TSTP Solution File: SWV111+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV111+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Thu Sep 29 15:10:01 EDT 2022
% Result : Theorem 0.13s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : SWV111+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.28 % Computer : n026.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Sun Sep 4 01:39:24 EDT 2022
% 0.07/0.28 % CPUTime :
% 0.07/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.29 Usage: tptp [options] [-file:]file
% 0.07/0.29 -h, -? prints this message.
% 0.07/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.29 -m, -model generate model.
% 0.07/0.29 -p, -proof generate proof.
% 0.07/0.29 -c, -core generate unsat core of named formulas.
% 0.07/0.29 -st, -statistics display statistics.
% 0.07/0.29 -t:timeout set timeout (in second).
% 0.07/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.29 -<param>:<value> configuration parameter and value.
% 0.07/0.29 -o:<output-file> file to place output in.
% 0.13/0.47 % SZS status Theorem
% 0.13/0.47 % SZS output start Proof
% 0.13/0.47 tff(leq_type, type, (
% 0.13/0.47 leq: ( $i * $i ) > $o)).
% 0.13/0.47 tff(minus_type, type, (
% 0.13/0.47 minus: ( $i * $i ) > $i)).
% 0.13/0.47 tff(succ_type, type, (
% 0.13/0.47 succ: $i > $i)).
% 0.13/0.47 tff(tptp_minus_1_type, type, (
% 0.13/0.47 tptp_minus_1: $i)).
% 0.13/0.47 tff(tptp_fun_P_17_type, type, (
% 0.13/0.47 tptp_fun_P_17: $i)).
% 0.13/0.47 tff(tptp_fun_O_18_type, type, (
% 0.13/0.47 tptp_fun_O_18: $i)).
% 0.13/0.47 tff(a_select3_type, type, (
% 0.13/0.47 a_select3: ( $i * $i * $i ) > $i)).
% 0.13/0.47 tff(pminus_ds1_filter_type, type, (
% 0.13/0.47 pminus_ds1_filter: $i)).
% 0.13/0.47 tff(tptp_fun_N_15_type, type, (
% 0.13/0.47 tptp_fun_N_15: $i)).
% 0.13/0.47 tff(tptp_fun_M_16_type, type, (
% 0.13/0.47 tptp_fun_M_16: $i)).
% 0.13/0.47 tff(r_ds1_filter_type, type, (
% 0.13/0.47 r_ds1_filter: $i)).
% 0.13/0.47 tff(n1_type, type, (
% 0.13/0.47 n1: $i)).
% 0.13/0.47 tff(n3_type, type, (
% 0.13/0.47 n3: $i)).
% 0.13/0.47 tff(n0_type, type, (
% 0.13/0.47 n0: $i)).
% 0.13/0.47 tff(id_ds1_filter_type, type, (
% 0.13/0.47 id_ds1_filter: $i)).
% 0.13/0.47 tff(n6_type, type, (
% 0.13/0.47 n6: $i)).
% 0.13/0.47 tff(pv57_type, type, (
% 0.13/0.47 pv57: $i)).
% 0.13/0.47 tff(lt_type, type, (
% 0.13/0.47 lt: ( $i * $i ) > $o)).
% 0.13/0.47 tff(plus_type, type, (
% 0.13/0.47 plus: ( $i * $i ) > $i)).
% 0.13/0.47 tff(q_ds1_filter_type, type, (
% 0.13/0.47 q_ds1_filter: $i)).
% 0.13/0.47 tff(n999_type, type, (
% 0.13/0.47 n999: $i)).
% 0.13/0.47 tff(pv5_type, type, (
% 0.13/0.47 pv5: $i)).
% 0.13/0.47 tff(tptp_fun_R_19_type, type, (
% 0.13/0.47 tptp_fun_R_19: $i)).
% 0.13/0.47 tff(tptp_fun_Q_20_type, type, (
% 0.13/0.47 tptp_fun_Q_20: $i)).
% 0.13/0.47 tff(pred_type, type, (
% 0.13/0.47 pred: $i > $i)).
% 0.13/0.47 tff(n5_type, type, (
% 0.13/0.47 n5: $i)).
% 0.13/0.47 tff(gt_type, type, (
% 0.13/0.47 gt: ( $i * $i ) > $o)).
% 0.13/0.47 tff(tptp_fun_L_13_type, type, (
% 0.13/0.47 tptp_fun_L_13: $i)).
% 0.13/0.47 tff(tptp_fun_K_14_type, type, (
% 0.13/0.47 tptp_fun_K_14: $i)).
% 0.13/0.47 tff(tptp_fun_S_21_type, type, (
% 0.13/0.47 tptp_fun_S_21: $i)).
% 0.13/0.47 tff(tptp_fun_T_22_type, type, (
% 0.13/0.47 tptp_fun_T_22: $i)).
% 0.13/0.47 tff(1,assumption,(~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.13/0.47 tff(2,plain,
% 0.13/0.47 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.47 inference(tautology,[status(thm)],[])).
% 0.13/0.47 tff(3,plain,
% 0.13/0.47 (leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.47 tff(4,plain,
% 0.13/0.47 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.47 inference(tautology,[status(thm)],[])).
% 0.13/0.47 tff(5,plain,
% 0.13/0.47 (leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.47 tff(6,plain,
% 0.13/0.47 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), N!15)),
% 0.13/0.47 inference(tautology,[status(thm)],[])).
% 0.13/0.47 tff(7,plain,
% 0.13/0.47 (leq(succ(tptp_minus_1), N!15)),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.13/0.47 tff(8,plain,
% 0.13/0.47 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), M!16)),
% 0.13/0.47 inference(tautology,[status(thm)],[])).
% 0.13/0.47 tff(9,plain,
% 0.13/0.47 (leq(succ(tptp_minus_1), M!16)),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.13/0.47 tff(10,plain,
% 0.13/0.47 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))),
% 0.13/0.47 inference(tautology,[status(thm)],[])).
% 0.13/0.47 tff(11,plain,
% 0.13/0.47 (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 0.13/0.47 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.13/0.47 tff(12,plain,
% 0.13/0.47 (^[C: $i, D: $i] : refl(((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.47 inference(bind,[status(th)],[])).
% 0.13/0.47 tff(13,plain,
% 0.13/0.47 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.47 tff(14,plain,
% 0.13/0.47 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(15,plain,
% 0.13/0.48 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.48 tff(16,plain,
% 0.13/0.48 (^[C: $i, D: $i] : 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))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(17,plain,
% 0.13/0.48 (![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(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.48 tff(18,plain,
% 0.13/0.48 (![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)))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(19,plain,
% 0.13/0.48 ((~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (((lt(H, plus(n1, minus(n6, n1))) & (G = pv57)) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & (lt(G, pv57) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, pv57)) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(pv57, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))) <=> (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(20,axiom,(~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (((lt(H, plus(n1, minus(n6, n1))) & (G = pv57)) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & (lt(G, pv57) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, pv57)) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(pv57, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_symm_0004')).
% 0.13/0.48 tff(21,plain,
% 0.13/0.48 (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.48 tff(22,plain,
% 0.13/0.48 (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.48 inference(or_elim,[status(thm)],[21])).
% 0.13/0.48 tff(23,plain,
% 0.13/0.48 (![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)))),
% 0.13/0.48 inference(and_elim,[status(thm)],[22])).
% 0.13/0.48 tff(24,plain,
% 0.13/0.48 (![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)))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.13/0.48 tff(25,plain,
% 0.13/0.48 (![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.13/0.48 tff(26,plain,(
% 0.13/0.48 ![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.13/0.48 inference(skolemize,[status(sab)],[25])).
% 0.13/0.48 tff(27,plain,
% 0.13/0.48 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.13/0.48 tff(28,plain,
% 0.13/0.48 (![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[27, 13])).
% 0.13/0.48 tff(29,plain,
% 0.13/0.48 (((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(30,plain,
% 0.13/0.48 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(quant_inst,[status(thm)],[])).
% 0.13/0.48 tff(31,plain,
% 0.13/0.48 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.48 tff(32,plain,
% 0.13/0.48 ($false),
% 0.13/0.48 inference(unit_resolution,[status(thm)],[31, 28, 11, 9, 7, 5, 3])).
% 0.13/0.48 tff(33,plain,((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.48 tff(34,plain,
% 0.13/0.48 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(35,plain,
% 0.13/0.48 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.13/0.48 inference(rewrite,[status(thm)],[])).
% 0.13/0.48 tff(36,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.13/0.48 tff(37,plain,
% 0.13/0.48 (![X: $i] : (pred(succ(X)) = X)),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.48 tff(38,plain,(
% 0.13/0.48 ![X: $i] : (pred(succ(X)) = X)),
% 0.13/0.48 inference(skolemize,[status(sab)],[37])).
% 0.13/0.48 tff(39,plain,
% 0.13/0.48 (![X: $i] : (pred(succ(X)) = X)),
% 0.13/0.48 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.48 tff(40,plain,
% 0.13/0.48 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) = succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.48 inference(quant_inst,[status(thm)],[])).
% 0.13/0.48 tff(41,plain,
% 0.13/0.48 (pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.13/0.48 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.48 tff(42,plain,
% 0.13/0.48 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(43,plain,
% 0.13/0.48 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.48 tff(44,plain,
% 0.13/0.48 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.13/0.48 inference(bind,[status(th)],[])).
% 0.13/0.48 tff(45,plain,
% 0.13/0.48 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.13/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.49 tff(46,plain,
% 0.13/0.49 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(47,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.13/0.49 tff(48,plain,
% 0.13/0.49 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.49 tff(49,plain,
% 0.13/0.49 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.13/0.49 tff(50,plain,(
% 0.13/0.49 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.13/0.49 inference(skolemize,[status(sab)],[49])).
% 0.13/0.49 tff(51,plain,
% 0.13/0.49 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.13/0.49 tff(52,plain,
% 0.13/0.49 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(53,plain,
% 0.13/0.49 (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.49 tff(54,plain,
% 0.13/0.49 (minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))) = succ(succ(succ(succ(succ(succ(tptp_minus_1))))))),
% 0.13/0.49 inference(transitivity,[status(thm)],[53, 41])).
% 0.13/0.49 tff(55,plain,
% 0.13/0.49 (leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) <=> leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.49 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.49 tff(56,plain,
% 0.13/0.49 (leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(symmetry,[status(thm)],[55])).
% 0.13/0.49 tff(57,plain,
% 0.13/0.49 (leq(pv57, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) <=> leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.49 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.49 tff(58,plain,
% 0.13/0.49 (leq(pv57, minus(n6, n1)) <=> leq(pv57, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(59,plain,
% 0.13/0.49 (leq(pv57, minus(n6, n1)) <=> leq(pv57, minus(n6, n1))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(60,plain,
% 0.13/0.49 (leq(pv57, minus(n6, n1))),
% 0.13/0.49 inference(and_elim,[status(thm)],[22])).
% 0.13/0.49 tff(61,plain,
% 0.13/0.49 (leq(pv57, minus(n6, n1))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.49 tff(62,plain,
% 0.13/0.49 (leq(pv57, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.13/0.49 tff(63,plain,
% 0.13/0.49 (leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.13/0.49 tff(64,assumption,(~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.13/0.49 tff(65,plain,
% 0.13/0.49 (((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(Q!20, pv57)),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(66,plain,
% 0.13/0.49 (leq(Q!20, pv57)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.49 tff(67,plain,
% 0.13/0.49 (![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)))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(68,plain,
% 0.13/0.49 (^[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)))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(69,plain,
% 0.13/0.49 (![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)))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.13/0.49 tff(70,plain,
% 0.13/0.49 (![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))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(71,plain,
% 0.13/0.49 (^[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)))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(72,plain,
% 0.13/0.49 (![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))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[71])).
% 0.13/0.49 tff(73,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.13/0.49 tff(74,plain,
% 0.13/0.49 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.13/0.49 tff(75,plain,
% 0.13/0.49 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.13/0.49 tff(76,plain,(
% 0.13/0.49 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.49 inference(skolemize,[status(sab)],[75])).
% 0.13/0.49 tff(77,plain,
% 0.13/0.49 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.13/0.49 tff(78,plain,
% 0.13/0.49 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.13/0.49 tff(79,plain,
% 0.13/0.49 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(80,plain,
% 0.13/0.49 ((leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (~leq(Q!20, pv57))) <=> ((~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(81,plain,
% 0.13/0.49 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (~leq(Q!20, pv57)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))))),
% 0.13/0.49 inference(monotonicity,[status(thm)],[80])).
% 0.13/0.49 tff(82,plain,
% 0.13/0.49 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (~leq(Q!20, pv57)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.49 inference(transitivity,[status(thm)],[81, 79])).
% 0.13/0.49 tff(83,plain,
% 0.13/0.49 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (~leq(Q!20, pv57)))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(84,plain,
% 0.13/0.49 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (~leq(pv57, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.49 tff(85,plain,
% 0.13/0.49 (leq(Q!20, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[84, 78, 66, 63])).
% 0.13/0.49 tff(86,plain,
% 0.13/0.49 (leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[85, 56])).
% 0.13/0.49 tff(87,plain,
% 0.13/0.49 (((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(88,plain,
% 0.13/0.49 (leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[87, 64])).
% 0.13/0.49 tff(89,plain,
% 0.13/0.49 (((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), R!19)),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(90,plain,
% 0.13/0.49 (leq(succ(tptp_minus_1), R!19)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[89, 64])).
% 0.13/0.49 tff(91,plain,
% 0.13/0.49 (((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), Q!20)),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(92,plain,
% 0.13/0.49 (leq(succ(tptp_minus_1), Q!20)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[91, 64])).
% 0.13/0.49 tff(93,plain,
% 0.13/0.49 (^[G: $i, H: $i] : refl(((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))) <=> ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(94,plain,
% 0.13/0.49 (![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))) <=> ![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[93])).
% 0.13/0.49 tff(95,plain,
% 0.13/0.49 (^[G: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57)) <=> (~((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))))), ((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) <=> (~(~((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))))))), rewrite((~(~((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))))) <=> ((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))), ((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) <=> ((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))))), (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> (((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))), rewrite((((~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))), (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) <=> ((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))))), ((((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) <=> (((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))), rewrite((((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) <=> (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))), ((((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) <=> (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))), (((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> (((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))))), rewrite((((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))) <=> ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))), (((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(96,plain,
% 0.13/0.49 (![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> ![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[95])).
% 0.13/0.50 tff(97,plain,
% 0.13/0.50 (^[G: $i, H: $i] : rewrite(((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(98,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[97])).
% 0.13/0.50 tff(99,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))))) <=> ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(100,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(and_elim,[status(thm)],[22])).
% 0.13/0.50 tff(101,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (((~(lt(H, plus(n1, minus(n6, n1))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.13/0.50 tff(102,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.13/0.50 tff(103,plain,(
% 0.13/0.50 ![G: $i, H: $i] : ((~(leq(succ(tptp_minus_1), G) & leq(succ(tptp_minus_1), H) & leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (((~(lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) & (G = pv57))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))),
% 0.13/0.50 inference(skolemize,[status(sab)],[102])).
% 0.13/0.50 tff(104,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.13/0.50 tff(105,plain,
% 0.13/0.50 (![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.13/0.50 tff(106,plain,
% 0.13/0.50 (((~![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))) | ((~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))))))) <=> ((~![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(107,plain,
% 0.13/0.50 ((~![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))) | ((~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(108,plain,
% 0.13/0.50 ((~![G: $i, H: $i] : ((~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)) | (~lt(H, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(G = pv57)))) | (~((~lt(G, pv57)) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))))))) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.13/0.50 tff(109,plain,
% 0.13/0.50 ((~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[108, 105, 92, 90, 88])).
% 0.13/0.50 tff(110,plain,
% 0.13/0.50 (~((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[109, 86])).
% 0.13/0.50 tff(111,plain,
% 0.13/0.50 (((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))))) | ((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(112,plain,
% 0.13/0.50 ((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.13/0.50 tff(113,plain,
% 0.13/0.50 (plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) = plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.50 tff(114,plain,
% 0.13/0.50 (plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50 inference(symmetry,[status(thm)],[113])).
% 0.13/0.50 tff(115,plain,
% 0.13/0.50 (^[X: $i] : refl((plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))) <=> (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(116,plain,
% 0.13/0.50 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[115])).
% 0.13/0.50 tff(117,plain,
% 0.13/0.50 (^[X: $i] : rewrite((plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X)))))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(118,plain,
% 0.13/0.50 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[117])).
% 0.13/0.50 tff(119,plain,
% 0.13/0.50 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X)))))) <=> ![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(120,axiom,(![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_plus_5_r')).
% 0.13/0.50 tff(121,plain,
% 0.13/0.50 (![X: $i] : (plus(X, n5) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.13/0.50 tff(122,plain,
% 0.13/0.50 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.13/0.50 tff(123,plain,(
% 0.13/0.50 ![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(skolemize,[status(sab)],[122])).
% 0.13/0.50 tff(124,plain,
% 0.13/0.50 (![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.13/0.50 tff(125,plain,
% 0.13/0.50 ((~![X: $i] : (plus(X, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(X))))))) | (plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(126,plain,
% 0.13/0.50 (plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.13/0.50 tff(127,plain,
% 0.13/0.50 (succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = plus(succ(succ(tptp_minus_1)), succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.50 inference(symmetry,[status(thm)],[126])).
% 0.13/0.50 tff(128,plain,
% 0.13/0.50 (succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) = plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50 inference(transitivity,[status(thm)],[127, 114])).
% 0.13/0.50 tff(129,plain,
% 0.13/0.50 (lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[128])).
% 0.13/0.50 tff(130,plain,
% 0.13/0.50 (^[X: $i, Y: $i] : refl((lt(X, Y) <=> gt(Y, X)) <=> (lt(X, Y) <=> gt(Y, X)))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(131,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[130])).
% 0.13/0.50 tff(132,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(133,axiom,(![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','lt_gt')).
% 0.13/0.50 tff(134,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.13/0.50 tff(135,plain,(
% 0.13/0.50 ![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))),
% 0.13/0.50 inference(skolemize,[status(sab)],[134])).
% 0.13/0.50 tff(136,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.13/0.50 tff(137,plain,
% 0.13/0.50 ((~![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))) | (lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(138,plain,
% 0.13/0.50 (lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.13/0.50 tff(139,plain,
% 0.13/0.50 (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(140,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[139])).
% 0.13/0.50 tff(141,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(142,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.13/0.50 tff(143,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.13/0.50 tff(144,plain,(
% 0.13/0.50 ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.13/0.50 inference(skolemize,[status(sab)],[143])).
% 0.13/0.50 tff(145,plain,
% 0.13/0.50 (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.13/0.50 tff(146,plain,
% 0.13/0.50 ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(147,plain,
% 0.13/0.50 (leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.13/0.50 tff(148,plain,
% 0.13/0.50 (pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) = minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))),
% 0.13/0.50 inference(symmetry,[status(thm)],[53])).
% 0.13/0.50 tff(149,plain,
% 0.13/0.50 (succ(succ(succ(succ(succ(succ(tptp_minus_1)))))) = pred(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.50 inference(symmetry,[status(thm)],[41])).
% 0.13/0.50 tff(150,plain,
% 0.13/0.50 (succ(succ(succ(succ(succ(succ(tptp_minus_1)))))) = minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))),
% 0.13/0.50 inference(transitivity,[status(thm)],[149, 148])).
% 0.13/0.50 tff(151,plain,
% 0.13/0.50 (leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[150])).
% 0.13/0.50 tff(152,plain,
% 0.13/0.50 (leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) <=> leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.50 inference(symmetry,[status(thm)],[151])).
% 0.13/0.50 tff(153,plain,
% 0.13/0.50 (leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[88, 152])).
% 0.13/0.50 tff(154,plain,
% 0.13/0.50 ((~(leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19))) | (~leq(R!19, succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19)),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(155,plain,
% 0.13/0.50 (gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[154, 153, 147])).
% 0.13/0.50 tff(156,plain,
% 0.13/0.50 ((~(lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) <=> gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19))) | lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1)))))))) | (~gt(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), R!19))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(157,plain,
% 0.13/0.50 (lt(R!19, succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[156, 155, 138])).
% 0.13/0.50 tff(158,plain,
% 0.13/0.50 (lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[157, 129])).
% 0.13/0.50 tff(159,plain,
% 0.13/0.50 (((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(160,plain,
% 0.13/0.50 (~(a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[159, 64])).
% 0.13/0.50 tff(161,plain,
% 0.13/0.50 ((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(162,plain,
% 0.13/0.50 ((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.13/0.50 tff(163,plain,
% 0.13/0.50 (~(Q!20 = pv57)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[162, 158, 112])).
% 0.13/0.50 tff(164,plain,
% 0.13/0.50 ((~![X: $i, Y: $i] : (lt(X, Y) <=> gt(Y, X))) | (lt(Q!20, pv57) <=> gt(pv57, Q!20))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(165,plain,
% 0.13/0.50 (lt(Q!20, pv57) <=> gt(pv57, Q!20)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[164, 136])).
% 0.13/0.50 tff(166,plain,
% 0.13/0.50 (((~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~lt(R!19, plus(succ(succ(tptp_minus_1)), minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(Q!20 = pv57)))) | (~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))))) | ((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(167,plain,
% 0.13/0.50 ((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[166, 110])).
% 0.13/0.50 tff(168,plain,
% 0.13/0.50 ((~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(169,plain,
% 0.13/0.50 ((~((~lt(Q!20, pv57)) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (~lt(Q!20, pv57))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[168, 160])).
% 0.13/0.50 tff(170,plain,
% 0.13/0.50 (~lt(Q!20, pv57)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.13/0.50 tff(171,plain,
% 0.13/0.50 ((~(lt(Q!20, pv57) <=> gt(pv57, Q!20))) | lt(Q!20, pv57) | (~gt(pv57, Q!20))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(172,plain,
% 0.13/0.50 ((~(lt(Q!20, pv57) <=> gt(pv57, Q!20))) | (~gt(pv57, Q!20))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.13/0.50 tff(173,plain,
% 0.13/0.50 (~gt(pv57, Q!20)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[172, 165])).
% 0.13/0.50 tff(174,plain,
% 0.13/0.50 (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(175,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[174])).
% 0.13/0.50 tff(176,plain,
% 0.13/0.50 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(177,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[176])).
% 0.13/0.50 tff(178,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(179,plain,
% 0.13/0.50 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(180,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[179])).
% 0.13/0.50 tff(181,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.13/0.50 tff(182,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.13/0.50 tff(183,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.13/0.50 tff(184,plain,(
% 0.13/0.50 ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.13/0.50 inference(skolemize,[status(sab)],[183])).
% 0.13/0.50 tff(185,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.13/0.50 tff(186,plain,
% 0.13/0.50 (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[185, 175])).
% 0.13/0.50 tff(187,plain,
% 0.13/0.50 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(188,plain,
% 0.13/0.51 (((Q!20 = pv57) | gt(pv57, Q!20) | (~leq(Q!20, pv57))) <=> ((~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(189,plain,
% 0.13/0.51 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((Q!20 = pv57) | gt(pv57, Q!20) | (~leq(Q!20, pv57)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20)))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[188])).
% 0.13/0.51 tff(190,plain,
% 0.13/0.51 (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((Q!20 = pv57) | gt(pv57, Q!20) | (~leq(Q!20, pv57)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20))),
% 0.13/0.51 inference(transitivity,[status(thm)],[189, 187])).
% 0.13/0.51 tff(191,plain,
% 0.13/0.51 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((Q!20 = pv57) | gt(pv57, Q!20) | (~leq(Q!20, pv57)))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(192,plain,
% 0.13/0.51 ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(Q!20, pv57)) | (Q!20 = pv57) | gt(pv57, Q!20)),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.13/0.51 tff(193,plain,
% 0.13/0.51 ((Q!20 = pv57) | gt(pv57, Q!20)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[192, 186, 66])).
% 0.13/0.51 tff(194,plain,
% 0.13/0.51 ($false),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[193, 173, 163])).
% 0.13/0.51 tff(195,plain,((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.51 tff(196,assumption,(~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.13/0.51 tff(197,plain,
% 0.13/0.51 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(198,plain,
% 0.13/0.51 (leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.13/0.51 tff(199,plain,
% 0.13/0.51 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(200,plain,
% 0.13/0.51 (leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[199, 196])).
% 0.13/0.51 tff(201,plain,
% 0.13/0.51 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), L!13)),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(202,plain,
% 0.13/0.51 (leq(succ(tptp_minus_1), L!13)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[201, 196])).
% 0.13/0.51 tff(203,plain,
% 0.13/0.51 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), K!14)),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(204,plain,
% 0.13/0.51 (leq(succ(tptp_minus_1), K!14)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[203, 196])).
% 0.13/0.51 tff(205,plain,
% 0.13/0.51 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(206,plain,
% 0.13/0.51 (~(a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[205, 196])).
% 0.13/0.51 tff(207,plain,
% 0.13/0.51 (^[A: $i, B: $i] : refl(((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.51 inference(bind,[status(th)],[])).
% 0.13/0.51 tff(208,plain,
% 0.13/0.51 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.51 inference(quant_intro,[status(thm)],[207])).
% 0.13/0.51 tff(209,plain,
% 0.13/0.51 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.51 inference(bind,[status(th)],[])).
% 0.13/0.51 tff(210,plain,
% 0.13/0.51 (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.51 inference(quant_intro,[status(thm)],[209])).
% 0.13/0.51 tff(211,plain,
% 0.13/0.51 (^[A: $i, B: $i] : rewrite(((~(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))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))),
% 0.13/0.51 inference(bind,[status(th)],[])).
% 0.13/0.51 tff(212,plain,
% 0.13/0.51 (![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))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.13/0.51 inference(quant_intro,[status(thm)],[211])).
% 0.13/0.51 tff(213,plain,
% 0.13/0.51 (![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))) <=> ![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)))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(214,plain,
% 0.13/0.51 (![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)))),
% 0.13/0.51 inference(and_elim,[status(thm)],[22])).
% 0.13/0.51 tff(215,plain,
% 0.13/0.51 (![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)))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.13/0.51 tff(216,plain,
% 0.13/0.51 (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.13/0.51 tff(217,plain,(
% 0.13/0.51 ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.13/0.51 inference(skolemize,[status(sab)],[216])).
% 0.13/0.51 tff(218,plain,
% 0.13/0.51 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.13/0.51 tff(219,plain,
% 0.13/0.51 (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[218, 208])).
% 0.13/0.51 tff(220,plain,
% 0.13/0.51 (((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.52 inference(rewrite,[status(thm)],[])).
% 0.13/0.52 tff(221,plain,
% 0.13/0.52 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(222,plain,
% 0.13/0.52 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.13/0.52 tff(223,plain,
% 0.13/0.52 ($false),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[222, 219, 206, 204, 202, 200, 198])).
% 0.13/0.52 tff(224,plain,((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.52 tff(225,assumption,(~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.13/0.52 tff(226,plain,
% 0.13/0.52 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))) | leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(227,plain,
% 0.13/0.52 (leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.13/0.52 tff(228,plain,
% 0.13/0.52 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), S!21)),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(229,plain,
% 0.13/0.52 (leq(succ(tptp_minus_1), S!21)),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.13/0.52 tff(230,plain,
% 0.13/0.52 (^[I: $i] : refl(((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(231,plain,
% 0.13/0.52 (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[230])).
% 0.13/0.52 tff(232,plain,
% 0.13/0.52 (^[I: $i] : rewrite(((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(233,plain,
% 0.13/0.52 (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[232])).
% 0.13/0.52 tff(234,plain,
% 0.13/0.52 (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.52 inference(transitivity,[status(thm)],[233, 231])).
% 0.13/0.52 tff(235,plain,
% 0.13/0.52 (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))))), quant_intro(proof_bind(^[J: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> (((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))), rewrite((((~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))), (![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))) <=> ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> (((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))), rewrite((((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(236,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[235])).
% 0.13/0.52 tff(237,plain,
% 0.13/0.52 (^[I: $i] : rewrite(((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(238,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[237])).
% 0.13/0.52 tff(239,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.52 inference(rewrite,[status(thm)],[])).
% 0.13/0.52 tff(240,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.52 inference(and_elim,[status(thm)],[22])).
% 0.13/0.52 tff(241,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.13/0.52 tff(242,plain,
% 0.13/0.52 (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[241, 238])).
% 0.13/0.52 tff(243,plain,(
% 0.13/0.52 ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, minus(pv57, succ(succ(tptp_minus_1)))))) | ![J: $i] : ((~(leq(succ(tptp_minus_1), J) & leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.53 inference(skolemize,[status(sab)],[242])).
% 0.13/0.53 tff(244,plain,
% 0.13/0.53 (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.53 inference(modus_ponens,[status(thm)],[243, 236])).
% 0.13/0.53 tff(245,plain,
% 0.13/0.53 (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.53 inference(modus_ponens,[status(thm)],[244, 234])).
% 0.13/0.53 tff(246,plain,
% 0.13/0.53 (((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) | ((~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.53 inference(rewrite,[status(thm)],[])).
% 0.13/0.53 tff(247,plain,
% 0.13/0.53 ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) | ((~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.53 inference(quant_inst,[status(thm)],[])).
% 0.13/0.53 tff(248,plain,
% 0.13/0.53 ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) | ![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.53 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.13/0.53 tff(249,plain,
% 0.13/0.53 (![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[248, 245, 229, 227])).
% 0.13/0.53 tff(250,plain,
% 0.13/0.53 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))) | leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.53 inference(tautology,[status(thm)],[])).
% 0.13/0.53 tff(251,plain,
% 0.13/0.53 (leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[250, 225])).
% 0.13/0.53 tff(252,plain,
% 0.13/0.53 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), T!22)),
% 0.13/0.53 inference(tautology,[status(thm)],[])).
% 0.13/0.53 tff(253,plain,
% 0.13/0.53 (leq(succ(tptp_minus_1), T!22)),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[252, 225])).
% 0.13/0.53 tff(254,plain,
% 0.13/0.53 (((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))) | (~(a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))),
% 0.13/0.53 inference(tautology,[status(thm)],[])).
% 0.13/0.53 tff(255,plain,
% 0.13/0.53 (~(a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[254, 225])).
% 0.13/0.53 tff(256,plain,
% 0.13/0.53 (((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.53 inference(rewrite,[status(thm)],[])).
% 0.13/0.53 tff(257,plain,
% 0.13/0.53 ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.13/0.53 inference(quant_inst,[status(thm)],[])).
% 0.13/0.53 tff(258,plain,
% 0.13/0.53 ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.53 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.13/0.53 tff(259,plain,
% 0.13/0.53 ($false),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[258, 255, 253, 251, 249])).
% 0.13/0.53 tff(260,plain,((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.53 tff(261,plain,
% 0.13/0.53 (((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))))) <=> ((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.53 inference(rewrite,[status(thm)],[])).
% 0.13/0.53 tff(262,plain,
% 0.13/0.53 ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))))),
% 0.13/0.53 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(263,plain,
% 0.45/0.54 ((~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(264,plain,
% 0.45/0.54 ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[263])).
% 0.45/0.54 tff(265,plain,
% 0.45/0.54 ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(transitivity,[status(thm)],[264, 262])).
% 0.45/0.54 tff(266,plain,
% 0.45/0.54 ((~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) <=> (~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(267,plain,
% 0.45/0.54 ((~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(268,plain,
% 0.45/0.54 ((~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(269,plain,
% 0.45/0.54 ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (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(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54 inference(rewrite,[status(thm)],[])).
% 0.45/0.54 tff(270,plain,
% 0.45/0.54 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))))),
% 0.45/0.54 inference(monotonicity,[status(thm)],[269, 268, 267, 266, 265])).
% 0.45/0.54 tff(271,plain,
% 0.45/0.54 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), S!21)) | (~leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, pv57)) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.45/0.54 inference(transitivity,[status(thm)],[270, 261])).
% 0.45/0.54 tff(272,plain,
% 0.45/0.54 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(273,plain,
% 0.45/0.55 (((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(274,plain,
% 0.45/0.55 ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))))),
% 0.45/0.55 inference(rewrite,[status(thm)],[])).
% 0.45/0.55 tff(275,plain,
% 0.45/0.55 (((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[274])).
% 0.45/0.55 tff(276,plain,
% 0.45/0.55 (((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))) <=> (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))),
% 0.45/0.55 inference(transitivity,[status(thm)],[275, 273])).
% 0.45/0.55 tff(277,plain,
% 0.45/0.55 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))))),
% 0.45/0.55 inference(monotonicity,[status(thm)],[276])).
% 0.48/0.56 tff(278,plain,
% 0.48/0.56 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (~((~(leq(succ(tptp_minus_1), Q!20) & leq(succ(tptp_minus_1), R!19) & leq(Q!20, pv57) & leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!20, R!19) = a_select3(id_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(pv57, succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), T!22) & leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))))))),
% 0.48/0.56 inference(transitivity,[status(thm)],[277, 272])).
% 0.48/0.56 tff(279,plain,
% 0.48/0.56 ((![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(280,plain,
% 0.48/0.56 ((~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.56 inference(monotonicity,[status(thm)],[279])).
% 0.48/0.56 tff(281,plain,
% 0.48/0.56 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(282,plain,
% 0.48/0.57 ((![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(283,plain,
% 0.48/0.57 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[282])).
% 0.48/0.57 tff(284,plain,
% 0.48/0.57 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(285,plain,
% 0.48/0.57 ((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(286,plain,
% 0.48/0.57 ((leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(287,plain,
% 0.48/0.58 ((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[286])).
% 0.48/0.58 tff(288,plain,
% 0.48/0.58 (~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(or_elim,[status(thm)],[21])).
% 0.48/0.58 tff(289,plain,
% 0.48/0.58 (~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.48/0.58 tff(290,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.48/0.58 tff(291,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[290, 284])).
% 0.48/0.58 tff(292,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, pv57) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(pv57, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[291, 283])).
% 0.48/0.58 tff(293,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[292, 281])).
% 0.48/0.58 tff(294,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[293, 280])).
% 0.48/0.58 tff(295,plain,
% 0.48/0.58 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[294, 280])).
% 0.48/0.59 tff(296,plain,
% 0.48/0.59 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(succ(tptp_minus_1), R) & leq(Q, pv57) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(pv57, succ(succ(tptp_minus_1)))))) | ![T: $i] : ((~(leq(succ(tptp_minus_1), T) & leq(T, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[295, 280])).
% 0.48/0.59 unexpected number of arguments: (let ((a!1 (forall ((K $i) (L $i))
% 0.48/0.59 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.59 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.48/0.59 (succ (succ tptp_minus_1)))))
% 0.48/0.59 (let ((a!3 (not (and (leq (succ tptp_minus_1) K)
% 0.48/0.59 (leq (succ tptp_minus_1) L)
% 0.48/0.59 (leq K a!2)
% 0.48/0.59 (leq L a!2)))))
% 0.48/0.59 (or a!3
% 0.48/0.59 (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))))
% 0.48/0.59 (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.48/0.59 (a!6 (forall ((M $i) (N $i))
% 0.48/0.59 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.59 (let ((a!2 (leq M (minus a!1 (succ (succ tptp_minus_1)))))
% 0.48/0.59 (a!3 (leq N (minus a!1 (succ (succ tptp_minus_1))))))
% 0.48/0.59 (let ((a!4 (not (and (leq (succ tptp_minus_1) M)
% 0.48/0.59 (leq (succ tptp_minus_1) N)
% 0.48/0.59 a!2
% 0.48/0.59 a!3))))
% 0.48/0.59 (or a!4
% 0.48/0.59 (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))))
% 0.48/0.59 (a!11 (forall ((O $i) (P $i))
% 0.48/0.59 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.59 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.48/0.59 (succ (succ tptp_minus_1)))))
% 0.48/0.59 (let ((a!3 (not (and (leq (succ tptp_minus_1) O)
% 0.48/0.59 (leq (succ tptp_minus_1) P)
% 0.48/0.59 (leq O a!2)
% 0.48/0.59 (leq P a!2)))))
% 0.48/0.59 (or a!3
% 0.48/0.59 (= (a_select3 pminus_ds1_filter O P)
% 0.48/0.59 (a_select3 pminus_ds1_filter P O))))))))
% 0.48/0.59 (a!14 (forall ((Q $i) (R $i))
% 0.48/0.59 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.59 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.48/0.59 (succ (succ tptp_minus_1)))))
% 0.48/0.59 (let ((a!3 (not (and (leq (succ tptp_minus_1) Q)
% 0.48/0.59 (leq (succ tptp_minus_1) R)
% 0.48/0.59 (leq Q pv57)
% 0.48/0.60 (leq R a!2)))))
% 0.48/0.60 (or a!3
% 0.48/0.60 (= (a_select3 id_ds1_filter Q R)
% 0.48/0.60 (a_select3 id_ds1_filter R Q))))))))
% 0.48/0.60 (a!17 (forall ((S $i))
% 0.48/0.60 (let ((a!1 (leq S (minus pv57 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (a!3 (forall ((T $i))
% 0.48/0.60 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.60 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.48/0.60 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (let ((a!3 (not (and (leq (succ tptp_minus_1) T)
% 0.48/0.60 (leq T a!2)))))
% 0.48/0.60 (or a!3
% 0.48/0.60 (= (a_select3 id_ds1_filter S T)
% 0.48/0.60 (a_select3 id_ds1_filter T S)))))))))
% 0.48/0.60 (let ((a!2 (not (and (leq (succ tptp_minus_1) S) a!1))))
% 0.48/0.60 (or a!2 a!3)))))
% 0.48/0.60 (a!18 (leq S!21 (minus pv57 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (a!20 (forall ((T $i))
% 0.48/0.60 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.48/0.60 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.48/0.60 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (let ((a!3 (not (and (leq (succ tptp_minus_1) T) (leq T a!2)))))
% 0.48/0.60 (or a!3
% 0.48/0.60 (= (a_select3 id_ds1_filter S!21 T)
% 0.48/0.60 (a_select3 id_ds1_filter T S!21)))))))))
% 0.48/0.60 (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.48/0.60 (a!7 (leq M!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (a!8 (leq N!15 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.48/0.60 (a!19 (not (and (leq (succ tptp_minus_1) S!21) a!18))))
% 0.48/0.60 (let ((a!4 (not (and (leq (succ tptp_minus_1) K!14)
% 0.48/0.60 (leq (succ tptp_minus_1) L!13)
% 0.48/0.60 (leq K!14 a!3)
% 0.48/0.60 (leq L!13 a!3))))
% 0.48/0.60 (a!9 (not (and (leq (succ tptp_minus_1) M!16)
% 0.48/0.60 (leq (succ tptp_minus_1) N!15)
% 0.48/0.60 a!7
% 0.48/0.60 a!8)))
% 0.48/0.60 (a!12 (not (and (leq (succ tptp_minus_1) O!18)
% 0.48/0.60 (leq (succ tptp_minus_1) P!17)
% 0.48/0.60 (leq O!18 a!3)
% 0.48/0.60 (leq P!17 a!3))))
% 0.48/0.60 (a!15 (not (and (leq (succ tptp_minus_1) Q!20)
% 0.48/0.60 (leq (succ tptp_minus_1) R!19)
% 0.48/0.60 (leq Q!20 pv57)
% 0.48/0.60 (leq R!19 a!3))))
% 0.48/0.60 (a!21 (sk (~ (not a!17) (not (or a!19 a!20)))))
% 0.48/0.60 (a!22 (not (and (leq (succ tptp_minus_1) T!22) (leq T!22 a!3)))))
% 0.48/0.60 (let ((a!5 (not (or a!4
% 0.48/0.60 (= (a_select3 q_ds1_filter K!14 L!13)
% 0.48/0.60 (a_select3 q_ds1_filter L!13 K!14)))))
% 0.48/0.60 (a!10 (not (or a!9
% 0.48/0.60 (= (a_select3 r_ds1_filter M!16 N!15)
% 0.48/0.60 (a_select3 r_ds1_filter N!15 M!16)))))
% 0.48/0.60 (a!13 (not (or a!12
% 0.48/0.60 (= (a_select3 pminus_ds1_filter O!18 P!17)
% 0.48/0.60 (a_select3 pminus_ds1_filter P!17 O!18)))))
% 0.48/0.60 (a!16 (not (or a!15
% 0.48/0.60 (= (a_select3 id_ds1_filter Q!20 R!19)
% 0.48/0.60 (a_select3 id_ds1_filter R!19 Q!20)))))
% 0.48/0.60 (a!23 (not (or a!22
% 0.48/0.60 (= (a_select3 id_ds1_filter S!21 T!22)
% 0.48/0.60 (a_select3 id_ds1_filter T!22 S!21))))))
% 0.48/0.60 (let ((a!24 (nnf-neg (refl (~ (not a!19) (not a!19)))
% 0.48/0.60 (sk (~ (not a!20) a!23))
% 0.48/0.60 (~ (not (or a!19 a!20)) (and (not a!19) a!23))))
% 0.48/0.60 (a!26 (~ (not (and a!1 a!6 a!11 a!14 a!17))
% 0.48/0.60 (or a!5 a!10 a!13 a!16 (and (not a!19) a!23)))))
% 0.48/0.60 (let ((a!25 (trans a!21 a!24 (~ (not a!17) (and (not a!19) a!23)))))
% 0.48/0.60 (nnf-neg (sk (~ (not a!1) a!5))
% 0.48/0.60 (sk (~ (not a!6) a!10))
% 0.48/0.60 (sk (~ (not a!11) a!13))
% 0.48/0.60 (sk (~ (not a!14) a!16))
% 0.48/0.60 a!25
% 0.48/0.60 a!26)))))))
% 0.48/0.60 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------