%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV115+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 15:10:02 EDT 2022

% Result   : Theorem 0.13s 0.48s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : SWV115+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.02/0.09  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.28  % Computer : n020.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Sun Sep  4 01:29:44 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 0.08/0.29  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29  Usage: tptp [options] [-file:]file
% 0.08/0.29    -h, -?       prints this message.
% 0.08/0.29    -smt2        print SMT-LIB2 benchmark.
% 0.08/0.29    -m, -model   generate model.
% 0.08/0.29    -p, -proof   generate proof.
% 0.08/0.29    -c, -core    generate unsat core of named formulas.
% 0.08/0.29    -st, -statistics display statistics.
% 0.08/0.29    -t:timeout   set timeout (in second).
% 0.08/0.29    -smt2status  display status in smt2 format instead of SZS.
% 0.08/0.29    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29    -<param>:<value> configuration parameter and value.
% 0.08/0.29    -o:<output-file> file to place output in.
% 0.13/0.48  % SZS status Theorem
% 0.13/0.48  % SZS output start Proof
% 0.13/0.48  tff(leq_type, type, (
% 0.13/0.48     leq: ( $i * $i ) > $o)).
% 0.13/0.48  tff(minus_type, type, (
% 0.13/0.48     minus: ( $i * $i ) > $i)).
% 0.13/0.48  tff(succ_type, type, (
% 0.13/0.48     succ: $i > $i)).
% 0.13/0.48  tff(tptp_minus_1_type, type, (
% 0.13/0.48     tptp_minus_1: $i)).
% 0.13/0.48  tff(tptp_fun_L_13_type, type, (
% 0.13/0.48     tptp_fun_L_13: $i)).
% 0.13/0.48  tff(tptp_fun_K_14_type, type, (
% 0.13/0.48     tptp_fun_K_14: $i)).
% 0.13/0.48  tff(a_select3_type, type, (
% 0.13/0.48     a_select3: ( $i * $i * $i ) > $i)).
% 0.13/0.48  tff(q_ds1_filter_type, type, (
% 0.13/0.48     q_ds1_filter: $i)).
% 0.13/0.48  tff(tptp_fun_S_21_type, type, (
% 0.13/0.48     tptp_fun_S_21: $i)).
% 0.13/0.48  tff(tptp_fun_T_22_type, type, (
% 0.13/0.48     tptp_fun_T_22: $i)).
% 0.13/0.48  tff(id_ds1_filter_type, type, (
% 0.13/0.48     id_ds1_filter: $i)).
% 0.13/0.48  tff(n1_type, type, (
% 0.13/0.48     n1: $i)).
% 0.13/0.48  tff(n6_type, type, (
% 0.13/0.48     n6: $i)).
% 0.13/0.48  tff(n0_type, type, (
% 0.13/0.48     n0: $i)).
% 0.13/0.48  tff(pminus_ds1_filter_type, type, (
% 0.13/0.48     pminus_ds1_filter: $i)).
% 0.13/0.48  tff(r_ds1_filter_type, type, (
% 0.13/0.48     r_ds1_filter: $i)).
% 0.13/0.48  tff(n3_type, type, (
% 0.13/0.48     n3: $i)).
% 0.13/0.48  tff(n999_type, type, (
% 0.13/0.48     n999: $i)).
% 0.13/0.48  tff(pv5_type, type, (
% 0.13/0.48     pv5: $i)).
% 0.13/0.48  tff(tptp_fun_R_19_type, type, (
% 0.13/0.48     tptp_fun_R_19: $i)).
% 0.13/0.48  tff(tptp_fun_Q_20_type, type, (
% 0.13/0.48     tptp_fun_Q_20: $i)).
% 0.13/0.48  tff(tptp_fun_P_17_type, type, (
% 0.13/0.48     tptp_fun_P_17: $i)).
% 0.13/0.48  tff(tptp_fun_O_18_type, type, (
% 0.13/0.48     tptp_fun_O_18: $i)).
% 0.13/0.48  tff(tptp_fun_N_15_type, type, (
% 0.13/0.48     tptp_fun_N_15: $i)).
% 0.13/0.48  tff(tptp_fun_M_16_type, type, (
% 0.13/0.48     tptp_fun_M_16: $i)).
% 0.13/0.48  tff(1,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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.13/0.48  tff(2,plain,
% 0.13/0.48      (((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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.48      inference(tautology,[status(thm)],[])).
% 0.13/0.48  tff(3,plain,
% 0.13/0.48      (leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.48      inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.48  tff(4,plain,
% 0.13/0.48      (((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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), S!21)),
% 0.13/0.48      inference(tautology,[status(thm)],[])).
% 0.13/0.48  tff(5,plain,
% 0.13/0.48      (leq(succ(tptp_minus_1), S!21)),
% 0.13/0.48      inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.48  tff(6,plain,
% 0.13/0.48      (^[I: $i] : refl(((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))))),
% 0.13/0.48      inference(bind,[status(th)],[])).
% 0.13/0.48  tff(7,plain,
% 0.13/0.48      (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.48      inference(quant_intro,[status(thm)],[6])).
% 0.13/0.48  tff(8,plain,
% 0.13/0.48      (^[I: $i] : rewrite(((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))))),
% 0.13/0.48      inference(bind,[status(th)],[])).
% 0.13/0.48  tff(9,plain,
% 0.13/0.48      (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.48      inference(quant_intro,[status(thm)],[8])).
% 0.13/0.48  tff(10,plain,
% 0.13/0.48      (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.48      inference(transitivity,[status(thm)],[9, 7])).
% 0.13/0.48  tff(11,plain,
% 0.13/0.48      (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), I) & leq(I, 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), I) & leq(I, 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(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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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)))) <=> (((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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)))) <=> ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))))),
% 0.13/0.49      inference(bind,[status(th)],[])).
% 0.13/0.49  tff(12,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, 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)))) <=> ![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.49      inference(quant_intro,[status(thm)],[11])).
% 0.13/0.49  tff(13,plain,
% 0.13/0.49      (^[I: $i] : rewrite(((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ((~(leq(succ(tptp_minus_1), I) & leq(I, 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)))))),
% 0.13/0.49      inference(bind,[status(th)],[])).
% 0.13/0.49  tff(14,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, 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))))),
% 0.13/0.49      inference(quant_intro,[status(thm)],[13])).
% 0.13/0.49  tff(15,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))) <=> ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.49      inference(rewrite,[status(thm)],[])).
% 0.13/0.49  tff(16,plain,
% 0.13/0.49      ((~(((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, minus(n6, n1))) & leq(R, minus(n6, n1))) => (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(n6, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))) <=> (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))))),
% 0.13/0.49      inference(rewrite,[status(thm)],[])).
% 0.13/0.49  tff(17,axiom,(~(((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(n6, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => ((((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i, R: $i] : ((((leq(n0, Q) & leq(n0, R)) & leq(Q, minus(n6, n1))) & leq(R, minus(n6, n1))) => (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q)))) & ![S: $i] : ((leq(n0, S) & leq(S, minus(n6, n1))) => ![T: $i] : ((leq(n0, T) & leq(T, minus(n6, n1))) => (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0008')).
% 0.13/0.49  tff(18,plain,
% 0.13/0.49      (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.49  tff(19,plain,
% 0.13/0.49      (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.49      inference(or_elim,[status(thm)],[18])).
% 0.13/0.49  tff(20,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.49      inference(and_elim,[status(thm)],[19])).
% 0.13/0.49  tff(21,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(n0, I) & leq(I, minus(n6, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[20, 15])).
% 0.13/0.49  tff(22,plain,
% 0.13/0.49      (![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, 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))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.49  tff(23,plain,(
% 0.13/0.49      ![I: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(I, 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))))),
% 0.13/0.49      inference(skolemize,[status(sab)],[22])).
% 0.13/0.49  tff(24,plain,
% 0.13/0.49      (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[23, 12])).
% 0.13/0.49  tff(25,plain,
% 0.13/0.49      (![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[24, 10])).
% 0.13/0.49  tff(26,plain,
% 0.13/0.49      (((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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)))))))) <=> ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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)))))))),
% 0.13/0.49      inference(rewrite,[status(thm)],[])).
% 0.13/0.49  tff(27,plain,
% 0.13/0.49      ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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)))))))),
% 0.13/0.49      inference(quant_inst,[status(thm)],[])).
% 0.13/0.49  tff(28,plain,
% 0.13/0.49      ((~![I: $i] : ((~leq(succ(tptp_minus_1), I)) | (~leq(I, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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))))))),
% 0.13/0.49      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.49  tff(29,plain,
% 0.13/0.49      (![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))))))),
% 0.13/0.49      inference(unit_resolution,[status(thm)],[28, 25, 5, 3])).
% 0.13/0.49  tff(30,plain,
% 0.13/0.49      (((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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.49      inference(tautology,[status(thm)],[])).
% 0.13/0.49  tff(31,plain,
% 0.13/0.49      (leq(T!22, 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)],[30, 1])).
% 0.13/0.49  tff(32,plain,
% 0.13/0.49      (((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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), T!22)),
% 0.13/0.49      inference(tautology,[status(thm)],[])).
% 0.13/0.49  tff(33,plain,
% 0.13/0.49      (leq(succ(tptp_minus_1), T!22)),
% 0.13/0.49      inference(unit_resolution,[status(thm)],[32, 1])).
% 0.13/0.49  tff(34,plain,
% 0.13/0.49      (((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(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)))),
% 0.13/0.49      inference(tautology,[status(thm)],[])).
% 0.13/0.49  tff(35,plain,
% 0.13/0.49      (~(a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21))),
% 0.13/0.49      inference(unit_resolution,[status(thm)],[34, 1])).
% 0.13/0.49  tff(36,plain,
% 0.13/0.49      (((~![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))))))),
% 0.13/0.49      inference(rewrite,[status(thm)],[])).
% 0.13/0.49  tff(37,plain,
% 0.13/0.49      ((~![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))))))),
% 0.13/0.50      inference(quant_inst,[status(thm)],[])).
% 0.13/0.50  tff(38,plain,
% 0.13/0.50      ((~![J: $i] : ((a_select3(id_ds1_filter, S!21, J) = a_select3(id_ds1_filter, J, S!21)) | (~leq(succ(tptp_minus_1), J)) | (~leq(J, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(id_ds1_filter, S!21, T!22) = a_select3(id_ds1_filter, T!22, S!21)) | (~leq(succ(tptp_minus_1), T!22)) | (~leq(T!22, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.50  tff(39,plain,
% 0.13/0.50      ($false),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[38, 35, 33, 31, 29])).
% 0.13/0.50  tff(40,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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.50  tff(41,assumption,(~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))), introduced(assumption)).
% 0.13/0.50  tff(42,plain,
% 0.13/0.50      (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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)))))) | leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(43,plain,
% 0.13/0.50      (leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.50  tff(44,plain,
% 0.13/0.50      (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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)))))) | leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(45,plain,
% 0.13/0.50      (leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[44, 41])).
% 0.13/0.50  tff(46,plain,
% 0.13/0.50      (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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)))))) | leq(succ(tptp_minus_1), R!19)),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(47,plain,
% 0.13/0.50      (leq(succ(tptp_minus_1), R!19)),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[46, 41])).
% 0.13/0.50  tff(48,plain,
% 0.13/0.50      (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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)))))) | leq(succ(tptp_minus_1), Q!20)),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(49,plain,
% 0.13/0.50      (leq(succ(tptp_minus_1), Q!20)),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[48, 41])).
% 0.13/0.50  tff(50,plain,
% 0.13/0.50      (((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(51,plain,
% 0.13/0.50      (~(a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[50, 41])).
% 0.13/0.50  tff(52,plain,
% 0.13/0.50      (^[G: $i, H: $i] : refl(((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, G, H) = a_select3(pminus_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)))))))),
% 0.13/0.50      inference(bind,[status(th)],[])).
% 0.13/0.50  tff(53,plain,
% 0.13/0.50      (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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)))))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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))))))),
% 0.13/0.50      inference(quant_intro,[status(thm)],[52])).
% 0.13/0.50  tff(54,plain,
% 0.13/0.50      (^[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)))))))), (((~(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(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(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)))))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(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))))))))),
% 0.13/0.50      inference(bind,[status(th)],[])).
% 0.13/0.50  tff(55,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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(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))))))),
% 0.13/0.50      inference(quant_intro,[status(thm)],[54])).
% 0.13/0.50  tff(56,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)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))))),
% 0.13/0.50      inference(bind,[status(th)],[])).
% 0.13/0.50  tff(57,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)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(quant_intro,[status(thm)],[56])).
% 0.13/0.50  tff(58,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)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G))) <=> ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(rewrite,[status(thm)],[])).
% 0.13/0.50  tff(59,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)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(and_elim,[status(thm)],[19])).
% 0.13/0.50  tff(60,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)))) | (a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[59, 58])).
% 0.13/0.50  tff(61,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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[60, 57])).
% 0.13/0.50  tff(62,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(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)))),
% 0.13/0.50      inference(skolemize,[status(sab)],[61])).
% 0.13/0.50  tff(63,plain,
% 0.13/0.50      (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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))))))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[62, 55])).
% 0.13/0.50  tff(64,plain,
% 0.13/0.50      (![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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))))))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[63, 53])).
% 0.13/0.50  tff(65,plain,
% 0.13/0.50      (((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))) <=> ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))),
% 0.13/0.50      inference(rewrite,[status(thm)],[])).
% 0.13/0.50  tff(66,plain,
% 0.13/0.50      ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))),
% 0.13/0.50      inference(quant_inst,[status(thm)],[])).
% 0.13/0.50  tff(67,plain,
% 0.13/0.50      ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(succ(tptp_minus_1), Q!20)) | (~leq(succ(tptp_minus_1), R!19)) | (~leq(Q!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(R!19, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.50      inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.50  tff(68,plain,
% 0.13/0.50      ($false),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[67, 64, 51, 49, 47, 45, 43])).
% 0.13/0.50  tff(69,plain,((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.50  tff(70,assumption,(~((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))))))), introduced(assumption)).
% 0.13/0.50  tff(71,plain,
% 0.13/0.50      (((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)))))) | leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(72,plain,
% 0.13/0.50      (leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[71, 70])).
% 0.13/0.50  tff(73,plain,
% 0.13/0.50      (((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)))))) | leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(74,plain,
% 0.13/0.50      (leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[73, 70])).
% 0.13/0.50  tff(75,plain,
% 0.13/0.50      (((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)))))) | leq(succ(tptp_minus_1), P!17)),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(76,plain,
% 0.13/0.50      (leq(succ(tptp_minus_1), P!17)),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[75, 70])).
% 0.13/0.50  tff(77,plain,
% 0.13/0.50      (((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)))))) | leq(succ(tptp_minus_1), O!18)),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(78,plain,
% 0.13/0.50      (leq(succ(tptp_minus_1), O!18)),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[77, 70])).
% 0.13/0.50  tff(79,plain,
% 0.13/0.50      (((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(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))),
% 0.13/0.50      inference(tautology,[status(thm)],[])).
% 0.13/0.50  tff(80,plain,
% 0.13/0.50      (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18))),
% 0.13/0.50      inference(unit_resolution,[status(thm)],[79, 70])).
% 0.13/0.50  tff(81,plain,
% 0.13/0.50      (((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(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))))))) <=> ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(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))))))),
% 0.13/0.50      inference(rewrite,[status(thm)],[])).
% 0.13/0.50  tff(82,plain,
% 0.13/0.50      ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_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(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))))))),
% 0.13/0.51      inference(quant_inst,[status(thm)],[])).
% 0.13/0.51  tff(83,plain,
% 0.13/0.51      ((~![G: $i, H: $i] : ((a_select3(pminus_ds1_filter, G, H) = a_select3(pminus_ds1_filter, H, G)) | (~leq(succ(tptp_minus_1), G)) | (~leq(succ(tptp_minus_1), H)) | (~leq(G, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.51  tff(84,plain,
% 0.13/0.51      ($false),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[83, 64, 80, 78, 76, 74, 72])).
% 0.13/0.51  tff(85,plain,((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)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.51  tff(86,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)).
% 0.13/0.51  tff(87,plain,
% 0.13/0.51      (((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))))),
% 0.13/0.51      inference(tautology,[status(thm)],[])).
% 0.13/0.51  tff(88,plain,
% 0.13/0.51      (leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[87, 86])).
% 0.13/0.51  tff(89,plain,
% 0.13/0.51      (((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))))),
% 0.13/0.51      inference(tautology,[status(thm)],[])).
% 0.13/0.51  tff(90,plain,
% 0.13/0.51      (leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[89, 86])).
% 0.13/0.51  tff(91,plain,
% 0.13/0.51      (((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)),
% 0.13/0.51      inference(tautology,[status(thm)],[])).
% 0.13/0.51  tff(92,plain,
% 0.13/0.51      (leq(succ(tptp_minus_1), N!15)),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[91, 86])).
% 0.13/0.51  tff(93,plain,
% 0.13/0.51      (((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)),
% 0.13/0.51      inference(tautology,[status(thm)],[])).
% 0.13/0.51  tff(94,plain,
% 0.13/0.51      (leq(succ(tptp_minus_1), M!16)),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[93, 86])).
% 0.13/0.51  tff(95,plain,
% 0.13/0.51      (((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)))),
% 0.13/0.51      inference(tautology,[status(thm)],[])).
% 0.13/0.51  tff(96,plain,
% 0.13/0.51      (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[95, 86])).
% 0.13/0.51  tff(97,plain,
% 0.13/0.51      (^[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)))))))),
% 0.13/0.51      inference(bind,[status(th)],[])).
% 0.13/0.51  tff(98,plain,
% 0.13/0.51      (![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))))))),
% 0.13/0.51      inference(quant_intro,[status(thm)],[97])).
% 0.13/0.51  tff(99,plain,
% 0.13/0.51      (^[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))))))))),
% 0.13/0.51      inference(bind,[status(th)],[])).
% 0.13/0.51  tff(100,plain,
% 0.13/0.51      (![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))))))),
% 0.13/0.51      inference(quant_intro,[status(thm)],[99])).
% 0.13/0.51  tff(101,plain,
% 0.13/0.51      (^[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))))),
% 0.13/0.51      inference(bind,[status(th)],[])).
% 0.13/0.51  tff(102,plain,
% 0.13/0.51      (![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)))),
% 0.13/0.51      inference(quant_intro,[status(thm)],[101])).
% 0.13/0.51  tff(103,plain,
% 0.13/0.51      (![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)))),
% 0.13/0.51      inference(rewrite,[status(thm)],[])).
% 0.13/0.51  tff(104,plain,
% 0.13/0.51      (![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)))),
% 0.13/0.51      inference(and_elim,[status(thm)],[19])).
% 0.13/0.51  tff(105,plain,
% 0.13/0.51      (![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)))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[104, 103])).
% 0.13/0.51  tff(106,plain,
% 0.13/0.51      (![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)))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[105, 102])).
% 0.13/0.51  tff(107,plain,(
% 0.13/0.51      ![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)))),
% 0.13/0.51      inference(skolemize,[status(sab)],[106])).
% 0.13/0.51  tff(108,plain,
% 0.13/0.51      (![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))))))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[107, 100])).
% 0.13/0.51  tff(109,plain,
% 0.13/0.51      (![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))))))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[108, 98])).
% 0.13/0.51  tff(110,plain,
% 0.13/0.51      (((~![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))))))),
% 0.13/0.51      inference(rewrite,[status(thm)],[])).
% 0.13/0.51  tff(111,plain,
% 0.13/0.51      ((~![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))))))),
% 0.13/0.51      inference(quant_inst,[status(thm)],[])).
% 0.13/0.51  tff(112,plain,
% 0.13/0.51      ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.13/0.51      inference(modus_ponens,[status(thm)],[111, 110])).
% 0.13/0.51  tff(113,plain,
% 0.13/0.51      ($false),
% 0.13/0.51      inference(unit_resolution,[status(thm)],[112, 109, 96, 94, 92, 90, 88])).
% 0.13/0.51  tff(114,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,[]))).
% 0.13/0.51  tff(115,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(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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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, 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(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_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(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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))))),
% 0.13/0.51      inference(rewrite,[status(thm)],[])).
% 0.13/0.51  tff(116,plain,
% 0.13/0.51      ((leq(succ(tptp_minus_1), S!21) & leq(S!21, 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)))))))) <=> (~((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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.51      inference(rewrite,[status(thm)],[])).
% 0.13/0.51  tff(117,plain,
% 0.13/0.51      ((~((~(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)))))))),
% 0.13/0.51      inference(rewrite,[status(thm)],[])).
% 0.13/0.51  tff(118,plain,
% 0.13/0.51      ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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))))))))),
% 0.13/0.51      inference(monotonicity,[status(thm)],[117])).
% 0.13/0.51  tff(119,plain,
% 0.13/0.51      ((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.13/0.51      inference(transitivity,[status(thm)],[118, 116])).
% 0.13/0.51  tff(120,plain,
% 0.13/0.51      ((~((~(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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) <=> (~((a_select3(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~leq(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)))))))),
% 0.13/0.52      inference(rewrite,[status(thm)],[])).
% 0.13/0.52  tff(121,plain,
% 0.13/0.52      ((~((~(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)))))))),
% 0.13/0.52      inference(rewrite,[status(thm)],[])).
% 0.13/0.52  tff(122,plain,
% 0.13/0.52      ((~((~(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)))))))),
% 0.13/0.52      inference(rewrite,[status(thm)],[])).
% 0.13/0.52  tff(123,plain,
% 0.13/0.52      ((~((~(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)))))))),
% 0.13/0.52      inference(rewrite,[status(thm)],[])).
% 0.13/0.52  tff(124,plain,
% 0.13/0.52      (((~((~(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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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, 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.13/0.52      inference(monotonicity,[status(thm)],[123, 122, 121, 120, 119])).
% 0.13/0.52  tff(125,plain,
% 0.13/0.52      (((~((~(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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)) | (~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))))))))),
% 0.13/0.52      inference(transitivity,[status(thm)],[124, 115])).
% 0.13/0.52  tff(126,plain,
% 0.13/0.52      (((~((~(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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))),
% 0.13/0.53      inference(rewrite,[status(thm)],[])).
% 0.13/0.53  tff(127,plain,
% 0.13/0.53      (((leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.53      inference(rewrite,[status(thm)],[])).
% 0.13/0.53  tff(128,plain,
% 0.13/0.53      ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, 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(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(129,plain,
% 0.13/0.53      (((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.53      inference(monotonicity,[status(thm)],[128])).
% 0.13/0.53  tff(130,plain,
% 0.13/0.53      (((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.53      inference(transitivity,[status(thm)],[129, 127])).
% 0.13/0.53  tff(131,plain,
% 0.13/0.53      (((~((~(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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))),
% 0.13/0.53      inference(monotonicity,[status(thm)],[130])).
% 0.13/0.53  tff(132,plain,
% 0.13/0.53      (((~((~(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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | ((~(~(leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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, 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(pminus_ds1_filter, Q!20, R!19) = a_select3(pminus_ds1_filter, R!19, Q!20)))) | (leq(succ(tptp_minus_1), S!21) & leq(S!21, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))),
% 0.13/0.53      inference(transitivity,[status(thm)],[131, 126])).
% 0.13/0.53  tff(133,plain,
% 0.13/0.53      ((![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.54      inference(rewrite,[status(thm)],[])).
% 0.13/0.54  tff(134,plain,
% 0.13/0.54      ((~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))),
% 0.13/0.54      inference(monotonicity,[status(thm)],[133])).
% 0.13/0.54  tff(135,plain,
% 0.13/0.54      ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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))))))),
% 0.13/0.54      inference(rewrite,[status(thm)],[])).
% 0.13/0.54  tff(136,plain,
% 0.13/0.54      ((![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.54      inference(rewrite,[status(thm)],[])).
% 0.13/0.54  tff(137,plain,
% 0.13/0.54      ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.54      inference(monotonicity,[status(thm)],[136])).
% 0.13/0.54  tff(138,plain,
% 0.13/0.54      ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.55      inference(rewrite,[status(thm)],[])).
% 0.13/0.55  tff(139,plain,
% 0.13/0.55      ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.55      inference(rewrite,[status(thm)],[])).
% 0.13/0.55  tff(140,plain,
% 0.13/0.55      ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(rewrite,[status(thm)],[])).
% 0.13/0.55  tff(141,plain,
% 0.13/0.55      ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S))))))),
% 0.13/0.55      inference(monotonicity,[status(thm)],[140])).
% 0.13/0.55  tff(142,plain,
% 0.13/0.55      (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(or_elim,[status(thm)],[18])).
% 0.13/0.55  tff(143,plain,
% 0.13/0.55      (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(modus_ponens,[status(thm)],[142, 141])).
% 0.13/0.55  tff(144,plain,
% 0.13/0.55      (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(modus_ponens,[status(thm)],[143, 139])).
% 0.13/0.55  tff(145,plain,
% 0.13/0.55      (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(modus_ponens,[status(thm)],[144, 138])).
% 0.13/0.55  tff(146,plain,
% 0.13/0.55      (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i, R: $i] : ((~(leq(n0, Q) & leq(n0, R) & leq(Q, minus(n6, n1)) & leq(R, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(n0, S) & leq(S, minus(n6, n1)))) | ![T: $i] : ((~(leq(n0, T) & leq(T, minus(n6, n1)))) | (a_select3(id_ds1_filter, S, T) = a_select3(id_ds1_filter, T, S)))))),
% 0.13/0.55      inference(modus_ponens,[status(thm)],[145, 137])).
% 0.13/0.55  tff(147,plain,
% 0.13/0.55      (~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.56      inference(modus_ponens,[status(thm)],[146, 135])).
% 0.13/0.56  tff(148,plain,
% 0.13/0.56      (~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.13/0.56      inference(modus_ponens,[status(thm)],[147, 134])).
% 0.13/0.56  tff(149,plain,
% 0.13/0.56      (~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.49/0.57      inference(modus_ponens,[status(thm)],[148, 134])).
% 0.49/0.57  tff(150,plain,
% 0.49/0.57      (~(![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, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, Q, R) = a_select3(pminus_ds1_filter, R, Q))) & ![S: $i] : ((~(leq(succ(tptp_minus_1), S) & leq(S, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), 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)))))),
% 0.49/0.57      inference(modus_ponens,[status(thm)],[149, 134])).
% 0.49/0.57  unexpected number of arguments: (let ((a!1 (forall ((K $i) (L $i))
% 0.49/0.57               (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57               (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                 (succ (succ tptp_minus_1)))))
% 0.49/0.57               (let ((a!3 (not (and (leq (succ tptp_minus_1) K)
% 0.49/0.57                                    (leq (succ tptp_minus_1) L)
% 0.49/0.57                                    (leq K a!2)
% 0.49/0.57                                    (leq L a!2)))))
% 0.49/0.57                 (or a!3
% 0.49/0.57                     (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))))
% 0.49/0.57        (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.49/0.57        (a!6 (forall ((M $i) (N $i))
% 0.49/0.57               (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57               (let ((a!2 (leq M (minus a!1 (succ (succ tptp_minus_1)))))
% 0.49/0.57                     (a!3 (leq N (minus a!1 (succ (succ tptp_minus_1))))))
% 0.49/0.57               (let ((a!4 (not (and (leq (succ tptp_minus_1) M)
% 0.49/0.57                                    (leq (succ tptp_minus_1) N)
% 0.49/0.57                                    a!2
% 0.49/0.57                                    a!3))))
% 0.49/0.57                 (or a!4
% 0.49/0.57                     (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))))
% 0.49/0.57        (a!11 (forall ((O $i) (P $i))
% 0.49/0.57                (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                  (succ (succ tptp_minus_1)))))
% 0.49/0.57                (let ((a!3 (not (and (leq (succ tptp_minus_1) O)
% 0.49/0.57                                     (leq (succ tptp_minus_1) P)
% 0.49/0.57                                     (leq O a!2)
% 0.49/0.57                                     (leq P a!2)))))
% 0.49/0.57                  (or a!3
% 0.49/0.57                      (= (a_select3 pminus_ds1_filter O P)
% 0.49/0.57                         (a_select3 pminus_ds1_filter P O))))))))
% 0.49/0.57        (a!14 (forall ((Q $i) (R $i))
% 0.49/0.57                (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                  (succ (succ tptp_minus_1)))))
% 0.49/0.57                (let ((a!3 (not (and (leq (succ tptp_minus_1) Q)
% 0.49/0.57                                     (leq (succ tptp_minus_1) R)
% 0.49/0.57                                     (leq Q a!2)
% 0.49/0.57                                     (leq R a!2)))))
% 0.49/0.57                  (or a!3
% 0.49/0.57                      (= (a_select3 pminus_ds1_filter Q R)
% 0.49/0.57                         (a_select3 pminus_ds1_filter R Q))))))))
% 0.49/0.57        (a!17 (forall ((S $i))
% 0.49/0.57                (let ((a!1 (succ (succ (succ (succ tptp_minus_1)))))
% 0.49/0.57                      (a!4 (forall ((T $i))
% 0.49/0.57                             (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57                             (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                               (succ (succ tptp_minus_1)))))
% 0.49/0.57                             (let ((a!3 (not (and (leq (succ tptp_minus_1) T)
% 0.49/0.57                                                  (leq T a!2)))))
% 0.49/0.57                               (or a!3
% 0.49/0.57                                   (= (a_select3 id_ds1_filter S T)
% 0.49/0.57                                      (a_select3 id_ds1_filter T S)))))))))
% 0.49/0.57                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                  (succ (succ tptp_minus_1)))))
% 0.49/0.57                (let ((a!3 (not (and (leq (succ tptp_minus_1) S) (leq S a!2)))))
% 0.49/0.57                  (or a!3 a!4))))))
% 0.49/0.57        (a!19 (forall ((T $i))
% 0.49/0.57                (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.49/0.57                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.49/0.57                                  (succ (succ tptp_minus_1)))))
% 0.49/0.57                (let ((a!3 (not (and (leq (succ tptp_minus_1) T) (leq T a!2)))))
% 0.49/0.57                  (or a!3
% 0.49/0.57                      (= (a_select3 id_ds1_filter S!21 T)
% 0.49/0.57                         (a_select3 id_ds1_filter T S!21)))))))))
% 0.49/0.57  (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.49/0.57        (a!7 (leq M!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.49/0.57        (a!8 (leq N!15 (minus a!2 (succ (succ tptp_minus_1))))))
% 0.49/0.57  (let ((a!4 (not (and (leq (succ tptp_minus_1) K!14)
% 0.49/0.57                       (leq (succ tptp_minus_1) L!13)
% 0.49/0.57                       (leq K!14 a!3)
% 0.49/0.57                       (leq L!13 a!3))))
% 0.49/0.57        (a!9 (not (and (leq (succ tptp_minus_1) M!16)
% 0.49/0.57                       (leq (succ tptp_minus_1) N!15)
% 0.49/0.57                       a!7
% 0.49/0.57                       a!8)))
% 0.49/0.57        (a!12 (not (and (leq (succ tptp_minus_1) O!18)
% 0.49/0.57                        (leq (succ tptp_minus_1) P!17)
% 0.49/0.57                        (leq O!18 a!3)
% 0.49/0.57                        (leq P!17 a!3))))
% 0.49/0.57        (a!15 (not (and (leq (succ tptp_minus_1) Q!20)
% 0.49/0.57                        (leq (succ tptp_minus_1) R!19)
% 0.49/0.57                        (leq Q!20 a!3)
% 0.49/0.57                        (leq R!19 a!3))))
% 0.49/0.57        (a!18 (not (and (leq (succ tptp_minus_1) S!21) (leq S!21 a!3))))
% 0.49/0.57        (a!21 (not (and (leq (succ tptp_minus_1) T!22) (leq T!22 a!3)))))
% 0.49/0.57  (let ((a!5 (not (or a!4
% 0.49/0.57                      (= (a_select3 q_ds1_filter K!14 L!13)
% 0.49/0.57                         (a_select3 q_ds1_filter L!13 K!14)))))
% 0.49/0.57        (a!10 (not (or a!9
% 0.49/0.57                       (= (a_select3 r_ds1_filter M!16 N!15)
% 0.49/0.57                          (a_select3 r_ds1_filter N!15 M!16)))))
% 0.49/0.57        (a!13 (not (or a!12
% 0.49/0.57                       (= (a_select3 pminus_ds1_filter O!18 P!17)
% 0.49/0.57                          (a_select3 pminus_ds1_filter P!17 O!18)))))
% 0.49/0.57        (a!16 (not (or a!15
% 0.49/0.57                       (= (a_select3 pminus_ds1_filter Q!20 R!19)
% 0.49/0.57                          (a_select3 pminus_ds1_filter R!19 Q!20)))))
% 0.49/0.57        (a!20 (sk (~ (not a!17) (not (or a!18 a!19)))))
% 0.49/0.57        (a!22 (not (or a!21
% 0.49/0.57                       (= (a_select3 id_ds1_filter S!21 T!22)
% 0.49/0.57                          (a_select3 id_ds1_filter T!22 S!21))))))
% 0.49/0.57  (let ((a!23 (nnf-neg (refl (~ (not a!18) (not a!18)))
% 0.49/0.57                       (sk (~ (not a!19) a!22))
% 0.49/0.57                       (~ (not (or a!18 a!19)) (and (not a!18) a!22))))
% 0.49/0.57        (a!25 (~ (not (and a!1 a!6 a!11 a!14 a!17))
% 0.49/0.57                 (or a!5 a!10 a!13 a!16 (and (not a!18) a!22)))))
% 0.49/0.57  (let ((a!24 (trans a!20 a!23 (~ (not a!17) (and (not a!18) a!22)))))
% 0.49/0.57    (nnf-neg (sk (~ (not a!1) a!5))
% 0.49/0.57             (sk (~ (not a!6) a!10))
% 0.49/0.57             (sk (~ (not a!11) a!13))
% 0.49/0.57             (sk (~ (not a!14) a!16))
% 0.49/0.57             a!24
% 0.49/0.57             a!25)))))))
% 0.49/0.57  Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------