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 0.02/0.23 % Computer : n156.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 05:26:54 CDT 2018 0.02/0.23 % CPUTime : 249.31/249.53 % SZS status Theorem 249.31/249.53 249.31/249.53 % SZS output start Proof 249.31/249.53 Take the following subset of the input axioms: 249.36/249.55 fof(aA1, axiom, ![Y, X]: s_e(X, Y, Y, X)). 249.36/249.55 fof(aA2, axiom, 249.36/249.55 ![Y, Z, X, V, Z2, V2]: 249.36/249.55 (~s_e(X, Y, Z, V) | (~s_e(X, Y, Z2, V2) | s_e(Z, V, Z2, V2)))). 249.36/249.55 fof(aSatz2_2, axiom, 249.36/249.55 ![Xa, Xb, Xc, Xd]: (s_e(Xc, Xd, Xa, Xb) | ~s_e(Xa, Xb, Xc, Xd))). 249.36/249.55 fof(aSatz2_5, axiom, 249.36/249.55 ![Xa, Xb, Xc, Xd]: (~s_e(Xa, Xb, Xc, Xd) | s_e(Xa, Xb, Xd, Xc))). 249.36/249.55 fof(aSatz7_13, axiom, 249.36/249.55 ![Xa, Xp, Xq]: s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))). 249.36/249.55 fof(aSatz7_7, axiom, ![Xa, Xp]: Xp=s(Xa, s(Xa, Xp))). 249.36/249.55 fof(aSatz8_2, conjecture, 249.36/249.55 ![Xa, Xb, Xc]: (s_r(Xc, Xb, Xa) | ~s_r(Xa, Xb, Xc))). 249.36/249.55 fof(d_Defn8_1, axiom, 249.36/249.55 ![Xa, Xb, Xc]: 249.36/249.55 ((s_e(Xa, Xc, Xa, s(Xb, Xc)) | ~s_r(Xa, Xb, Xc)) 249.36/249.55 & (s_r(Xa, Xb, Xc) | ~s_e(Xa, Xc, Xa, s(Xb, Xc))))). 249.36/249.55 249.36/249.55 Now clausify the problem and encode Horn clauses using encoding 3 of 249.36/249.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 249.36/249.55 We repeatedly replace C & s=t => u=v by the two clauses: 249.36/249.55 $$fresh(y, y, x1...xn) = u 249.36/249.55 C => $$fresh(s, t, x1...xn) = v 249.36/249.55 where $$fresh is a fresh function symbol and x1..xn are the free 249.36/249.55 variables of u and v. 249.36/249.55 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 249.36/249.55 input problem has no model of domain size 1). 249.36/249.55 249.36/249.55 The encoding turns the above axioms into the following unit equations and goals: 249.36/249.55 249.36/249.55 Axiom 1 (aA2): $$fresh144(X, X, Y, Z, W, V, U, T) = s_e(W, V, U, T). 249.36/249.55 Axiom 2 (aA2): $$fresh143(X, X, Y, Z, W, V) = $$true2. 249.36/249.55 Axiom 21 (aSatz2_2): $$fresh135(X, X, Y, Z, W, V) = $$true2. 249.36/249.55 Axiom 25 (aSatz2_5): $$fresh131(X, X, Y, Z, W, V) = $$true2. 249.36/249.55 Axiom 188 (d_Defn8_1): $$fresh28(X, X, Y, Z, W) = $$true2. 249.36/249.55 Axiom 196 (d_Defn8_1_1): $$fresh22(X, X, Y, Z, W) = $$true2. 249.36/249.55 Axiom 198 (aA1): s_e(X, Y, Y, X) = $$true2. 249.36/249.55 Axiom 202 (aA2): $$fresh144(s_e(X, Y, Z, W), $$true2, X, Y, V, U, Z, W) = $$fresh143(s_e(X, Y, V, U), $$true2, V, U, Z, W). 249.36/249.55 Axiom 218 (d_Defn8_1_1): $$fresh22(s_r(X, Y, Z), $$true2, X, Y, Z) = s_e(X, Z, X, s(Y, Z)). 249.36/249.55 Axiom 219 (d_Defn8_1): $$fresh28(s_e(X, Y, X, s(Z, Y)), $$true2, X, Z, Y) = s_r(X, Z, Y). 249.36/249.55 Axiom 225 (aSatz2_5): $$fresh131(s_e(X, Y, Z, W), $$true2, X, Y, Z, W) = s_e(X, Y, W, Z). 249.36/249.55 Axiom 291 (aSatz7_7): X = s(Y, s(Y, X)). 249.36/249.55 Axiom 307 (aSatz7_13): s_e(X, Y, s(Z, X), s(Z, Y)) = $$true2. 249.36/249.55 Axiom 310 (aSatz2_2): $$fresh135(s_e(X, Y, Z, W), $$true2, X, Y, Z, W) = s_e(Z, W, X, Y). 249.36/249.57 Axiom 333 (aSatz8_2): s_r(sK3_aSatz8_2_Xa, sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc) = $$true2. 249.36/249.57 249.36/249.57 Goal 1 (aSatz8_2_1): s_r(sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) = $$true2. 249.36/249.57 Proof: 249.36/249.57 s_r(sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 219 (d_Defn8_1) } 249.36/249.57 $$fresh28(s_e(sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 1 (aA2) } 249.36/249.57 $$fresh28($$fresh144($$true2, $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 198 (aA1) } 249.36/249.57 $$fresh28($$fresh144(s_e(s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 202 (aA2) } 249.36/249.57 $$fresh28($$fresh143(s_e(s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 225 (aSatz2_5) } 249.36/249.57 $$fresh28($$fresh143($$fresh131(s_e(s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 1 (aA2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144($$true2, $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 21 (aSatz2_2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144($$fresh135($$true2, $$true2, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc)), $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 196 (d_Defn8_1_1) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144($$fresh135($$fresh22($$true2, $$true2, sK3_aSatz8_2_Xa, sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), $$true2, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc)), $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 333 (aSatz8_2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144($$fresh135($$fresh22(s_r(sK3_aSatz8_2_Xa, sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), $$true2, sK3_aSatz8_2_Xa, sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), $$true2, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc)), $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 218 (d_Defn8_1_1) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144($$fresh135(s_e(sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc)), $$true2, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc)), $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 310 (aSatz2_2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh144(s_e(sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 202 (aA2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh143(s_e(sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 291 (aSatz7_7) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh143(s_e(sK3_aSatz8_2_Xa, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc), s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), s(sK2_aSatz8_2_Xb, s(sK2_aSatz8_2_Xb, sK1_aSatz8_2_Xc))), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 307 (aSatz7_13) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$fresh143($$true2, $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 2 (aA2) } 249.36/249.57 $$fresh28($$fresh143($$fresh131($$true2, $$true2, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa), sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc), $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 25 (aSatz2_5) } 249.36/249.57 $$fresh28($$fresh143($$true2, $$true2, sK1_aSatz8_2_Xc, sK3_aSatz8_2_Xa, sK1_aSatz8_2_Xc, s(sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa)), $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 2 (aA2) } 249.36/249.57 $$fresh28($$true2, $$true2, sK1_aSatz8_2_Xc, sK2_aSatz8_2_Xb, sK3_aSatz8_2_Xa) 249.36/249.57 = { by axiom 188 (d_Defn8_1) } 249.36/249.57 $$true2 249.36/249.57 % SZS output end Proof 249.36/249.57 249.36/249.57 RESULT: Theorem (the conjecture is true). 249.36/249.63 EOF