0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.13/0.34 % Computer : n026.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Thu Jul 2 09:01:09 EDT 2020 0.13/0.35 % CPUTime : 320.36/40.61 % SZS status Theorem 320.36/40.61 320.36/40.61 % SZS output start Proof 320.36/40.61 Take the following subset of the input axioms: 321.00/40.65 fof(goals, conjecture, ![X2, X3, X4, X5]: (d(product(X2, X4), product(X3, X5)) <= (d(X4, X5) & d(X2, X3)))). 321.00/40.65 fof(sos01, axiom, ![A, C, B]: product(A, product(B, C))=product(product(A, B), C)). 321.00/40.65 fof(sos02, axiom, ![A]: A=product(A, A)). 321.00/40.65 fof(sos03, axiom, ![X0, X1]: ((X1=product(X1, product(X0, X1)) & product(X0, product(X1, X0))=X0) <=> d(X0, X1))). 321.00/40.65 321.00/40.65 Now clausify the problem and encode Horn clauses using encoding 3 of 321.00/40.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 321.00/40.65 We repeatedly replace C & s=t => u=v by the two clauses: 321.00/40.65 fresh(y, y, x1...xn) = u 321.00/40.65 C => fresh(s, t, x1...xn) = v 321.00/40.65 where fresh is a fresh function symbol and x1..xn are the free 321.00/40.65 variables of u and v. 321.00/40.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the 321.00/40.65 input problem has no model of domain size 1). 321.00/40.65 321.00/40.65 The encoding turns the above axioms into the following unit equations and goals: 321.00/40.65 321.00/40.65 Axiom 1 (sos03): fresh3(X, X, Y, Z) = d(Y, Z). 321.00/40.65 Axiom 2 (sos03): fresh4(X, X, Y, Z) = true. 321.00/40.65 Axiom 3 (sos03_1): fresh(X, X, Y, Z) = Y. 321.00/40.65 Axiom 4 (sos03_2): fresh2(X, X, Y, Z) = Z. 321.00/40.65 Axiom 5 (sos01): product(X, product(Y, Z)) = product(product(X, Y), Z). 321.00/40.65 Axiom 6 (sos03_2): fresh2(d(X, Y), true, X, Y) = product(Y, product(X, Y)). 321.00/40.65 Axiom 7 (sos03_1): fresh(d(X, Y), true, X, Y) = product(X, product(Y, X)). 321.00/40.65 Axiom 8 (sos03): fresh3(X, product(X, product(Y, X)), Y, X) = fresh4(product(Y, product(X, Y)), Y, Y, X). 321.00/40.65 Axiom 9 (sos02): X = product(X, X). 321.00/40.65 Axiom 10 (goals): d(sK4_goals_X4, sK3_goals_X5) = true. 321.00/40.65 Axiom 11 (goals_1): d(sK2_goals_X2, sK1_goals_X3) = true. 321.00/40.65 321.00/40.65 Lemma 12: product(sK4_goals_X4, product(sK3_goals_X5, sK4_goals_X4)) = sK4_goals_X4. 321.00/40.65 Proof: 321.00/40.65 product(sK4_goals_X4, product(sK3_goals_X5, sK4_goals_X4)) 321.00/40.65 = { by axiom 7 (sos03_1) } 321.00/40.65 fresh(d(sK4_goals_X4, sK3_goals_X5), true, sK4_goals_X4, sK3_goals_X5) 321.00/40.65 = { by axiom 10 (goals) } 321.00/40.65 fresh(true, true, sK4_goals_X4, sK3_goals_X5) 321.00/40.65 = { by axiom 3 (sos03_1) } 321.00/40.65 sK4_goals_X4 321.00/40.65 321.00/40.65 Lemma 13: product(sK4_goals_X4, product(sK3_goals_X5, product(sK4_goals_X4, X))) = product(sK4_goals_X4, X). 321.00/40.65 Proof: 321.00/40.65 product(sK4_goals_X4, product(sK3_goals_X5, product(sK4_goals_X4, X))) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.65 product(sK4_goals_X4, product(product(sK3_goals_X5, sK4_goals_X4), X)) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.65 product(product(sK4_goals_X4, product(sK3_goals_X5, sK4_goals_X4)), X) 321.00/40.65 = { by lemma 12 } 321.00/40.65 product(sK4_goals_X4, X) 321.00/40.65 321.00/40.65 Lemma 14: product(Z, product(Y, product(Z, product(Y, X)))) = product(Z, product(Y, X)). 321.00/40.65 Proof: 321.00/40.65 product(Z, product(Y, product(Z, product(Y, X)))) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.65 product(Z, product(Y, product(product(Z, Y), X))) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.65 product(product(Z, Y), product(product(Z, Y), X)) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.65 product(product(product(Z, Y), product(Z, Y)), X) 321.00/40.65 = { by axiom 9 (sos02) } 321.00/40.65 product(product(Z, Y), X) 321.00/40.65 = { by axiom 5 (sos01) } 321.00/40.66 product(Z, product(Y, X)) 321.00/40.66 321.00/40.66 Lemma 15: product(W, product(Z, product(Y, product(W, product(Z, product(Y, X)))))) = product(W, product(Z, product(Y, X))). 321.00/40.66 Proof: 321.00/40.66 product(W, product(Z, product(Y, product(W, product(Z, product(Y, X)))))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(W, product(Z, product(Y, product(product(W, Z), product(Y, X))))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(W, Z), product(Y, product(product(W, Z), product(Y, X)))) 321.00/40.66 = { by lemma 14 } 321.00/40.66 product(product(W, Z), product(Y, X)) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(W, product(Z, product(Y, X))) 321.00/40.66 321.00/40.66 Lemma 16: product(sK2_goals_X2, product(sK1_goals_X3, product(sK2_goals_X2, X))) = product(sK2_goals_X2, X). 321.00/40.66 Proof: 321.00/40.66 product(sK2_goals_X2, product(sK1_goals_X3, product(sK2_goals_X2, X))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(sK2_goals_X2, product(product(sK1_goals_X3, sK2_goals_X2), X)) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(sK2_goals_X2, product(sK1_goals_X3, sK2_goals_X2)), X) 321.00/40.66 = { by axiom 7 (sos03_1) } 321.00/40.66 product(fresh(d(sK2_goals_X2, sK1_goals_X3), true, sK2_goals_X2, sK1_goals_X3), X) 321.00/40.66 = { by axiom 11 (goals_1) } 321.00/40.66 product(fresh(true, true, sK2_goals_X2, sK1_goals_X3), X) 321.00/40.66 = { by axiom 3 (sos03_1) } 321.00/40.66 product(sK2_goals_X2, X) 321.00/40.66 321.00/40.66 Lemma 17: product(Y, product(sK2_goals_X2, product(sK1_goals_X3, product(Y, product(sK2_goals_X2, X))))) = product(Y, product(sK2_goals_X2, X)). 321.00/40.66 Proof: 321.00/40.66 product(Y, product(sK2_goals_X2, product(sK1_goals_X3, product(Y, product(sK2_goals_X2, X))))) 321.00/40.66 = { by lemma 16 } 321.00/40.66 product(Y, product(sK2_goals_X2, product(sK1_goals_X3, product(Y, product(sK2_goals_X2, product(sK1_goals_X3, product(sK2_goals_X2, X))))))) 321.00/40.66 = { by lemma 15 } 321.00/40.66 product(Y, product(sK2_goals_X2, product(sK1_goals_X3, product(sK2_goals_X2, X)))) 321.00/40.66 = { by lemma 16 } 321.00/40.66 product(Y, product(sK2_goals_X2, X)) 321.00/40.66 321.00/40.66 Lemma 18: product(Y, product(X, product(Y, X))) = product(Y, X). 321.00/40.66 Proof: 321.00/40.66 product(Y, product(X, product(Y, X))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(Y, X), product(Y, X)) 321.00/40.66 = { by axiom 9 (sos02) } 321.00/40.66 product(Y, X) 321.00/40.66 321.00/40.66 Lemma 19: product(Z, product(Y, product(X, product(Z, product(Y, X))))) = product(Z, product(Y, X)). 321.00/40.66 Proof: 321.00/40.66 product(Z, product(Y, product(X, product(Z, product(Y, X))))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(Z, product(Y, product(X, product(product(Z, Y), X)))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(Z, Y), product(X, product(product(Z, Y), X))) 321.00/40.66 = { by lemma 18 } 321.00/40.66 product(product(Z, Y), X) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(Z, product(Y, X)) 321.00/40.66 321.00/40.66 Lemma 20: product(W, product(Z, product(Y, product(X, product(W, product(Z, product(Y, X))))))) = product(W, product(Z, product(Y, X))). 321.00/40.66 Proof: 321.00/40.66 product(W, product(Z, product(Y, product(X, product(W, product(Z, product(Y, X))))))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(W, product(Z, product(Y, product(X, product(product(W, Z), product(Y, X)))))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(W, Z), product(Y, product(X, product(product(W, Z), product(Y, X))))) 321.00/40.66 = { by lemma 19 } 321.00/40.66 product(product(W, Z), product(Y, X)) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(W, product(Z, product(Y, X))) 321.00/40.66 321.00/40.66 Lemma 21: product(sK3_goals_X5, product(sK4_goals_X4, sK3_goals_X5)) = sK3_goals_X5. 321.00/40.66 Proof: 321.00/40.66 product(sK3_goals_X5, product(sK4_goals_X4, sK3_goals_X5)) 321.00/40.66 = { by axiom 6 (sos03_2) } 321.00/40.66 fresh2(d(sK4_goals_X4, sK3_goals_X5), true, sK4_goals_X4, sK3_goals_X5) 321.00/40.66 = { by axiom 10 (goals) } 321.00/40.66 fresh2(true, true, sK4_goals_X4, sK3_goals_X5) 321.00/40.66 = { by axiom 4 (sos03_2) } 321.00/40.66 sK3_goals_X5 321.00/40.66 321.00/40.66 Lemma 22: product(sK3_goals_X5, product(sK4_goals_X4, product(sK3_goals_X5, X))) = product(sK3_goals_X5, X). 321.00/40.66 Proof: 321.00/40.66 product(sK3_goals_X5, product(sK4_goals_X4, product(sK3_goals_X5, X))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(sK3_goals_X5, product(product(sK4_goals_X4, sK3_goals_X5), X)) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(sK3_goals_X5, product(sK4_goals_X4, sK3_goals_X5)), X) 321.00/40.66 = { by lemma 21 } 321.00/40.66 product(sK3_goals_X5, X) 321.00/40.66 321.00/40.66 Lemma 23: product(sK1_goals_X3, product(sK2_goals_X2, product(sK1_goals_X3, X))) = product(sK1_goals_X3, X). 321.00/40.66 Proof: 321.00/40.66 product(sK1_goals_X3, product(sK2_goals_X2, product(sK1_goals_X3, X))) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(sK1_goals_X3, product(product(sK2_goals_X2, sK1_goals_X3), X)) 321.00/40.66 = { by axiom 5 (sos01) } 321.00/40.66 product(product(sK1_goals_X3, product(sK2_goals_X2, sK1_goals_X3)), X) 321.00/40.66 = { by axiom 6 (sos03_2) } 321.00/40.66 product(fresh2(d(sK2_goals_X2, sK1_goals_X3), true, sK2_goals_X2, sK1_goals_X3), X) 321.00/40.66 = { by axiom 11 (goals_1) } 321.00/40.66 product(fresh2(true, true, sK2_goals_X2, sK1_goals_X3), X) 321.00/40.66 = { by axiom 4 (sos03_2) } 321.00/40.66 product(sK1_goals_X3, X) 321.00/40.66 321.00/40.66 Lemma 24: product(Y, product(sK1_goals_X3, product(sK2_goals_X2, product(Y, product(sK1_goals_X3, X))))) = product(Y, product(sK1_goals_X3, X)). 321.00/40.66 Proof: 321.00/40.66 product(Y, product(sK1_goals_X3, product(sK2_goals_X2, product(Y, product(sK1_goals_X3, X))))) 321.00/40.66 = { by lemma 23 } 321.00/40.66 product(Y, product(sK1_goals_X3, product(sK2_goals_X2, product(Y, product(sK1_goals_X3, product(sK2_goals_X2, product(sK1_goals_X3, X))))))) 321.00/40.66 = { by lemma 15 } 321.00/40.66 product(Y, product(sK1_goals_X3, product(sK2_goals_X2, product(sK1_goals_X3, X)))) 321.00/40.66 = { by lemma 23 } 321.00/40.70 product(Y, product(sK1_goals_X3, X)) 321.00/40.70 321.00/40.70 Goal 1 (goals_2): d(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)) = true. 321.00/40.70 Proof: 321.00/40.70 d(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 12 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, sK4_goals_X4))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 15 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, sK4_goals_X4)))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 12 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4)))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 17 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 20 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 17 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4)))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 13 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4)))))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 15 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 13 } 321.00/40.70 d(product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by axiom 5 (sos01) } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4)))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 19 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, sK3_goals_X5)) 321.00/40.70 = { by lemma 21 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, sK3_goals_X5)))) 321.00/40.70 = { by lemma 15 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, sK3_goals_X5))))))) 321.00/40.70 = { by lemma 21 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by lemma 24 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5)))))))) 321.00/40.70 = { by lemma 20 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5)))))))))))) 321.00/40.70 = { by lemma 24 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5))))))))) 321.00/40.70 = { by lemma 22 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5))))))))))) 321.00/40.70 = { by lemma 15 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK4_goals_X4, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5)))))))) 321.00/40.70 = { by lemma 22 } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, product(sK4_goals_X4, product(sK1_goals_X3, sK3_goals_X5)))))) 321.00/40.70 = { by axiom 5 (sos01) } 321.00/40.70 d(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by axiom 1 (sos03) } 321.00/40.70 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by lemma 18 } 321.00/40.70 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, sK3_goals_X5), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by axiom 5 (sos01) } 321.00/40.70 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by axiom 5 (sos01) } 321.00/40.70 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK1_goals_X3, product(product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.70 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by lemma 19 } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by lemma 14 } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4)), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(sK2_goals_X2, sK4_goals_X4))))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, sK3_goals_X5), product(sK2_goals_X2, sK4_goals_X4)))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(sK3_goals_X5, product(product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)), product(sK2_goals_X2, sK4_goals_X4))))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, product(product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))), product(sK2_goals_X2, sK4_goals_X4)))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh3(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 8 (sos03) } 321.00/40.71 fresh4(product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by lemma 18 } 321.00/40.71 fresh4(product(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh4(product(product(sK2_goals_X2, sK4_goals_X4), product(product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4)), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4)))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 5 (sos01) } 321.00/40.71 fresh4(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by lemma 14 } 321.00/40.71 fresh4(product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(product(sK2_goals_X2, sK4_goals_X4), product(product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5)))), product(sK2_goals_X2, sK4_goals_X4))), product(sK1_goals_X3, product(sK3_goals_X5, product(product(sK2_goals_X2, sK4_goals_X4), product(sK1_goals_X3, sK3_goals_X5))))) 321.00/40.71 = { by axiom 2 (sos03) } 321.00/40.71 true 321.00/40.71 % SZS output end Proof 321.00/40.71 321.00/40.71 RESULT: Theorem (the conjecture is true). 321.00/40.74 EOF