%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV114+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 15:10:01 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV114+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Sep  4 01:27:56 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.51  % SZS status Theorem
% 0.20/0.51  % SZS output start Proof
% 0.20/0.51  tff(gt_type, type, (
% 0.20/0.51     gt: ( $i * $i ) > $o)).
% 0.20/0.51  tff(succ_type, type, (
% 0.20/0.51     succ: $i > $i)).
% 0.20/0.51  tff(tptp_minus_1_type, type, (
% 0.20/0.51     tptp_minus_1: $i)).
% 0.20/0.51  tff(leq_type, type, (
% 0.20/0.51     leq: ( $i * $i ) > $o)).
% 0.20/0.51  tff(tptp_fun_M_19_type, type, (
% 0.20/0.51     tptp_fun_M_19: $i)).
% 0.20/0.51  tff(minus_type, type, (
% 0.20/0.51     minus: ( $i * $i ) > $i)).
% 0.20/0.51  tff(pred_type, type, (
% 0.20/0.51     pred: $i > $i)).
% 0.20/0.51  tff(n1_type, type, (
% 0.20/0.51     n1: $i)).
% 0.20/0.51  tff(tptp_fun_N_20_type, type, (
% 0.20/0.51     tptp_fun_N_20: $i)).
% 0.20/0.51  tff(a_select3_type, type, (
% 0.20/0.51     a_select3: ( $i * $i * $i ) > $i)).
% 0.20/0.51  tff(id_ds1_filter_type, type, (
% 0.20/0.51     id_ds1_filter: $i)).
% 0.20/0.51  tff(tptp_fun_L_17_type, type, (
% 0.20/0.51     tptp_fun_L_17: $i)).
% 0.20/0.51  tff(tptp_fun_K_18_type, type, (
% 0.20/0.51     tptp_fun_K_18: $i)).
% 0.20/0.51  tff(pminus_ds1_filter_type, type, (
% 0.20/0.51     pminus_ds1_filter: $i)).
% 0.20/0.51  tff(n6_type, type, (
% 0.20/0.51     n6: $i)).
% 0.20/0.51  tff(n0_type, type, (
% 0.20/0.51     n0: $i)).
% 0.20/0.51  tff(r_ds1_filter_type, type, (
% 0.20/0.51     r_ds1_filter: $i)).
% 0.20/0.51  tff(n3_type, type, (
% 0.20/0.51     n3: $i)).
% 0.20/0.51  tff(q_ds1_filter_type, type, (
% 0.20/0.51     q_ds1_filter: $i)).
% 0.20/0.51  tff(n999_type, type, (
% 0.20/0.51     n999: $i)).
% 0.20/0.51  tff(pv5_type, type, (
% 0.20/0.51     pv5: $i)).
% 0.20/0.51  tff(tptp_fun_J_15_type, type, (
% 0.20/0.51     tptp_fun_J_15: $i)).
% 0.20/0.51  tff(tptp_fun_I_16_type, type, (
% 0.20/0.51     tptp_fun_I_16: $i)).
% 0.20/0.51  tff(tptp_fun_H_13_type, type, (
% 0.20/0.51     tptp_fun_H_13: $i)).
% 0.20/0.51  tff(tptp_fun_G_14_type, type, (
% 0.20/0.51     tptp_fun_G_14: $i)).
% 0.20/0.51  tff(1,plain,
% 0.20/0.51      (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(2,plain,
% 0.20/0.51      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.51  tff(3,plain,
% 0.20/0.51      (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(4,plain,
% 0.20/0.51      (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.51  tff(5,plain,
% 0.20/0.51      (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(6,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.20/0.51  tff(7,plain,
% 0.20/0.51      (![X: $i] : (minus(X, n1) = pred(X))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.51  tff(8,plain,
% 0.20/0.51      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.51  tff(9,plain,(
% 0.20/0.51      ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.51      inference(skolemize,[status(sab)],[8])).
% 0.20/0.51  tff(10,plain,
% 0.20/0.51      (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.51  tff(11,plain,
% 0.20/0.51      ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(12,plain,
% 0.20/0.51      (minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.51  tff(13,plain,
% 0.20/0.51      (pred(succ(tptp_minus_1)) = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.20/0.51      inference(symmetry,[status(thm)],[12])).
% 0.20/0.51  tff(14,plain,
% 0.20/0.51      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(15,plain,
% 0.20/0.51      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(16,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.20/0.51  tff(17,plain,
% 0.20/0.51      (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.51  tff(18,plain,(
% 0.20/0.51      ![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.51      inference(skolemize,[status(sab)],[17])).
% 0.20/0.51  tff(19,plain,
% 0.20/0.51      (![X: $i] : (pred(succ(X)) = X)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.51  tff(20,plain,
% 0.20/0.51      ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(21,plain,
% 0.20/0.51      (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.52  tff(22,plain,
% 0.20/0.52      (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 0.20/0.52      inference(symmetry,[status(thm)],[21])).
% 0.20/0.52  tff(23,plain,
% 0.20/0.52      (tptp_minus_1 = minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))),
% 0.20/0.52      inference(transitivity,[status(thm)],[22, 13])).
% 0.20/0.52  tff(24,plain,
% 0.20/0.52      (leq(M!19, tptp_minus_1) <=> leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))),
% 0.20/0.52      inference(monotonicity,[status(thm)],[23])).
% 0.20/0.52  tff(25,plain,
% 0.20/0.52      (leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) <=> leq(M!19, tptp_minus_1)),
% 0.20/0.52      inference(symmetry,[status(thm)],[24])).
% 0.20/0.52  tff(26,assumption,(~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.20/0.52  tff(27,plain,
% 0.20/0.52      (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.20/0.52      inference(tautology,[status(thm)],[])).
% 0.20/0.52  tff(28,plain,
% 0.20/0.52      (leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.52  tff(29,plain,
% 0.20/0.52      (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.20/0.52      inference(tautology,[status(thm)],[])).
% 0.20/0.52  tff(30,plain,
% 0.20/0.52      (leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[29, 26])).
% 0.20/0.52  tff(31,plain,
% 0.20/0.52      (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), L!17)),
% 0.20/0.52      inference(tautology,[status(thm)],[])).
% 0.20/0.52  tff(32,plain,
% 0.20/0.52      (leq(succ(tptp_minus_1), L!17)),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[31, 26])).
% 0.20/0.52  tff(33,plain,
% 0.20/0.52      (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), K!18)),
% 0.20/0.52      inference(tautology,[status(thm)],[])).
% 0.20/0.52  tff(34,plain,
% 0.20/0.52      (leq(succ(tptp_minus_1), K!18)),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[33, 26])).
% 0.20/0.52  tff(35,plain,
% 0.20/0.52      (((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))),
% 0.20/0.52      inference(tautology,[status(thm)],[])).
% 0.20/0.52  tff(36,plain,
% 0.20/0.52      (~(a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18))),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[35, 26])).
% 0.20/0.52  tff(37,plain,
% 0.20/0.52      (^[E: $i, F: $i] : refl(((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(38,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[37])).
% 0.20/0.52  tff(39,plain,
% 0.20/0.52      (^[E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> (((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))), rewrite((((~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(40,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[39])).
% 0.20/0.52  tff(41,plain,
% 0.20/0.52      (^[E: $i, F: $i] : rewrite(((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))),
% 0.20/0.52      inference(bind,[status(th)],[])).
% 0.20/0.52  tff(42,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[41])).
% 0.20/0.52  tff(43,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) <=> ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(44,plain,
% 0.20/0.52      ((~(((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G)))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n3, n1))) & leq(J, minus(n3, n1))) => (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K)))) & ![M: $i] : ((leq(n0, M) & leq(M, minus(n0, n1))) => ![N: $i] : ((leq(n0, N) & leq(N, minus(n6, n1))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))) <=> (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(45,axiom,(~(((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G)))) & ![I: $i, J: $i] : ((((leq(n0, I) & leq(n0, J)) & leq(I, minus(n3, n1))) & leq(J, minus(n3, n1))) => (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I)))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K)))) & ![M: $i] : ((leq(n0, M) & leq(M, minus(n0, n1))) => ![N: $i] : ((leq(n0, N) & leq(N, minus(n6, n1))) => (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_symm_0007')).
% 0.20/0.52  tff(46,plain,
% 0.20/0.52      (~((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.52  tff(47,plain,
% 0.20/0.52      (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)))),
% 0.20/0.52      inference(or_elim,[status(thm)],[46])).
% 0.20/0.52  tff(48,plain,
% 0.20/0.52      (![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)))),
% 0.20/0.52      inference(and_elim,[status(thm)],[47])).
% 0.20/0.52  tff(49,plain,
% 0.20/0.52      (![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)))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[48, 43])).
% 0.20/0.52  tff(50,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.52  tff(51,plain,(
% 0.20/0.52      ![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))),
% 0.20/0.52      inference(skolemize,[status(sab)],[50])).
% 0.20/0.52  tff(52,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[51, 40])).
% 0.20/0.52  tff(53,plain,
% 0.20/0.52      (![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[52, 38])).
% 0.20/0.53  tff(54,plain,
% 0.20/0.53      (((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.53      inference(rewrite,[status(thm)],[])).
% 0.20/0.53  tff(55,plain,
% 0.20/0.53      ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.20/0.53      inference(quant_inst,[status(thm)],[])).
% 0.20/0.53  tff(56,plain,
% 0.20/0.53      ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.20/0.53      inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.53  tff(57,plain,
% 0.20/0.53      ($false),
% 0.20/0.53      inference(unit_resolution,[status(thm)],[56, 53, 36, 34, 32, 30, 28])).
% 0.20/0.53  tff(58,plain,((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53  tff(59,assumption,(~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.45/0.53  tff(60,plain,
% 0.45/0.53      (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.45/0.53      inference(tautology,[status(thm)],[])).
% 0.45/0.53  tff(61,plain,
% 0.45/0.53      (leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[60, 59])).
% 0.45/0.53  tff(62,plain,
% 0.45/0.53      (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.45/0.53      inference(tautology,[status(thm)],[])).
% 0.45/0.53  tff(63,plain,
% 0.45/0.53      (leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[62, 59])).
% 0.45/0.53  tff(64,plain,
% 0.45/0.53      (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), J!15)),
% 0.45/0.53      inference(tautology,[status(thm)],[])).
% 0.45/0.53  tff(65,plain,
% 0.45/0.53      (leq(succ(tptp_minus_1), J!15)),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[64, 59])).
% 0.45/0.53  tff(66,plain,
% 0.45/0.53      (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), I!16)),
% 0.45/0.53      inference(tautology,[status(thm)],[])).
% 0.45/0.53  tff(67,plain,
% 0.45/0.53      (leq(succ(tptp_minus_1), I!16)),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[66, 59])).
% 0.45/0.53  tff(68,plain,
% 0.45/0.53      (((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (~(a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))),
% 0.45/0.53      inference(tautology,[status(thm)],[])).
% 0.45/0.53  tff(69,plain,
% 0.45/0.53      (~(a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16))),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[68, 59])).
% 0.45/0.53  tff(70,plain,
% 0.45/0.53      (^[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)))))))),
% 0.45/0.53      inference(bind,[status(th)],[])).
% 0.45/0.53  tff(71,plain,
% 0.45/0.53      (![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))))))),
% 0.45/0.53      inference(quant_intro,[status(thm)],[70])).
% 0.45/0.53  tff(72,plain,
% 0.45/0.53      (^[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))))))))),
% 0.45/0.53      inference(bind,[status(th)],[])).
% 0.45/0.53  tff(73,plain,
% 0.45/0.53      (![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))))))),
% 0.45/0.53      inference(quant_intro,[status(thm)],[72])).
% 0.45/0.53  tff(74,plain,
% 0.45/0.53      (^[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))))),
% 0.45/0.53      inference(bind,[status(th)],[])).
% 0.45/0.53  tff(75,plain,
% 0.45/0.53      (![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)))),
% 0.45/0.53      inference(quant_intro,[status(thm)],[74])).
% 0.45/0.53  tff(76,plain,
% 0.45/0.53      (![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)))),
% 0.45/0.53      inference(rewrite,[status(thm)],[])).
% 0.45/0.53  tff(77,plain,
% 0.45/0.53      (![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)))),
% 0.45/0.53      inference(and_elim,[status(thm)],[47])).
% 0.45/0.53  tff(78,plain,
% 0.45/0.53      (![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)))),
% 0.45/0.53      inference(modus_ponens,[status(thm)],[77, 76])).
% 0.45/0.53  tff(79,plain,
% 0.45/0.53      (![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)))),
% 0.45/0.53      inference(modus_ponens,[status(thm)],[78, 75])).
% 0.45/0.53  tff(80,plain,(
% 0.45/0.53      ![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)))),
% 0.45/0.53      inference(skolemize,[status(sab)],[79])).
% 0.45/0.53  tff(81,plain,
% 0.45/0.53      (![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))))))),
% 0.45/0.53      inference(modus_ponens,[status(thm)],[80, 73])).
% 0.45/0.53  tff(82,plain,
% 0.45/0.53      (![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))))))),
% 0.45/0.53      inference(modus_ponens,[status(thm)],[81, 71])).
% 0.45/0.53  tff(83,plain,
% 0.45/0.53      (((~![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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.45/0.53      inference(rewrite,[status(thm)],[])).
% 0.45/0.53  tff(84,plain,
% 0.45/0.53      ((~![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, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.45/0.53      inference(quant_inst,[status(thm)],[])).
% 0.45/0.53  tff(85,plain,
% 0.45/0.53      ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.45/0.53      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.45/0.53  tff(86,plain,
% 0.45/0.53      ($false),
% 0.45/0.53      inference(unit_resolution,[status(thm)],[85, 82, 69, 67, 65, 63, 61])).
% 0.45/0.53  tff(87,plain,((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.53  tff(88,assumption,(~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.45/0.53  tff(89,plain,
% 0.45/0.53      (((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.45/0.54      inference(tautology,[status(thm)],[])).
% 0.45/0.54  tff(90,plain,
% 0.45/0.54      (leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.45/0.54  tff(91,plain,
% 0.45/0.54      (((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.45/0.54      inference(tautology,[status(thm)],[])).
% 0.45/0.54  tff(92,plain,
% 0.45/0.54      (leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[91, 88])).
% 0.45/0.54  tff(93,plain,
% 0.45/0.54      (((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), H!13)),
% 0.45/0.54      inference(tautology,[status(thm)],[])).
% 0.45/0.54  tff(94,plain,
% 0.45/0.54      (leq(succ(tptp_minus_1), H!13)),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[93, 88])).
% 0.45/0.54  tff(95,plain,
% 0.45/0.54      (((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), G!14)),
% 0.45/0.54      inference(tautology,[status(thm)],[])).
% 0.45/0.54  tff(96,plain,
% 0.45/0.54      (leq(succ(tptp_minus_1), G!14)),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[95, 88])).
% 0.45/0.54  tff(97,plain,
% 0.45/0.54      (((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))),
% 0.45/0.54      inference(tautology,[status(thm)],[])).
% 0.45/0.54  tff(98,plain,
% 0.45/0.54      (~(a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14))),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[97, 88])).
% 0.45/0.54  tff(99,plain,
% 0.45/0.54      (^[A: $i, B: $i] : refl(((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54      inference(bind,[status(th)],[])).
% 0.45/0.54  tff(100,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(quant_intro,[status(thm)],[99])).
% 0.45/0.54  tff(101,plain,
% 0.45/0.54      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.45/0.54      inference(bind,[status(th)],[])).
% 0.45/0.54  tff(102,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(quant_intro,[status(thm)],[101])).
% 0.45/0.54  tff(103,plain,
% 0.45/0.54      (^[A: $i, B: $i] : rewrite(((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))))),
% 0.45/0.54      inference(bind,[status(th)],[])).
% 0.45/0.54  tff(104,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(quant_intro,[status(thm)],[103])).
% 0.45/0.54  tff(105,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(rewrite,[status(thm)],[])).
% 0.45/0.54  tff(106,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(and_elim,[status(thm)],[47])).
% 0.45/0.54  tff(107,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(modus_ponens,[status(thm)],[106, 105])).
% 0.45/0.54  tff(108,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(modus_ponens,[status(thm)],[107, 104])).
% 0.45/0.54  tff(109,plain,(
% 0.45/0.54      ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))),
% 0.45/0.54      inference(skolemize,[status(sab)],[108])).
% 0.45/0.54  tff(110,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(modus_ponens,[status(thm)],[109, 102])).
% 0.45/0.54  tff(111,plain,
% 0.45/0.54      (![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(modus_ponens,[status(thm)],[110, 100])).
% 0.45/0.54  tff(112,plain,
% 0.45/0.54      (((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(rewrite,[status(thm)],[])).
% 0.45/0.54  tff(113,plain,
% 0.45/0.54      ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.45/0.54      inference(quant_inst,[status(thm)],[])).
% 0.45/0.54  tff(114,plain,
% 0.45/0.54      ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.45/0.54      inference(modus_ponens,[status(thm)],[113, 112])).
% 0.45/0.54  tff(115,plain,
% 0.45/0.54      ($false),
% 0.45/0.54      inference(unit_resolution,[status(thm)],[114, 111, 98, 96, 94, 92, 90])).
% 0.45/0.54  tff(116,plain,((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.45/0.54  tff(117,plain,
% 0.45/0.54      (((~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))))) <=> ((~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.45/0.54      inference(rewrite,[status(thm)],[])).
% 0.45/0.54  tff(118,plain,
% 0.45/0.54      ((leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))))),
% 0.45/0.54      inference(rewrite,[status(thm)],[])).
% 0.45/0.54  tff(119,plain,
% 0.45/0.54      ((~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.55      inference(rewrite,[status(thm)],[])).
% 0.45/0.55  tff(120,plain,
% 0.45/0.55      ((leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.45/0.55      inference(monotonicity,[status(thm)],[119])).
% 0.45/0.55  tff(121,plain,
% 0.45/0.55      ((leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))))),
% 0.45/0.55      inference(transitivity,[status(thm)],[120, 118])).
% 0.45/0.55  tff(122,plain,
% 0.45/0.55      ((~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) <=> (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.55      inference(rewrite,[status(thm)],[])).
% 0.45/0.55  tff(123,plain,
% 0.45/0.55      ((~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) <=> (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.55      inference(rewrite,[status(thm)],[])).
% 0.45/0.55  tff(124,plain,
% 0.45/0.55      ((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) <=> (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.45/0.55      inference(rewrite,[status(thm)],[])).
% 0.45/0.55  tff(125,plain,
% 0.46/0.55      (((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))))),
% 0.46/0.55      inference(monotonicity,[status(thm)],[124, 123, 122, 121])).
% 0.46/0.55  tff(126,plain,
% 0.46/0.55      (((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~((a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)) | (~leq(succ(tptp_minus_1), N!20)) | (~leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), M!19)) | (~leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)) | (~leq(succ(tptp_minus_1), G!14)) | (~leq(succ(tptp_minus_1), H!13)) | (~leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.46/0.55      inference(transitivity,[status(thm)],[125, 117])).
% 0.46/0.55  tff(127,plain,
% 0.46/0.55      (((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(128,plain,
% 0.46/0.55      (((leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(129,plain,
% 0.46/0.55      ((~(~(leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))),
% 0.46/0.55      inference(rewrite,[status(thm)],[])).
% 0.46/0.55  tff(130,plain,
% 0.46/0.55      (((~(~(leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> ((leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))),
% 0.46/0.55      inference(monotonicity,[status(thm)],[129])).
% 0.46/0.55  tff(131,plain,
% 0.46/0.55      (((~(~(leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))) <=> (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))),
% 0.46/0.55      inference(transitivity,[status(thm)],[130, 128])).
% 0.46/0.55  tff(132,plain,
% 0.46/0.55      (((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | ((~(~(leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))))),
% 0.46/0.56      inference(monotonicity,[status(thm)],[131])).
% 0.46/0.56  tff(133,plain,
% 0.46/0.56      (((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | ((~(~(leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), G!14) & leq(succ(tptp_minus_1), H!13) & leq(G!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(H!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, G!14, H!13) = a_select3(q_ds1_filter, H!13, G!14)))) | (~((~(leq(succ(tptp_minus_1), I!16) & leq(succ(tptp_minus_1), J!15) & leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)))) | (~((~(leq(succ(tptp_minus_1), K!18) & leq(succ(tptp_minus_1), L!17) & leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)))) | (leq(succ(tptp_minus_1), M!19) & leq(M!19, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), N!20) & leq(N!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M!19, N!20) = a_select3(id_ds1_filter, N!20, M!19))))))),
% 0.46/0.56      inference(transitivity,[status(thm)],[132, 127])).
% 0.46/0.56  tff(134,plain,
% 0.46/0.56      ((![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))) <=> (![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.56      inference(rewrite,[status(thm)],[])).
% 0.46/0.56  tff(135,plain,
% 0.46/0.56      ((~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.56      inference(monotonicity,[status(thm)],[134])).
% 0.46/0.56  tff(136,plain,
% 0.46/0.56      ((~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.56      inference(rewrite,[status(thm)],[])).
% 0.46/0.56  tff(137,plain,
% 0.46/0.56      ((![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))) <=> (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.56      inference(rewrite,[status(thm)],[])).
% 0.46/0.56  tff(138,plain,
% 0.46/0.56      ((~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.56      inference(monotonicity,[status(thm)],[137])).
% 0.46/0.56  tff(139,plain,
% 0.46/0.56      ((~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.56      inference(rewrite,[status(thm)],[])).
% 0.46/0.56  tff(140,plain,
% 0.46/0.56      ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.57      inference(rewrite,[status(thm)],[])).
% 0.46/0.57  tff(141,plain,
% 0.46/0.57      ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(rewrite,[status(thm)],[])).
% 0.46/0.57  tff(142,plain,
% 0.46/0.57      ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M))))))),
% 0.46/0.57      inference(monotonicity,[status(thm)],[141])).
% 0.46/0.57  tff(143,plain,
% 0.46/0.57      (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(or_elim,[status(thm)],[46])).
% 0.46/0.57  tff(144,plain,
% 0.46/0.57      (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[143, 142])).
% 0.46/0.57  tff(145,plain,
% 0.46/0.57      (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[144, 140])).
% 0.46/0.57  tff(146,plain,
% 0.46/0.57      (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[145, 139])).
% 0.46/0.57  tff(147,plain,
% 0.46/0.57      (~(![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(n0, I) & leq(n0, J) & leq(I, minus(n3, n1)) & leq(J, minus(n3, n1)))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(n0, M) & leq(M, minus(n0, n1)))) | ![N: $i] : ((~(leq(n0, N) & leq(N, minus(n6, n1)))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[146, 138])).
% 0.46/0.57  tff(148,plain,
% 0.46/0.57      (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[147, 136])).
% 0.46/0.57  tff(149,plain,
% 0.46/0.57      (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[148, 135])).
% 0.46/0.57  tff(150,plain,
% 0.46/0.57      (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.57      inference(modus_ponens,[status(thm)],[149, 135])).
% 0.46/0.58  tff(151,plain,
% 0.46/0.58      (~(![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(q_ds1_filter, G, H) = a_select3(q_ds1_filter, H, G))) & ![I: $i, J: $i] : ((~(leq(succ(tptp_minus_1), I) & leq(succ(tptp_minus_1), J) & leq(I, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(J, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, I, J) = a_select3(r_ds1_filter, J, I))) & ![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(pminus_ds1_filter, K, L) = a_select3(pminus_ds1_filter, L, K))) & ![M: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(M, minus(succ(tptp_minus_1), succ(succ(tptp_minus_1)))))) | ![N: $i] : ((~(leq(succ(tptp_minus_1), N) & leq(N, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, M, N) = a_select3(id_ds1_filter, N, M)))))),
% 0.46/0.58      inference(modus_ponens,[status(thm)],[150, 135])).
% 0.46/0.58  unexpected number of arguments: (let ((a!1 (forall ((G $i) (H $i))
% 0.46/0.58               (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.46/0.58               (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.46/0.58                                 (succ (succ tptp_minus_1)))))
% 0.46/0.58               (let ((a!3 (not (and (leq (succ tptp_minus_1) G)
% 0.46/0.58                                    (leq (succ tptp_minus_1) H)
% 0.46/0.58                                    (leq G a!2)
% 0.46/0.58                                    (leq H a!2)))))
% 0.46/0.58                 (or a!3
% 0.46/0.58                     (= (a_select3 q_ds1_filter G H) (a_select3 q_ds1_filter H G))))))))
% 0.46/0.58        (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.46/0.58        (a!6 (forall ((I $i) (J $i))
% 0.46/0.58               (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.46/0.58               (let ((a!2 (leq I (minus a!1 (succ (succ tptp_minus_1)))))
% 0.46/0.58                     (a!3 (leq J (minus a!1 (succ (succ tptp_minus_1))))))
% 0.46/0.58               (let ((a!4 (not (and (leq (succ tptp_minus_1) I)
% 0.46/0.58                                    (leq (succ tptp_minus_1) J)
% 0.46/0.58                                    a!2
% 0.46/0.58                                    a!3))))
% 0.46/0.58                 (or a!4
% 0.46/0.58                     (= (a_select3 r_ds1_filter I J) (a_select3 r_ds1_filter J I))))))))
% 0.46/0.58        (a!11 (forall ((K $i) (L $i))
% 0.46/0.58                (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.46/0.58                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.46/0.58                                  (succ (succ tptp_minus_1)))))
% 0.46/0.58                (let ((a!3 (not (and (leq (succ tptp_minus_1) K)
% 0.46/0.58                                     (leq (succ tptp_minus_1) L)
% 0.46/0.58                                     (leq K a!2)
% 0.46/0.58                                     (leq L a!2)))))
% 0.46/0.58                  (or a!3
% 0.46/0.58                      (= (a_select3 pminus_ds1_filter K L)
% 0.46/0.58                         (a_select3 pminus_ds1_filter L K))))))))
% 0.46/0.58        (a!14 (forall ((M $i))
% 0.46/0.58                (let ((a!1 (leq M
% 0.46/0.58                                (minus (succ tptp_minus_1)
% 0.46/0.58                                       (succ (succ tptp_minus_1)))))
% 0.46/0.58                      (a!3 (forall ((N $i))
% 0.46/0.58                             (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.46/0.58                             (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.46/0.58                                               (succ (succ tptp_minus_1)))))
% 0.46/0.58                             (let ((a!3 (not (and (leq (succ tptp_minus_1) N)
% 0.46/0.58                                                  (leq N a!2)))))
% 0.46/0.58                               (or a!3
% 0.46/0.58                                   (= (a_select3 id_ds1_filter M N)
% 0.46/0.58                                      (a_select3 id_ds1_filter N M)))))))))
% 0.46/0.58                (let ((a!2 (not (and (leq (succ tptp_minus_1) M) a!1))))
% 0.46/0.58                  (or a!2 a!3)))))
% 0.46/0.58        (a!15 (leq M!19 (minus (succ tptp_minus_1) (succ (succ tptp_minus_1)))))
% 0.46/0.58        (a!17 (forall ((N $i))
% 0.46/0.58                (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.46/0.58                (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.46/0.58                                  (succ (succ tptp_minus_1)))))
% 0.46/0.58                (let ((a!3 (not (and (leq (succ tptp_minus_1) N) (leq N a!2)))))
% 0.46/0.58                  (or a!3
% 0.46/0.58                      (= (a_select3 id_ds1_filter M!19 N)
% 0.46/0.58                         (a_select3 id_ds1_filter N M!19)))))))))
% 0.46/0.58  (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.46/0.58        (a!7 (leq I!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.46/0.58        (a!8 (leq J!15 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.46/0.58        (a!16 (not (and (leq (succ tptp_minus_1) M!19) a!15))))
% 0.46/0.58  (let ((a!4 (not (and (leq (succ tptp_minus_1) G!14)
% 0.46/0.58                       (leq (succ tptp_minus_1) H!13)
% 0.46/0.58                       (leq G!14 a!3)
% 0.46/0.58                       (leq H!13 a!3))))
% 0.46/0.58        (a!9 (not (and (leq (succ tptp_minus_1) I!16)
% 0.46/0.58                       (leq (succ tptp_minus_1) J!15)
% 0.46/0.58                       a!7
% 0.46/0.58                       a!8)))
% 0.46/0.58        (a!12 (not (and (leq (succ tptp_minus_1) K!18)
% 0.46/0.58                        (leq (succ tptp_minus_1) L!17)
% 0.46/0.58                        (leq K!18 a!3)
% 0.46/0.58                        (leq L!17 a!3))))
% 0.46/0.58        (a!18 (sk (~ (not a!14) (not (or a!16 a!17)))))
% 0.46/0.58        (a!19 (not (and (leq (succ tptp_minus_1) N!20) (leq N!20 a!3)))))
% 0.46/0.58  (let ((a!5 (not (or a!4
% 0.46/0.58                      (= (a_select3 q_ds1_filter G!14 H!13)
% 0.46/0.58                         (a_select3 q_ds1_filter H!13 G!14)))))
% 0.46/0.58        (a!10 (not (or a!9
% 0.46/0.58                       (= (a_select3 r_ds1_filter I!16 J!15)
% 0.46/0.58                          (a_select3 r_ds1_filter J!15 I!16)))))
% 0.46/0.58        (a!13 (not (or a!12
% 0.46/0.58                       (= (a_select3 pminus_ds1_filter K!18 L!17)
% 0.46/0.58                          (a_select3 pminus_ds1_filter L!17 K!18)))))
% 0.46/0.58        (a!20 (not (or a!19
% 0.46/0.58                       (= (a_select3 id_ds1_filter M!19 N!20)
% 0.46/0.58                          (a_select3 id_ds1_filter N!20 M!19))))))
% 0.46/0.58  (let ((a!21 (nnf-neg (refl (~ (not a!16) (not a!16)))
% 0.46/0.58                       (sk (~ (not a!17) a!20))
% 0.46/0.58                       (~ (not (or a!16 a!17)) (and (not a!16) a!20))))
% 0.46/0.58        (a!23 (~ (not (and a!1 a!6 a!11 a!14))
% 0.46/0.58                 (or a!5 a!10 a!13 (and (not a!16) a!20)))))
% 0.46/0.58  (let ((a!22 (trans a!18 a!21 (~ (not a!14) (and (not a!16) a!20)))))
% 0.46/0.58    (nnf-neg (sk (~ (not a!1) a!5))
% 0.46/0.58             (sk (~ (not a!6) a!10))
% 0.46/0.58             (sk (~ (not a!11) a!13))
% 0.46/0.58             a!22
% 0.46/0.58             a!23)))))))
% 0.46/0.58  Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------