%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV109+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:31 AM UTC 2025
% Result : Theorem 250.95s 251.12s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWV109+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n012.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Fri Jun 20 09:26:55 EDT 2025
% 0.16/0.32 % CPUTime :
% 250.95/251.12 % SZS status Theorem
% 250.95/251.12 % SZS output start Proof
% 250.95/251.12 tff(leq_type, type, (
% 250.95/251.12 leq: ( $i * $i ) > $o)).
% 250.95/251.12 tff(minus_type, type, (
% 250.95/251.12 minus: ( $i * $i ) > $i)).
% 250.95/251.12 tff(n1_type, type, (
% 250.95/251.12 n1: $i)).
% 250.95/251.12 tff(n6_type, type, (
% 250.95/251.12 n6: $i)).
% 250.95/251.12 tff(tptp_fun_L_13_type, type, (
% 250.95/251.12 tptp_fun_L_13: $i)).
% 250.95/251.12 tff(tptp_fun_K_14_type, type, (
% 250.95/251.12 tptp_fun_K_14: $i)).
% 250.95/251.12 tff(n0_type, type, (
% 250.95/251.12 n0: $i)).
% 250.95/251.12 tff(a_select3_type, type, (
% 250.95/251.12 a_select3: ( $i * $i * $i ) > $i)).
% 250.95/251.12 tff(q_ds1_filter_type, type, (
% 250.95/251.12 q_ds1_filter: $i)).
% 250.95/251.12 tff(tptp_fun_R_19_type, type, (
% 250.95/251.12 tptp_fun_R_19: $i)).
% 250.95/251.12 tff(tptp_fun_Q_20_type, type, (
% 250.95/251.12 tptp_fun_Q_20: $i)).
% 250.95/251.12 tff(pminus_ds1_filter_type, type, (
% 250.95/251.12 pminus_ds1_filter: $i)).
% 250.95/251.12 tff(id_ds1_filter_type, type, (
% 250.95/251.12 id_ds1_filter: $i)).
% 250.95/251.12 tff(r_ds1_filter_type, type, (
% 250.95/251.12 r_ds1_filter: $i)).
% 250.95/251.12 tff(n3_type, type, (
% 250.95/251.12 n3: $i)).
% 250.95/251.12 tff(pv47_type, type, (
% 250.95/251.12 pv47: $i)).
% 250.95/251.12 tff(n999_type, type, (
% 250.95/251.12 n999: $i)).
% 250.95/251.12 tff(pv5_type, type, (
% 250.95/251.12 pv5: $i)).
% 250.95/251.12 tff(tptp_fun_P_17_type, type, (
% 250.95/251.12 tptp_fun_P_17: $i)).
% 250.95/251.12 tff(tptp_fun_O_18_type, type, (
% 250.95/251.12 tptp_fun_O_18: $i)).
% 250.95/251.13 tff(tptp_fun_N_15_type, type, (
% 250.95/251.13 tptp_fun_N_15: $i)).
% 250.95/251.13 tff(tptp_fun_M_16_type, type, (
% 250.95/251.13 tptp_fun_M_16: $i)).
% 250.95/251.13 tff(tptp_fun_S_21_type, type, (
% 250.95/251.13 tptp_fun_S_21: $i)).
% 250.95/251.13 tff(tptp_fun_T_22_type, type, (
% 250.95/251.13 tptp_fun_T_22: $i)).
% 250.95/251.13 tff(1,assumption,(~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))), introduced(assumption)).
% 250.95/251.13 tff(2,plain,
% 250.95/251.13 (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))) | leq(R!19, minus(n6, n1))),
% 250.95/251.13 inference(tautology,[status(thm)],[])).
% 250.95/251.13 tff(3,plain,
% 250.95/251.13 (leq(R!19, minus(n6, n1))),
% 250.95/251.13 inference(unit_resolution,[status(thm)],[2, 1])).
% 250.95/251.13 tff(4,plain,
% 250.95/251.13 (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))) | leq(Q!20, minus(n6, n1))),
% 250.95/251.13 inference(tautology,[status(thm)],[])).
% 250.95/251.13 tff(5,plain,
% 250.95/251.13 (leq(Q!20, minus(n6, n1))),
% 250.95/251.13 inference(unit_resolution,[status(thm)],[4, 1])).
% 250.95/251.13 tff(6,plain,
% 250.95/251.13 (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))) | leq(n0, R!19)),
% 250.95/251.13 inference(tautology,[status(thm)],[])).
% 250.95/251.13 tff(7,plain,
% 250.95/251.13 (leq(n0, R!19)),
% 250.95/251.13 inference(unit_resolution,[status(thm)],[6, 1])).
% 250.95/251.13 tff(8,plain,
% 250.95/251.13 (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))) | leq(n0, Q!20)),
% 250.95/251.13 inference(tautology,[status(thm)],[])).
% 250.95/251.13 tff(9,plain,
% 250.95/251.13 (leq(n0, Q!20)),
% 250.95/251.13 inference(unit_resolution,[status(thm)],[8, 1])).
% 250.95/251.13 tff(10,plain,
% 250.95/251.13 (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))) | (~(a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))),
% 250.95/251.13 inference(tautology,[status(thm)],[])).
% 250.95/251.13 tff(11,plain,
% 250.95/251.13 (~(a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20))),
% 250.95/251.13 inference(unit_resolution,[status(thm)],[10, 1])).
% 250.95/251.13 tff(12,plain,
% 250.95/251.13 (^[G: $i, H: $i] : refl(((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))),
% 250.95/251.13 inference(bind,[status(th)],[])).
% 250.95/251.13 tff(13,plain,
% 250.95/251.13 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 250.95/251.13 inference(quant_intro,[status(thm)],[12])).
% 250.95/251.13 tff(14,plain,
% 250.95/251.13 (^[G: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1))) <=> (~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))), ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) <=> (~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))))), rewrite((~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))), ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))), (((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> (((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))))), rewrite((((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))), (((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))))),
% 250.95/251.13 inference(bind,[status(th)],[])).
% 250.95/251.13 tff(15,plain,
% 250.95/251.13 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 250.95/251.13 inference(quant_intro,[status(thm)],[14])).
% 250.95/251.13 tff(16,plain,
% 250.95/251.13 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 250.95/251.13 inference(rewrite,[status(thm)],[])).
% 250.95/251.13 tff(17,plain,
% 250.95/251.13 ((~(((((((((leq(n0, pv5) & leq(n0, pv47)) & leq(pv5, minus(n999, n1))) & leq(pv47, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, minus(n6, n1))) & leq(R, minus(n6, n1))) => (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(n6, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))) <=> (~((~(leq(n0, pv5) & leq(n0, pv47) & leq(pv5, minus(n999, n1)) & leq(pv47, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))))),
% 250.95/251.13 inference(rewrite,[status(thm)],[])).
% 250.95/251.13 tff(18,axiom,(~(((((((((leq(n0, pv5) & leq(n0, pv47)) & leq(pv5, minus(n999, n1))) & leq(pv47, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, minus(n6, n1))) & leq(R, minus(n6, n1))) => (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(n6, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0002')).
% 250.95/251.13 tff(19,plain,
% 250.95/251.13 (~((~(leq(n0, pv5) & leq(n0, pv47) & leq(pv5, minus(n999, n1)) & leq(pv47, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 250.95/251.13 inference(modus_ponens,[status(thm)],[18, 17])).
% 250.95/251.13 tff(20,plain,
% 250.95/251.13 (leq(n0, pv5) & leq(n0, pv47) & leq(pv5, minus(n999, n1)) & leq(pv47, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 250.95/251.13 inference(or_elim,[status(thm)],[19])).
% 250.95/251.13 tff(21,plain,
% 250.95/251.13 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 250.95/251.13 inference(and_elim,[status(thm)],[20])).
% 250.95/251.13 tff(22,plain,
% 250.95/251.13 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 250.95/251.13 inference(modus_ponens,[status(thm)],[21, 16])).
% 250.95/251.13 tff(23,plain,(
% 250.95/251.13 ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 250.95/251.13 inference(skolemize,[status(sab)],[22])).
% 250.95/251.14 tff(24,plain,
% 250.95/251.14 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 250.95/251.14 inference(modus_ponens,[status(thm)],[23, 15])).
% 250.95/251.14 tff(25,plain,
% 250.95/251.14 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 250.95/251.14 inference(modus_ponens,[status(thm)],[24, 13])).
% 250.95/251.14 tff(26,plain,
% 250.95/251.14 (((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))) <=> ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))),
% 250.95/251.14 inference(rewrite,[status(thm)],[])).
% 250.95/251.14 tff(27,plain,
% 250.95/251.14 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))),
% 250.95/251.14 inference(quant_inst,[status(thm)],[])).
% 250.95/251.14 tff(28,plain,
% 250.95/251.14 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))),
% 250.95/251.14 inference(modus_ponens,[status(thm)],[27, 26])).
% 250.95/251.14 tff(29,plain,
% 250.95/251.14 ($false),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[28, 25, 11, 9, 7, 5, 3])).
% 250.95/251.14 tff(30,plain,((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))), inference(lemma,lemma(discharge,[]))).
% 250.95/251.14 tff(31,assumption,(~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))), introduced(assumption)).
% 250.95/251.14 tff(32,plain,
% 250.95/251.14 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))) | leq(P!17, minus(n6, n1))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(33,plain,
% 250.95/251.14 (leq(P!17, minus(n6, n1))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[32, 31])).
% 250.95/251.14 tff(34,plain,
% 250.95/251.14 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))) | leq(O!18, minus(n6, n1))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(35,plain,
% 250.95/251.14 (leq(O!18, minus(n6, n1))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[34, 31])).
% 250.95/251.14 tff(36,plain,
% 250.95/251.14 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))) | leq(n0, P!17)),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(37,plain,
% 250.95/251.14 (leq(n0, P!17)),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[36, 31])).
% 250.95/251.14 tff(38,plain,
% 250.95/251.14 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))) | leq(n0, O!18)),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(39,plain,
% 250.95/251.14 (leq(n0, O!18)),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[38, 31])).
% 250.95/251.14 tff(40,plain,
% 250.95/251.14 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))) | (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(41,plain,
% 250.95/251.14 (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[40, 31])).
% 250.95/251.14 tff(42,plain,
% 250.95/251.14 (((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) <=> ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))),
% 250.95/251.14 inference(rewrite,[status(thm)],[])).
% 250.95/251.14 tff(43,plain,
% 250.95/251.14 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))),
% 250.95/251.14 inference(quant_inst,[status(thm)],[])).
% 250.95/251.14 tff(44,plain,
% 250.95/251.14 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))),
% 250.95/251.14 inference(modus_ponens,[status(thm)],[43, 42])).
% 250.95/251.14 tff(45,plain,
% 250.95/251.14 ($false),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[44, 25, 41, 39, 37, 35, 33])).
% 250.95/251.14 tff(46,plain,((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))), inference(lemma,lemma(discharge,[]))).
% 250.95/251.14 tff(47,assumption,(~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))), introduced(assumption)).
% 250.95/251.14 tff(48,plain,
% 250.95/251.14 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))) | leq(N!15, minus(n3, n1))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(49,plain,
% 250.95/251.14 (leq(N!15, minus(n3, n1))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[48, 47])).
% 250.95/251.14 tff(50,plain,
% 250.95/251.14 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))) | leq(M!16, minus(n3, n1))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(51,plain,
% 250.95/251.14 (leq(M!16, minus(n3, n1))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[50, 47])).
% 250.95/251.14 tff(52,plain,
% 250.95/251.14 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))) | leq(n0, N!15)),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(53,plain,
% 250.95/251.14 (leq(n0, N!15)),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[52, 47])).
% 250.95/251.14 tff(54,plain,
% 250.95/251.14 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))) | leq(n0, M!16)),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(55,plain,
% 250.95/251.14 (leq(n0, M!16)),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[54, 47])).
% 250.95/251.14 tff(56,plain,
% 250.95/251.14 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))) | (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))),
% 250.95/251.14 inference(tautology,[status(thm)],[])).
% 250.95/251.14 tff(57,plain,
% 250.95/251.14 (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 250.95/251.14 inference(unit_resolution,[status(thm)],[56, 47])).
% 250.95/251.14 tff(58,plain,
% 250.95/251.14 (^[C: $i, D: $i] : refl(((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))))),
% 250.95/251.14 inference(bind,[status(th)],[])).
% 250.95/251.14 tff(59,plain,
% 250.95/251.14 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))) <=> ![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))),
% 250.95/251.14 inference(quant_intro,[status(thm)],[58])).
% 250.95/251.14 tff(60,plain,
% 250.95/251.14 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1))) <=> (~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))))), ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) <=> (~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))))))), rewrite((~(~((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))), ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) <=> ((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))))), (((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> (((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))))), rewrite((((~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))), (((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))))),
% 250.95/251.14 inference(bind,[status(th)],[])).
% 250.95/251.14 tff(61,plain,
% 250.95/251.14 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))),
% 250.95/251.14 inference(quant_intro,[status(thm)],[60])).
% 250.95/251.14 tff(62,plain,
% 250.95/251.14 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 250.95/251.14 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(63,plain,
% 250.95/251.15 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 250.95/251.15 inference(and_elim,[status(thm)],[20])).
% 250.95/251.15 tff(64,plain,
% 250.95/251.15 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[63, 62])).
% 250.95/251.15 tff(65,plain,(
% 250.95/251.15 ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 250.95/251.15 inference(skolemize,[status(sab)],[64])).
% 250.95/251.15 tff(66,plain,
% 250.95/251.15 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[65, 61])).
% 250.95/251.15 tff(67,plain,
% 250.95/251.15 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[66, 59])).
% 250.95/251.15 tff(68,plain,
% 250.95/251.15 (((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))) <=> ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(69,plain,
% 250.95/251.15 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))),
% 250.95/251.15 inference(quant_inst,[status(thm)],[])).
% 250.95/251.15 tff(70,plain,
% 250.95/251.15 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[69, 68])).
% 250.95/251.15 tff(71,plain,
% 250.95/251.15 ($false),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[70, 67, 57, 55, 53, 51, 49])).
% 250.95/251.15 tff(72,plain,((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))), inference(lemma,lemma(discharge,[]))).
% 250.95/251.15 tff(73,assumption,(~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))))), introduced(assumption)).
% 250.95/251.15 tff(74,plain,
% 250.95/251.15 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))) | leq(S!21, minus(n6, n1))),
% 250.95/251.15 inference(tautology,[status(thm)],[])).
% 250.95/251.15 tff(75,plain,
% 250.95/251.15 (leq(S!21, minus(n6, n1))),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[74, 73])).
% 250.95/251.15 tff(76,plain,
% 250.95/251.15 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))) | leq(n0, S!21)),
% 250.95/251.15 inference(tautology,[status(thm)],[])).
% 250.95/251.15 tff(77,plain,
% 250.95/251.15 (leq(n0, S!21)),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[76, 73])).
% 250.95/251.15 tff(78,plain,
% 250.95/251.15 (^[I: $i] : refl(((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))))),
% 250.95/251.15 inference(bind,[status(th)],[])).
% 250.95/251.15 tff(79,plain,
% 250.95/251.15 (![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(quant_intro,[status(thm)],[78])).
% 250.95/251.15 tff(80,plain,
% 250.95/251.15 (^[I: $i] : rewrite(((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))))),
% 250.95/251.15 inference(bind,[status(th)],[])).
% 250.95/251.15 tff(81,plain,
% 250.95/251.15 (![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(quant_intro,[status(thm)],[80])).
% 250.95/251.15 tff(82,plain,
% 250.95/251.15 (![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(transitivity,[status(thm)],[81, 79])).
% 250.95/251.15 tff(83,plain,
% 250.95/251.15 (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, I) & leq(I, minus(n6, n1))) <=> (~((~leq(n0, I)) | (~leq(I, minus(n6, n1)))))), ((~(leq(n0, I) & leq(I, minus(n6, n1)))) <=> (~(~((~leq(n0, I)) | (~leq(I, minus(n6, n1)))))))), rewrite((~(~((~leq(n0, I)) | (~leq(I, minus(n6, n1)))))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1))))), ((~(leq(n0, I) & leq(I, minus(n6, n1)))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1)))))), quant_intro(proof_bind(^[J: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, J) & leq(J, minus(n6, n1))) <=> (~((~leq(n0, J)) | (~leq(J, minus(n6, n1)))))), ((~(leq(n0, J) & leq(J, minus(n6, n1)))) <=> (~(~((~leq(n0, J)) | (~leq(J, minus(n6, n1)))))))), rewrite((~(~((~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) <=> ((~leq(n0, J)) | (~leq(J, minus(n6, n1))))), ((~(leq(n0, J) & leq(J, minus(n6, n1)))) <=> ((~leq(n0, J)) | (~leq(J, minus(n6, n1)))))), (((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> (((~leq(n0, J)) | (~leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))), rewrite((((~leq(n0, J)) | (~leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))), (((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))))), (![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))), (((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> (((~leq(n0, I)) | (~leq(I, minus(n6, n1)))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))))), rewrite((((~leq(n0, I)) | (~leq(I, minus(n6, n1)))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))), (((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))))),
% 250.95/251.15 inference(bind,[status(th)],[])).
% 250.95/251.15 tff(84,plain,
% 250.95/251.15 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(quant_intro,[status(thm)],[83])).
% 250.95/251.15 tff(85,plain,
% 250.95/251.15 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(86,plain,
% 250.95/251.15 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 250.95/251.15 inference(and_elim,[status(thm)],[20])).
% 250.95/251.15 tff(87,plain,
% 250.95/251.15 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[86, 85])).
% 250.95/251.15 tff(88,plain,(
% 250.95/251.15 ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 250.95/251.15 inference(skolemize,[status(sab)],[87])).
% 250.95/251.15 tff(89,plain,
% 250.95/251.15 (![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[88, 84])).
% 250.95/251.15 tff(90,plain,
% 250.95/251.15 (![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[89, 82])).
% 250.95/251.15 tff(91,plain,
% 250.95/251.15 (((~![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) | ((~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) <=> ((~![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(92,plain,
% 250.95/251.15 ((~![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) | ((~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))),
% 250.95/251.15 inference(quant_inst,[status(thm)],[])).
% 250.95/251.15 tff(93,plain,
% 250.95/251.15 ((~![I: $i] : ((~leq(n0, I)) | (~leq(I, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1)))))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[92, 91])).
% 250.95/251.15 tff(94,plain,
% 250.95/251.15 (![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[93, 90, 77, 75])).
% 250.95/251.15 tff(95,plain,
% 250.95/251.15 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))) | leq(T!22, minus(n6, n1))),
% 250.95/251.15 inference(tautology,[status(thm)],[])).
% 250.95/251.15 tff(96,plain,
% 250.95/251.15 (leq(T!22, minus(n6, n1))),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[95, 73])).
% 250.95/251.15 tff(97,plain,
% 250.95/251.15 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))) | leq(n0, T!22)),
% 250.95/251.15 inference(tautology,[status(thm)],[])).
% 250.95/251.15 tff(98,plain,
% 250.95/251.15 (leq(n0, T!22)),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[97, 73])).
% 250.95/251.15 tff(99,plain,
% 250.95/251.15 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))) | (~(a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))),
% 250.95/251.15 inference(tautology,[status(thm)],[])).
% 250.95/251.15 tff(100,plain,
% 250.95/251.15 (~(a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[99, 73])).
% 250.95/251.15 tff(101,plain,
% 250.95/251.15 (((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) | ((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))))) <=> ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))))),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(102,plain,
% 250.95/251.15 ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) | ((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))))),
% 250.95/251.15 inference(quant_inst,[status(thm)],[])).
% 250.95/251.15 tff(103,plain,
% 250.95/251.15 ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(n0, J)) | (~leq(J, minus(n6, n1))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1)))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[102, 101])).
% 250.95/251.15 tff(104,plain,
% 250.95/251.15 ($false),
% 250.95/251.15 inference(unit_resolution,[status(thm)],[103, 100, 98, 96, 94])).
% 250.95/251.15 tff(105,plain,((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))), inference(lemma,lemma(discharge,[]))).
% 250.95/251.15 tff(106,plain,
% 250.95/251.15 (leq(pv5, minus(n999, n1)) <=> leq(pv5, minus(n999, n1))),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(107,plain,
% 250.95/251.15 (leq(pv5, minus(n999, n1))),
% 250.95/251.15 inference(and_elim,[status(thm)],[20])).
% 250.95/251.15 tff(108,plain,
% 250.95/251.15 (leq(pv5, minus(n999, n1))),
% 250.95/251.15 inference(modus_ponens,[status(thm)],[107, 106])).
% 250.95/251.15 tff(109,plain,
% 250.95/251.15 (leq(n0, pv5) <=> leq(n0, pv5)),
% 250.95/251.15 inference(rewrite,[status(thm)],[])).
% 250.95/251.15 tff(110,plain,
% 250.95/251.15 (leq(n0, pv5)),
% 250.95/251.15 inference(and_elim,[status(thm)],[20])).
% 250.95/251.16 tff(111,plain,
% 250.95/251.16 (leq(n0, pv5)),
% 250.95/251.16 inference(modus_ponens,[status(thm)],[110, 109])).
% 250.95/251.16 tff(112,plain,
% 250.95/251.16 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(n0, K!14)) | (~leq(n0, L!13)) | (~leq(K!14, minus(n6, n1))) | (~leq(L!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) | (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(n0, K!14)) | (~leq(n0, L!13)) | (~leq(K!14, minus(n6, n1))) | (~leq(L!13, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) | (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(113,plain,
% 250.95/251.16 ((leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1)))))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(114,plain,
% 250.95/251.16 ((~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(115,plain,
% 250.95/251.16 ((leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))))))),
% 250.95/251.16 inference(monotonicity,[status(thm)],[114])).
% 250.95/251.16 tff(116,plain,
% 250.95/251.16 ((leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1)))))),
% 250.95/251.16 inference(transitivity,[status(thm)],[115, 113])).
% 250.95/251.16 tff(117,plain,
% 250.95/251.16 ((~((~(leq(n0, Q!20) & leq(n0, R!19) & leq(Q!20, minus(n6, n1)) & leq(R!19, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) <=> (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(118,plain,
% 250.95/251.16 ((~((~(leq(n0, O!18) & leq(n0, P!17) & leq(O!18, minus(n6, n1)) & leq(P!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) <=> (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(119,plain,
% 250.95/251.16 ((~((~(leq(n0, M!16) & leq(n0, N!15) & leq(M!16, minus(n3, n1)) & leq(N!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) <=> (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(120,plain,
% 250.95/251.16 ((~((~(leq(n0, K!14) & leq(n0, L!13) & leq(K!14, minus(n6, n1)) & leq(L!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) <=> (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(n0, K!14)) | (~leq(n0, L!13)) | (~leq(K!14, minus(n6, n1))) | (~leq(L!13, minus(n6, n1)))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(121,plain,
% 250.95/251.16 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, K!14) & leq(n0, L!13) & leq(K!14, minus(n6, n1)) & leq(L!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(n0, M!16) & leq(n0, N!15) & leq(M!16, minus(n3, n1)) & leq(N!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(n0, O!18) & leq(n0, P!17) & leq(O!18, minus(n6, n1)) & leq(P!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(n0, Q!20) & leq(n0, R!19) & leq(Q!20, minus(n6, n1)) & leq(R!19, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(n0, K!14)) | (~leq(n0, L!13)) | (~leq(K!14, minus(n6, n1))) | (~leq(L!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) | (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))))))),
% 250.95/251.16 inference(monotonicity,[status(thm)],[120, 119, 118, 117, 116])).
% 250.95/251.16 tff(122,plain,
% 250.95/251.16 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, K!14) & leq(n0, L!13) & leq(K!14, minus(n6, n1)) & leq(L!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(n0, M!16) & leq(n0, N!15) & leq(M!16, minus(n3, n1)) & leq(N!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(n0, O!18) & leq(n0, P!17) & leq(O!18, minus(n6, n1)) & leq(P!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(n0, Q!20) & leq(n0, R!19) & leq(Q!20, minus(n6, n1)) & leq(R!19, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(n0, K!14)) | (~leq(n0, L!13)) | (~leq(K!14, minus(n6, n1))) | (~leq(L!13, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(n0, T!22)) | (~leq(T!22, minus(n6, n1))) | (~leq(n0, S!21)) | (~leq(S!21, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) | (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(n0, Q!20)) | (~leq(n0, R!19)) | (~leq(Q!20, minus(n6, n1))) | (~leq(R!19, minus(n6, n1))))))),
% 250.95/251.16 inference(transitivity,[status(thm)],[121, 112])).
% 250.95/251.16 tff(123,plain,
% 250.95/251.16 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, K!14) & leq(n0, L!13) & leq(K!14, minus(n6, n1)) & leq(L!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(n0, M!16) & leq(n0, N!15) & leq(M!16, minus(n3, n1)) & leq(N!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(n0, O!18) & leq(n0, P!17) & leq(O!18, minus(n6, n1)) & leq(P!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(n0, Q!20) & leq(n0, R!19) & leq(Q!20, minus(n6, n1)) & leq(R!19, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | ((leq(n0, S!21) & leq(S!21, minus(n6, n1))) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, K!14) & leq(n0, L!13) & leq(K!14, minus(n6, n1)) & leq(L!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(n0, M!16) & leq(n0, N!15) & leq(M!16, minus(n3, n1)) & leq(N!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(n0, O!18) & leq(n0, P!17) & leq(O!18, minus(n6, n1)) & leq(P!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(n0, Q!20) & leq(n0, R!19) & leq(Q!20, minus(n6, n1)) & leq(R!19, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(n0, S!21) & leq(S!21, minus(n6, n1)) & (~((~(leq(n0, T!22) & leq(T!22, minus(n6, n1)))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))))),
% 250.95/251.16 inference(rewrite,[status(thm)],[])).
% 250.95/251.16 tff(124,plain,
% 250.95/251.16 ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 250.95/251.17 inference(rewrite,[status(thm)],[])).
% 250.95/251.17 tff(125,plain,
% 250.95/251.17 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 250.95/251.17 inference(monotonicity,[status(thm)],[124])).
% 250.95/251.17 tff(126,plain,
% 250.95/251.17 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 250.95/251.17 inference(rewrite,[status(thm)],[])).
% 250.95/251.17 tff(127,plain,
% 250.95/251.17 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 250.95/251.17 inference(or_elim,[status(thm)],[19])).
% 250.95/251.17 tff(128,plain,
% 250.95/251.17 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 250.95/251.17 inference(modus_ponens,[status(thm)],[127, 125])).
% 250.95/251.17 tff(129,plain,
% 250.95/251.17 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 250.95/251.17 inference(modus_ponens,[status(thm)],[128, 126])).
% 250.95/251.17 tff(130,plain,
% 250.95/251.17 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 250.95/251.18 inference(modus_ponens,[status(thm)],[129, 125])).
% 250.95/251.18 unexpected number of arguments: (let ((a!1 (refl (~ (not (leq n0 pv5)) (not (leq n0 pv5)))))
% 250.95/251.18 (a!2 (~ (not (leq pv5 (minus n999 n1))) (not (leq pv5 (minus n999 n1)))))
% 250.95/251.18 (a!3 (forall ((K $i) (L $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 K)
% 250.95/251.18 (leq n0 L)
% 250.95/251.18 (leq K (minus n6 n1))
% 250.95/251.18 (leq L (minus n6 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))
% 250.95/251.18 (a!4 (not (and (leq n0 K!14)
% 250.95/251.18 (leq n0 L!13)
% 250.95/251.18 (leq K!14 (minus n6 n1))
% 250.95/251.18 (leq L!13 (minus n6 n1)))))
% 250.95/251.18 (a!6 (forall ((M $i) (N $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 M)
% 250.95/251.18 (leq n0 N)
% 250.95/251.18 (leq M (minus n3 n1))
% 250.95/251.18 (leq N (minus n3 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))
% 250.95/251.18 (a!7 (not (and (leq n0 M!16)
% 250.95/251.18 (leq n0 N!15)
% 250.95/251.18 (leq M!16 (minus n3 n1))
% 250.95/251.18 (leq N!15 (minus n3 n1)))))
% 250.95/251.18 (a!9 (forall ((O $i) (P $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 O)
% 250.95/251.18 (leq n0 P)
% 250.95/251.18 (leq O (minus n6 n1))
% 250.95/251.18 (leq P (minus n6 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 pminus_ds1_filter O P)
% 250.95/251.18 (a_select3 pminus_ds1_filter P O))))))
% 250.95/251.18 (a!10 (not (and (leq n0 O!18)
% 250.95/251.18 (leq n0 P!17)
% 250.95/251.18 (leq O!18 (minus n6 n1))
% 250.95/251.18 (leq P!17 (minus n6 n1)))))
% 250.95/251.18 (a!12 (forall ((Q $i) (R $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 Q)
% 250.95/251.18 (leq n0 R)
% 250.95/251.18 (leq Q (minus n6 n1))
% 250.95/251.18 (leq R (minus n6 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 pminus_ds1_filter Q R)
% 250.95/251.18 (a_select3 pminus_ds1_filter R Q))))))
% 250.95/251.18 (a!13 (not (and (leq n0 Q!20)
% 250.95/251.18 (leq n0 R!19)
% 250.95/251.18 (leq Q!20 (minus n6 n1))
% 250.95/251.18 (leq R!19 (minus n6 n1)))))
% 250.95/251.18 (a!15 (forall ((S $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 S) (leq S (minus n6 n1)))))
% 250.95/251.18 (a!2 (forall ((T $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 T)
% 250.95/251.18 (leq T (minus n6 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 id_ds1_filter S T)
% 250.95/251.18 (a_select3 id_ds1_filter T S)))))))
% 250.95/251.18 (or a!1 a!2))))
% 250.95/251.18 (a!16 (not (and (leq n0 S!21) (leq S!21 (minus n6 n1)))))
% 250.95/251.18 (a!17 (forall ((T $i))
% 250.95/251.18 (let ((a!1 (not (and (leq n0 T) (leq T (minus n6 n1))))))
% 250.95/251.18 (or a!1
% 250.95/251.18 (= (a_select3 id_ds1_filter S!21 T)
% 250.95/251.18 (a_select3 id_ds1_filter T S!21))))))
% 250.95/251.18 (a!19 (~ (and (leq n0 S!21) (leq S!21 (minus n6 n1)))
% 250.95/251.18 (and (leq n0 S!21) (leq S!21 (minus n6 n1)))))
% 250.95/251.18 (a!20 (not (and (leq n0 T!22) (leq T!22 (minus n6 n1))))))
% 250.95/251.18 (let ((a!5 (not (or a!4
% 250.95/251.18 (= (a_select3 q_ds1_filter K!14 L!13)
% 250.95/251.18 (a_select3 q_ds1_filter L!13 K!14)))))
% 250.95/251.18 (a!8 (not (or a!7
% 250.95/251.18 (= (a_select3 r_ds1_filter M!16 N!15)
% 250.95/251.18 (a_select3 r_ds1_filter N!15 M!16)))))
% 250.95/251.18 (a!11 (not (or a!10
% 250.95/251.18 (= (a_select3 pminus_ds1_filter O!18 P!17)
% 250.95/251.18 (a_select3 pminus_ds1_filter P!17 O!18)))))
% 250.95/251.18 (a!14 (not (or a!13
% 250.95/251.18 (= (a_select3 pminus_ds1_filter Q!20 R!19)
% 250.95/251.18 (a_select3 pminus_ds1_filter R!19 Q!20)))))
% 250.95/251.18 (a!18 (sk (~ (not a!15) (not (or a!16 a!17)))))
% 250.95/251.18 (a!21 (not (or a!20
% 250.95/251.18 (= (a_select3 id_ds1_filter S!21 T!22)
% 250.95/251.18 (a_select3 id_ds1_filter T!22 S!21)))))
% 250.95/251.18 (a!24 (not (and (leq n0 pv5)
% 250.95/251.18 (leq pv5 (minus n999 n1))
% 250.95/251.18 a!3
% 250.95/251.18 a!6
% 250.95/251.18 a!9
% 250.95/251.18 a!12
% 250.95/251.18 a!15))))
% 250.95/251.18 (let ((a!22 (and (and (leq n0 S!21) (leq S!21 (minus n6 n1))) a!21)))
% 250.95/251.18 (let ((a!23 (nnf-neg (refl a!19)
% 250.95/251.18 (sk (~ (not a!17) a!21))
% 250.95/251.18 (~ (not (or a!16 a!17)) a!22)))
% 250.95/251.18 (a!25 (or (not (leq n0 pv5))
% 250.95/251.18 (not (leq pv5 (minus n999 n1)))
% 250.95/251.18 a!5
% 250.95/251.18 a!8
% 250.95/251.18 a!11
% 250.95/251.18 a!14
% 250.95/251.18 a!22)))
% 250.95/251.18 (nnf-neg a!1
% 250.95/251.18 (refl a!2)
% 250.95/251.18 (sk (~ (not a!3) a!5))
% 250.95/251.18 (sk (~ (not a!6) a!8))
% 250.95/251.18 (sk (~ (not a!9) a!11))
% 250.95/251.18 (sk (~ (not a!12) a!14))
% 250.95/251.18 (trans a!18 a!23 (~ (not a!15) a!22))
% 250.95/251.18 (~ a!24 a!25))))))
% 250.95/251.18 Proof display could not be completed: unexpected number of arguments
% 251.75/251.98 % E exiting
%------------------------------------------------------------------------------