0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.09/0.30 % Computer : n031.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Thu Jul 2 08:35:17 EDT 2020 0.09/0.30 % CPUTime : 460.31/58.17 % SZS status Theorem 460.31/58.17 460.31/58.17 % SZS output start Proof 460.31/58.17 Take the following subset of the input axioms: 460.31/58.18 fof(aA2, axiom, ![Y, Z, X, V, Z2, V2]: (~s_e(X, Y, Z2, V2) | (s_e(Z, V, Z2, V2) | ~s_e(X, Y, Z, V)))). 460.31/58.18 fof(aSatz10_12b, axiom, ![Xb, Xa, Xc, Xa1]: (~s_r(Xa, Xb, Xc) | (~s_e(Xa, Xb, Xa1, Xb) | (s_e(Xa, Xc, Xa1, Xc) | ~s_r(Xa1, Xb, Xc))))). 460.31/58.18 fof(aSatz10_12c, conjecture, ![Xb, Xa, Xc, Xa1, Xc1]: (~s_r(Xa1, Xb, Xc1) | (Xc=Xc1 | (midpoint(Xc, Xc1)!=Xb | (s_e(Xa, Xc, Xa1, Xc1) | (~s_e(Xb, Xc, Xb, Xc1) | (~s_e(Xa, Xb, Xa1, Xb) | ~s_r(Xa, Xb, Xc)))))))). 460.56/58.18 fof(aSatz2_2, axiom, ![Xb, Xa, Xc, Xd]: (s_e(Xc, Xd, Xa, Xb) | ~s_e(Xa, Xb, Xc, Xd))). 460.56/58.18 fof(aSatz7_6, axiom, ![Xa, Xp, Xq]: (s(Xa, Xp)=Xq | ~s_m(Xp, Xa, Xq))). 460.56/58.18 fof(aSatz7_7, axiom, ![Xa, Xp]: Xp=s(Xa, s(Xa, Xp))). 460.56/58.18 fof(aSatz8_22, axiom, ![Xb, Xa]: s_m(Xa, midpoint(Xa, Xb), Xb)). 460.56/58.18 fof(aSatz8_4, axiom, ![Xb, Xa, Xc]: (~s_r(Xa, Xb, Xc) | s_r(Xa, Xb, s(Xb, Xc)))). 460.56/58.18 fof(d_Defn8_1, axiom, ![Xb, Xa, Xc]: ((~s_r(Xa, Xb, Xc) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | ~s_e(Xa, Xc, Xa, s(Xb, Xc))))). 460.56/58.18 460.56/58.18 Now clausify the problem and encode Horn clauses using encoding 3 of 460.56/58.18 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 460.56/58.18 We repeatedly replace C & s=t => u=v by the two clauses: 460.56/58.18 fresh(y, y, x1...xn) = u 460.56/58.18 C => fresh(s, t, x1...xn) = v 460.56/58.18 where fresh is a fresh function symbol and x1..xn are the free 460.56/58.18 variables of u and v. 460.56/58.18 A predicate p(X) is encoded as p(X)=true (this is sound, because the 460.56/58.18 input problem has no model of domain size 1). 460.56/58.18 460.56/58.18 The encoding turns the above axioms into the following unit equations and goals: 460.56/58.18 460.56/58.18 Axiom 1 (aA2): fresh183(X, X, Y, Z, W, V, U, T) = s_e(W, V, U, T). 460.56/58.19 Axiom 2 (aA2): fresh184(X, X, Y, Z, W, V) = true2. 460.56/58.19 Axiom 3 (aSatz10_12b): fresh174(X, X, Y, Z, W, V) = s_e(Y, W, V, W). 460.56/58.19 Axiom 4 (aSatz10_12b): fresh284(X, X, Y, Z, W) = true2. 460.56/58.19 Axiom 5 (aSatz10_12b): fresh283(X, X, Y, Z, W, V) = fresh284(s_e(Y, Z, V, Z), true2, Y, W, V). 460.56/58.19 Axiom 6 (aSatz2_2): fresh172(X, X, Y, Z, W, V) = true2. 460.56/58.19 Axiom 7 (aSatz7_6): fresh13(X, X, Y, Z, W) = W. 460.56/58.19 Axiom 8 (aSatz8_4): fresh92(X, X, Y, Z, W) = true2. 460.56/58.19 Axiom 9 (d_Defn8_1_1): fresh35(X, X, Y, Z, W) = true2. 460.56/58.19 Axiom 10 (aA2): fresh183(s_e(X, Y, Z, W), true2, X, Y, V, U, Z, W) = fresh184(s_e(X, Y, V, U), true2, V, U, Z, W). 460.56/58.19 Axiom 11 (aSatz10_12b): fresh283(s_r(X, Y, Z), true2, W, Y, Z, X) = fresh174(s_r(W, Y, Z), true2, W, Y, Z, X). 460.56/58.19 Axiom 12 (aSatz8_4): fresh92(s_r(X, Y, Z), true2, X, Y, Z) = s_r(X, Y, s(Y, Z)). 460.56/58.19 Axiom 13 (aSatz2_2): fresh172(s_e(X, Y, Z, W), true2, X, Y, Z, W) = s_e(Z, W, X, Y). 460.56/58.19 Axiom 14 (aSatz7_7): X = s(Y, s(Y, X)). 460.56/58.19 Axiom 15 (aSatz8_22): s_m(X, midpoint(X, Y), Y) = true2. 460.56/58.19 Axiom 16 (aSatz7_6): fresh13(s_m(X, Y, Z), true2, X, Y, Z) = s(Y, X). 460.56/58.19 Axiom 17 (d_Defn8_1_1): fresh35(s_r(X, Y, Z), true2, X, Y, Z) = s_e(X, Z, X, s(Y, Z)). 460.56/58.19 Axiom 18 (aSatz10_12c): midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1) = sK5_aSatz10_12c_Xb. 460.56/58.19 Axiom 19 (aSatz10_12c_2): s_e(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb) = true2. 460.56/58.19 Axiom 20 (aSatz10_12c_3): s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) = true2. 460.56/58.19 Axiom 21 (aSatz10_12c_4): s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = true2. 460.56/58.19 460.56/58.19 Lemma 22: s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = sK2_aSatz10_12c_Xc1. 460.56/58.19 Proof: 460.56/58.19 s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) 460.56/58.19 = { by axiom 16 (aSatz7_6) } 460.56/58.19 fresh13(s_m(sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 18 (aSatz10_12c) } 460.56/58.19 fresh13(s_m(sK4_aSatz10_12c_Xc, midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1), sK2_aSatz10_12c_Xc1), true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 15 (aSatz8_22) } 460.56/58.19 fresh13(true2, true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 7 (aSatz7_6) } 460.56/58.19 sK2_aSatz10_12c_Xc1 460.56/58.19 460.56/58.19 Lemma 23: s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = true2. 460.56/58.19 Proof: 460.56/58.19 s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) 460.56/58.19 = { by axiom 14 (aSatz7_7) } 460.56/58.19 s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc))) 460.56/58.19 = { by lemma 22 } 460.56/58.19 s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)) 460.56/58.19 = { by axiom 12 (aSatz8_4) } 460.56/58.19 fresh92(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 20 (aSatz10_12c_3) } 460.56/58.19 fresh92(true2, true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 8 (aSatz8_4) } 460.56/58.19 true2 460.56/58.19 460.56/58.19 Goal 1 (aSatz10_12c_6): s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) = true2. 460.56/58.19 Proof: 460.56/58.19 s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 1 (aA2) } 460.56/58.19 fresh183(true2, true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 9 (d_Defn8_1_1) } 460.56/58.19 fresh183(fresh35(true2, true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by lemma 23 } 460.56/58.19 fresh183(fresh35(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 17 (d_Defn8_1_1) } 460.56/58.19 fresh183(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by lemma 22 } 460.56/58.19 fresh183(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 10 (aA2) } 460.56/58.19 fresh184(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 13 (aSatz2_2) } 460.56/58.19 fresh184(fresh172(s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 3 (aSatz10_12b) } 460.56/58.19 fresh184(fresh172(fresh174(true2, true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.19 = { by axiom 21 (aSatz10_12c_4) } 460.56/58.20 fresh184(fresh172(fresh174(s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 11 (aSatz10_12b) } 460.56/58.20 fresh184(fresh172(fresh283(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by lemma 23 } 460.56/58.20 fresh184(fresh172(fresh283(true2, true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 5 (aSatz10_12b) } 460.56/58.20 fresh184(fresh172(fresh284(s_e(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 19 (aSatz10_12c_2) } 460.56/58.20 fresh184(fresh172(fresh284(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 4 (aSatz10_12b) } 460.56/58.20 fresh184(fresh172(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 6 (aSatz2_2) } 460.56/58.20 fresh184(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) 460.56/58.20 = { by axiom 2 (aA2) } 460.56/58.20 true2 460.56/58.20 % SZS output end Proof 460.56/58.20 460.56/58.20 RESULT: Theorem (the conjecture is true). 460.56/58.27 EOF