0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.14/0.36 % Computer : n025.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Thu Jul 2 07:31:03 EDT 2020 0.14/0.36 % CPUTime : 0.22/0.45 % SZS status Theorem 0.22/0.45 0.22/0.45 % SZS output start Proof 0.22/0.45 Take the following subset of the input axioms: 0.22/0.45 fof(ax55, axiom, ![U, V, W, X, Y]: insert_pq(i(triple(U, V, W)), X)=i(triple(U, insert_slb(V, pair(X, Y)), W))). 0.22/0.45 fof(l2_co, conjecture, ![U]: (![Z, X1, X2, X3, X4, X5]: i(triple(Z, insert_slb(U, pair(X4, X5)), X2))=i(triple(X1, insert_slb(U, pair(X4, X5)), X3)) <= ![V, W, X, Y]: i(triple(V, U, X))=i(triple(W, U, Y)))). 0.22/0.45 0.22/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of 0.22/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 0.22/0.45 We repeatedly replace C & s=t => u=v by the two clauses: 0.22/0.45 fresh(y, y, x1...xn) = u 0.22/0.45 C => fresh(s, t, x1...xn) = v 0.22/0.45 where fresh is a fresh function symbol and x1..xn are the free 0.22/0.45 variables of u and v. 0.22/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the 0.22/0.45 input problem has no model of domain size 1). 0.22/0.45 0.22/0.45 The encoding turns the above axioms into the following unit equations and goals: 0.22/0.45 0.22/0.45 Axiom 1 (ax55): insert_pq(i(triple(X, Y, Z)), W) = i(triple(X, insert_slb(Y, pair(W, V)), Z)). 0.22/0.45 Axiom 2 (l2_co): i(triple(X, sK7_l2_co_U, Y)) = i(triple(Z, sK7_l2_co_U, W)). 0.22/0.45 0.22/0.45 Lemma 3: i(triple(X, sK7_l2_co_U, Y)) = i(triple(?, sK7_l2_co_U, ?)). 0.22/0.45 Proof: 0.22/0.45 i(triple(X, sK7_l2_co_U, Y)) 0.22/0.45 = { by axiom 2 (l2_co) } 0.22/0.45 i(triple(Z, sK7_l2_co_U, W)) 0.22/0.45 = { by axiom 2 (l2_co) } 0.22/0.45 i(triple(?, sK7_l2_co_U, ?)) 0.22/0.45 0.22/0.45 Goal 1 (l2_co_1): i(triple(sK6_l2_co_Z, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK4_l2_co_X2)) = i(triple(sK5_l2_co_X1, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK3_l2_co_X3)). 0.22/0.45 Proof: 0.22/0.45 i(triple(sK6_l2_co_Z, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK4_l2_co_X2)) 0.22/0.45 = { by axiom 1 (ax55) } 0.22/0.45 insert_pq(i(triple(sK6_l2_co_Z, sK7_l2_co_U, sK4_l2_co_X2)), sK2_l2_co_X4) 0.22/0.45 = { by lemma 3 } 0.22/0.46 insert_pq(i(triple(?, sK7_l2_co_U, ?)), sK2_l2_co_X4) 0.22/0.46 = { by lemma 3 } 0.22/0.46 insert_pq(i(triple(sK5_l2_co_X1, sK7_l2_co_U, sK3_l2_co_X3)), sK2_l2_co_X4) 0.22/0.46 = { by axiom 1 (ax55) } 0.22/0.46 i(triple(sK5_l2_co_X1, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK3_l2_co_X3)) 0.22/0.46 % SZS output end Proof 0.22/0.46 0.22/0.46 RESULT: Theorem (the conjecture is true). 0.22/0.46 EOF