0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.10 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.30 % Computer : n012.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 960 0.10/0.30 % WCLimit : 120 0.10/0.30 % DateTime : Thu Jul 2 06:51:21 EDT 2020 0.10/0.30 % CPUTime : 11.71/1.81 % SZS status Theorem 11.71/1.81 11.71/1.81 % SZS output start Proof 11.71/1.81 Take the following subset of the input axioms: 11.71/1.82 fof(less_entry_point_neg_neg, axiom, ![X, Y, RDN_X, RDN_Y]: ((rdn_translate(Y, rdn_neg(RDN_Y)) & (rdn_translate(X, rdn_neg(RDN_X)) & rdn_positive_less(RDN_Y, RDN_X))) => less(X, Y))). 11.71/1.82 fof(less_property, axiom, ![X, Y]: ((X!=Y & ~less(Y, X)) <=> less(X, Y))). 11.71/1.82 fof(rdn_positive_less23, axiom, rdn_positive_less(rdnn(n2), rdnn(n3))). 11.71/1.82 fof(rdnn2, axiom, rdn_translate(nn2, rdn_neg(rdnn(n2)))). 11.71/1.82 fof(rdnn3, axiom, rdn_translate(nn3, rdn_neg(rdnn(n3)))). 11.71/1.82 fof(something_less_nn2, conjecture, ?[X]: less(X, nn2)). 11.71/1.82 11.71/1.82 Now clausify the problem and encode Horn clauses using encoding 3 of 11.71/1.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 11.71/1.82 We repeatedly replace C & s=t => u=v by the two clauses: 11.71/1.82 fresh(y, y, x1...xn) = u 11.71/1.82 C => fresh(s, t, x1...xn) = v 11.71/1.82 where fresh is a fresh function symbol and x1..xn are the free 11.71/1.82 variables of u and v. 11.71/1.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the 11.71/1.82 input problem has no model of domain size 1). 11.71/1.82 11.71/1.82 The encoding turns the above axioms into the following unit equations and goals: 11.71/1.82 11.71/1.82 Axiom 1 (less_entry_point_neg_neg): fresh26(X, X, Y, Z, W, V) = less(Y, Z). 11.71/1.82 Axiom 2 (less_entry_point_neg_neg): fresh69(X, X, Y, Z) = true2. 11.71/1.82 Axiom 3 (less_entry_point_neg_neg): fresh68(X, X, Y, Z, W, V) = fresh69(rdn_positive_less(V, W), true2, Y, Z). 11.71/1.82 Axiom 4 (rdnn2): rdn_translate(nn2, rdn_neg(rdnn(n2))) = true2. 11.71/1.82 Axiom 5 (rdnn3): rdn_translate(nn3, rdn_neg(rdnn(n3))) = true2. 11.71/1.82 Axiom 6 (less_entry_point_neg_neg): fresh68(rdn_translate(X, rdn_neg(Y)), true2, Z, X, W, Y) = fresh26(rdn_translate(Z, rdn_neg(W)), true2, Z, X, W, Y). 11.71/1.82 Axiom 7 (rdn_positive_less23): rdn_positive_less(rdnn(n2), rdnn(n3)) = true2. 11.71/1.82 11.71/1.82 Goal 1 (something_less_nn2): less(X, nn2) = true2. 11.71/1.82 The goal is true when: 11.71/1.82 X = nn3 11.71/1.82 11.71/1.82 Proof: 11.71/1.82 less(nn3, nn2) 11.71/1.82 = { by axiom 1 (less_entry_point_neg_neg) } 11.71/1.82 fresh26(true2, true2, nn3, nn2, rdnn(n3), rdnn(n2)) 11.71/1.82 = { by axiom 5 (rdnn3) } 11.71/1.82 fresh26(rdn_translate(nn3, rdn_neg(rdnn(n3))), true2, nn3, nn2, rdnn(n3), rdnn(n2)) 11.71/1.82 = { by axiom 6 (less_entry_point_neg_neg) } 11.71/1.82 fresh68(rdn_translate(nn2, rdn_neg(rdnn(n2))), true2, nn3, nn2, rdnn(n3), rdnn(n2)) 11.71/1.82 = { by axiom 4 (rdnn2) } 11.71/1.82 fresh68(true2, true2, nn3, nn2, rdnn(n3), rdnn(n2)) 11.71/1.82 = { by axiom 3 (less_entry_point_neg_neg) } 11.71/1.82 fresh69(rdn_positive_less(rdnn(n2), rdnn(n3)), true2, nn3, nn2) 11.71/1.82 = { by axiom 7 (rdn_positive_less23) } 11.71/1.82 fresh69(true2, true2, nn3, nn2) 11.71/1.82 = { by axiom 2 (less_entry_point_neg_neg) } 11.71/1.82 true2 11.71/1.82 % SZS output end Proof 11.71/1.82 11.71/1.82 RESULT: Theorem (the conjecture is true). 11.71/1.83 EOF