TSTP Solution File: SWV112+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV112+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 0.21s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV112+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 : n008.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 01:30:25 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.
% 0.21/0.58 % SZS status Theorem
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 tff(leq_type, type, (
% 0.21/0.58 leq: ( $i * $i ) > $o)).
% 0.21/0.58 tff(pv57_type, type, (
% 0.21/0.58 pv57: $i)).
% 0.21/0.58 tff(tptp_fun_Q_19_type, type, (
% 0.21/0.58 tptp_fun_Q_19: $i)).
% 0.21/0.58 tff(minus_type, type, (
% 0.21/0.58 minus: ( $i * $i ) > $i)).
% 0.21/0.58 tff(succ_type, type, (
% 0.21/0.58 succ: $i > $i)).
% 0.21/0.58 tff(tptp_minus_1_type, type, (
% 0.21/0.58 tptp_minus_1: $i)).
% 0.21/0.58 tff(plus_type, type, (
% 0.21/0.58 plus: ( $i * $i ) > $i)).
% 0.21/0.58 tff(n1_type, type, (
% 0.21/0.58 n1: $i)).
% 0.21/0.58 tff(pred_type, type, (
% 0.21/0.58 pred: $i > $i)).
% 0.21/0.58 tff(tptp_fun_R_20_type, type, (
% 0.21/0.58 tptp_fun_R_20: $i)).
% 0.21/0.58 tff(a_select3_type, type, (
% 0.21/0.58 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.58 tff(id_ds1_filter_type, type, (
% 0.21/0.58 id_ds1_filter: $i)).
% 0.21/0.58 tff(tptp_fun_P_17_type, type, (
% 0.21/0.58 tptp_fun_P_17: $i)).
% 0.21/0.58 tff(tptp_fun_O_18_type, type, (
% 0.21/0.58 tptp_fun_O_18: $i)).
% 0.21/0.58 tff(pminus_ds1_filter_type, type, (
% 0.21/0.58 pminus_ds1_filter: $i)).
% 0.21/0.58 tff(n6_type, type, (
% 0.21/0.58 n6: $i)).
% 0.21/0.58 tff(n0_type, type, (
% 0.21/0.58 n0: $i)).
% 0.21/0.58 tff(r_ds1_filter_type, type, (
% 0.21/0.58 r_ds1_filter: $i)).
% 0.21/0.58 tff(n3_type, type, (
% 0.21/0.58 n3: $i)).
% 0.21/0.58 tff(q_ds1_filter_type, type, (
% 0.21/0.58 q_ds1_filter: $i)).
% 0.21/0.58 tff(n999_type, type, (
% 0.21/0.58 n999: $i)).
% 0.21/0.58 tff(pv5_type, type, (
% 0.21/0.58 pv5: $i)).
% 0.21/0.58 tff(tptp_fun_N_15_type, type, (
% 0.21/0.58 tptp_fun_N_15: $i)).
% 0.21/0.58 tff(tptp_fun_M_16_type, type, (
% 0.21/0.58 tptp_fun_M_16: $i)).
% 0.21/0.58 tff(tptp_fun_L_13_type, type, (
% 0.21/0.58 tptp_fun_L_13: $i)).
% 0.21/0.58 tff(tptp_fun_K_14_type, type, (
% 0.21/0.58 tptp_fun_K_14: $i)).
% 0.21/0.58 tff(1,plain,
% 0.21/0.58 (^[X: $i] : refl((plus(succ(succ(tptp_minus_1)), X) = succ(X)) <=> (plus(succ(succ(tptp_minus_1)), X) = succ(X)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(2,plain,
% 0.21/0.58 (![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X)) <=> ![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.58 tff(3,plain,
% 0.21/0.58 (^[X: $i] : rewrite((plus(n1, X) = succ(X)) <=> (plus(succ(succ(tptp_minus_1)), X) = succ(X)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(4,plain,
% 0.21/0.58 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.58 tff(5,plain,
% 0.21/0.58 (![X: $i] : (plus(n1, X) = succ(X)) <=> ![X: $i] : (plus(n1, X) = succ(X))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(6,axiom,(![X: $i] : (plus(n1, X) = succ(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','succ_plus_1_l')).
% 0.21/0.58 tff(7,plain,
% 0.21/0.58 (![X: $i] : (plus(n1, X) = succ(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.58 tff(8,plain,
% 0.21/0.58 (![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.58 tff(9,plain,(
% 0.21/0.58 ![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))),
% 0.21/0.58 inference(skolemize,[status(sab)],[8])).
% 0.21/0.58 tff(10,plain,
% 0.21/0.58 (![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.58 tff(11,plain,
% 0.21/0.58 ((~![X: $i] : (plus(succ(succ(tptp_minus_1)), X) = succ(X))) | (plus(succ(succ(tptp_minus_1)), pv57) = succ(pv57))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(12,plain,
% 0.21/0.58 (plus(succ(succ(tptp_minus_1)), pv57) = succ(pv57)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.58 tff(13,plain,
% 0.21/0.58 (minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))) = minus(succ(pv57), succ(succ(tptp_minus_1)))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.58 tff(14,plain,
% 0.21/0.58 (minus(succ(pv57), succ(succ(tptp_minus_1))) = minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))),
% 0.21/0.58 inference(symmetry,[status(thm)],[13])).
% 0.21/0.58 tff(15,plain,
% 0.21/0.58 (^[X: $i] : refl((minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(16,plain,
% 0.21/0.58 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.58 tff(17,plain,
% 0.21/0.58 (^[X: $i] : rewrite((minus(X, n1) = pred(X)) <=> (minus(X, succ(succ(tptp_minus_1))) = pred(X)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(18,plain,
% 0.21/0.58 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.58 tff(19,plain,
% 0.21/0.58 (![X: $i] : (minus(X, n1) = pred(X)) <=> ![X: $i] : (minus(X, n1) = pred(X))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(20,axiom,(![X: $i] : (minus(X, n1) = pred(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_minus_1')).
% 0.21/0.58 tff(21,plain,
% 0.21/0.58 (![X: $i] : (minus(X, n1) = pred(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.58 tff(22,plain,
% 0.21/0.58 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.21/0.58 tff(23,plain,(
% 0.21/0.58 ![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.21/0.58 inference(skolemize,[status(sab)],[22])).
% 0.21/0.58 tff(24,plain,
% 0.21/0.58 (![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.58 tff(25,plain,
% 0.21/0.58 ((~![X: $i] : (minus(X, succ(succ(tptp_minus_1))) = pred(X))) | (minus(succ(pv57), succ(succ(tptp_minus_1))) = pred(succ(pv57)))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(26,plain,
% 0.21/0.58 (minus(succ(pv57), succ(succ(tptp_minus_1))) = pred(succ(pv57))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.21/0.58 tff(27,plain,
% 0.21/0.58 (pred(succ(pv57)) = minus(succ(pv57), succ(succ(tptp_minus_1)))),
% 0.21/0.58 inference(symmetry,[status(thm)],[26])).
% 0.21/0.58 tff(28,plain,
% 0.21/0.58 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(29,plain,
% 0.21/0.58 (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(30,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.21/0.58 tff(31,plain,
% 0.21/0.58 (![X: $i] : (pred(succ(X)) = X)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.58 tff(32,plain,(
% 0.21/0.58 ![X: $i] : (pred(succ(X)) = X)),
% 0.21/0.58 inference(skolemize,[status(sab)],[31])).
% 0.21/0.58 tff(33,plain,
% 0.21/0.58 (![X: $i] : (pred(succ(X)) = X)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.58 tff(34,plain,
% 0.21/0.58 ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(pv57)) = pv57)),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(35,plain,
% 0.21/0.58 (pred(succ(pv57)) = pv57),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.21/0.58 tff(36,plain,
% 0.21/0.58 (pv57 = pred(succ(pv57))),
% 0.21/0.58 inference(symmetry,[status(thm)],[35])).
% 0.21/0.58 tff(37,plain,
% 0.21/0.58 (pv57 = minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))),
% 0.21/0.58 inference(transitivity,[status(thm)],[36, 27, 14])).
% 0.21/0.58 tff(38,plain,
% 0.21/0.58 (leq(Q!19, pv57) <=> leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.58 tff(39,plain,
% 0.21/0.58 (leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) <=> leq(Q!19, pv57)),
% 0.21/0.58 inference(symmetry,[status(thm)],[38])).
% 0.21/0.58 tff(40,assumption,(~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.21/0.58 tff(41,plain,
% 0.21/0.58 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(42,plain,
% 0.21/0.58 (leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.58 tff(43,plain,
% 0.21/0.58 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(44,plain,
% 0.21/0.59 (leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.21/0.59 tff(45,plain,
% 0.21/0.59 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), P!17)),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(46,plain,
% 0.21/0.59 (leq(succ(tptp_minus_1), P!17)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.21/0.59 tff(47,plain,
% 0.21/0.59 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), O!18)),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(48,plain,
% 0.21/0.59 (leq(succ(tptp_minus_1), O!18)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[47, 40])).
% 0.21/0.59 tff(49,plain,
% 0.21/0.59 (((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(50,plain,
% 0.21/0.59 (~(a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[49, 40])).
% 0.21/0.59 tff(51,plain,
% 0.21/0.59 (^[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)))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(52,plain,
% 0.21/0.59 (![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))))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.59 tff(53,plain,
% 0.21/0.59 (^[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))))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(54,plain,
% 0.54/0.59 (![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))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[53])).
% 0.54/0.59 tff(55,plain,
% 0.54/0.59 (^[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))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(56,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[55])).
% 0.54/0.59 tff(57,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(58,plain,
% 0.54/0.59 ((~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, pv57)) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i] : ((leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1))) => ![R: $i] : ((leq(n0, R) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))) <=> (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(59,axiom,(~(((((((((leq(n0, pv5) & leq(n0, pv57)) & leq(pv5, minus(n999, n1))) & leq(pv57, minus(n6, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, minus(n6, n1))) & leq(B, minus(n6, n1))) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, minus(n3, n1))) & leq(D, minus(n3, n1))) => (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)))) & ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, minus(n6, n1))) & leq(F, minus(n6, n1))) => (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)))) & ![G: $i, H: $i] : ((((leq(n0, G) & leq(n0, H)) & leq(G, pv57)) & leq(H, minus(n6, n1))) => (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G)))) & ![I: $i] : ((leq(n0, I) & leq(I, minus(pv57, n1))) => ![J: $i] : ((leq(n0, J) & leq(J, minus(n6, n1))) => (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))) => (((((leq(n0, pv5) & leq(pv5, minus(n999, n1))) & ![K: $i, L: $i] : ((((leq(n0, K) & leq(n0, L)) & leq(K, minus(n6, n1))) & leq(L, minus(n6, n1))) => (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K)))) & ![M: $i, N: $i] : ((((leq(n0, M) & leq(n0, N)) & leq(M, minus(n3, n1))) & leq(N, minus(n3, n1))) => (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M)))) & ![O: $i, P: $i] : ((((leq(n0, O) & leq(n0, P)) & leq(O, minus(n6, n1))) & leq(P, minus(n6, n1))) => (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O)))) & ![Q: $i] : ((leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1))) => ![R: $i] : ((leq(n0, R) & leq(R, minus(n6, n1))) => (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0005')).
% 0.54/0.60 tff(60,plain,
% 0.54/0.60 (~((~(leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I)))))) | (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.54/0.60 tff(61,plain,
% 0.54/0.60 (leq(n0, pv5) & leq(n0, pv57) & leq(pv5, minus(n999, n1)) & leq(pv57, minus(n6, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, minus(n6, n1)) & leq(B, minus(n6, n1)))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, minus(n3, n1)) & leq(D, minus(n3, n1)))) | (a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C))) & ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, minus(n6, n1)) & leq(F, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E))) & ![G: $i, H: $i] : ((~(leq(n0, G) & leq(n0, H) & leq(G, pv57) & leq(H, minus(n6, n1)))) | (a_select3(id_ds1_filter, G, H) = a_select3(id_ds1_filter, H, G))) & ![I: $i] : ((~(leq(n0, I) & leq(I, minus(pv57, n1)))) | ![J: $i] : ((~(leq(n0, J) & leq(J, minus(n6, n1)))) | (a_select3(id_ds1_filter, I, J) = a_select3(id_ds1_filter, J, I))))),
% 0.54/0.60 inference(or_elim,[status(thm)],[60])).
% 0.54/0.60 tff(62,plain,
% 0.54/0.60 (![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)))),
% 0.54/0.60 inference(and_elim,[status(thm)],[61])).
% 0.54/0.60 tff(63,plain,
% 0.54/0.60 (![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)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.54/0.60 tff(64,plain,
% 0.54/0.60 (![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)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.54/0.60 tff(65,plain,(
% 0.54/0.60 ![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)))),
% 0.54/0.60 inference(skolemize,[status(sab)],[64])).
% 0.54/0.60 tff(66,plain,
% 0.54/0.60 (![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))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[65, 54])).
% 0.54/0.60 tff(67,plain,
% 0.54/0.60 (![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))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[66, 52])).
% 0.54/0.61 tff(68,plain,
% 0.54/0.61 (((~![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, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![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, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(69,plain,
% 0.54/0.61 ((~![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, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(70,plain,
% 0.54/0.61 ((~![E: $i, F: $i] : ((a_select3(pminus_ds1_filter, E, F) = a_select3(pminus_ds1_filter, F, E)) | (~leq(succ(tptp_minus_1), E)) | (~leq(succ(tptp_minus_1), F)) | (~leq(E, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(F, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.54/0.61 tff(71,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[70, 67, 50, 48, 46, 44, 42])).
% 0.54/0.61 tff(72,plain,((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(73,assumption,(~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.56/0.61 tff(74,plain,
% 0.56/0.61 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(75,plain,
% 0.56/0.61 (leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.56/0.61 tff(76,plain,
% 0.56/0.61 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(77,plain,
% 0.56/0.61 (leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.56/0.61 tff(78,plain,
% 0.56/0.61 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), N!15)),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(79,plain,
% 0.56/0.61 (leq(succ(tptp_minus_1), N!15)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[78, 73])).
% 0.56/0.61 tff(80,plain,
% 0.56/0.61 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), M!16)),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(81,plain,
% 0.56/0.61 (leq(succ(tptp_minus_1), M!16)),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[80, 73])).
% 0.56/0.61 tff(82,plain,
% 0.56/0.61 (((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))),
% 0.56/0.61 inference(tautology,[status(thm)],[])).
% 0.56/0.61 tff(83,plain,
% 0.56/0.61 (~(a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16))),
% 0.56/0.61 inference(unit_resolution,[status(thm)],[82, 73])).
% 0.56/0.61 tff(84,plain,
% 0.56/0.61 (^[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)))))))),
% 0.56/0.61 inference(bind,[status(th)],[])).
% 0.56/0.61 tff(85,plain,
% 0.56/0.61 (![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))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[84])).
% 0.56/0.62 tff(86,plain,
% 0.56/0.62 (^[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))))))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(87,plain,
% 0.56/0.62 (![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))))))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[86])).
% 0.56/0.62 tff(88,plain,
% 0.56/0.62 (^[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))))),
% 0.56/0.62 inference(bind,[status(th)],[])).
% 0.56/0.62 tff(89,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(quant_intro,[status(thm)],[88])).
% 0.56/0.62 tff(90,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(91,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(and_elim,[status(thm)],[61])).
% 0.56/0.62 tff(92,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.56/0.62 tff(93,plain,
% 0.56/0.62 (![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)))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.56/0.62 tff(94,plain,(
% 0.56/0.62 ![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)))),
% 0.56/0.62 inference(skolemize,[status(sab)],[93])).
% 0.56/0.62 tff(95,plain,
% 0.56/0.62 (![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))))))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.56/0.62 tff(96,plain,
% 0.56/0.62 (![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))))))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.56/0.62 tff(97,plain,
% 0.56/0.62 (((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) <=> ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.56/0.62 inference(rewrite,[status(thm)],[])).
% 0.56/0.62 tff(98,plain,
% 0.56/0.62 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | ((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))),
% 0.56/0.62 inference(quant_inst,[status(thm)],[])).
% 0.56/0.62 tff(99,plain,
% 0.56/0.62 ((~![C: $i, D: $i] : ((a_select3(r_ds1_filter, C, D) = a_select3(r_ds1_filter, D, C)) | (~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(D, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))),
% 0.56/0.62 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.56/0.62 tff(100,plain,
% 0.56/0.62 ($false),
% 0.56/0.62 inference(unit_resolution,[status(thm)],[99, 96, 83, 81, 79, 77, 75])).
% 0.56/0.62 tff(101,plain,((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.62 tff(102,assumption,(~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))), introduced(assumption)).
% 0.56/0.62 tff(103,plain,
% 0.56/0.62 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.56/0.63 inference(tautology,[status(thm)],[])).
% 0.56/0.63 tff(104,plain,
% 0.56/0.63 (leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.56/0.63 tff(105,plain,
% 0.56/0.63 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.56/0.63 inference(tautology,[status(thm)],[])).
% 0.56/0.63 tff(106,plain,
% 0.56/0.63 (leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.56/0.63 tff(107,plain,
% 0.56/0.63 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), L!13)),
% 0.56/0.63 inference(tautology,[status(thm)],[])).
% 0.56/0.63 tff(108,plain,
% 0.56/0.63 (leq(succ(tptp_minus_1), L!13)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[107, 102])).
% 0.56/0.63 tff(109,plain,
% 0.56/0.63 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | leq(succ(tptp_minus_1), K!14)),
% 0.56/0.63 inference(tautology,[status(thm)],[])).
% 0.56/0.63 tff(110,plain,
% 0.56/0.63 (leq(succ(tptp_minus_1), K!14)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[109, 102])).
% 0.56/0.63 tff(111,plain,
% 0.56/0.63 (((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (~(a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))),
% 0.56/0.63 inference(tautology,[status(thm)],[])).
% 0.56/0.63 tff(112,plain,
% 0.56/0.63 (~(a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14))),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[111, 102])).
% 0.56/0.63 tff(113,plain,
% 0.56/0.63 (^[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)))))))),
% 0.56/0.63 inference(bind,[status(th)],[])).
% 0.56/0.63 tff(114,plain,
% 0.56/0.63 (![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))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[113])).
% 0.58/0.63 tff(115,plain,
% 0.58/0.63 (^[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))))))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(116,plain,
% 0.58/0.63 (![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))))))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[115])).
% 0.58/0.63 tff(117,plain,
% 0.58/0.63 (^[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))))),
% 0.58/0.63 inference(bind,[status(th)],[])).
% 0.58/0.63 tff(118,plain,
% 0.58/0.63 (![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)))),
% 0.58/0.63 inference(quant_intro,[status(thm)],[117])).
% 0.58/0.63 tff(119,plain,
% 0.58/0.63 (![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)))),
% 0.58/0.63 inference(rewrite,[status(thm)],[])).
% 0.58/0.63 tff(120,plain,
% 0.58/0.63 (![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)))),
% 0.58/0.63 inference(and_elim,[status(thm)],[61])).
% 0.58/0.63 tff(121,plain,
% 0.58/0.63 (![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)))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.58/0.63 tff(122,plain,
% 0.58/0.63 (![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)))),
% 0.58/0.63 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.58/0.63 tff(123,plain,(
% 0.58/0.63 ![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)))),
% 0.58/0.64 inference(skolemize,[status(sab)],[122])).
% 0.58/0.64 tff(124,plain,
% 0.58/0.64 (![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))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.58/0.64 tff(125,plain,
% 0.58/0.64 (![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))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.58/0.64 tff(126,plain,
% 0.58/0.64 (((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) <=> ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(127,plain,
% 0.58/0.64 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | ((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(128,plain,
% 0.58/0.64 ((~![A: $i, B: $i] : ((a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)) | (~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(B, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.58/0.64 tff(129,plain,
% 0.58/0.64 ($false),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[128, 125, 112, 110, 108, 106, 104])).
% 0.58/0.64 tff(130,plain,((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.64 tff(131,plain,
% 0.58/0.64 (((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))))) <=> ((~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(132,plain,
% 0.58/0.64 ((leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(133,plain,
% 0.58/0.64 ((~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(134,plain,
% 0.58/0.65 ((leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[133])).
% 0.58/0.65 tff(135,plain,
% 0.58/0.65 ((leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))))),
% 0.58/0.65 inference(transitivity,[status(thm)],[134, 132])).
% 0.58/0.65 tff(136,plain,
% 0.58/0.65 ((~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) <=> (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(137,plain,
% 0.58/0.65 ((~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) <=> (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(138,plain,
% 0.58/0.65 ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) <=> (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(139,plain,
% 0.58/0.65 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[138, 137, 136, 135])).
% 0.58/0.65 tff(140,plain,
% 0.58/0.65 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~((a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)) | (~leq(succ(tptp_minus_1), R!20)) | (~leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), Q!19)) | (~leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) | (~((a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)) | (~leq(succ(tptp_minus_1), K!14)) | (~leq(succ(tptp_minus_1), L!13)) | (~leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))) | (~((a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)) | (~leq(succ(tptp_minus_1), M!16)) | (~leq(succ(tptp_minus_1), N!15)) | (~leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))) | (~leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1))))))) | (~((a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)) | (~leq(succ(tptp_minus_1), O!18)) | (~leq(succ(tptp_minus_1), P!17)) | (~leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))) | (~leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1))))))))),
% 0.58/0.65 inference(transitivity,[status(thm)],[139, 131])).
% 0.58/0.65 tff(141,plain,
% 0.58/0.65 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(142,plain,
% 0.58/0.66 (((leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(143,plain,
% 0.58/0.66 ((~(~(leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) <=> (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))),
% 0.58/0.66 inference(rewrite,[status(thm)],[])).
% 0.58/0.66 tff(144,plain,
% 0.58/0.66 (((~(~(leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> ((leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))),
% 0.58/0.66 inference(monotonicity,[status(thm)],[143])).
% 0.58/0.66 tff(145,plain,
% 0.58/0.66 (((~(~(leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))) <=> (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))),
% 0.58/0.66 inference(transitivity,[status(thm)],[144, 142])).
% 0.58/0.66 tff(146,plain,
% 0.58/0.66 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | ((~(~(leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))))),
% 0.58/0.66 inference(monotonicity,[status(thm)],[145])).
% 0.58/0.66 tff(147,plain,
% 0.58/0.66 (((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | ((~(~(leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1))))))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19)))))) <=> ((~((~(leq(succ(tptp_minus_1), K!14) & leq(succ(tptp_minus_1), L!13) & leq(K!14, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L!13, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K!14, L!13) = a_select3(q_ds1_filter, L!13, K!14)))) | (~((~(leq(succ(tptp_minus_1), M!16) & leq(succ(tptp_minus_1), N!15) & leq(M!16, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N!15, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M!16, N!15) = a_select3(r_ds1_filter, N!15, M!16)))) | (~((~(leq(succ(tptp_minus_1), O!18) & leq(succ(tptp_minus_1), P!17) & leq(O!18, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P!17, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O!18, P!17) = a_select3(pminus_ds1_filter, P!17, O!18)))) | (leq(succ(tptp_minus_1), Q!19) & leq(Q!19, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))) & (~((~(leq(succ(tptp_minus_1), R!20) & leq(R!20, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q!19, R!20) = a_select3(id_ds1_filter, R!20, Q!19))))))),
% 0.58/0.67 inference(transitivity,[status(thm)],[146, 141])).
% 0.58/0.67 tff(148,plain,
% 0.58/0.67 ((![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))) <=> (![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(149,plain,
% 0.58/0.67 ((~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.67 inference(monotonicity,[status(thm)],[148])).
% 0.58/0.67 tff(150,plain,
% 0.58/0.67 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(151,plain,
% 0.58/0.68 ((![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))) <=> (![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(152,plain,
% 0.58/0.68 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[151])).
% 0.58/0.68 tff(153,plain,
% 0.58/0.68 ((~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(154,plain,
% 0.58/0.68 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(155,plain,
% 0.58/0.68 ((leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))) <=> (leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.68 inference(rewrite,[status(thm)],[])).
% 0.58/0.68 tff(156,plain,
% 0.58/0.68 ((~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))) <=> (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q))))))),
% 0.58/0.69 inference(monotonicity,[status(thm)],[155])).
% 0.58/0.69 tff(157,plain,
% 0.58/0.69 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(or_elim,[status(thm)],[60])).
% 0.58/0.69 tff(158,plain,
% 0.58/0.69 (~(leq(n0, pv5) & leq(pv5, minus(n999, n1)) & ![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.58/0.69 tff(159,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.58/0.69 tff(160,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[159, 153])).
% 0.58/0.69 tff(161,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(n0, K) & leq(n0, L) & leq(K, minus(n6, n1)) & leq(L, minus(n6, n1)))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(n0, M) & leq(n0, N) & leq(M, minus(n3, n1)) & leq(N, minus(n3, n1)))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(n0, O) & leq(n0, P) & leq(O, minus(n6, n1)) & leq(P, minus(n6, n1)))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(n0, Q) & leq(Q, minus(plus(n1, pv57), n1)))) | ![R: $i] : ((~(leq(n0, R) & leq(R, minus(n6, n1)))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[160, 152])).
% 0.58/0.69 tff(162,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[161, 150])).
% 0.58/0.69 tff(163,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[162, 149])).
% 0.58/0.69 tff(164,plain,
% 0.58/0.69 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[163, 149])).
% 0.58/0.70 tff(165,plain,
% 0.58/0.70 (~(![K: $i, L: $i] : ((~(leq(succ(tptp_minus_1), K) & leq(succ(tptp_minus_1), L) & leq(K, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(L, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(q_ds1_filter, K, L) = a_select3(q_ds1_filter, L, K))) & ![M: $i, N: $i] : ((~(leq(succ(tptp_minus_1), M) & leq(succ(tptp_minus_1), N) & leq(M, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))) & leq(N, minus(succ(succ(succ(succ(tptp_minus_1)))), succ(succ(tptp_minus_1)))))) | (a_select3(r_ds1_filter, M, N) = a_select3(r_ds1_filter, N, M))) & ![O: $i, P: $i] : ((~(leq(succ(tptp_minus_1), O) & leq(succ(tptp_minus_1), P) & leq(O, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))) & leq(P, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(pminus_ds1_filter, O, P) = a_select3(pminus_ds1_filter, P, O))) & ![Q: $i] : ((~(leq(succ(tptp_minus_1), Q) & leq(Q, minus(plus(succ(succ(tptp_minus_1)), pv57), succ(succ(tptp_minus_1)))))) | ![R: $i] : ((~(leq(succ(tptp_minus_1), R) & leq(R, minus(succ(succ(succ(succ(succ(succ(succ(tptp_minus_1))))))), succ(succ(tptp_minus_1)))))) | (a_select3(id_ds1_filter, Q, R) = a_select3(id_ds1_filter, R, Q)))))),
% 0.58/0.70 inference(modus_ponens,[status(thm)],[164, 149])).
% 0.58/0.70 unexpected number of arguments: (let ((a!1 (forall ((K $i) (L $i))
% 0.58/0.70 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.58/0.70 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (let ((a!3 (not (and (leq (succ tptp_minus_1) K)
% 0.58/0.70 (leq (succ tptp_minus_1) L)
% 0.58/0.70 (leq K a!2)
% 0.58/0.70 (leq L a!2)))))
% 0.58/0.70 (or a!3
% 0.58/0.70 (= (a_select3 q_ds1_filter K L) (a_select3 q_ds1_filter L K))))))))
% 0.58/0.70 (a!2 (succ (succ (succ (succ tptp_minus_1)))))
% 0.58/0.70 (a!6 (forall ((M $i) (N $i))
% 0.58/0.70 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!2 (leq M (minus a!1 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (a!3 (leq N (minus a!1 (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!4 (not (and (leq (succ tptp_minus_1) M)
% 0.58/0.70 (leq (succ tptp_minus_1) N)
% 0.58/0.70 a!2
% 0.58/0.70 a!3))))
% 0.58/0.70 (or a!4
% 0.58/0.70 (= (a_select3 r_ds1_filter M N) (a_select3 r_ds1_filter N M))))))))
% 0.58/0.70 (a!11 (forall ((O $i) (P $i))
% 0.58/0.70 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.58/0.70 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (let ((a!3 (not (and (leq (succ tptp_minus_1) O)
% 0.58/0.70 (leq (succ tptp_minus_1) P)
% 0.58/0.70 (leq O a!2)
% 0.58/0.70 (leq P a!2)))))
% 0.58/0.70 (or a!3
% 0.58/0.70 (= (a_select3 pminus_ds1_filter O P)
% 0.58/0.70 (a_select3 pminus_ds1_filter P O))))))))
% 0.58/0.70 (a!14 (forall ((Q $i))
% 0.58/0.70 (let ((a!1 (minus (plus (succ (succ tptp_minus_1)) pv57)
% 0.58/0.70 (succ (succ tptp_minus_1))))
% 0.58/0.70 (a!3 (forall ((R $i))
% 0.58/0.70 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.58/0.70 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (let ((a!3 (not (and (leq (succ tptp_minus_1) R)
% 0.58/0.70 (leq R a!2)))))
% 0.58/0.70 (or a!3
% 0.58/0.70 (= (a_select3 id_ds1_filter Q R)
% 0.58/0.70 (a_select3 id_ds1_filter R Q)))))))))
% 0.58/0.70 (let ((a!2 (not (and (leq (succ tptp_minus_1) Q) (leq Q a!1)))))
% 0.58/0.70 (or a!2 a!3)))))
% 0.58/0.70 (a!15 (minus (plus (succ (succ tptp_minus_1)) pv57)
% 0.58/0.70 (succ (succ tptp_minus_1))))
% 0.58/0.70 (a!17 (forall ((R $i))
% 0.58/0.70 (let ((a!1 (succ (succ (succ (succ tptp_minus_1))))))
% 0.58/0.70 (let ((a!2 (minus (succ (succ (succ a!1)))
% 0.58/0.70 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (let ((a!3 (not (and (leq (succ tptp_minus_1) R) (leq R a!2)))))
% 0.58/0.70 (or a!3
% 0.58/0.70 (= (a_select3 id_ds1_filter Q!19 R)
% 0.58/0.70 (a_select3 id_ds1_filter R Q!19)))))))))
% 0.58/0.70 (let ((a!3 (minus (succ (succ (succ a!2))) (succ (succ tptp_minus_1))))
% 0.58/0.70 (a!7 (leq M!16 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (a!8 (leq N!15 (minus a!2 (succ (succ tptp_minus_1)))))
% 0.58/0.70 (a!16 (not (and (leq (succ tptp_minus_1) Q!19) (leq Q!19 a!15)))))
% 0.58/0.70 (let ((a!4 (not (and (leq (succ tptp_minus_1) K!14)
% 0.58/0.70 (leq (succ tptp_minus_1) L!13)
% 0.58/0.70 (leq K!14 a!3)
% 0.58/0.70 (leq L!13 a!3))))
% 0.58/0.70 (a!9 (not (and (leq (succ tptp_minus_1) M!16)
% 0.58/0.70 (leq (succ tptp_minus_1) N!15)
% 0.58/0.70 a!7
% 0.58/0.70 a!8)))
% 0.58/0.70 (a!12 (not (and (leq (succ tptp_minus_1) O!18)
% 0.58/0.70 (leq (succ tptp_minus_1) P!17)
% 0.58/0.70 (leq O!18 a!3)
% 0.58/0.70 (leq P!17 a!3))))
% 0.58/0.70 (a!18 (sk (~ (not a!14) (not (or a!16 a!17)))))
% 0.58/0.70 (a!19 (not (and (leq (succ tptp_minus_1) R!20) (leq R!20 a!3)))))
% 0.58/0.70 (let ((a!5 (not (or a!4
% 0.58/0.70 (= (a_select3 q_ds1_filter K!14 L!13)
% 0.58/0.70 (a_select3 q_ds1_filter L!13 K!14)))))
% 0.58/0.70 (a!10 (not (or a!9
% 0.58/0.70 (= (a_select3 r_ds1_filter M!16 N!15)
% 0.58/0.70 (a_select3 r_ds1_filter N!15 M!16)))))
% 0.58/0.70 (a!13 (not (or a!12
% 0.58/0.70 (= (a_select3 pminus_ds1_filter O!18 P!17)
% 0.58/0.70 (a_select3 pminus_ds1_filter P!17 O!18)))))
% 0.58/0.70 (a!20 (not (or a!19
% 0.58/0.70 (= (a_select3 id_ds1_filter Q!19 R!20)
% 0.58/0.70 (a_select3 id_ds1_filter R!20 Q!19))))))
% 0.58/0.70 (let ((a!21 (nnf-neg (refl (~ (not a!16) (not a!16)))
% 0.58/0.70 (sk (~ (not a!17) a!20))
% 0.58/0.70 (~ (not (or a!16 a!17)) (and (not a!16) a!20))))
% 0.58/0.70 (a!23 (~ (not (and a!1 a!6 a!11 a!14))
% 0.58/0.70 (or a!5 a!10 a!13 (and (not a!16) a!20)))))
% 0.58/0.70 (let ((a!22 (trans a!18 a!21 (~ (not a!14) (and (not a!16) a!20)))))
% 0.58/0.70 (nnf-neg (sk (~ (not a!1) a!5))
% 0.58/0.70 (sk (~ (not a!6) a!10))
% 0.58/0.70 (sk (~ (not a!11) a!13))
% 0.58/0.70 a!22
% 0.58/0.70 a!23)))))))
% 0.58/0.71 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------