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 12 (prove_1) } 0.06/0.44 tuple(Thersandros, $$fresh(?, ?, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, $$fresh(?, ?, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by lemma 32 } 0.06/0.44 tuple(Thersandros, $$fresh($$true2, $$true2, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by lemma 37 } 0.06/0.44 tuple(Thersandros, $$fresh(patricide(Polyneikes), $$true2, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, $$fresh(patricide(sK3_background_D), $$true2, Iokaste, Polyneikes, Thersandros)) 0.06/0.44 = { by axiom 22 (background_4) } 0.06/0.44 tuple(Thersandros, $$fresh(patricide(sK3_background_D), $$true2, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 28 (prove_1) } 0.06/0.44 tuple(Thersandros, $$fresh6(relation(sK3_background_D, of, Thersandros), $$true2, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 18 (background_8) } 0.06/0.44 tuple(Thersandros, $$fresh6($$true2, $$true2, Iokaste, sK3_background_D, Thersandros)) 0.06/0.44 = { by axiom 9 (prove_1) } 0.06/0.44 tuple(Thersandros, $$fresh5(Iokaste, Iokaste, Thersandros)) 0.06/0.44 = { by axiom 8 (prove_1) } 0.06/0.44 tuple(Thersandros, $$true2) 0.06/0.44 % SZS output end Proof 0.06/0.44 0.06/0.44 RESULT: Theorem (the conjecture is true). 0.06/0.46 EOF