%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV112+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 142.08s 142.33s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV112+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:27:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 142.08/142.33 % SZS status Theorem
% 142.08/142.33 % SZS output start Proof
% 142.08/142.33 tff(leq_type, type, (
% 142.08/142.33 leq: ( $i * $i ) > $o)).
% 142.08/142.33 tff(minus_type, type, (
% 142.08/142.33 minus: ( $i * $i ) > $i)).
% 142.08/142.33 tff(n1_type, type, (
% 142.08/142.33 n1: $i)).
% 142.08/142.33 tff(n6_type, type, (
% 142.08/142.33 n6: $i)).
% 142.08/142.33 tff(tptp_fun_L_13_type, type, (
% 142.08/142.33 tptp_fun_L_13: $i)).
% 142.08/142.33 tff(tptp_fun_K_14_type, type, (
% 142.08/142.33 tptp_fun_K_14: $i)).
% 142.08/142.33 tff(n0_type, type, (
% 142.08/142.33 n0: $i)).
% 142.08/142.33 tff(a_select3_type, type, (
% 142.08/142.33 a_select3: ( $i * $i * $i ) > $i)).
% 142.08/142.33 tff(q_ds1_filter_type, type, (
% 142.08/142.33 q_ds1_filter: $i)).
% 142.08/142.33 tff(tptp_fun_P_17_type, type, (
% 142.08/142.33 tptp_fun_P_17: $i)).
% 142.08/142.33 tff(tptp_fun_O_18_type, type, (
% 142.08/142.33 tptp_fun_O_18: $i)).
% 142.08/142.33 tff(pminus_ds1_filter_type, type, (
% 142.08/142.33 pminus_ds1_filter: $i)).
% 142.08/142.33 tff(id_ds1_filter_type, type, (
% 142.08/142.33 id_ds1_filter: $i)).
% 142.08/142.33 tff(pv57_type, type, (
% 142.08/142.33 pv57: $i)).
% 142.08/142.33 tff(r_ds1_filter_type, type, (
% 142.08/142.33 r_ds1_filter: $i)).
% 142.08/142.33 tff(n3_type, type, (
% 142.08/142.33 n3: $i)).
% 142.08/142.33 tff(n999_type, type, (
% 142.08/142.33 n999: $i)).
% 142.08/142.33 tff(pv5_type, type, (
% 142.08/142.33 pv5: $i)).
% 142.08/142.33 tff(plus_type, type, (
% 142.08/142.33 plus: ( $i * $i ) > $i)).
% 142.08/142.33 tff(tptp_fun_N_15_type, type, (
% 142.08/142.33 tptp_fun_N_15: $i)).
% 142.08/142.33 tff(tptp_fun_M_16_type, type, (
% 142.08/142.33 tptp_fun_M_16: $i)).
% 142.08/142.33 tff(tptp_fun_Q_19_type, type, (
% 142.08/142.33 tptp_fun_Q_19: $i)).
% 142.08/142.33 tff(tptp_fun_R_20_type, type, (
% 142.08/142.33 tptp_fun_R_20: $i)).
% 142.08/142.33 tff(succ_type, type, (
% 142.08/142.33 succ: $i > $i)).
% 142.08/142.33 tff(pred_type, type, (
% 142.08/142.33 pred: $i > $i)).
% 142.08/142.33 tff(1,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)).
% 142.08/142.33 tff(2,plain,
% 142.08/142.33 (((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))),
% 142.08/142.33 inference(tautology,[status(thm)],[])).
% 142.08/142.33 tff(3,plain,
% 142.08/142.33 (leq(P!17, minus(n6, n1))),
% 142.08/142.33 inference(unit_resolution,[status(thm)],[2, 1])).
% 142.08/142.33 tff(4,plain,
% 142.08/142.33 (((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))),
% 142.08/142.33 inference(tautology,[status(thm)],[])).
% 142.08/142.33 tff(5,plain,
% 142.08/142.33 (leq(O!18, minus(n6, n1))),
% 142.08/142.33 inference(unit_resolution,[status(thm)],[4, 1])).
% 142.08/142.33 tff(6,plain,
% 142.08/142.33 (((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)),
% 142.08/142.33 inference(tautology,[status(thm)],[])).
% 142.08/142.33 tff(7,plain,
% 142.08/142.33 (leq(n0, P!17)),
% 142.08/142.33 inference(unit_resolution,[status(thm)],[6, 1])).
% 142.08/142.33 tff(8,plain,
% 142.08/142.33 (((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)),
% 142.08/142.33 inference(tautology,[status(thm)],[])).
% 142.08/142.33 tff(9,plain,
% 142.08/142.33 (leq(n0, O!18)),
% 142.08/142.33 inference(unit_resolution,[status(thm)],[8, 1])).
% 142.08/142.33 tff(10,plain,
% 142.08/142.33 (((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)))),
% 142.08/142.33 inference(tautology,[status(thm)],[])).
% 142.08/142.33 tff(11,plain,
% 142.08/142.33 (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18))),
% 142.08/142.33 inference(unit_resolution,[status(thm)],[10, 1])).
% 142.08/142.33 tff(12,plain,
% 142.08/142.33 (^[E: $i, F: $i] : refl(((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~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)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))))),
% 142.08/142.33 inference(bind,[status(th)],[])).
% 142.08/142.33 tff(13,plain,
% 142.08/142.33 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))),
% 142.08/142.33 inference(quant_intro,[status(thm)],[12])).
% 142.08/142.33 tff(14,plain,
% 142.08/142.33 (^[E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1))) <=> (~((~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))))), ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) <=> (~(~((~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))))))), rewrite((~(~((~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))))) <=> ((~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))), ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) <=> ((~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1)))))), (((~(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))) <=> (((~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))))), rewrite((((~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))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))), (((~(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))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))))),
% 142.08/142.33 inference(bind,[status(th)],[])).
% 142.08/142.33 tff(15,plain,
% 142.08/142.33 (![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))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))),
% 142.08/142.33 inference(quant_intro,[status(thm)],[14])).
% 142.08/142.33 tff(16,plain,
% 142.08/142.33 (![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))) <=> ![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)))),
% 142.08/142.33 inference(rewrite,[status(thm)],[])).
% 142.08/142.33 tff(17,plain,
% 142.08/142.33 ((~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, 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, pv57)) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, 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] : ((leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1))) => ![R: $i] : ((leq(n0, R) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))) <=> (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, 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, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, 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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))))),
% 142.08/142.34 inference(rewrite,[status(thm)],[])).
% 142.08/142.34 tff(18,axiom,(~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, 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, pv57)) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, 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] : ((leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1))) => ![R: $i] : ((leq(n0, R) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_symm_0005')).
% 142.08/142.34 tff(19,plain,
% 142.08/142.34 (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, 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, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, 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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[18, 17])).
% 142.08/142.34 tff(20,plain,
% 142.08/142.34 (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, 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, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, 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))))),
% 142.08/142.34 inference(or_elim,[status(thm)],[19])).
% 142.08/142.34 tff(21,plain,
% 142.08/142.34 (![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)))),
% 142.08/142.34 inference(and_elim,[status(thm)],[20])).
% 142.08/142.34 tff(22,plain,
% 142.08/142.34 (![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)))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[21, 16])).
% 142.08/142.34 tff(23,plain,(
% 142.08/142.34 ![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)))),
% 142.08/142.34 inference(skolemize,[status(sab)],[22])).
% 142.08/142.34 tff(24,plain,
% 142.08/142.34 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[23, 15])).
% 142.08/142.34 tff(25,plain,
% 142.08/142.34 (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[24, 13])).
% 142.08/142.34 tff(26,plain,
% 142.08/142.34 (((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, 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))))) <=> ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, 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))))),
% 142.08/142.34 inference(rewrite,[status(thm)],[])).
% 142.08/142.34 tff(27,plain,
% 142.08/142.34 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, 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))))),
% 142.08/142.34 inference(quant_inst,[status(thm)],[])).
% 142.08/142.34 tff(28,plain,
% 142.08/142.34 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[27, 26])).
% 142.08/142.34 tff(29,plain,
% 142.08/142.34 ($false),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[28, 25, 11, 9, 7, 5, 3])).
% 142.08/142.34 tff(30,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,[]))).
% 142.08/142.34 tff(31,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)).
% 142.08/142.34 tff(32,plain,
% 142.08/142.34 (((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))),
% 142.08/142.34 inference(tautology,[status(thm)],[])).
% 142.08/142.34 tff(33,plain,
% 142.08/142.34 (leq(N!15, minus(n3, n1))),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[32, 31])).
% 142.08/142.34 tff(34,plain,
% 142.08/142.34 (((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))),
% 142.08/142.34 inference(tautology,[status(thm)],[])).
% 142.08/142.34 tff(35,plain,
% 142.08/142.34 (leq(M!16, minus(n3, n1))),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[34, 31])).
% 142.08/142.34 tff(36,plain,
% 142.08/142.34 (((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)),
% 142.08/142.34 inference(tautology,[status(thm)],[])).
% 142.08/142.34 tff(37,plain,
% 142.08/142.34 (leq(n0, N!15)),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[36, 31])).
% 142.08/142.34 tff(38,plain,
% 142.08/142.34 (((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)),
% 142.08/142.34 inference(tautology,[status(thm)],[])).
% 142.08/142.34 tff(39,plain,
% 142.08/142.34 (leq(n0, M!16)),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[38, 31])).
% 142.08/142.34 tff(40,plain,
% 142.08/142.34 (((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)))),
% 142.08/142.34 inference(tautology,[status(thm)],[])).
% 142.08/142.34 tff(41,plain,
% 142.08/142.34 (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 142.08/142.34 inference(unit_resolution,[status(thm)],[40, 31])).
% 142.08/142.34 tff(42,plain,
% 142.08/142.34 (^[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)))))),
% 142.08/142.34 inference(bind,[status(th)],[])).
% 142.08/142.34 tff(43,plain,
% 142.08/142.34 (![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))))),
% 142.08/142.34 inference(quant_intro,[status(thm)],[42])).
% 142.08/142.34 tff(44,plain,
% 142.08/142.34 (^[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))))))),
% 142.08/142.34 inference(bind,[status(th)],[])).
% 142.08/142.34 tff(45,plain,
% 142.08/142.34 (![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))))),
% 142.08/142.34 inference(quant_intro,[status(thm)],[44])).
% 142.08/142.34 tff(46,plain,
% 142.08/142.34 (![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)))),
% 142.08/142.34 inference(rewrite,[status(thm)],[])).
% 142.08/142.34 tff(47,plain,
% 142.08/142.34 (![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)))),
% 142.08/142.34 inference(and_elim,[status(thm)],[20])).
% 142.08/142.34 tff(48,plain,
% 142.08/142.34 (![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)))),
% 142.08/142.34 inference(modus_ponens,[status(thm)],[47, 46])).
% 142.08/142.34 tff(49,plain,(
% 142.08/142.34 ![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)))),
% 142.08/142.34 inference(skolemize,[status(sab)],[48])).
% 142.08/142.34 tff(50,plain,
% 142.08/142.34 (![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))))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[49, 45])).
% 142.08/142.35 tff(51,plain,
% 142.08/142.35 (![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))))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[50, 43])).
% 142.08/142.35 tff(52,plain,
% 142.08/142.35 (((~![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))))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(53,plain,
% 142.08/142.35 ((~![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))))),
% 142.08/142.35 inference(quant_inst,[status(thm)],[])).
% 142.08/142.35 tff(54,plain,
% 142.08/142.35 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[53, 52])).
% 142.08/142.35 tff(55,plain,
% 142.08/142.35 ($false),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[54, 51, 41, 39, 37, 35, 33])).
% 142.08/142.35 tff(56,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,[]))).
% 142.08/142.35 tff(57,plain,
% 142.08/142.35 (^[X: $i] : refl((plus(n1, X) = succ(X)) <=> (plus(n1, X) = succ(X)))),
% 142.08/142.35 inference(bind,[status(th)],[])).
% 142.08/142.35 tff(58,plain,
% 142.08/142.35 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 142.08/142.35 inference(quant_intro,[status(thm)],[57])).
% 142.08/142.35 tff(59,plain,
% 142.08/142.35 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(60,axiom,(![X: $i] : (plus(n1, X) = succ(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_plus_1_l')).
% 142.08/142.35 tff(61,plain,
% 142.08/142.35 (![X: $i] : (plus(n1, X) = succ(X))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[60, 59])).
% 142.08/142.35 tff(62,plain,(
% 142.08/142.35 ![X: $i] : (plus(n1, X) = succ(X))),
% 142.08/142.35 inference(skolemize,[status(sab)],[61])).
% 142.08/142.35 tff(63,plain,
% 142.08/142.35 (![X: $i] : (plus(n1, X) = succ(X))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[62, 58])).
% 142.08/142.35 tff(64,plain,
% 142.08/142.35 ((~![X: $i] : (plus(n1, X) = succ(X))) | (plus(n1, pv57) = succ(pv57))),
% 142.08/142.35 inference(quant_inst,[status(thm)],[])).
% 142.08/142.35 tff(65,plain,
% 142.08/142.35 (plus(n1, pv57) = succ(pv57)),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[64, 63])).
% 142.08/142.35 tff(66,plain,
% 142.08/142.35 (minus(plus(n1, pv57), n1) = minus(succ(pv57), n1)),
% 142.08/142.35 inference(monotonicity,[status(thm)],[65])).
% 142.08/142.35 tff(67,plain,
% 142.08/142.35 (minus(succ(pv57), n1) = minus(plus(n1, pv57), n1)),
% 142.08/142.35 inference(symmetry,[status(thm)],[66])).
% 142.08/142.35 tff(68,plain,
% 142.08/142.35 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 142.08/142.35 inference(bind,[status(th)],[])).
% 142.08/142.35 tff(69,plain,
% 142.08/142.35 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 142.08/142.35 inference(quant_intro,[status(thm)],[68])).
% 142.08/142.35 tff(70,plain,
% 142.08/142.35 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(71,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 142.08/142.35 tff(72,plain,
% 142.08/142.35 (![X: $i] : (minus(X, n1) = pred(X))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[71, 70])).
% 142.08/142.35 tff(73,plain,(
% 142.08/142.35 ![X: $i] : (minus(X, n1) = pred(X))),
% 142.08/142.35 inference(skolemize,[status(sab)],[72])).
% 142.08/142.35 tff(74,plain,
% 142.08/142.35 (![X: $i] : (minus(X, n1) = pred(X))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[73, 69])).
% 142.08/142.35 tff(75,plain,
% 142.08/142.35 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(succ(pv57), n1) = pred(succ(pv57)))),
% 142.08/142.35 inference(quant_inst,[status(thm)],[])).
% 142.08/142.35 tff(76,plain,
% 142.08/142.35 (minus(succ(pv57), n1) = pred(succ(pv57))),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[75, 74])).
% 142.08/142.35 tff(77,plain,
% 142.08/142.35 (pred(succ(pv57)) = minus(succ(pv57), n1)),
% 142.08/142.35 inference(symmetry,[status(thm)],[76])).
% 142.08/142.35 tff(78,plain,
% 142.08/142.35 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(79,plain,
% 142.08/142.35 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(80,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 142.08/142.35 tff(81,plain,
% 142.08/142.35 (![X: $i] : (pred(succ(X)) = X)),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[80, 79])).
% 142.08/142.35 tff(82,plain,(
% 142.08/142.35 ![X: $i] : (pred(succ(X)) = X)),
% 142.08/142.35 inference(skolemize,[status(sab)],[81])).
% 142.08/142.35 tff(83,plain,
% 142.08/142.35 (![X: $i] : (pred(succ(X)) = X)),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[82, 78])).
% 142.08/142.35 tff(84,plain,
% 142.08/142.35 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(pv57)) = pv57)),
% 142.08/142.35 inference(quant_inst,[status(thm)],[])).
% 142.08/142.35 tff(85,plain,
% 142.08/142.35 (pred(succ(pv57)) = pv57),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[84, 83])).
% 142.08/142.35 tff(86,plain,
% 142.08/142.35 (pv57 = pred(succ(pv57))),
% 142.08/142.35 inference(symmetry,[status(thm)],[85])).
% 142.08/142.35 tff(87,plain,
% 142.08/142.35 (pv57 = minus(plus(n1, pv57), n1)),
% 142.08/142.35 inference(transitivity,[status(thm)],[86, 77, 67])).
% 142.08/142.35 tff(88,plain,
% 142.08/142.35 (leq(Q!19, pv57) <=> leq(Q!19, minus(plus(n1, pv57), n1))),
% 142.08/142.35 inference(monotonicity,[status(thm)],[87])).
% 142.08/142.35 tff(89,plain,
% 142.08/142.35 (leq(Q!19, minus(plus(n1, pv57), n1)) <=> leq(Q!19, pv57)),
% 142.08/142.35 inference(symmetry,[status(thm)],[88])).
% 142.08/142.35 tff(90,assumption,(~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1))))), introduced(assumption)).
% 142.08/142.35 tff(91,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))) | leq(Q!19, minus(plus(n1, pv57), n1))),
% 142.08/142.35 inference(tautology,[status(thm)],[])).
% 142.08/142.35 tff(92,plain,
% 142.08/142.35 (leq(Q!19, minus(plus(n1, pv57), n1))),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[91, 90])).
% 142.08/142.35 tff(93,plain,
% 142.08/142.35 (leq(Q!19, pv57)),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[92, 89])).
% 142.08/142.35 tff(94,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))) | leq(n0, Q!19)),
% 142.08/142.35 inference(tautology,[status(thm)],[])).
% 142.08/142.35 tff(95,plain,
% 142.08/142.35 (leq(n0, Q!19)),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[94, 90])).
% 142.08/142.35 tff(96,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))) | leq(R!20, minus(n6, n1))),
% 142.08/142.35 inference(tautology,[status(thm)],[])).
% 142.08/142.35 tff(97,plain,
% 142.08/142.35 (leq(R!20, minus(n6, n1))),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[96, 90])).
% 142.08/142.35 tff(98,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))) | leq(n0, R!20)),
% 142.08/142.35 inference(tautology,[status(thm)],[])).
% 142.08/142.35 tff(99,plain,
% 142.08/142.35 (leq(n0, R!20)),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[98, 90])).
% 142.08/142.35 tff(100,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))) | (~(a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))),
% 142.08/142.35 inference(tautology,[status(thm)],[])).
% 142.08/142.35 tff(101,plain,
% 142.08/142.35 (~(a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[100, 90])).
% 142.08/142.35 tff(102,plain,
% 142.08/142.35 (^[G: $i, H: $i] : refl(((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))) <=> ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))))),
% 142.08/142.35 inference(bind,[status(th)],[])).
% 142.08/142.35 tff(103,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))) <=> ![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))),
% 142.08/142.35 inference(quant_intro,[status(thm)],[102])).
% 142.08/142.35 tff(104,plain,
% 142.08/142.35 (^[G: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1))) <=> (~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))))), ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) <=> (~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))))))), rewrite((~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))), ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))))), (((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> (((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))), rewrite((((~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))), (((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))))),
% 142.08/142.35 inference(bind,[status(th)],[])).
% 142.08/142.35 tff(105,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))),
% 142.08/142.35 inference(quant_intro,[status(thm)],[104])).
% 142.08/142.35 tff(106,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(107,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))),
% 142.08/142.35 inference(and_elim,[status(thm)],[20])).
% 142.08/142.35 tff(108,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[107, 106])).
% 142.08/142.35 tff(109,plain,(
% 142.08/142.35 ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))),
% 142.08/142.35 inference(skolemize,[status(sab)],[108])).
% 142.08/142.35 tff(110,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[109, 105])).
% 142.08/142.35 tff(111,plain,
% 142.08/142.35 (![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[110, 103])).
% 142.08/142.35 tff(112,plain,
% 142.08/142.35 (((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57)))) <=> ((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57)))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(113,plain,
% 142.08/142.35 (((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(Q!19, pv57))) <=> ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57)))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(114,plain,
% 142.08/142.35 (((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(Q!19, pv57)))) <=> ((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57))))),
% 142.08/142.35 inference(monotonicity,[status(thm)],[113])).
% 142.08/142.35 tff(115,plain,
% 142.08/142.35 (((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(Q!19, pv57)))) <=> ((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57)))),
% 142.08/142.35 inference(transitivity,[status(thm)],[114, 112])).
% 142.08/142.35 tff(116,plain,
% 142.08/142.35 ((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | ((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(Q!19, pv57)))),
% 142.08/142.35 inference(quant_inst,[status(thm)],[])).
% 142.08/142.35 tff(117,plain,
% 142.08/142.35 ((~![G: $i, H: $i] : ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(H, minus(n6, n1))) | (~leq(G, pv57)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, pv57))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[116, 115])).
% 142.08/142.35 tff(118,plain,
% 142.08/142.35 (~leq(Q!19, pv57)),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[117, 111, 101, 99, 97, 95])).
% 142.08/142.35 tff(119,plain,
% 142.08/142.35 ($false),
% 142.08/142.35 inference(unit_resolution,[status(thm)],[118, 93])).
% 142.08/142.35 tff(120,plain,((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))), inference(lemma,lemma(discharge,[]))).
% 142.08/142.35 tff(121,plain,
% 142.08/142.35 (leq(pv5, minus(n999, n1)) <=> leq(pv5, minus(n999, n1))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(122,plain,
% 142.08/142.35 (leq(pv5, minus(n999, n1))),
% 142.08/142.35 inference(and_elim,[status(thm)],[20])).
% 142.08/142.35 tff(123,plain,
% 142.08/142.35 (leq(pv5, minus(n999, n1))),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[122, 121])).
% 142.08/142.35 tff(124,plain,
% 142.08/142.35 (leq(n0, pv5) <=> leq(n0, pv5)),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(125,plain,
% 142.08/142.35 (leq(n0, pv5)),
% 142.08/142.35 inference(and_elim,[status(thm)],[20])).
% 142.08/142.35 tff(126,plain,
% 142.08/142.35 (leq(n0, pv5)),
% 142.08/142.35 inference(modus_ponens,[status(thm)],[125, 124])).
% 142.08/142.35 tff(127,plain,
% 142.08/142.35 (((~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(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), 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))))))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(128,plain,
% 142.08/142.35 ((leq(n0, Q!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1)))))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(129,plain,
% 142.08/142.35 ((~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1)))))),
% 142.08/142.35 inference(rewrite,[status(thm)],[])).
% 142.08/142.35 tff(130,plain,
% 142.08/142.35 ((leq(n0, Q!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (leq(n0, Q!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))))))),
% 142.08/142.35 inference(monotonicity,[status(thm)],[129])).
% 142.08/142.35 tff(131,plain,
% 142.08/142.35 ((leq(n0, Q!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1)))))),
% 142.08/142.36 inference(transitivity,[status(thm)],[130, 128])).
% 142.08/142.36 tff(132,plain,
% 142.08/142.36 ((~((~(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)))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(133,plain,
% 142.08/142.36 ((~((~(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)))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(134,plain,
% 142.08/142.36 ((~((~(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)))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(135,plain,
% 142.08/142.36 (((~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!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~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(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), n1))))))),
% 142.08/142.36 inference(monotonicity,[status(thm)],[134, 133, 132, 131])).
% 142.08/142.36 tff(136,plain,
% 142.08/142.36 (((~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!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(n0, R!20)) | (~leq(R!20, minus(n6, n1))) | (~leq(n0, Q!19)) | (~leq(Q!19, minus(plus(n1, pv57), 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))))))),
% 142.08/142.36 inference(transitivity,[status(thm)],[135, 127])).
% 142.08/142.36 tff(137,plain,
% 142.08/142.36 (((~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!19) & leq(Q!19, minus(plus(n1, pv57), n1))) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~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!19) & leq(Q!19, minus(plus(n1, pv57), n1)) & (~((~(leq(n0, R!20) & leq(R!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(138,plain,
% 142.08/142.36 ((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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))) <=> (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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(139,plain,
% 142.08/142.36 ((~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 142.08/142.36 inference(monotonicity,[status(thm)],[138])).
% 142.08/142.36 tff(140,plain,
% 142.08/142.36 ((~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 142.08/142.36 inference(rewrite,[status(thm)],[])).
% 142.08/142.36 tff(141,plain,
% 142.08/142.36 (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 142.08/142.36 inference(or_elim,[status(thm)],[19])).
% 142.08/142.36 tff(142,plain,
% 142.08/142.36 (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 142.08/142.37 inference(modus_ponens,[status(thm)],[141, 139])).
% 142.08/142.37 tff(143,plain,
% 142.08/142.37 (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 142.08/142.37 inference(modus_ponens,[status(thm)],[142, 140])).
% 142.08/142.37 tff(144,plain,
% 142.08/142.37 (~(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] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 142.08/142.37 inference(modus_ponens,[status(thm)],[143, 139])).
% 142.08/142.37 unexpected number of arguments: (let ((a!1 (refl (~ (not (leq n0 pv5)) (not (leq n0 pv5)))))
% 142.08/142.37 (a!2 (~ (not (leq pv5 (minus n999 n1))) (not (leq pv5 (minus n999 n1)))))
% 142.08/142.37 (a!3 (forall ((K $i) (L $i))
% 142.08/142.37 (let ((a!1 (not (and (leq n0 K)
% 142.08/142.37 (leq n0 L)
% 142.08/142.37 (leq K (minus n6 n1))
% 142.08/142.37 (leq L (minus n6 n1))))))
% 142.08/142.37 (or a!1
% 142.08/142.37 (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))
% 142.08/142.37 (a!4 (not (and (leq n0 K!14)
% 142.08/142.37 (leq n0 L!13)
% 142.08/142.37 (leq K!14 (minus n6 n1))
% 142.08/142.37 (leq L!13 (minus n6 n1)))))
% 142.08/142.37 (a!6 (forall ((M $i) (N $i))
% 142.08/142.37 (let ((a!1 (not (and (leq n0 M)
% 142.08/142.37 (leq n0 N)
% 142.08/142.37 (leq M (minus n3 n1))
% 142.08/142.37 (leq N (minus n3 n1))))))
% 142.08/142.37 (or a!1
% 142.08/142.37 (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))
% 142.08/142.37 (a!7 (not (and (leq n0 M!16)
% 142.08/142.37 (leq n0 N!15)
% 142.08/142.37 (leq M!16 (minus n3 n1))
% 142.08/142.37 (leq N!15 (minus n3 n1)))))
% 142.08/142.37 (a!9 (forall ((O $i) (P $i))
% 142.08/142.37 (let ((a!1 (not (and (leq n0 O)
% 142.08/142.37 (leq n0 P)
% 142.08/142.37 (leq O (minus n6 n1))
% 142.08/142.37 (leq P (minus n6 n1))))))
% 142.08/142.37 (or a!1
% 142.08/142.37 (= (a_select3 pminus_ds1_filter O P)
% 142.08/142.37 (a_select3 pminus_ds1_filter P O))))))
% 142.08/142.37 (a!10 (not (and (leq n0 O!18)
% 142.08/142.37 (leq n0 P!17)
% 142.08/142.37 (leq O!18 (minus n6 n1))
% 142.08/142.37 (leq P!17 (minus n6 n1)))))
% 142.08/142.37 (a!12 (forall ((Q $i))
% 142.08/142.37 (let ((a!1 (and (leq n0 Q) (leq Q (minus (plus n1 pv57) n1))))
% 142.08/142.37 (a!2 (forall ((R $i))
% 142.08/142.37 (let ((a!1 (not (and (leq n0 R)
% 142.08/142.37 (leq R (minus n6 n1))))))
% 142.08/142.37 (or a!1
% 142.08/142.37 (= (a_select3 id_ds1_filter Q R)
% 142.08/142.37 (a_select3 id_ds1_filter R Q)))))))
% 142.08/142.37 (or (not a!1) a!2))))
% 142.08/142.37 (a!13 (and (leq n0 Q!19) (leq Q!19 (minus (plus n1 pv57) n1))))
% 142.08/142.37 (a!14 (forall ((R $i))
% 142.08/142.37 (let ((a!1 (not (and (leq n0 R) (leq R (minus n6 n1))))))
% 142.08/142.37 (or a!1
% 142.08/142.37 (= (a_select3 id_ds1_filter Q!19 R)
% 142.08/142.37 (a_select3 id_ds1_filter R Q!19))))))
% 142.08/142.37 (a!16 (not (and (leq n0 R!20) (leq R!20 (minus n6 n1))))))
% 142.08/142.37 (let ((a!5 (not (or a!4
% 142.08/142.37 (= (a_select3 q_ds1_filter K!14 L!13)
% 142.08/142.37 (a_select3 q_ds1_filter L!13 K!14)))))
% 142.08/142.37 (a!8 (not (or a!7
% 142.08/142.37 (= (a_select3 r_ds1_filter M!16 N!15)
% 142.08/142.37 (a_select3 r_ds1_filter N!15 M!16)))))
% 142.08/142.37 (a!11 (not (or a!10
% 142.08/142.37 (= (a_select3 pminus_ds1_filter O!18 P!17)
% 142.08/142.37 (a_select3 pminus_ds1_filter P!17 O!18)))))
% 142.08/142.37 (a!15 (~ (not a!12) (not (or (not a!13) a!14))))
% 142.08/142.37 (a!17 (not (or a!16
% 142.08/142.37 (= (a_select3 id_ds1_filter Q!19 R!20)
% 142.08/142.37 (a_select3 id_ds1_filter R!20 Q!19)))))
% 142.08/142.37 (a!20 (not (and (leq n0 pv5) (leq pv5 (minus n999 n1)) a!3 a!6 a!9 a!12))))
% 142.08/142.37 (let ((a!18 (~ (not (or (not a!13) a!14)) (and a!13 a!17)))
% 142.08/142.37 (a!21 (or (not (leq n0 pv5))
% 142.08/142.37 (not (leq pv5 (minus n999 n1)))
% 142.08/142.37 a!5
% 142.08/142.37 a!8
% 142.08/142.37 a!11
% 142.08/142.37 (and a!13 a!17))))
% 142.08/142.37 (let ((a!19 (nnf-neg (refl (~ a!13 a!13)) (sk (~ (not a!14) a!17)) a!18)))
% 142.08/142.37 (nnf-neg a!1
% 142.08/142.37 (refl a!2)
% 142.08/142.37 (sk (~ (not a!3) a!5))
% 142.08/142.37 (sk (~ (not a!6) a!8))
% 142.08/142.37 (sk (~ (not a!9) a!11))
% 142.08/142.37 (trans (sk a!15) a!19 (~ (not a!12) (and a!13 a!17)))
% 142.08/142.37 (~ a!20 a!21))))))
% 142.08/142.37 Proof display could not be completed: unexpected number of arguments
% 142.56/142.89 % E exiting
%------------------------------------------------------------------------------