%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV114+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:31:32 AM UTC 2025
% Result : Theorem 80.87s 81.11s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV114+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:27:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 80.87/81.11 % SZS status Theorem
% 80.87/81.11 % SZS output start Proof
% 80.87/81.11 tff(leq_type, type, (
% 80.87/81.11 leq: ( $i * $i ) > $o)).
% 80.87/81.11 tff(minus_type, type, (
% 80.87/81.11 minus: ( $i * $i ) > $i)).
% 80.87/81.11 tff(n1_type, type, (
% 80.87/81.11 n1: $i)).
% 80.87/81.11 tff(n6_type, type, (
% 80.87/81.11 n6: $i)).
% 80.87/81.11 tff(tptp_fun_H_13_type, type, (
% 80.87/81.11 tptp_fun_H_13: $i)).
% 80.87/81.11 tff(tptp_fun_G_14_type, type, (
% 80.87/81.11 tptp_fun_G_14: $i)).
% 80.87/81.11 tff(n0_type, type, (
% 80.87/81.11 n0: $i)).
% 80.87/81.11 tff(a_select3_type, type, (
% 80.87/81.11 a_select3: ( $i * $i * $i ) > $i)).
% 80.87/81.11 tff(q_ds1_filter_type, type, (
% 80.87/81.11 q_ds1_filter: $i)).
% 80.87/81.11 tff(tptp_fun_L_17_type, type, (
% 80.87/81.11 tptp_fun_L_17: $i)).
% 80.87/81.11 tff(tptp_fun_K_18_type, type, (
% 80.87/81.11 tptp_fun_K_18: $i)).
% 80.87/81.11 tff(pminus_ds1_filter_type, type, (
% 80.87/81.11 pminus_ds1_filter: $i)).
% 80.87/81.11 tff(r_ds1_filter_type, type, (
% 80.87/81.11 r_ds1_filter: $i)).
% 80.87/81.11 tff(n3_type, type, (
% 80.87/81.11 n3: $i)).
% 80.87/81.11 tff(n999_type, type, (
% 80.87/81.11 n999: $i)).
% 80.87/81.11 tff(pv5_type, type, (
% 80.87/81.11 pv5: $i)).
% 80.87/81.11 tff(id_ds1_filter_type, type, (
% 80.87/81.11 id_ds1_filter: $i)).
% 80.87/81.11 tff(tptp_fun_J_15_type, type, (
% 80.87/81.11 tptp_fun_J_15: $i)).
% 80.87/81.11 tff(tptp_fun_I_16_type, type, (
% 80.87/81.11 tptp_fun_I_16: $i)).
% 80.87/81.11 tff(tptp_fun_M_19_type, type, (
% 80.87/81.11 tptp_fun_M_19: $i)).
% 80.87/81.11 tff(tptp_fun_N_20_type, type, (
% 80.87/81.11 tptp_fun_N_20: $i)).
% 80.87/81.11 tff(tptp_minus_1_type, type, (
% 80.87/81.11 tptp_minus_1: $i)).
% 80.87/81.11 tff(pred_type, type, (
% 80.87/81.11 pred: $i > $i)).
% 80.87/81.11 tff(succ_type, type, (
% 80.87/81.11 succ: $i > $i)).
% 80.87/81.11 tff(gt_type, type, (
% 80.87/81.11 gt: ( $i * $i ) > $o)).
% 80.87/81.11 tff(1,assumption,(~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))), introduced(assumption)).
% 80.87/81.11 tff(2,plain,
% 80.87/81.11 (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))) | leq(L!17, minus(n6, n1))),
% 80.87/81.11 inference(tautology,[status(thm)],[])).
% 80.87/81.11 tff(3,plain,
% 80.87/81.11 (leq(L!17, minus(n6, n1))),
% 80.87/81.11 inference(unit_resolution,[status(thm)],[2, 1])).
% 80.87/81.11 tff(4,plain,
% 80.87/81.11 (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))) | leq(K!18, minus(n6, n1))),
% 80.87/81.11 inference(tautology,[status(thm)],[])).
% 80.87/81.11 tff(5,plain,
% 80.87/81.11 (leq(K!18, minus(n6, n1))),
% 80.87/81.11 inference(unit_resolution,[status(thm)],[4, 1])).
% 80.87/81.11 tff(6,plain,
% 80.87/81.11 (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))) | leq(n0, L!17)),
% 80.87/81.11 inference(tautology,[status(thm)],[])).
% 80.87/81.11 tff(7,plain,
% 80.87/81.11 (leq(n0, L!17)),
% 80.87/81.11 inference(unit_resolution,[status(thm)],[6, 1])).
% 80.87/81.11 tff(8,plain,
% 80.87/81.11 (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))) | leq(n0, K!18)),
% 80.87/81.11 inference(tautology,[status(thm)],[])).
% 80.87/81.11 tff(9,plain,
% 80.87/81.11 (leq(n0, K!18)),
% 80.87/81.11 inference(unit_resolution,[status(thm)],[8, 1])).
% 80.87/81.11 tff(10,plain,
% 80.87/81.11 (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))) | (~(a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))),
% 80.87/81.11 inference(tautology,[status(thm)],[])).
% 80.87/81.11 tff(11,plain,
% 80.87/81.11 (~(a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18))),
% 80.87/81.11 inference(unit_resolution,[status(thm)],[10, 1])).
% 80.87/81.11 tff(12,plain,
% 80.87/81.11 (^[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)))))),
% 80.87/81.11 inference(bind,[status(th)],[])).
% 80.87/81.11 tff(13,plain,
% 80.87/81.11 (![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))))),
% 80.87/81.11 inference(quant_intro,[status(thm)],[12])).
% 80.87/81.11 tff(14,plain,
% 80.87/81.11 (^[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))))))),
% 80.87/81.11 inference(bind,[status(th)],[])).
% 80.87/81.11 tff(15,plain,
% 80.87/81.11 (![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))))),
% 80.87/81.11 inference(quant_intro,[status(thm)],[14])).
% 80.87/81.11 tff(16,plain,
% 80.87/81.11 (![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)))),
% 80.87/81.11 inference(rewrite,[status(thm)],[])).
% 80.87/81.11 tff(17,plain,
% 80.87/81.11 ((~(((((leq(n0, pv5) & leq(pv5, minus(n999, 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)))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G)))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n3, n1))) & leq(J, minus(n3, n1))) => (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K)))) & ![M: $i] : ((leq(n0, M) & leq(M, minus(n0, n1))) => ![N: $i] : ((leq(n0, N) & leq(N, minus(n6, n1))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))) <=> (~((~(leq(n0, pv5) & leq(pv5, minus(n999, 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))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))))),
% 80.87/81.11 inference(rewrite,[status(thm)],[])).
% 80.87/81.11 tff(18,axiom,(~(((((leq(n0, pv5) & leq(pv5, minus(n999, 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)))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G)))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n3, n1))) & leq(J, minus(n3, n1))) => (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K)))) & ![M: $i] : ((leq(n0, M) & leq(M, minus(n0, n1))) => ![N: $i] : ((leq(n0, N) & leq(N, minus(n6, n1))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0007')).
% 80.87/81.11 tff(19,plain,
% 80.87/81.11 (~((~(leq(n0, pv5) & leq(pv5, minus(n999, 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))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 80.87/81.12 inference(modus_ponens,[status(thm)],[18, 17])).
% 80.87/81.12 tff(20,plain,
% 80.87/81.12 (leq(n0, pv5) & leq(pv5, minus(n999, 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)))),
% 80.87/81.12 inference(or_elim,[status(thm)],[19])).
% 80.87/81.12 tff(21,plain,
% 80.87/81.12 (![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)))),
% 80.87/81.12 inference(and_elim,[status(thm)],[20])).
% 80.87/81.12 tff(22,plain,
% 80.87/81.12 (![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)))),
% 80.87/81.12 inference(modus_ponens,[status(thm)],[21, 16])).
% 80.87/81.12 tff(23,plain,(
% 80.87/81.12 ![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)))),
% 80.87/81.12 inference(skolemize,[status(sab)],[22])).
% 80.87/81.12 tff(24,plain,
% 80.87/81.12 (![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))))),
% 80.87/81.12 inference(modus_ponens,[status(thm)],[23, 15])).
% 80.87/81.12 tff(25,plain,
% 80.87/81.12 (![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))))),
% 80.87/81.12 inference(modus_ponens,[status(thm)],[24, 13])).
% 80.87/81.12 tff(26,plain,
% 80.87/81.12 (((~![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, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!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, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))),
% 80.87/81.12 inference(rewrite,[status(thm)],[])).
% 80.87/81.12 tff(27,plain,
% 80.87/81.12 ((~![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, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))),
% 80.87/81.12 inference(quant_inst,[status(thm)],[])).
% 80.87/81.12 tff(28,plain,
% 80.87/81.12 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(n0, E)) | (~leq(n0, F)) | (~leq(E, minus(n6, n1))) | (~leq(F, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))),
% 80.87/81.12 inference(modus_ponens,[status(thm)],[27, 26])).
% 80.87/81.12 tff(29,plain,
% 80.87/81.12 ($false),
% 80.87/81.12 inference(unit_resolution,[status(thm)],[28, 25, 11, 9, 7, 5, 3])).
% 80.87/81.12 tff(30,plain,((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))), inference(lemma,lemma(discharge,[]))).
% 80.87/81.12 tff(31,assumption,(~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))), introduced(assumption)).
% 80.92/81.12 tff(32,plain,
% 80.92/81.12 (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))) | leq(J!15, minus(n3, n1))),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(33,plain,
% 80.92/81.12 (leq(J!15, minus(n3, n1))),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[32, 31])).
% 80.92/81.12 tff(34,plain,
% 80.92/81.12 (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))) | leq(I!16, minus(n3, n1))),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(35,plain,
% 80.92/81.12 (leq(I!16, minus(n3, n1))),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[34, 31])).
% 80.92/81.12 tff(36,plain,
% 80.92/81.12 (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))) | leq(n0, J!15)),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(37,plain,
% 80.92/81.12 (leq(n0, J!15)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[36, 31])).
% 80.92/81.12 tff(38,plain,
% 80.92/81.12 (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))) | leq(n0, I!16)),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(39,plain,
% 80.92/81.12 (leq(n0, I!16)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[38, 31])).
% 80.92/81.12 tff(40,plain,
% 80.92/81.12 (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))) | (~(a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(41,plain,
% 80.92/81.12 (~(a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16))),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[40, 31])).
% 80.92/81.12 tff(42,plain,
% 80.92/81.12 (^[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)))))),
% 80.92/81.12 inference(bind,[status(th)],[])).
% 80.92/81.12 tff(43,plain,
% 80.92/81.12 (![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))))),
% 80.92/81.12 inference(quant_intro,[status(thm)],[42])).
% 80.92/81.12 tff(44,plain,
% 80.92/81.12 (^[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))))))),
% 80.92/81.12 inference(bind,[status(th)],[])).
% 80.92/81.12 tff(45,plain,
% 80.92/81.12 (![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))))),
% 80.92/81.12 inference(quant_intro,[status(thm)],[44])).
% 80.92/81.12 tff(46,plain,
% 80.92/81.12 (![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)))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(47,plain,
% 80.92/81.12 (![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)))),
% 80.92/81.12 inference(and_elim,[status(thm)],[20])).
% 80.92/81.12 tff(48,plain,
% 80.92/81.12 (![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)))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[47, 46])).
% 80.92/81.12 tff(49,plain,(
% 80.92/81.12 ![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)))),
% 80.92/81.12 inference(skolemize,[status(sab)],[48])).
% 80.92/81.12 tff(50,plain,
% 80.92/81.12 (![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))))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[49, 45])).
% 80.92/81.12 tff(51,plain,
% 80.92/81.12 (![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))))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[50, 43])).
% 80.92/81.12 tff(52,plain,
% 80.92/81.12 (((~![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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(53,plain,
% 80.92/81.12 ((~![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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))),
% 80.92/81.12 inference(quant_inst,[status(thm)],[])).
% 80.92/81.12 tff(54,plain,
% 80.92/81.12 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[53, 52])).
% 80.92/81.12 tff(55,plain,
% 80.92/81.12 ($false),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[54, 51, 41, 39, 37, 35, 33])).
% 80.92/81.12 tff(56,plain,((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))), inference(lemma,lemma(discharge,[]))).
% 80.92/81.12 tff(57,plain,
% 80.92/81.12 (^[X: $i] : refl((minus(X, n1) = pred(X)) <=> (minus(X, n1) = pred(X)))),
% 80.92/81.12 inference(bind,[status(th)],[])).
% 80.92/81.12 tff(58,plain,
% 80.92/81.12 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 80.92/81.12 inference(quant_intro,[status(thm)],[57])).
% 80.92/81.12 tff(59,plain,
% 80.92/81.12 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(60,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 80.92/81.12 tff(61,plain,
% 80.92/81.12 (![X: $i] : (minus(X, n1) = pred(X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[60, 59])).
% 80.92/81.12 tff(62,plain,(
% 80.92/81.12 ![X: $i] : (minus(X, n1) = pred(X))),
% 80.92/81.12 inference(skolemize,[status(sab)],[61])).
% 80.92/81.12 tff(63,plain,
% 80.92/81.12 (![X: $i] : (minus(X, n1) = pred(X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[62, 58])).
% 80.92/81.12 tff(64,plain,
% 80.92/81.12 ((~![X: $i] : (minus(X, n1) = pred(X))) | (minus(n0, n1) = pred(n0))),
% 80.92/81.12 inference(quant_inst,[status(thm)],[])).
% 80.92/81.12 tff(65,plain,
% 80.92/81.12 (minus(n0, n1) = pred(n0)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[64, 63])).
% 80.92/81.12 tff(66,plain,
% 80.92/81.12 (pred(n0) = minus(n0, n1)),
% 80.92/81.12 inference(symmetry,[status(thm)],[65])).
% 80.92/81.12 tff(67,plain,
% 80.92/81.12 ((succ(tptp_minus_1) = n0) <=> (succ(tptp_minus_1) = n0)),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(68,axiom,(succ(tptp_minus_1) = n0), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_tptp_minus_1')).
% 80.92/81.12 tff(69,plain,
% 80.92/81.12 (succ(tptp_minus_1) = n0),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[68, 67])).
% 80.92/81.12 tff(70,plain,
% 80.92/81.12 (n0 = succ(tptp_minus_1)),
% 80.92/81.12 inference(symmetry,[status(thm)],[69])).
% 80.92/81.12 tff(71,plain,
% 80.92/81.12 (pred(n0) = pred(succ(tptp_minus_1))),
% 80.92/81.12 inference(monotonicity,[status(thm)],[70])).
% 80.92/81.12 tff(72,plain,
% 80.92/81.12 (pred(succ(tptp_minus_1)) = pred(n0)),
% 80.92/81.12 inference(symmetry,[status(thm)],[71])).
% 80.92/81.12 tff(73,plain,
% 80.92/81.12 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(74,plain,
% 80.92/81.12 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(75,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 80.92/81.12 tff(76,plain,
% 80.92/81.12 (![X: $i] : (pred(succ(X)) = X)),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[75, 74])).
% 80.92/81.12 tff(77,plain,(
% 80.92/81.12 ![X: $i] : (pred(succ(X)) = X)),
% 80.92/81.12 inference(skolemize,[status(sab)],[76])).
% 80.92/81.12 tff(78,plain,
% 80.92/81.12 (![X: $i] : (pred(succ(X)) = X)),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[77, 73])).
% 80.92/81.12 tff(79,plain,
% 80.92/81.12 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 80.92/81.12 inference(quant_inst,[status(thm)],[])).
% 80.92/81.12 tff(80,plain,
% 80.92/81.12 (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[79, 78])).
% 80.92/81.12 tff(81,plain,
% 80.92/81.12 (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 80.92/81.12 inference(symmetry,[status(thm)],[80])).
% 80.92/81.12 tff(82,plain,
% 80.92/81.12 (tptp_minus_1 = minus(n0, n1)),
% 80.92/81.12 inference(transitivity,[status(thm)],[81, 72, 66])).
% 80.92/81.12 tff(83,plain,
% 80.92/81.12 (leq(M!19, tptp_minus_1) <=> leq(M!19, minus(n0, n1))),
% 80.92/81.12 inference(monotonicity,[status(thm)],[82])).
% 80.92/81.12 tff(84,plain,
% 80.92/81.12 (leq(M!19, minus(n0, n1)) <=> leq(M!19, tptp_minus_1)),
% 80.92/81.12 inference(symmetry,[status(thm)],[83])).
% 80.92/81.12 tff(85,assumption,(~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1))))), introduced(assumption)).
% 80.92/81.12 tff(86,plain,
% 80.92/81.12 (((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))) | leq(M!19, minus(n0, n1))),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(87,plain,
% 80.92/81.12 (leq(M!19, minus(n0, n1))),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[86, 85])).
% 80.92/81.12 tff(88,plain,
% 80.92/81.12 (leq(M!19, tptp_minus_1)),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[87, 84])).
% 80.92/81.12 tff(89,plain,
% 80.92/81.12 (pred(n0) = tptp_minus_1),
% 80.92/81.12 inference(transitivity,[status(thm)],[71, 80])).
% 80.92/81.12 tff(90,plain,
% 80.92/81.12 (leq(n0, pred(n0)) <=> leq(n0, tptp_minus_1)),
% 80.92/81.12 inference(monotonicity,[status(thm)],[89])).
% 80.92/81.12 tff(91,plain,
% 80.92/81.12 ((~leq(n0, pred(n0))) <=> (~leq(n0, tptp_minus_1))),
% 80.92/81.12 inference(monotonicity,[status(thm)],[90])).
% 80.92/81.12 tff(92,plain,
% 80.92/81.12 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 80.92/81.12 inference(bind,[status(th)],[])).
% 80.92/81.12 tff(93,plain,
% 80.92/81.12 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 80.92/81.12 inference(quant_intro,[status(thm)],[92])).
% 80.92/81.12 tff(94,plain,
% 80.92/81.12 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(95,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 80.92/81.12 tff(96,plain,
% 80.92/81.12 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[95, 94])).
% 80.92/81.12 tff(97,plain,(
% 80.92/81.12 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 80.92/81.12 inference(skolemize,[status(sab)],[96])).
% 80.92/81.12 tff(98,plain,
% 80.92/81.12 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[97, 93])).
% 80.92/81.12 tff(99,plain,
% 80.92/81.12 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(n0, pred(n0)) <=> gt(n0, n0))),
% 80.92/81.12 inference(quant_inst,[status(thm)],[])).
% 80.92/81.12 tff(100,plain,
% 80.92/81.12 (leq(n0, pred(n0)) <=> gt(n0, n0)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[99, 98])).
% 80.92/81.12 tff(101,plain,
% 80.92/81.12 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 80.92/81.12 inference(bind,[status(th)],[])).
% 80.92/81.12 tff(102,plain,
% 80.92/81.12 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 80.92/81.12 inference(quant_intro,[status(thm)],[101])).
% 80.92/81.12 tff(103,plain,
% 80.92/81.12 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(104,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 80.92/81.12 tff(105,plain,
% 80.92/81.12 (![X: $i] : (~gt(X, X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[104, 103])).
% 80.92/81.12 tff(106,plain,(
% 80.92/81.12 ![X: $i] : (~gt(X, X))),
% 80.92/81.12 inference(skolemize,[status(sab)],[105])).
% 80.92/81.12 tff(107,plain,
% 80.92/81.12 (![X: $i] : (~gt(X, X))),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[106, 102])).
% 80.92/81.12 tff(108,plain,
% 80.92/81.12 ((~![X: $i] : (~gt(X, X))) | (~gt(n0, n0))),
% 80.92/81.12 inference(quant_inst,[status(thm)],[])).
% 80.92/81.12 tff(109,plain,
% 80.92/81.12 (~gt(n0, n0)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[108, 107])).
% 80.92/81.12 tff(110,plain,
% 80.92/81.12 ((~(leq(n0, pred(n0)) <=> gt(n0, n0))) | (~leq(n0, pred(n0))) | gt(n0, n0)),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(111,plain,
% 80.92/81.12 (~leq(n0, pred(n0))),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[110, 109, 100])).
% 80.92/81.12 tff(112,plain,
% 80.92/81.12 (~leq(n0, tptp_minus_1)),
% 80.92/81.12 inference(modus_ponens,[status(thm)],[111, 91])).
% 80.92/81.12 tff(113,plain,
% 80.92/81.12 (((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))) | leq(n0, M!19)),
% 80.92/81.12 inference(tautology,[status(thm)],[])).
% 80.92/81.12 tff(114,plain,
% 80.92/81.12 (leq(n0, M!19)),
% 80.92/81.12 inference(unit_resolution,[status(thm)],[113, 85])).
% 80.92/81.12 tff(115,plain,
% 80.92/81.12 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 80.92/81.12 inference(rewrite,[status(thm)],[])).
% 80.92/81.12 tff(116,plain,
% 80.92/81.12 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 80.92/81.13 inference(bind,[status(th)],[])).
% 80.92/81.13 tff(117,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 80.92/81.13 inference(quant_intro,[status(thm)],[116])).
% 80.92/81.13 tff(118,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(119,plain,
% 80.92/81.13 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 80.92/81.13 inference(bind,[status(th)],[])).
% 80.92/81.13 tff(120,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 80.92/81.13 inference(quant_intro,[status(thm)],[119])).
% 80.92/81.13 tff(121,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 80.92/81.13 tff(122,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[121, 120])).
% 80.92/81.13 tff(123,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[122, 118])).
% 80.92/81.13 tff(124,plain,(
% 80.92/81.13 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 80.92/81.13 inference(skolemize,[status(sab)],[123])).
% 80.92/81.13 tff(125,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[124, 117])).
% 80.92/81.13 tff(126,plain,
% 80.92/81.13 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[125, 115])).
% 80.92/81.13 tff(127,plain,
% 80.92/81.13 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(128,plain,
% 80.92/81.13 ((leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)) | (~leq(n0, M!19))) <=> ((~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(129,plain,
% 80.92/81.13 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)) | (~leq(n0, M!19)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1))))),
% 80.92/81.13 inference(monotonicity,[status(thm)],[128])).
% 80.92/81.13 tff(130,plain,
% 80.92/81.13 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)) | (~leq(n0, M!19)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)))),
% 80.92/81.13 inference(transitivity,[status(thm)],[129, 127])).
% 80.92/81.13 tff(131,plain,
% 80.92/81.13 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1)) | (~leq(n0, M!19)))),
% 80.92/81.13 inference(quant_inst,[status(thm)],[])).
% 80.92/81.13 tff(132,plain,
% 80.92/81.13 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(n0, M!19)) | leq(n0, tptp_minus_1) | (~leq(M!19, tptp_minus_1))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[131, 130])).
% 80.92/81.13 tff(133,plain,
% 80.92/81.13 (~leq(M!19, tptp_minus_1)),
% 80.92/81.13 inference(unit_resolution,[status(thm)],[132, 126, 114, 112])).
% 80.92/81.13 tff(134,plain,
% 80.92/81.13 ($false),
% 80.92/81.13 inference(unit_resolution,[status(thm)],[133, 88])).
% 80.92/81.13 tff(135,plain,((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))), inference(lemma,lemma(discharge,[]))).
% 80.92/81.13 tff(136,plain,
% 80.92/81.13 (leq(pv5, minus(n999, n1)) <=> leq(pv5, minus(n999, n1))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(137,plain,
% 80.92/81.13 (leq(pv5, minus(n999, n1))),
% 80.92/81.13 inference(and_elim,[status(thm)],[20])).
% 80.92/81.13 tff(138,plain,
% 80.92/81.13 (leq(pv5, minus(n999, n1))),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[137, 136])).
% 80.92/81.13 tff(139,plain,
% 80.92/81.13 (leq(n0, pv5) <=> leq(n0, pv5)),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(140,plain,
% 80.92/81.13 (leq(n0, pv5)),
% 80.92/81.13 inference(and_elim,[status(thm)],[20])).
% 80.92/81.13 tff(141,plain,
% 80.92/81.13 (leq(n0, pv5)),
% 80.92/81.13 inference(modus_ponens,[status(thm)],[140, 139])).
% 80.92/81.13 tff(142,plain,
% 80.92/81.13 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(n0, G!14)) | (~leq(n0, H!13)) | (~leq(G!14, minus(n6, n1))) | (~leq(H!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1))))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(n0, G!14)) | (~leq(n0, H!13)) | (~leq(G!14, minus(n6, n1))) | (~leq(H!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(143,plain,
% 80.92/81.13 ((leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1)))))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(144,plain,
% 80.92/81.13 ((~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1)))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(145,plain,
% 80.92/81.13 ((leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))))))),
% 80.92/81.13 inference(monotonicity,[status(thm)],[144])).
% 80.92/81.13 tff(146,plain,
% 80.92/81.13 ((leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1)))))),
% 80.92/81.13 inference(transitivity,[status(thm)],[145, 143])).
% 80.92/81.13 tff(147,plain,
% 80.92/81.13 ((~((~(leq(n0, K!18) & leq(n0, L!17) & leq(K!18, minus(n6, n1)) & leq(L!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) <=> (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1)))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(148,plain,
% 80.92/81.13 ((~((~(leq(n0, I!16) & leq(n0, J!15) & leq(I!16, minus(n3, n1)) & leq(J!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) <=> (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1)))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(149,plain,
% 80.92/81.13 ((~((~(leq(n0, G!14) & leq(n0, H!13) & leq(G!14, minus(n6, n1)) & leq(H!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) <=> (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(n0, G!14)) | (~leq(n0, H!13)) | (~leq(G!14, minus(n6, n1))) | (~leq(H!13, minus(n6, n1)))))),
% 80.92/81.13 inference(rewrite,[status(thm)],[])).
% 80.92/81.13 tff(150,plain,
% 80.92/81.13 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, G!14) & leq(n0, H!13) & leq(G!14, minus(n6, n1)) & leq(H!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(n0, I!16) & leq(n0, J!15) & leq(I!16, minus(n3, n1)) & leq(J!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(n0, K!18) & leq(n0, L!17) & leq(K!18, minus(n6, n1)) & leq(L!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(n0, G!14)) | (~leq(n0, H!13)) | (~leq(G!14, minus(n6, n1))) | (~leq(H!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1))))))),
% 80.92/81.13 inference(monotonicity,[status(thm)],[149, 148, 147, 146])).
% 80.92/81.13 tff(151,plain,
% 80.92/81.13 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, G!14) & leq(n0, H!13) & leq(G!14, minus(n6, n1)) & leq(H!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(n0, I!16) & leq(n0, J!15) & leq(I!16, minus(n3, n1)) & leq(J!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(n0, K!18) & leq(n0, L!17) & leq(K!18, minus(n6, n1)) & leq(L!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(n0, N!20)) | (~leq(N!20, minus(n6, n1))) | (~leq(n0, M!19)) | (~leq(M!19, minus(n0, n1))))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(n0, G!14)) | (~leq(n0, H!13)) | (~leq(G!14, minus(n6, n1))) | (~leq(H!13, minus(n6, n1))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(n0, I!16)) | (~leq(n0, J!15)) | (~leq(I!16, minus(n3, n1))) | (~leq(J!15, minus(n3, n1))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(n0, K!18)) | (~leq(n0, L!17)) | (~leq(K!18, minus(n6, n1))) | (~leq(L!17, minus(n6, n1))))))),
% 80.92/81.14 inference(transitivity,[status(thm)],[150, 142])).
% 80.92/81.14 tff(152,plain,
% 80.92/81.14 (((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, G!14) & leq(n0, H!13) & leq(G!14, minus(n6, n1)) & leq(H!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(n0, I!16) & leq(n0, J!15) & leq(I!16, minus(n3, n1)) & leq(J!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(n0, K!18) & leq(n0, L!17) & leq(K!18, minus(n6, n1)) & leq(L!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | ((leq(n0, M!19) & leq(M!19, minus(n0, n1))) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~leq(n0, pv5)) | (~leq(pv5, minus(n999, n1))) | (~((~(leq(n0, G!14) & leq(n0, H!13) & leq(G!14, minus(n6, n1)) & leq(H!13, minus(n6, n1)))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(n0, I!16) & leq(n0, J!15) & leq(I!16, minus(n3, n1)) & leq(J!15, minus(n3, n1)))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(n0, K!18) & leq(n0, L!17) & leq(K!18, minus(n6, n1)) & leq(L!17, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(n0, M!19) & leq(M!19, minus(n0, n1)) & (~((~(leq(n0, N!20) & leq(N!20, minus(n6, n1)))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))))),
% 80.92/81.14 inference(rewrite,[status(thm)],[])).
% 80.92/81.14 tff(153,plain,
% 80.92/81.14 ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 80.92/81.14 inference(rewrite,[status(thm)],[])).
% 80.92/81.14 tff(154,plain,
% 80.92/81.14 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 80.92/81.14 inference(monotonicity,[status(thm)],[153])).
% 80.92/81.14 tff(155,plain,
% 80.92/81.14 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 80.92/81.14 inference(rewrite,[status(thm)],[])).
% 80.92/81.14 tff(156,plain,
% 80.92/81.14 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 80.92/81.14 inference(or_elim,[status(thm)],[19])).
% 80.92/81.14 tff(157,plain,
% 80.92/81.14 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 80.92/81.14 inference(modus_ponens,[status(thm)],[156, 154])).
% 80.92/81.14 tff(158,plain,
% 80.92/81.14 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 80.92/81.14 inference(modus_ponens,[status(thm)],[157, 155])).
% 80.92/81.14 tff(159,plain,
% 80.92/81.14 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 80.92/81.14 inference(modus_ponens,[status(thm)],[158, 154])).
% 80.92/81.14 unexpected number of arguments: (let ((a!1 (refl (~ (not (leq n0 pv5)) (not (leq n0 pv5)))))
% 80.92/81.14 (a!2 (~ (not (leq pv5 (minus n999 n1))) (not (leq pv5 (minus n999 n1)))))
% 80.92/81.14 (a!3 (forall ((G $i) (H $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 G)
% 80.92/81.14 (leq n0 H)
% 80.92/81.14 (leq G (minus n6 n1))
% 80.92/81.14 (leq H (minus n6 n1))))))
% 80.92/81.14 (or a!1
% 80.92/81.14 (= (a_select3 q_ds1_filter G H) (a_select3 q_ds1_filter H G))))))
% 80.92/81.14 (a!4 (not (and (leq n0 G!14)
% 80.92/81.14 (leq n0 H!13)
% 80.92/81.14 (leq G!14 (minus n6 n1))
% 80.92/81.14 (leq H!13 (minus n6 n1)))))
% 80.92/81.14 (a!6 (forall ((I $i) (J $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 I)
% 80.92/81.14 (leq n0 J)
% 80.92/81.14 (leq I (minus n3 n1))
% 80.92/81.14 (leq J (minus n3 n1))))))
% 80.92/81.14 (or a!1
% 80.92/81.14 (= (a_select3 r_ds1_filter I J) (a_select3 r_ds1_filter J I))))))
% 80.92/81.14 (a!7 (not (and (leq n0 I!16)
% 80.92/81.14 (leq n0 J!15)
% 80.92/81.14 (leq I!16 (minus n3 n1))
% 80.92/81.14 (leq J!15 (minus n3 n1)))))
% 80.92/81.14 (a!9 (forall ((K $i) (L $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 K)
% 80.92/81.14 (leq n0 L)
% 80.92/81.14 (leq K (minus n6 n1))
% 80.92/81.14 (leq L (minus n6 n1))))))
% 80.92/81.14 (or a!1
% 80.92/81.14 (= (a_select3 pminus_ds1_filter K L)
% 80.92/81.14 (a_select3 pminus_ds1_filter L K))))))
% 80.92/81.14 (a!10 (not (and (leq n0 K!18)
% 80.92/81.14 (leq n0 L!17)
% 80.92/81.14 (leq K!18 (minus n6 n1))
% 80.92/81.14 (leq L!17 (minus n6 n1)))))
% 80.92/81.14 (a!12 (forall ((M $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 M) (leq M (minus n0 n1)))))
% 80.92/81.14 (a!2 (forall ((N $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 N)
% 80.92/81.14 (leq N (minus n6 n1))))))
% 80.92/81.14 (or a!1
% 80.92/81.14 (= (a_select3 id_ds1_filter M N)
% 80.92/81.14 (a_select3 id_ds1_filter N M)))))))
% 80.92/81.14 (or a!1 a!2))))
% 80.92/81.14 (a!13 (not (and (leq n0 M!19) (leq M!19 (minus n0 n1)))))
% 80.92/81.14 (a!14 (forall ((N $i))
% 80.92/81.14 (let ((a!1 (not (and (leq n0 N) (leq N (minus n6 n1))))))
% 80.92/81.14 (or a!1
% 80.92/81.14 (= (a_select3 id_ds1_filter M!19 N)
% 80.92/81.14 (a_select3 id_ds1_filter N M!19))))))
% 80.92/81.14 (a!16 (~ (and (leq n0 M!19) (leq M!19 (minus n0 n1)))
% 80.92/81.14 (and (leq n0 M!19) (leq M!19 (minus n0 n1)))))
% 80.92/81.14 (a!17 (not (and (leq n0 N!20) (leq N!20 (minus n6 n1))))))
% 80.92/81.14 (let ((a!5 (not (or a!4
% 80.92/81.14 (= (a_select3 q_ds1_filter G!14 H!13)
% 80.92/81.15 (a_select3 q_ds1_filter H!13 G!14)))))
% 80.92/81.15 (a!8 (not (or a!7
% 80.92/81.15 (= (a_select3 r_ds1_filter I!16 J!15)
% 80.92/81.15 (a_select3 r_ds1_filter J!15 I!16)))))
% 80.92/81.15 (a!11 (not (or a!10
% 80.92/81.15 (= (a_select3 pminus_ds1_filter K!18 L!17)
% 80.92/81.15 (a_select3 pminus_ds1_filter L!17 K!18)))))
% 80.92/81.15 (a!15 (sk (~ (not a!12) (not (or a!13 a!14)))))
% 80.92/81.15 (a!18 (not (or a!17
% 80.92/81.15 (= (a_select3 id_ds1_filter M!19 N!20)
% 80.92/81.15 (a_select3 id_ds1_filter N!20 M!19)))))
% 80.92/81.15 (a!21 (not (and (leq n0 pv5) (leq pv5 (minus n999 n1)) a!3 a!6 a!9 a!12))))
% 80.92/81.15 (let ((a!19 (and (and (leq n0 M!19) (leq M!19 (minus n0 n1))) a!18)))
% 80.92/81.15 (let ((a!20 (nnf-neg (refl a!16)
% 80.92/81.15 (sk (~ (not a!14) a!18))
% 80.92/81.15 (~ (not (or a!13 a!14)) a!19)))
% 80.92/81.15 (a!22 (or (not (leq n0 pv5))
% 80.92/81.15 (not (leq pv5 (minus n999 n1)))
% 80.92/81.15 a!5
% 80.92/81.15 a!8
% 80.92/81.15 a!11
% 80.92/81.15 a!19)))
% 80.92/81.15 (nnf-neg a!1
% 80.92/81.15 (refl a!2)
% 80.92/81.15 (sk (~ (not a!3) a!5))
% 80.92/81.15 (sk (~ (not a!6) a!8))
% 80.92/81.15 (sk (~ (not a!9) a!11))
% 80.92/81.15 (trans a!15 a!20 (~ (not a!12) a!19))
% 80.92/81.15 (~ a!21 a!22))))))
% 80.92/81.15 Proof display could not be completed: unexpected number of arguments
% 81.26/81.49 % E exiting
%------------------------------------------------------------------------------