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 0.09/0.31 % Computer : n020.cluster.edu 0.09/0.31 % Model : x86_64 x86_64 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.31 % Memory : 8042.1875MB 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 960 0.09/0.31 % WCLimit : 120 0.09/0.31 % DateTime : Thu Jul 2 06:49:02 EDT 2020 0.09/0.31 % CPUTime : 14.99/2.30 % SZS status Theorem 14.99/2.30 14.99/2.30 % SZS output start Proof 14.99/2.30 Take the following subset of the input axioms: 14.99/2.32 fof(quaternion_ds1_symm_0401, conjecture, ![M]: (![N]: (((M!=pv57 & ~(pv57=N & M=N)) => a_select3(id_ds1_filter, M, N)=a_select3(id_ds1_filter, N, M)) <= (leq(N, n5) & leq(n0, N))) <= (leq(M, pred(pv57)) & leq(n0, M))) <= (leq(pv5, n998) & (leq(pv58, n5) & (![G, H]: (((pv57=G & gt(pv58, H)) => a_select3(id_ds1_filter, G, H)=a_select3(id_ds1_filter, H, G)) <= (leq(n0, G) & (leq(G, n5) & (leq(H, n5) & leq(n0, H))))) & (![I, J]: ((a_select3(id_ds1_filter, J, I)=a_select3(id_ds1_filter, I, J) <= gt(pv57, I)) <= (leq(I, n5) & (leq(J, n5) & (leq(n0, J) & leq(n0, I))))) & (![K]: ((leq(K, pred(pv57)) & leq(n0, K)) => ![L]: (a_select3(id_ds1_filter, L, K)=a_select3(id_ds1_filter, K, L) <= (leq(L, n5) & leq(n0, L)))) & (![F, E]: (a_select3(pminus_ds1_filter, E, F)=a_select3(pminus_ds1_filter, F, E) <= (leq(E, n5) & (leq(F, n5) & (leq(n0, F) & leq(n0, E))))) & (![C, D]: ((leq(C, n2) & (leq(D, n2) & (leq(n0, D) & leq(n0, C)))) => a_select3(r_ds1_filter, C, D)=a_select3(r_ds1_filter, D, C)) & (![A, B]: (a_select3(q_ds1_filter, B, A)=a_select3(q_ds1_filter, A, B) <= (leq(n0, B) & (leq(B, n5) & (leq(A, n5) & leq(n0, A))))) & (gt(pv58, pv57) & (leq(pv57, n5) & (leq(n0, pv57) & leq(n0, pv5))))))))))))). 14.99/2.32 14.99/2.32 Now clausify the problem and encode Horn clauses using encoding 3 of 14.99/2.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 14.99/2.32 We repeatedly replace C & s=t => u=v by the two clauses: 14.99/2.32 fresh(y, y, x1...xn) = u 14.99/2.32 C => fresh(s, t, x1...xn) = v 14.99/2.32 where fresh is a fresh function symbol and x1..xn are the free 14.99/2.32 variables of u and v. 14.99/2.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the 14.99/2.32 input problem has no model of domain size 1). 14.99/2.32 14.99/2.32 The encoding turns the above axioms into the following unit equations and goals: 14.99/2.32 14.99/2.32 Axiom 1 (quaternion_ds1_symm_0401_15): fresh11(X, X, Y, Z) = a_select3(id_ds1_filter, Y, Z). 14.99/2.32 Axiom 2 (quaternion_ds1_symm_0401_15): fresh56(X, X, Y, Z) = a_select3(id_ds1_filter, Z, Y). 14.99/2.32 Axiom 3 (quaternion_ds1_symm_0401_15): fresh55(X, X, Y, Z) = fresh56(leq(Z, n5), true3, Y, Z). 14.99/2.32 Axiom 4 (quaternion_ds1_symm_0401_15): fresh54(X, X, Y, Z) = fresh55(leq(n0, Y), true3, Y, Z). 14.99/2.32 Axiom 5 (quaternion_ds1_symm_0401_2): leq(n0, sK2_quaternion_ds1_symm_0401_M) = true3. 14.99/2.32 Axiom 6 (quaternion_ds1_symm_0401_3): leq(n0, sK1_quaternion_ds1_symm_0401_N) = true3. 14.99/2.32 Axiom 7 (quaternion_ds1_symm_0401_7): leq(sK2_quaternion_ds1_symm_0401_M, pred(pv57)) = true3. 14.99/2.32 Axiom 8 (quaternion_ds1_symm_0401_8): leq(sK1_quaternion_ds1_symm_0401_N, n5) = true3. 14.99/2.32 Axiom 9 (quaternion_ds1_symm_0401_15): fresh54(leq(n0, X), true3, Y, X) = fresh11(leq(Y, pred(pv57)), true3, Y, X). 14.99/2.32 14.99/2.32 Goal 1 (quaternion_ds1_symm_0401_11): a_select3(id_ds1_filter, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) = a_select3(id_ds1_filter, sK1_quaternion_ds1_symm_0401_N, sK2_quaternion_ds1_symm_0401_M). 14.99/2.32 Proof: 14.99/2.32 a_select3(id_ds1_filter, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 1 (quaternion_ds1_symm_0401_15) } 14.99/2.32 fresh11(true3, true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 7 (quaternion_ds1_symm_0401_7) } 14.99/2.32 fresh11(leq(sK2_quaternion_ds1_symm_0401_M, pred(pv57)), true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 9 (quaternion_ds1_symm_0401_15) } 14.99/2.32 fresh54(leq(n0, sK1_quaternion_ds1_symm_0401_N), true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 6 (quaternion_ds1_symm_0401_3) } 14.99/2.32 fresh54(true3, true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 4 (quaternion_ds1_symm_0401_15) } 14.99/2.32 fresh55(leq(n0, sK2_quaternion_ds1_symm_0401_M), true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 5 (quaternion_ds1_symm_0401_2) } 14.99/2.32 fresh55(true3, true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 3 (quaternion_ds1_symm_0401_15) } 14.99/2.32 fresh56(leq(sK1_quaternion_ds1_symm_0401_N, n5), true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 8 (quaternion_ds1_symm_0401_8) } 14.99/2.32 fresh56(true3, true3, sK2_quaternion_ds1_symm_0401_M, sK1_quaternion_ds1_symm_0401_N) 14.99/2.32 = { by axiom 2 (quaternion_ds1_symm_0401_15) } 14.99/2.33 a_select3(id_ds1_filter, sK1_quaternion_ds1_symm_0401_N, sK2_quaternion_ds1_symm_0401_M) 14.99/2.33 % SZS output end Proof 14.99/2.33 14.99/2.33 RESULT: Theorem (the conjecture is true). 14.99/2.34 EOF