%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV116+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 35.14s 35.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV116+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:27:39 EDT 2025
% 0.19/0.34 % CPUTime :
% 35.14/35.37 % SZS status Theorem
% 35.14/35.37 % SZS output start Proof
% 35.14/35.37 tff(leq_type, type, (
% 35.14/35.37 leq: ( $i * $i ) > $o)).
% 35.14/35.37 tff(minus_type, type, (
% 35.14/35.37 minus: ( $i * $i ) > $i)).
% 35.14/35.37 tff(n1_type, type, (
% 35.14/35.37 n1: $i)).
% 35.14/35.37 tff(n6_type, type, (
% 35.14/35.37 n6: $i)).
% 35.14/35.37 tff(tptp_fun_L_13_type, type, (
% 35.14/35.37 tptp_fun_L_13: $i)).
% 35.14/35.37 tff(tptp_fun_K_14_type, type, (
% 35.14/35.37 tptp_fun_K_14: $i)).
% 35.14/35.37 tff(n0_type, type, (
% 35.14/35.37 n0: $i)).
% 35.14/35.37 tff(a_select3_type, type, (
% 35.14/35.37 a_select3: ( $i * $i * $i ) > $i)).
% 35.14/35.37 tff(q_ds1_filter_type, type, (
% 35.14/35.37 q_ds1_filter: $i)).
% 35.14/35.37 tff(tptp_fun_P_17_type, type, (
% 35.14/35.37 tptp_fun_P_17: $i)).
% 35.14/35.37 tff(tptp_fun_O_18_type, type, (
% 35.14/35.37 tptp_fun_O_18: $i)).
% 35.14/35.37 tff(pminus_ds1_filter_type, type, (
% 35.14/35.37 pminus_ds1_filter: $i)).
% 35.14/35.37 tff(id_ds1_filter_type, type, (
% 35.14/35.37 id_ds1_filter: $i)).
% 35.14/35.37 tff(r_ds1_filter_type, type, (
% 35.14/35.37 r_ds1_filter: $i)).
% 35.14/35.37 tff(n3_type, type, (
% 35.14/35.37 n3: $i)).
% 35.14/35.37 tff(n999_type, type, (
% 35.14/35.37 n999: $i)).
% 35.14/35.37 tff(pv5_type, type, (
% 35.14/35.37 pv5: $i)).
% 35.14/35.37 tff(tptp_fun_N_15_type, type, (
% 35.14/35.37 tptp_fun_N_15: $i)).
% 35.14/35.37 tff(tptp_fun_M_16_type, type, (
% 35.14/35.37 tptp_fun_M_16: $i)).
% 35.14/35.37 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)).
% 35.14/35.37 tff(2,plain,
% 35.14/35.37 (((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))),
% 35.14/35.37 inference(tautology,[status(thm)],[])).
% 35.14/35.37 tff(3,plain,
% 35.14/35.37 (leq(P!17, minus(n6, n1))),
% 35.14/35.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 35.14/35.37 tff(4,plain,
% 35.14/35.37 (((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))),
% 35.14/35.37 inference(tautology,[status(thm)],[])).
% 35.14/35.37 tff(5,plain,
% 35.14/35.37 (leq(O!18, minus(n6, n1))),
% 35.14/35.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 35.14/35.37 tff(6,plain,
% 35.14/35.37 (((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)),
% 35.14/35.37 inference(tautology,[status(thm)],[])).
% 35.14/35.37 tff(7,plain,
% 35.14/35.37 (leq(n0, P!17)),
% 35.14/35.37 inference(unit_resolution,[status(thm)],[6, 1])).
% 35.14/35.37 tff(8,plain,
% 35.14/35.37 (((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)),
% 35.14/35.37 inference(tautology,[status(thm)],[])).
% 35.14/35.37 tff(9,plain,
% 35.14/35.37 (leq(n0, O!18)),
% 35.14/35.37 inference(unit_resolution,[status(thm)],[8, 1])).
% 35.14/35.37 tff(10,plain,
% 35.14/35.37 (((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)))),
% 35.14/35.37 inference(tautology,[status(thm)],[])).
% 35.14/35.37 tff(11,plain,
% 35.14/35.37 (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18))),
% 35.14/35.37 inference(unit_resolution,[status(thm)],[10, 1])).
% 35.14/35.37 tff(12,plain,
% 35.14/35.37 (^[G: $i, H: $i] : refl(((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))),
% 35.14/35.37 inference(bind,[status(th)],[])).
% 35.14/35.37 tff(13,plain,
% 35.14/35.37 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 35.14/35.37 inference(quant_intro,[status(thm)],[12])).
% 35.14/35.37 tff(14,plain,
% 35.14/35.37 (^[G: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1))) <=> (~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))), ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) <=> (~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))))), rewrite((~(~((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))), ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) <=> ((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))))), (((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> (((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))))), rewrite((((~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))), (((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))))),
% 35.14/35.37 inference(bind,[status(th)],[])).
% 35.14/35.37 tff(15,plain,
% 35.14/35.37 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 35.14/35.37 inference(quant_intro,[status(thm)],[14])).
% 35.14/35.37 tff(16,plain,
% 35.14/35.37 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 35.14/35.37 inference(rewrite,[status(thm)],[])).
% 35.14/35.37 tff(17,plain,
% 35.14/35.37 ((~(((((((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)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((![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)))))) <=> (~((~(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))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (![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))))))),
% 35.14/35.38 inference(rewrite,[status(thm)],[])).
% 35.14/35.38 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)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((![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)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_symm_0009')).
% 35.14/35.38 tff(19,plain,
% 35.14/35.38 (~((~(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))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (![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)))))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 35.14/35.38 tff(20,plain,
% 35.14/35.38 (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))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 35.14/35.38 inference(or_elim,[status(thm)],[19])).
% 35.14/35.38 tff(21,plain,
% 35.14/35.38 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 35.14/35.38 inference(and_elim,[status(thm)],[20])).
% 35.14/35.38 tff(22,plain,
% 35.14/35.38 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[21, 16])).
% 35.14/35.38 tff(23,plain,(
% 35.14/35.38 ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 35.14/35.38 inference(skolemize,[status(sab)],[22])).
% 35.14/35.38 tff(24,plain,
% 35.14/35.38 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[23, 15])).
% 35.14/35.38 tff(25,plain,
% 35.14/35.38 (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[24, 13])).
% 35.14/35.38 tff(26,plain,
% 35.14/35.38 (((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))) <=> ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))),
% 35.14/35.38 inference(rewrite,[status(thm)],[])).
% 35.14/35.38 tff(27,plain,
% 35.14/35.38 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | ((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1))))),
% 35.14/35.38 inference(quant_inst,[status(thm)],[])).
% 35.14/35.38 tff(28,plain,
% 35.14/35.38 ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(n0, G)) | (~leq(n0, H)) | (~leq(G, minus(n6, n1))) | (~leq(H, minus(n6, n1))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(n0, O!18)) | (~leq(n0, P!17)) | (~leq(O!18, minus(n6, n1))) | (~leq(P!17, minus(n6, n1)))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 35.14/35.38 tff(29,plain,
% 35.14/35.38 ($false),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[28, 25, 11, 9, 7, 5, 3])).
% 35.14/35.38 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,[]))).
% 35.14/35.38 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)).
% 35.14/35.38 tff(32,plain,
% 35.14/35.38 (((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))),
% 35.14/35.38 inference(tautology,[status(thm)],[])).
% 35.14/35.38 tff(33,plain,
% 35.14/35.38 (leq(N!15, minus(n3, n1))),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 35.14/35.38 tff(34,plain,
% 35.14/35.38 (((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))),
% 35.14/35.38 inference(tautology,[status(thm)],[])).
% 35.14/35.38 tff(35,plain,
% 35.14/35.38 (leq(M!16, minus(n3, n1))),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[34, 31])).
% 35.14/35.38 tff(36,plain,
% 35.14/35.38 (((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)),
% 35.14/35.38 inference(tautology,[status(thm)],[])).
% 35.14/35.38 tff(37,plain,
% 35.14/35.38 (leq(n0, N!15)),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[36, 31])).
% 35.14/35.38 tff(38,plain,
% 35.14/35.38 (((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)),
% 35.14/35.38 inference(tautology,[status(thm)],[])).
% 35.14/35.38 tff(39,plain,
% 35.14/35.38 (leq(n0, M!16)),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[38, 31])).
% 35.14/35.38 tff(40,plain,
% 35.14/35.38 (((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)))),
% 35.14/35.38 inference(tautology,[status(thm)],[])).
% 35.14/35.38 tff(41,plain,
% 35.14/35.38 (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 35.14/35.38 inference(unit_resolution,[status(thm)],[40, 31])).
% 35.14/35.38 tff(42,plain,
% 35.14/35.38 (^[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)))))),
% 35.14/35.38 inference(bind,[status(th)],[])).
% 35.14/35.38 tff(43,plain,
% 35.14/35.38 (![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))))),
% 35.14/35.38 inference(quant_intro,[status(thm)],[42])).
% 35.14/35.38 tff(44,plain,
% 35.14/35.38 (^[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))))))),
% 35.14/35.38 inference(bind,[status(th)],[])).
% 35.14/35.38 tff(45,plain,
% 35.14/35.38 (![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))))),
% 35.14/35.38 inference(quant_intro,[status(thm)],[44])).
% 35.14/35.38 tff(46,plain,
% 35.14/35.38 (![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)))),
% 35.14/35.38 inference(rewrite,[status(thm)],[])).
% 35.14/35.38 tff(47,plain,
% 35.14/35.38 (![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)))),
% 35.14/35.38 inference(and_elim,[status(thm)],[20])).
% 35.14/35.38 tff(48,plain,
% 35.14/35.38 (![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)))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 35.14/35.38 tff(49,plain,(
% 35.14/35.38 ![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)))),
% 35.14/35.38 inference(skolemize,[status(sab)],[48])).
% 35.14/35.38 tff(50,plain,
% 35.14/35.38 (![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))))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[49, 45])).
% 35.14/35.38 tff(51,plain,
% 35.14/35.38 (![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))))),
% 35.14/35.38 inference(modus_ponens,[status(thm)],[50, 43])).
% 35.14/35.38 tff(52,plain,
% 35.14/35.38 (((~![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))))),
% 35.14/35.38 inference(rewrite,[status(thm)],[])).
% 35.14/35.38 tff(53,plain,
% 35.14/35.38 ((~![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))))),
% 35.14/35.39 inference(quant_inst,[status(thm)],[])).
% 35.14/35.39 tff(54,plain,
% 35.14/35.39 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(n0, C)) | (~leq(n0, D)) | (~leq(C, minus(n3, n1))) | (~leq(D, minus(n3, n1))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(n0, M!16)) | (~leq(n0, N!15)) | (~leq(M!16, minus(n3, n1))) | (~leq(N!15, minus(n3, n1)))),
% 35.14/35.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 35.14/35.39 tff(55,plain,
% 35.14/35.39 ($false),
% 35.14/35.39 inference(unit_resolution,[status(thm)],[54, 51, 41, 39, 37, 35, 33])).
% 35.14/35.39 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,[]))).
% 35.14/35.39 tff(57,plain,
% 35.14/35.39 (((~((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(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))))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(58,plain,
% 35.14/35.39 ((~((~(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)))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(59,plain,
% 35.14/35.39 ((~((~(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)))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(60,plain,
% 35.14/35.39 ((~((~(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)))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(61,plain,
% 35.14/35.39 (((~((~(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))))) <=> ((~((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))))))),
% 35.14/35.39 inference(monotonicity,[status(thm)],[60, 59, 58])).
% 35.14/35.39 tff(62,plain,
% 35.14/35.39 (((~((~(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))))) <=> ((~((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))))))),
% 35.14/35.39 inference(transitivity,[status(thm)],[61, 57])).
% 35.14/35.39 tff(63,plain,
% 35.14/35.39 ((![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)))) <=> (![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))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(64,plain,
% 35.14/35.39 ((~(![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))))) <=> (~(![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)))))),
% 35.14/35.39 inference(monotonicity,[status(thm)],[63])).
% 35.14/35.39 tff(65,plain,
% 35.14/35.39 ((~(![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))))) <=> (~(![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)))))),
% 35.14/35.39 inference(rewrite,[status(thm)],[])).
% 35.14/35.39 tff(66,plain,
% 35.14/35.39 (~(![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))))),
% 35.14/35.39 inference(or_elim,[status(thm)],[19])).
% 35.14/35.39 tff(67,plain,
% 35.14/35.39 (~(![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))))),
% 35.14/35.39 inference(modus_ponens,[status(thm)],[66, 64])).
% 35.14/35.39 tff(68,plain,
% 35.14/35.39 (~(![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))))),
% 35.14/35.39 inference(modus_ponens,[status(thm)],[67, 65])).
% 35.14/35.39 tff(69,plain,
% 35.14/35.39 (~(![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))))),
% 35.14/35.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 35.14/35.39 unexpected number of arguments: (let ((a!1 (forall ((K $i) (L $i))
% 35.14/35.39 (let ((a!1 (not (and (leq n0 K)
% 35.14/35.39 (leq n0 L)
% 35.14/35.39 (leq K (minus n6 n1))
% 35.14/35.39 (leq L (minus n6 n1))))))
% 35.14/35.39 (or a!1
% 35.14/35.39 (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))
% 35.14/35.39 (a!2 (not (and (leq n0 K!14)
% 35.14/35.39 (leq n0 L!13)
% 35.14/35.39 (leq K!14 (minus n6 n1))
% 35.14/35.39 (leq L!13 (minus n6 n1)))))
% 35.14/35.39 (a!4 (forall ((M $i) (N $i))
% 35.14/35.39 (let ((a!1 (not (and (leq n0 M)
% 35.14/35.39 (leq n0 N)
% 35.14/35.39 (leq M (minus n3 n1))
% 35.14/35.39 (leq N (minus n3 n1))))))
% 35.14/35.39 (or a!1
% 35.14/35.39 (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))
% 35.14/35.39 (a!5 (not (and (leq n0 M!16)
% 35.14/35.39 (leq n0 N!15)
% 35.14/35.39 (leq M!16 (minus n3 n1))
% 35.14/35.39 (leq N!15 (minus n3 n1)))))
% 35.14/35.39 (a!7 (forall ((O $i) (P $i))
% 35.14/35.39 (let ((a!1 (not (and (leq n0 O)
% 35.14/35.39 (leq n0 P)
% 35.14/35.39 (leq O (minus n6 n1))
% 35.14/35.39 (leq P (minus n6 n1))))))
% 35.14/35.39 (or a!1
% 35.14/35.39 (= (a_select3 pminus_ds1_filter O P)
% 35.14/35.39 (a_select3 pminus_ds1_filter P O))))))
% 35.14/35.39 (a!8 (not (and (leq n0 O!18)
% 35.14/35.39 (leq n0 P!17)
% 35.14/35.39 (leq O!18 (minus n6 n1))
% 35.14/35.39 (leq P!17 (minus n6 n1))))))
% 35.14/35.39 (let ((a!3 (not (or a!2
% 35.14/35.39 (= (a_select3 q_ds1_filter K!14 L!13)
% 35.14/35.39 (a_select3 q_ds1_filter L!13 K!14)))))
% 35.14/35.39 (a!6 (not (or a!5
% 35.14/35.39 (= (a_select3 r_ds1_filter M!16 N!15)
% 35.14/35.39 (a_select3 r_ds1_filter N!15 M!16)))))
% 35.14/35.39 (a!9 (not (or a!8
% 35.14/35.39 (= (a_select3 pminus_ds1_filter O!18 P!17)
% 35.14/35.39 (a_select3 pminus_ds1_filter P!17 O!18))))))
% 35.14/35.39 (nnf-neg (sk (~ (not a!1) a!3))
% 35.14/35.39 (sk (~ (not a!4) a!6))
% 35.14/35.39 (sk (~ (not a!7) a!9))
% 35.14/35.39 (~ (not (and a!1 a!4 a!7)) (or a!3 a!6 a!9)))))
% 35.14/35.39 Proof display could not be completed: unexpected number of arguments
% 35.33/35.57 % E exiting
%------------------------------------------------------------------------------