TSTP Solution File: SWV122+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV122+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 15:10:03 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWV122+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.28 % Computer : n006.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sun Sep 4 01:28:53 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % SZS output start Proof
% 0.14/0.36 tff(leq_type, type, (
% 0.14/0.36 leq: ( $i * $i ) > $o)).
% 0.14/0.36 tff(minus_type, type, (
% 0.14/0.36 minus: ( $i * $i ) > $i)).
% 0.14/0.36 tff(succ_type, type, (
% 0.14/0.36 succ: $i > $i)).
% 0.14/0.36 tff(tptp_minus_1_type, type, (
% 0.14/0.36 tptp_minus_1: $i)).
% 0.14/0.36 tff(tptp_fun_H_13_type, type, (
% 0.14/0.36 tptp_fun_H_13: $i)).
% 0.14/0.36 tff(tptp_fun_G_14_type, type, (
% 0.14/0.36 tptp_fun_G_14: $i)).
% 0.14/0.36 tff(a_select3_type, type, (
% 0.14/0.36 a_select3: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(q_ds1_filter_type, type, (
% 0.14/0.36 q_ds1_filter: $i)).
% 0.14/0.36 tff(tptp_fun_L_17_type, type, (
% 0.14/0.36 tptp_fun_L_17: $i)).
% 0.14/0.36 tff(tptp_fun_K_18_type, type, (
% 0.14/0.36 tptp_fun_K_18: $i)).
% 0.14/0.36 tff(pminus_ds1_filter_type, type, (
% 0.14/0.36 pminus_ds1_filter: $i)).
% 0.14/0.36 tff(n1_type, type, (
% 0.14/0.36 n1: $i)).
% 0.14/0.36 tff(n6_type, type, (
% 0.14/0.36 n6: $i)).
% 0.14/0.36 tff(n0_type, type, (
% 0.14/0.36 n0: $i)).
% 0.14/0.36 tff(r_ds1_filter_type, type, (
% 0.14/0.36 r_ds1_filter: $i)).
% 0.14/0.36 tff(n3_type, type, (
% 0.14/0.36 n3: $i)).
% 0.14/0.36 tff(tptp_fun_J_15_type, type, (
% 0.14/0.36 tptp_fun_J_15: $i)).
% 0.14/0.36 tff(tptp_fun_I_16_type, type, (
% 0.14/0.36 tptp_fun_I_16: $i)).
% 0.14/0.36 tff(1,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)).
% 0.14/0.36 tff(2,plain,
% 0.14/0.36 (((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))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(3,plain,
% 0.14/0.36 (leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.14/0.36 tff(4,plain,
% 0.14/0.36 (((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))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(5,plain,
% 0.14/0.36 (leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.14/0.36 tff(6,plain,
% 0.14/0.36 (((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)),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(7,plain,
% 0.14/0.36 (leq(succ(tptp_minus_1), L!17)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.14/0.36 tff(8,plain,
% 0.14/0.36 (((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)),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(9,plain,
% 0.14/0.36 (leq(succ(tptp_minus_1), K!18)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.14/0.36 tff(10,plain,
% 0.14/0.36 (((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)))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(11,plain,
% 0.14/0.36 (~(a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[10, 1])).
% 0.14/0.36 tff(12,plain,
% 0.14/0.36 (^[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)))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(13,plain,
% 0.14/0.36 (![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))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.14/0.36 tff(14,plain,
% 0.14/0.36 (^[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))))))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(15,plain,
% 0.14/0.36 (![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))))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.36 tff(16,plain,
% 0.14/0.36 (^[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))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(17,plain,
% 0.14/0.36 (![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)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.37 tff(18,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(19,plain,
% 0.14/0.37 ((~(((![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) => ((![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(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)))))) <=> (~((~(![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))) | (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(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))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(20,axiom,(~(((![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) => ((![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, minus(n6, n1))) & leq(H, minus(n6, n1))) => (a_select3(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)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0015')).
% 0.14/0.37 tff(21,plain,
% 0.14/0.37 (~((~(![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))))) | (![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, minus(n6, n1)) & leq(H, minus(n6, n1)))) | (a_select3(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)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.37 tff(22,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(or_elim,[status(thm)],[21])).
% 0.14/0.37 tff(23,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(and_elim,[status(thm)],[22])).
% 0.14/0.37 tff(24,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.14/0.37 tff(25,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.14/0.37 tff(26,plain,(
% 0.14/0.37 ![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)))),
% 0.14/0.37 inference(skolemize,[status(sab)],[25])).
% 0.14/0.37 tff(27,plain,
% 0.14/0.37 (![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))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.14/0.37 tff(28,plain,
% 0.14/0.37 (![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))))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[27, 13])).
% 0.14/0.37 tff(29,plain,
% 0.14/0.37 (((~![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))))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(30,plain,
% 0.14/0.37 ((~![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))))))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(31,plain,
% 0.14/0.37 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, K!18, L!17) = a_select3(pminus_ds1_filter, L!17, K!18)) | (~leq(succ(tptp_minus_1), K!18)) | (~leq(succ(tptp_minus_1), L!17)) | (~leq(K!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.14/0.37 tff(32,plain,
% 0.14/0.37 ($false),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[31, 28, 11, 9, 7, 5, 3])).
% 0.14/0.37 tff(33,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,[]))).
% 0.14/0.37 tff(34,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)).
% 0.14/0.37 tff(35,plain,
% 0.14/0.37 (((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))))),
% 0.14/0.37 inference(tautology,[status(thm)],[])).
% 0.14/0.37 tff(36,plain,
% 0.14/0.37 (leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.14/0.38 tff(37,plain,
% 0.14/0.38 (((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))))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 (leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.14/0.38 tff(39,plain,
% 0.14/0.38 (((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)),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(40,plain,
% 0.14/0.38 (leq(succ(tptp_minus_1), J!15)),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.14/0.38 tff(41,plain,
% 0.14/0.38 (((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)),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(42,plain,
% 0.14/0.38 (leq(succ(tptp_minus_1), I!16)),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[41, 34])).
% 0.14/0.38 tff(43,plain,
% 0.14/0.38 (((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)))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(44,plain,
% 0.14/0.38 (~(a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.14/0.38 tff(45,plain,
% 0.14/0.38 (^[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)))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(46,plain,
% 0.14/0.38 (![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))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.38 tff(47,plain,
% 0.14/0.38 (^[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))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(48,plain,
% 0.14/0.38 (![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))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.38 tff(49,plain,
% 0.14/0.38 (^[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))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(50,plain,
% 0.14/0.38 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((~(leq(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)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.14/0.38 tff(51,plain,
% 0.14/0.38 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) <=> ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(52,plain,
% 0.14/0.38 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.14/0.38 inference(and_elim,[status(thm)],[22])).
% 0.14/0.38 tff(53,plain,
% 0.14/0.38 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.38 tff(54,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.14/0.38 tff(55,plain,(
% 0.14/0.38 ![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)))),
% 0.14/0.38 inference(skolemize,[status(sab)],[54])).
% 0.14/0.38 tff(56,plain,
% 0.14/0.38 (![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))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.14/0.38 tff(57,plain,
% 0.14/0.38 (![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))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.14/0.38 tff(58,plain,
% 0.14/0.38 (((~![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))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(59,plain,
% 0.14/0.38 ((~![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))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(60,plain,
% 0.14/0.38 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, I!16, J!15) = a_select3(r_ds1_filter, J!15, I!16)) | (~leq(succ(tptp_minus_1), I!16)) | (~leq(succ(tptp_minus_1), J!15)) | (~leq(I!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(J!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.14/0.38 tff(61,plain,
% 0.14/0.38 ($false),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[60, 57, 44, 42, 40, 38, 36])).
% 0.14/0.38 tff(62,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,[]))).
% 0.14/0.38 tff(63,plain,
% 0.14/0.38 (((~((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(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))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(64,plain,
% 0.14/0.39 ((~((~(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)))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(65,plain,
% 0.14/0.39 ((~((~(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)))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(66,plain,
% 0.14/0.39 ((~((~(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)))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(67,plain,
% 0.14/0.39 (((~((~(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))))) <=> ((~((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))))))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[66, 65, 64])).
% 0.14/0.39 tff(68,plain,
% 0.14/0.39 (((~((~(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))))) <=> ((~((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))))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[67, 63])).
% 0.14/0.39 tff(69,plain,
% 0.14/0.39 (((~((~(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), 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)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(70,plain,
% 0.14/0.39 ((![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)))) <=> (![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))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(71,plain,
% 0.14/0.39 ((~(![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))))) <=> (~(![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)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 ((~(![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))))) <=> (~(![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)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(73,plain,
% 0.14/0.40 ((![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)))) <=> (![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 ((~(![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))))) <=> (~(![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)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 ((~(![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))))) <=> (~(![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)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(or_elim,[status(thm)],[21])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[80, 71])).
% 0.14/0.40 tff(82,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 (~(![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))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[82, 71])).
% 0.14/0.41 unexpected number of arguments: (let ((a!1 (forall ((G $i) (H $i))
% 0.14/0.41 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.14/0.41 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.14/0.41 (succ (succ tptp_minus_1)))))
% 0.14/0.41 (let ((a!3 (not (and (leq (succ tptp_minus_1) G)
% 0.14/0.41 (leq (succ tptp_minus_1) H)
% 0.14/0.41 (leq G a!2)
% 0.14/0.41 (leq H a!2)))))
% 0.14/0.41 (or a!3
% 0.14/0.41 (= (a_select3 q_ds1_filter G H) (a_select3 q_ds1_filter H G))))))))
% 0.14/0.41 (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.14/0.41 (a!6 (forall ((I $i) (J $i))
% 0.14/0.41 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.14/0.41 (let ((a!2 (leq I (minus a!1 (succ (succ tptp_minus_1)))))
% 0.14/0.41 (a!3 (leq J (minus a!1 (succ (succ tptp_minus_1))))))
% 0.14/0.41 (let ((a!4 (not (and (leq (succ tptp_minus_1) I)
% 0.14/0.41 (leq (succ tptp_minus_1) J)
% 0.14/0.41 a!2
% 0.14/0.41 a!3))))
% 0.14/0.41 (or a!4
% 0.14/0.41 (= (a_select3 r_ds1_filter I J) (a_select3 r_ds1_filter J I))))))))
% 0.14/0.41 (a!11 (forall ((K $i) (L $i))
% 0.14/0.41 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.14/0.41 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.14/0.41 (succ (succ tptp_minus_1)))))
% 0.14/0.41 (let ((a!3 (not (and (leq (succ tptp_minus_1) K)
% 0.14/0.41 (leq (succ tptp_minus_1) L)
% 0.14/0.41 (leq K a!2)
% 0.14/0.41 (leq L a!2)))))
% 0.14/0.41 (or a!3
% 0.14/0.41 (= (a_select3 pminus_ds1_filter K L)
% 0.14/0.41 (a_select3 pminus_ds1_filter L K)))))))))
% 0.14/0.41 (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.14/0.41 (a!7 (leq I!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.14/0.41 (a!8 (leq J!15 (minus a!2 (succ (succ tptp_minus_1))))))
% 0.14/0.41 (let ((a!4 (not (and (leq (succ tptp_minus_1) G!14)
% 0.14/0.41 (leq (succ tptp_minus_1) H!13)
% 0.14/0.41 (leq G!14 a!3)
% 0.14/0.41 (leq H!13 a!3))))
% 0.14/0.41 (a!9 (not (and (leq (succ tptp_minus_1) I!16)
% 0.14/0.41 (leq (succ tptp_minus_1) J!15)
% 0.14/0.41 a!7
% 0.14/0.41 a!8)))
% 0.14/0.41 (a!12 (not (and (leq (succ tptp_minus_1) K!18)
% 0.14/0.41 (leq (succ tptp_minus_1) L!17)
% 0.14/0.41 (leq K!18 a!3)
% 0.14/0.41 (leq L!17 a!3)))))
% 0.14/0.41 (let ((a!5 (not (or a!4
% 0.14/0.41 (= (a_select3 q_ds1_filter G!14 H!13)
% 0.14/0.41 (a_select3 q_ds1_filter H!13 G!14)))))
% 0.14/0.41 (a!10 (not (or a!9
% 0.14/0.41 (= (a_select3 r_ds1_filter I!16 J!15)
% 0.14/0.41 (a_select3 r_ds1_filter J!15 I!16)))))
% 0.14/0.41 (a!13 (not (or a!12
% 0.14/0.41 (= (a_select3 pminus_ds1_filter K!18 L!17)
% 0.14/0.41 (a_select3 pminus_ds1_filter L!17 K!18))))))
% 0.14/0.41 (nnf-neg (sk (~ (not a!1) a!5))
% 0.14/0.41 (sk (~ (not a!6) a!10))
% 0.14/0.41 (sk (~ (not a!11) a!13))
% 0.14/0.41 (~ (not (and a!1 a!6 a!11)) (or a!5 a!10 a!13)))))))
% 0.14/0.41 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------