TSTP Solution File: SWV198+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWV198+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 15:10:20 EDT 2022

% Result   : Theorem 0.57s 0.62s
% Output   : Proof 0.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV198+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n011.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 01:40:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.57/0.62  % SZS status Theorem
% 0.57/0.62  % SZS output start Proof
% 0.57/0.62  tff(a_select3_type, type, (
% 0.57/0.62     a_select3: ( $i * $i * $i ) > $i)).
% 0.57/0.62  tff(succ_type, type, (
% 0.57/0.62     succ: $i > $i)).
% 0.57/0.62  tff(tptp_minus_1_type, type, (
% 0.57/0.62     tptp_minus_1: $i)).
% 0.57/0.62  tff(u_defuse_type, type, (
% 0.57/0.62     u_defuse: $i)).
% 0.57/0.62  tff(tptp_fun_F_13_type, type, (
% 0.57/0.62     tptp_fun_F_13: $i)).
% 0.57/0.62  tff(tptp_fun_E_14_type, type, (
% 0.57/0.62     tptp_fun_E_14: $i)).
% 0.57/0.62  tff(a_select2_type, type, (
% 0.57/0.62     a_select2: ( $i * $i ) > $i)).
% 0.57/0.62  tff(sigma_defuse_type, type, (
% 0.57/0.62     sigma_defuse: $i)).
% 0.57/0.62  tff(rho_defuse_type, type, (
% 0.57/0.62     rho_defuse: $i)).
% 0.57/0.62  tff(use_type, type, (
% 0.57/0.62     use: $i)).
% 0.57/0.62  tff(n0_type, type, (
% 0.57/0.62     n0: $i)).
% 0.57/0.62  tff(n2_type, type, (
% 0.57/0.62     n2: $i)).
% 0.57/0.62  tff(z_defuse_type, type, (
% 0.57/0.62     z_defuse: $i)).
% 0.57/0.62  tff(leq_type, type, (
% 0.57/0.62     leq: ( $i * $i ) > $o)).
% 0.57/0.62  tff(pred_type, type, (
% 0.57/0.62     pred: $i > $i)).
% 0.57/0.62  tff(pv5_type, type, (
% 0.57/0.62     pv5: $i)).
% 0.57/0.62  tff(n998_type, type, (
% 0.57/0.62     n998: $i)).
% 0.57/0.62  tff(n5_type, type, (
% 0.57/0.62     n5: $i)).
% 0.57/0.62  tff(xinit_noise_defuse_type, type, (
% 0.57/0.62     xinit_noise_defuse: $i)).
% 0.57/0.62  tff(n4_type, type, (
% 0.57/0.62     n4: $i)).
% 0.57/0.62  tff(n3_type, type, (
% 0.57/0.62     n3: $i)).
% 0.57/0.62  tff(n1_type, type, (
% 0.57/0.63     n1: $i)).
% 0.57/0.63  tff(xinit_mean_defuse_type, type, (
% 0.57/0.63     xinit_mean_defuse: $i)).
% 0.57/0.63  tff(xinit_defuse_type, type, (
% 0.57/0.63     xinit_defuse: $i)).
% 0.57/0.63  tff(plus_type, type, (
% 0.57/0.63     plus: ( $i * $i ) > $i)).
% 0.57/0.63  tff(gt_type, type, (
% 0.57/0.63     gt: ( $i * $i ) > $o)).
% 0.57/0.63  tff(1,plain,
% 0.57/0.63      ((a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.57/0.63      inference(rewrite,[status(thm)],[])).
% 0.57/0.63  tff(2,plain,
% 0.57/0.63      ((a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.57/0.63      inference(rewrite,[status(thm)],[])).
% 0.57/0.63  tff(3,plain,
% 0.57/0.63      ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.57/0.63      inference(rewrite,[status(thm)],[])).
% 0.57/0.63  tff(4,plain,
% 0.57/0.63      ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, n2, n0) = use)),
% 0.57/0.63      inference(rewrite,[status(thm)],[])).
% 0.57/0.63  tff(5,plain,
% 0.57/0.63      ((~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => (a_select3(u_defuse, E, F) = use)))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(6,axiom,(~(((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => (a_select3(u_defuse, E, F) = use)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0009')).
% 0.62/0.63  tff(7,plain,
% 0.62/0.63      (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use)))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.62/0.63  tff(8,plain,
% 0.62/0.63      ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.62/0.63      inference(or_elim,[status(thm)],[7])).
% 0.62/0.63  tff(9,plain,
% 0.62/0.63      (a_select3(u_defuse, n2, n0) = use),
% 0.62/0.63      inference(and_elim,[status(thm)],[8])).
% 0.62/0.63  tff(10,plain,
% 0.62/0.63      (a_select3(u_defuse, n2, n0) = use),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[9, 4])).
% 0.62/0.63  tff(11,plain,
% 0.62/0.63      (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[10, 3])).
% 0.62/0.63  tff(12,plain,
% 0.62/0.63      (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[11, 2])).
% 0.62/0.63  tff(13,plain,
% 0.62/0.63      (a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[12, 1])).
% 0.62/0.63  tff(14,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(15,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(16,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(17,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(18,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(19,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))) <=> (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(20,plain,
% 0.62/0.63      ((~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))) <=> (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use)))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(21,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.62/0.63      inference(or_elim,[status(thm)],[7])).
% 0.62/0.63  tff(22,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[21, 20])).
% 0.62/0.63  tff(23,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[22, 20])).
% 0.62/0.63  tff(24,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[23, 20])).
% 0.62/0.63  tff(25,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[24, 19])).
% 0.62/0.63  tff(26,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[25, 18])).
% 0.62/0.63  tff(27,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[26, 17])).
% 0.62/0.63  tff(28,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[27, 16])).
% 0.62/0.63  tff(29,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[28, 15])).
% 0.62/0.63  tff(30,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[29, 14])).
% 0.62/0.63  tff(31,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[30, 14])).
% 0.62/0.63  tff(32,plain,
% 0.62/0.63      (~![E: $i, F: $i] : ((~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[31, 14])).
% 0.62/0.63  tff(33,plain,(
% 0.62/0.63      ~((~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.63      inference(skolemize,[status(sab)],[32])).
% 0.62/0.63  tff(34,plain,
% 0.62/0.63      (leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5)),
% 0.62/0.63      inference(or_elim,[status(thm)],[33])).
% 0.62/0.63  tff(35,plain,
% 0.62/0.63      (leq(F!13, pv5)),
% 0.62/0.63      inference(and_elim,[status(thm)],[34])).
% 0.62/0.63  tff(36,plain,
% 0.62/0.63      (leq(pv5, n0) <=> leq(pv5, succ(tptp_minus_1))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(37,plain,
% 0.62/0.63      (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(38,plain,
% 0.62/0.63      (leq(pv5, n0)),
% 0.62/0.63      inference(and_elim,[status(thm)],[8])).
% 0.62/0.63  tff(39,plain,
% 0.62/0.63      (leq(pv5, n0)),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.62/0.63  tff(40,plain,
% 0.62/0.63      (leq(pv5, succ(tptp_minus_1))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[39, 36])).
% 0.62/0.63  tff(41,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(42,plain,
% 0.62/0.63      (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.62/0.63      inference(bind,[status(th)],[])).
% 0.62/0.63  tff(43,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.62/0.63      inference(quant_intro,[status(thm)],[42])).
% 0.62/0.63  tff(44,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.62/0.63      inference(rewrite,[status(thm)],[])).
% 0.62/0.63  tff(45,plain,
% 0.62/0.63      (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.62/0.63      inference(bind,[status(th)],[])).
% 0.62/0.63  tff(46,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.62/0.63      inference(quant_intro,[status(thm)],[45])).
% 0.62/0.63  tff(47,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.62/0.63  tff(48,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[47, 46])).
% 0.62/0.63  tff(49,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.62/0.63      inference(modus_ponens,[status(thm)],[48, 44])).
% 0.62/0.63  tff(50,plain,(
% 0.62/0.63      ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.62/0.63      inference(skolemize,[status(sab)],[49])).
% 0.62/0.63  tff(51,plain,
% 0.62/0.63      (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[50, 43])).
% 0.62/0.64  tff(52,plain,
% 0.62/0.64      (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[51, 41])).
% 0.62/0.64  tff(53,plain,
% 0.62/0.64      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(54,plain,
% 0.62/0.64      ((leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5))) <=> ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(55,plain,
% 0.62/0.64      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[54])).
% 0.62/0.64  tff(56,plain,
% 0.62/0.64      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.62/0.64      inference(transitivity,[status(thm)],[55, 53])).
% 0.62/0.64  tff(57,plain,
% 0.62/0.64      ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(58,plain,
% 0.62/0.64      ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[57, 56])).
% 0.62/0.64  tff(59,plain,
% 0.62/0.64      (leq(F!13, succ(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[58, 52, 40, 35])).
% 0.62/0.64  tff(60,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), F!13)),
% 0.62/0.64      inference(and_elim,[status(thm)],[34])).
% 0.62/0.64  tff(61,plain,
% 0.62/0.64      (^[X: $i] : refl(((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(62,plain,
% 0.62/0.64      (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[61])).
% 0.62/0.64  tff(63,plain,
% 0.62/0.64      (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> (((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))), rewrite((((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(64,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[63])).
% 0.62/0.64  tff(65,plain,
% 0.62/0.64      (^[X: $i] : rewrite(((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(66,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[65])).
% 0.62/0.64  tff(67,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(68,plain,
% 0.62/0.64      (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(69,plain,
% 0.62/0.64      (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[68])).
% 0.62/0.64  tff(70,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_0')).
% 0.62/0.64  tff(71,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[70, 69])).
% 0.62/0.64  tff(72,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[71, 67])).
% 0.62/0.64  tff(73,plain,
% 0.62/0.64      (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[72, 66])).
% 0.62/0.64  tff(74,plain,(
% 0.62/0.64      ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.62/0.64      inference(skolemize,[status(sab)],[73])).
% 0.62/0.64  tff(75,plain,
% 0.62/0.64      (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[74, 64])).
% 0.62/0.64  tff(76,plain,
% 0.62/0.64      (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[75, 62])).
% 0.62/0.64  tff(77,plain,
% 0.62/0.64      (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(78,plain,
% 0.62/0.64      (((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(79,plain,
% 0.62/0.64      (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[78])).
% 0.62/0.64  tff(80,plain,
% 0.62/0.64      (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.62/0.64      inference(transitivity,[status(thm)],[79, 77])).
% 0.62/0.64  tff(81,plain,
% 0.62/0.64      ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(82,plain,
% 0.62/0.64      ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[81, 80])).
% 0.62/0.64  tff(83,plain,
% 0.62/0.64      ((F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[82, 76, 60])).
% 0.62/0.64  tff(84,plain,
% 0.62/0.64      (F!13 = succ(tptp_minus_1)),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[83, 59])).
% 0.62/0.64  tff(85,plain,
% 0.62/0.64      (^[X: $i] : refl((plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))) <=> (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(86,plain,
% 0.62/0.64      (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))) <=> ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[85])).
% 0.62/0.64  tff(87,plain,
% 0.62/0.64      (^[X: $i] : rewrite((plus(X, n2) = succ(succ(X))) <=> (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(88,plain,
% 0.62/0.64      (![X: $i] : (plus(X, n2) = succ(succ(X))) <=> ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[87])).
% 0.62/0.64  tff(89,plain,
% 0.62/0.64      (![X: $i] : (plus(X, n2) = succ(succ(X))) <=> ![X: $i] : (plus(X, n2) = succ(succ(X)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(90,axiom,(![X: $i] : (plus(X, n2) = succ(succ(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_plus_2_r')).
% 0.62/0.64  tff(91,plain,
% 0.62/0.64      (![X: $i] : (plus(X, n2) = succ(succ(X)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.62/0.64  tff(92,plain,
% 0.62/0.64      (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[91, 88])).
% 0.62/0.64  tff(93,plain,(
% 0.62/0.64      ![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.62/0.64      inference(skolemize,[status(sab)],[92])).
% 0.62/0.64  tff(94,plain,
% 0.62/0.64      (![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[93, 86])).
% 0.62/0.64  tff(95,plain,
% 0.62/0.64      ((~![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))) | (plus(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(tptp_minus_1))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(96,plain,
% 0.62/0.64      (plus(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1)))) = succ(succ(succ(tptp_minus_1)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[95, 94])).
% 0.62/0.64  tff(97,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : refl((leq(X, Y) <=> gt(succ(Y), X)) <=> (leq(X, Y) <=> gt(succ(Y), X)))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(98,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[97])).
% 0.62/0.64  tff(99,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X)) <=> ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(100,axiom,(![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_gt_equiv')).
% 0.62/0.64  tff(101,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[100, 99])).
% 0.62/0.64  tff(102,plain,(
% 0.62/0.64      ![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.62/0.64      inference(skolemize,[status(sab)],[101])).
% 0.62/0.64  tff(103,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[102, 98])).
% 0.62/0.64  tff(104,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : (leq(X, Y) <=> gt(succ(Y), X))) | (leq(pred(pred(E!14)), tptp_minus_1) <=> gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(105,plain,
% 0.62/0.64      (leq(pred(pred(E!14)), tptp_minus_1) <=> gt(succ(tptp_minus_1), pred(pred(E!14)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[104, 103])).
% 0.62/0.64  tff(106,plain,
% 0.62/0.64      ((a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))) <=> (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(107,plain,
% 0.62/0.64      ((a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))) <=> (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(108,plain,
% 0.62/0.64      ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(109,plain,
% 0.62/0.64      ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, n1, n0) = use)),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(110,plain,
% 0.62/0.64      (a_select3(u_defuse, n1, n0) = use),
% 0.62/0.64      inference(and_elim,[status(thm)],[8])).
% 0.62/0.64  tff(111,plain,
% 0.62/0.64      (a_select3(u_defuse, n1, n0) = use),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[110, 109])).
% 0.62/0.64  tff(112,plain,
% 0.62/0.64      (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(rho_defuse, succ(tptp_minus_1))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[111, 108])).
% 0.62/0.64  tff(113,plain,
% 0.62/0.64      (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select2(sigma_defuse, succ(tptp_minus_1))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[112, 107])).
% 0.62/0.64  tff(114,plain,
% 0.62/0.64      (a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1)) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[113, 106])).
% 0.62/0.64  tff(115,plain,
% 0.62/0.64      ((~![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))) | (plus(tptp_minus_1, succ(succ(succ(tptp_minus_1)))) = succ(succ(tptp_minus_1)))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(116,plain,
% 0.62/0.64      (plus(tptp_minus_1, succ(succ(succ(tptp_minus_1)))) = succ(succ(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[115, 94])).
% 0.62/0.64  tff(117,assumption,(pred(pred(E!14)) = tptp_minus_1), introduced(assumption)).
% 0.62/0.64  tff(118,plain,
% 0.62/0.64      (plus(pred(pred(E!14)), succ(succ(succ(tptp_minus_1)))) = plus(tptp_minus_1, succ(succ(succ(tptp_minus_1))))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[117])).
% 0.62/0.64  tff(119,plain,
% 0.62/0.64      ((~![X: $i] : (plus(X, succ(succ(succ(tptp_minus_1)))) = succ(succ(X)))) | (plus(pred(pred(E!14)), succ(succ(succ(tptp_minus_1)))) = succ(succ(pred(pred(E!14)))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(120,plain,
% 0.62/0.64      (plus(pred(pred(E!14)), succ(succ(succ(tptp_minus_1)))) = succ(succ(pred(pred(E!14))))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[119, 94])).
% 0.62/0.64  tff(121,plain,
% 0.62/0.64      (succ(succ(pred(pred(E!14)))) = plus(pred(pred(E!14)), succ(succ(succ(tptp_minus_1))))),
% 0.62/0.64      inference(symmetry,[status(thm)],[120])).
% 0.62/0.64  tff(122,plain,
% 0.62/0.64      (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(123,plain,
% 0.62/0.64      (![X: $i] : (succ(pred(X)) = X) <=> ![X: $i] : (succ(pred(X)) = X)),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(124,axiom,(![X: $i] : (succ(pred(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','succ_pred')).
% 0.62/0.64  tff(125,plain,
% 0.62/0.64      (![X: $i] : (succ(pred(X)) = X)),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[124, 123])).
% 0.62/0.64  tff(126,plain,(
% 0.62/0.64      ![X: $i] : (succ(pred(X)) = X)),
% 0.62/0.64      inference(skolemize,[status(sab)],[125])).
% 0.62/0.64  tff(127,plain,
% 0.62/0.64      (![X: $i] : (succ(pred(X)) = X)),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[126, 122])).
% 0.62/0.64  tff(128,plain,
% 0.62/0.64      ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(pred(E!14))) = pred(E!14))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(129,plain,
% 0.62/0.64      (succ(pred(pred(E!14))) = pred(E!14)),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[128, 127])).
% 0.62/0.64  tff(130,plain,
% 0.62/0.64      (pred(E!14) = succ(pred(pred(E!14)))),
% 0.62/0.64      inference(symmetry,[status(thm)],[129])).
% 0.62/0.64  tff(131,plain,
% 0.62/0.64      (succ(pred(E!14)) = succ(succ(pred(pred(E!14))))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[130])).
% 0.62/0.64  tff(132,plain,
% 0.62/0.64      ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(E!14)) = E!14)),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(133,plain,
% 0.62/0.64      (succ(pred(E!14)) = E!14),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[132, 127])).
% 0.62/0.64  tff(134,plain,
% 0.62/0.64      (E!14 = succ(pred(E!14))),
% 0.62/0.64      inference(symmetry,[status(thm)],[133])).
% 0.62/0.64  tff(135,plain,
% 0.62/0.64      (E!14 = succ(succ(tptp_minus_1))),
% 0.62/0.64      inference(transitivity,[status(thm)],[134, 131, 121, 118, 116])).
% 0.62/0.64  tff(136,plain,
% 0.62/0.64      (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(succ(tptp_minus_1)), succ(tptp_minus_1))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[135, 84])).
% 0.62/0.64  tff(137,plain,
% 0.62/0.64      (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.62/0.64      inference(transitivity,[status(thm)],[136, 114])).
% 0.62/0.64  tff(138,plain,
% 0.62/0.64      (~(a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.62/0.64      inference(or_elim,[status(thm)],[33])).
% 0.62/0.64  tff(139,plain,
% 0.62/0.64      ($false),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[138, 137])).
% 0.62/0.64  tff(140,plain,(~(pred(pred(E!14)) = tptp_minus_1)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64  tff(141,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(142,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[141])).
% 0.62/0.64  tff(143,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(144,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.62/0.64  tff(145,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.62/0.64  tff(146,plain,(
% 0.62/0.64      ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.62/0.64      inference(skolemize,[status(sab)],[145])).
% 0.62/0.64  tff(147,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[146, 142])).
% 0.62/0.64  tff(148,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(pred(pred(E!14)), pred(tptp_minus_1)) <=> gt(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(149,plain,
% 0.62/0.64      (leq(pred(pred(E!14)), pred(tptp_minus_1)) <=> gt(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[148, 147])).
% 0.62/0.64  tff(150,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : refl((leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> (leq(succ(X), succ(Y)) <=> leq(X, Y)))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(151,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[150])).
% 0.62/0.64  tff(152,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y)) <=> ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(153,axiom,(![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_succ_succ')).
% 0.62/0.64  tff(154,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[153, 152])).
% 0.62/0.64  tff(155,plain,(
% 0.62/0.64      ![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.62/0.64      inference(skolemize,[status(sab)],[154])).
% 0.62/0.64  tff(156,plain,
% 0.62/0.64      (![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[155, 151])).
% 0.62/0.64  tff(157,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(tptp_minus_1), succ(pred(pred(E!14)))) <=> leq(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(158,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), succ(pred(pred(E!14)))) <=> leq(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[157, 156])).
% 0.62/0.64  tff(159,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), succ(pred(pred(E!14)))) <=> leq(succ(tptp_minus_1), pred(E!14))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[129])).
% 0.62/0.64  tff(160,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), pred(E!14)) <=> leq(succ(tptp_minus_1), succ(pred(pred(E!14))))),
% 0.62/0.64      inference(symmetry,[status(thm)],[159])).
% 0.62/0.64  tff(161,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(succ(tptp_minus_1), pred(E!14)) <=> gt(E!14, succ(tptp_minus_1)))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(162,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), pred(E!14)) <=> gt(E!14, succ(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[161, 147])).
% 0.62/0.64  tff(163,assumption,(succ(tptp_minus_1) = E!14), introduced(assumption)).
% 0.62/0.64  tff(164,plain,
% 0.62/0.64      (E!14 = succ(tptp_minus_1)),
% 0.62/0.64      inference(symmetry,[status(thm)],[163])).
% 0.62/0.64  tff(165,plain,
% 0.62/0.64      (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[164, 84])).
% 0.62/0.64  tff(166,plain,
% 0.62/0.64      ($false),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[138, 165])).
% 0.62/0.64  tff(167,plain,(~(succ(tptp_minus_1) = E!14)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.64  tff(168,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), E!14)),
% 0.62/0.64      inference(and_elim,[status(thm)],[34])).
% 0.62/0.64  tff(169,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : refl(((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(170,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[169])).
% 0.62/0.64  tff(171,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & (~(X = Y))) <=> (~((~leq(X, Y)) | (X = Y)))), ((~(leq(X, Y) & (~(X = Y)))) <=> (~(~((~leq(X, Y)) | (X = Y)))))), rewrite((~(~((~leq(X, Y)) | (X = Y)))) <=> ((~leq(X, Y)) | (X = Y))), ((~(leq(X, Y) & (~(X = Y)))) <=> ((~leq(X, Y)) | (X = Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> (((~leq(X, Y)) | (X = Y)) | gt(Y, X)))), rewrite((((~leq(X, Y)) | (X = Y)) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))), (((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ((X = Y) | gt(Y, X) | (~leq(X, Y)))))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(172,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[171])).
% 0.62/0.64  tff(173,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(174,plain,
% 0.62/0.64      (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X)))),
% 0.62/0.64      inference(bind,[status(th)],[])).
% 0.62/0.64  tff(175,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.62/0.64      inference(quant_intro,[status(thm)],[174])).
% 0.62/0.64  tff(176,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & (~(X = Y))) => gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt2')).
% 0.62/0.64  tff(177,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[176, 175])).
% 0.62/0.64  tff(178,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[177, 173])).
% 0.62/0.64  tff(179,plain,(
% 0.62/0.64      ![X: $i, Y: $i] : ((~(leq(X, Y) & (~(X = Y)))) | gt(Y, X))),
% 0.62/0.64      inference(skolemize,[status(sab)],[178])).
% 0.62/0.64  tff(180,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[179, 172])).
% 0.62/0.64  tff(181,plain,
% 0.62/0.64      (![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[180, 170])).
% 0.62/0.64  tff(182,plain,
% 0.62/0.64      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(183,plain,
% 0.62/0.64      (((succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14))) <=> ((~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(184,plain,
% 0.62/0.64      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1))))),
% 0.62/0.64      inference(monotonicity,[status(thm)],[183])).
% 0.62/0.64  tff(185,plain,
% 0.62/0.64      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)))),
% 0.62/0.64      inference(transitivity,[status(thm)],[184, 182])).
% 0.62/0.64  tff(186,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), E!14)))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(187,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(succ(tptp_minus_1), E!14)) | (succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[186, 185])).
% 0.62/0.64  tff(188,plain,
% 0.62/0.64      ((succ(tptp_minus_1) = E!14) | gt(E!14, succ(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[187, 181, 168])).
% 0.62/0.64  tff(189,plain,
% 0.62/0.64      (gt(E!14, succ(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[188, 167])).
% 0.62/0.64  tff(190,plain,
% 0.62/0.64      ((~(leq(succ(tptp_minus_1), pred(E!14)) <=> gt(E!14, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(E!14)) | (~gt(E!14, succ(tptp_minus_1)))),
% 0.62/0.64      inference(tautology,[status(thm)],[])).
% 0.62/0.64  tff(191,plain,
% 0.62/0.64      ((~(leq(succ(tptp_minus_1), pred(E!14)) <=> gt(E!14, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(E!14))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[190, 189])).
% 0.62/0.64  tff(192,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), pred(E!14))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[191, 162])).
% 0.62/0.64  tff(193,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), succ(pred(pred(E!14))))),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[192, 160])).
% 0.62/0.64  tff(194,plain,
% 0.62/0.64      ((~(leq(succ(tptp_minus_1), succ(pred(pred(E!14)))) <=> leq(tptp_minus_1, pred(pred(E!14))))) | (~leq(succ(tptp_minus_1), succ(pred(pred(E!14))))) | leq(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.64      inference(tautology,[status(thm)],[])).
% 0.62/0.64  tff(195,plain,
% 0.62/0.64      (leq(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[194, 193, 158])).
% 0.62/0.64  tff(196,plain,
% 0.62/0.64      ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))) <=> leq(tptp_minus_1, pred(tptp_minus_1)))),
% 0.62/0.64      inference(quant_inst,[status(thm)],[])).
% 0.62/0.64  tff(197,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))) <=> leq(tptp_minus_1, pred(tptp_minus_1))),
% 0.62/0.64      inference(unit_resolution,[status(thm)],[196, 156])).
% 0.62/0.64  tff(198,plain,
% 0.62/0.64      (leq(n0, pv5) <=> leq(succ(tptp_minus_1), pv5)),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(199,plain,
% 0.62/0.64      (leq(n0, pv5) <=> leq(n0, pv5)),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.64  tff(200,plain,
% 0.62/0.64      (leq(n0, pv5)),
% 0.62/0.64      inference(and_elim,[status(thm)],[8])).
% 0.62/0.64  tff(201,plain,
% 0.62/0.64      (leq(n0, pv5)),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[200, 199])).
% 0.62/0.64  tff(202,plain,
% 0.62/0.64      (leq(succ(tptp_minus_1), pv5)),
% 0.62/0.64      inference(modus_ponens,[status(thm)],[201, 198])).
% 0.62/0.64  tff(203,plain,
% 0.62/0.64      (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))),
% 0.62/0.64      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(204,plain,
% 0.62/0.65      ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1))))),
% 0.62/0.65      inference(quant_inst,[status(thm)],[])).
% 0.62/0.65  tff(205,plain,
% 0.62/0.65      ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (pv5 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), pv5)) | (~leq(pv5, succ(tptp_minus_1)))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[204, 203])).
% 0.62/0.65  tff(206,plain,
% 0.62/0.65      (pv5 = succ(tptp_minus_1)),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[205, 76, 202, 40])).
% 0.62/0.65  tff(207,plain,
% 0.62/0.65      (pred(pv5) = pred(succ(tptp_minus_1))),
% 0.62/0.65      inference(monotonicity,[status(thm)],[206])).
% 0.62/0.65  tff(208,plain,
% 0.62/0.65      (pred(succ(tptp_minus_1)) = pred(pv5)),
% 0.62/0.65      inference(symmetry,[status(thm)],[207])).
% 0.62/0.65  tff(209,plain,
% 0.62/0.65      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(210,plain,
% 0.62/0.65      (![X: $i] : (pred(succ(X)) = X) <=> ![X: $i] : (pred(succ(X)) = X)),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(211,axiom,(![X: $i] : (pred(succ(X)) = X)), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','pred_succ')).
% 0.62/0.65  tff(212,plain,
% 0.62/0.65      (![X: $i] : (pred(succ(X)) = X)),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[211, 210])).
% 0.62/0.65  tff(213,plain,(
% 0.62/0.65      ![X: $i] : (pred(succ(X)) = X)),
% 0.62/0.65      inference(skolemize,[status(sab)],[212])).
% 0.62/0.65  tff(214,plain,
% 0.62/0.65      (![X: $i] : (pred(succ(X)) = X)),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[213, 209])).
% 0.62/0.65  tff(215,plain,
% 0.62/0.65      ((~![X: $i] : (pred(succ(X)) = X)) | (pred(succ(tptp_minus_1)) = tptp_minus_1)),
% 0.62/0.65      inference(quant_inst,[status(thm)],[])).
% 0.62/0.65  tff(216,plain,
% 0.62/0.65      (pred(succ(tptp_minus_1)) = tptp_minus_1),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[215, 214])).
% 0.62/0.65  tff(217,plain,
% 0.62/0.65      (tptp_minus_1 = pred(succ(tptp_minus_1))),
% 0.62/0.65      inference(symmetry,[status(thm)],[216])).
% 0.62/0.65  tff(218,plain,
% 0.62/0.65      ((~![X: $i] : (succ(pred(X)) = X)) | (succ(pred(tptp_minus_1)) = tptp_minus_1)),
% 0.62/0.65      inference(quant_inst,[status(thm)],[])).
% 0.62/0.65  tff(219,plain,
% 0.62/0.65      (succ(pred(tptp_minus_1)) = tptp_minus_1),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[218, 127])).
% 0.62/0.65  tff(220,plain,
% 0.62/0.65      (succ(pred(tptp_minus_1)) = pred(pv5)),
% 0.62/0.65      inference(transitivity,[status(thm)],[219, 217, 208])).
% 0.62/0.65  tff(221,plain,
% 0.62/0.65      (succ(tptp_minus_1) = F!13),
% 0.62/0.65      inference(symmetry,[status(thm)],[84])).
% 0.62/0.65  tff(222,plain,
% 0.62/0.65      (leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))) <=> leq(F!13, pred(pv5))),
% 0.62/0.65      inference(monotonicity,[status(thm)],[221, 220])).
% 0.62/0.65  tff(223,plain,
% 0.62/0.65      (leq(F!13, pred(pv5)) <=> leq(succ(tptp_minus_1), succ(pred(tptp_minus_1)))),
% 0.62/0.65      inference(symmetry,[status(thm)],[222])).
% 0.62/0.65  tff(224,plain,
% 0.62/0.65      ((~leq(F!13, pred(pv5))) <=> (~leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))))),
% 0.62/0.65      inference(monotonicity,[status(thm)],[223])).
% 0.62/0.65  tff(225,plain,
% 0.62/0.65      (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.62/0.65      inference(and_elim,[status(thm)],[34])).
% 0.62/0.65  tff(226,plain,
% 0.62/0.65      (^[A: $i, B: $i] : refl(((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))))),
% 0.62/0.65      inference(bind,[status(th)],[])).
% 0.62/0.65  tff(227,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))) <=> ![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))),
% 0.62/0.65      inference(quant_intro,[status(thm)],[226])).
% 0.62/0.65  tff(228,plain,
% 0.62/0.65      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5))) <=> (~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) <=> (~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))), ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))), (((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))))),
% 0.62/0.65      inference(bind,[status(th)],[])).
% 0.62/0.65  tff(229,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))),
% 0.62/0.65      inference(quant_intro,[status(thm)],[228])).
% 0.62/0.65  tff(230,plain,
% 0.62/0.65      (^[A: $i, B: $i] : rewrite(((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.62/0.65      inference(bind,[status(th)],[])).
% 0.62/0.65  tff(231,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.65      inference(quant_intro,[status(thm)],[230])).
% 0.62/0.65  tff(232,plain,
% 0.62/0.65      (^[A: $i, B: $i] : rewrite(((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.62/0.65      inference(bind,[status(th)],[])).
% 0.62/0.65  tff(233,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.62/0.65      inference(quant_intro,[status(thm)],[232])).
% 0.62/0.65  tff(234,plain,
% 0.62/0.65      (^[A: $i, B: $i] : rewrite(((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.62/0.65      inference(bind,[status(th)],[])).
% 0.62/0.65  tff(235,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.62/0.65      inference(quant_intro,[status(thm)],[234])).
% 0.62/0.65  tff(236,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(237,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.62/0.65      inference(and_elim,[status(thm)],[8])).
% 0.62/0.65  tff(238,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[237, 236])).
% 0.62/0.65  tff(239,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[238, 235])).
% 0.62/0.65  tff(240,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[239, 233])).
% 0.62/0.65  tff(241,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[240, 231])).
% 0.62/0.65  tff(242,plain,(
% 0.62/0.65      ![A: $i, B: $i] : ((~(leq(succ(tptp_minus_1), A) & leq(succ(tptp_minus_1), B) & leq(A, succ(succ(succ(tptp_minus_1)))) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.62/0.65      inference(skolemize,[status(sab)],[241])).
% 0.62/0.65  tff(243,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[242, 229])).
% 0.62/0.65  tff(244,plain,
% 0.62/0.65      (![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[243, 227])).
% 0.62/0.65  tff(245,plain,
% 0.62/0.65      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | ((a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(246,plain,
% 0.62/0.65      (((~leq(succ(tptp_minus_1), E!14)) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))) <=> ((a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(247,plain,
% 0.62/0.65      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | ((a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))))),
% 0.62/0.65      inference(monotonicity,[status(thm)],[246])).
% 0.62/0.65  tff(248,plain,
% 0.62/0.65      (((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))) <=> ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))),
% 0.62/0.65      inference(transitivity,[status(thm)],[247, 245])).
% 0.62/0.65  tff(249,plain,
% 0.62/0.65      ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5))))),
% 0.62/0.65      inference(quant_inst,[status(thm)],[])).
% 0.62/0.65  tff(250,plain,
% 0.62/0.65      ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[249, 248])).
% 0.62/0.65  tff(251,plain,
% 0.62/0.65      (~leq(F!13, pred(pv5))),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[250, 244, 168, 60, 225, 138])).
% 0.62/0.65  tff(252,plain,
% 0.62/0.65      (~leq(succ(tptp_minus_1), succ(pred(tptp_minus_1)))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[251, 224])).
% 0.62/0.65  tff(253,plain,
% 0.62/0.65      ((~(leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))) <=> leq(tptp_minus_1, pred(tptp_minus_1)))) | leq(succ(tptp_minus_1), succ(pred(tptp_minus_1))) | (~leq(tptp_minus_1, pred(tptp_minus_1)))),
% 0.62/0.65      inference(tautology,[status(thm)],[])).
% 0.62/0.65  tff(254,plain,
% 0.62/0.65      (~leq(tptp_minus_1, pred(tptp_minus_1))),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[253, 252, 197])).
% 0.62/0.65  tff(255,plain,
% 0.62/0.65      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))))),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(256,plain,
% 0.62/0.65      ((leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))) | (~leq(tptp_minus_1, pred(pred(E!14))))) <=> (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))))),
% 0.62/0.65      inference(rewrite,[status(thm)],[])).
% 0.62/0.65  tff(257,plain,
% 0.62/0.65      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))) | (~leq(tptp_minus_1, pred(pred(E!14)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1)))))),
% 0.62/0.65      inference(monotonicity,[status(thm)],[256])).
% 0.62/0.65  tff(258,plain,
% 0.62/0.65      (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))) | (~leq(tptp_minus_1, pred(pred(E!14)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))))),
% 0.62/0.65      inference(transitivity,[status(thm)],[257, 255])).
% 0.62/0.65  tff(259,plain,
% 0.62/0.65      ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(pred(pred(E!14)), pred(tptp_minus_1))) | (~leq(tptp_minus_1, pred(pred(E!14)))))),
% 0.62/0.65      inference(quant_inst,[status(thm)],[])).
% 0.62/0.65  tff(260,plain,
% 0.62/0.65      ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | leq(tptp_minus_1, pred(tptp_minus_1)) | (~leq(tptp_minus_1, pred(pred(E!14)))) | (~leq(pred(pred(E!14)), pred(tptp_minus_1)))),
% 0.62/0.65      inference(modus_ponens,[status(thm)],[259, 258])).
% 0.62/0.65  tff(261,plain,
% 0.62/0.65      (~leq(pred(pred(E!14)), pred(tptp_minus_1))),
% 0.62/0.65      inference(unit_resolution,[status(thm)],[260, 52, 254, 195])).
% 0.62/0.65  tff(262,plain,
% 0.62/0.65      ((~(leq(pred(pred(E!14)), pred(tptp_minus_1)) <=> gt(tptp_minus_1, pred(pred(E!14))))) | leq(pred(pred(E!14)), pred(tptp_minus_1)) | (~gt(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.66      inference(tautology,[status(thm)],[])).
% 0.62/0.66  tff(263,plain,
% 0.62/0.66      (~gt(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[262, 261, 149])).
% 0.62/0.66  tff(264,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.66      inference(rewrite,[status(thm)],[])).
% 0.62/0.66  tff(265,plain,
% 0.62/0.66      (((pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))) | (~leq(pred(pred(E!14)), tptp_minus_1))) <=> ((~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.66      inference(rewrite,[status(thm)],[])).
% 0.62/0.66  tff(266,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))) | (~leq(pred(pred(E!14)), tptp_minus_1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14)))))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[265])).
% 0.62/0.66  tff(267,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))) | (~leq(pred(pred(E!14)), tptp_minus_1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))))),
% 0.62/0.66      inference(transitivity,[status(thm)],[266, 264])).
% 0.62/0.66  tff(268,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14))) | (~leq(pred(pred(E!14)), tptp_minus_1)))),
% 0.62/0.66      inference(quant_inst,[status(thm)],[])).
% 0.62/0.66  tff(269,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1) | gt(tptp_minus_1, pred(pred(E!14)))),
% 0.62/0.66      inference(modus_ponens,[status(thm)],[268, 267])).
% 0.62/0.66  tff(270,plain,
% 0.62/0.66      ((~leq(pred(pred(E!14)), tptp_minus_1)) | (pred(pred(E!14)) = tptp_minus_1)),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[269, 181, 263])).
% 0.62/0.66  tff(271,plain,
% 0.62/0.66      (~leq(pred(pred(E!14)), tptp_minus_1)),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[270, 140])).
% 0.62/0.66  tff(272,plain,
% 0.62/0.66      ((~(leq(pred(pred(E!14)), tptp_minus_1) <=> gt(succ(tptp_minus_1), pred(pred(E!14))))) | leq(pred(pred(E!14)), tptp_minus_1) | (~gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.66      inference(tautology,[status(thm)],[])).
% 0.62/0.66  tff(273,plain,
% 0.62/0.66      ((~(leq(pred(pred(E!14)), tptp_minus_1) <=> gt(succ(tptp_minus_1), pred(pred(E!14))))) | (~gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[272, 271])).
% 0.62/0.66  tff(274,plain,
% 0.62/0.66      (~gt(succ(tptp_minus_1), pred(pred(E!14)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[273, 105])).
% 0.62/0.66  tff(275,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1))) <=> leq(pred(pred(E!14)), succ(tptp_minus_1)))),
% 0.62/0.66      inference(quant_inst,[status(thm)],[])).
% 0.62/0.66  tff(276,plain,
% 0.62/0.66      (leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1))) <=> leq(pred(pred(E!14)), succ(tptp_minus_1))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[275, 156])).
% 0.62/0.66  tff(277,plain,
% 0.62/0.66      (leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1))) <=> leq(pred(E!14), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[129])).
% 0.62/0.66  tff(278,plain,
% 0.62/0.66      (leq(pred(E!14), succ(succ(tptp_minus_1))) <=> leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(symmetry,[status(thm)],[277])).
% 0.62/0.66  tff(279,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : (leq(succ(X), succ(Y)) <=> leq(X, Y))) | (leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1)))) <=> leq(pred(E!14), succ(succ(tptp_minus_1))))),
% 0.62/0.66      inference(quant_inst,[status(thm)],[])).
% 0.62/0.66  tff(280,plain,
% 0.62/0.66      (leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1)))) <=> leq(pred(E!14), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[279, 156])).
% 0.62/0.66  tff(281,plain,
% 0.62/0.66      (leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1)))) <=> leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[133])).
% 0.62/0.66  tff(282,plain,
% 0.62/0.66      (leq(E!14, succ(succ(succ(tptp_minus_1)))) <=> leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1))))),
% 0.62/0.66      inference(symmetry,[status(thm)],[281])).
% 0.62/0.66  tff(283,plain,
% 0.62/0.66      (leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1))))),
% 0.62/0.66      inference(modus_ponens,[status(thm)],[225, 282])).
% 0.62/0.66  tff(284,plain,
% 0.62/0.66      ((~(leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1)))) <=> leq(pred(E!14), succ(succ(tptp_minus_1))))) | (~leq(succ(pred(E!14)), succ(succ(succ(tptp_minus_1))))) | leq(pred(E!14), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(tautology,[status(thm)],[])).
% 0.62/0.66  tff(285,plain,
% 0.62/0.66      (leq(pred(E!14), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[284, 283, 280])).
% 0.62/0.66  tff(286,plain,
% 0.62/0.66      (leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(modus_ponens,[status(thm)],[285, 278])).
% 0.62/0.66  tff(287,plain,
% 0.62/0.66      ((~(leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1))) <=> leq(pred(pred(E!14)), succ(tptp_minus_1)))) | (~leq(succ(pred(pred(E!14))), succ(succ(tptp_minus_1)))) | leq(pred(pred(E!14)), succ(tptp_minus_1))),
% 0.62/0.66      inference(tautology,[status(thm)],[])).
% 0.62/0.66  tff(288,plain,
% 0.62/0.66      (leq(pred(pred(E!14)), succ(tptp_minus_1))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[287, 286, 276])).
% 0.62/0.66  tff(289,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.66      inference(rewrite,[status(thm)],[])).
% 0.62/0.66  tff(290,plain,
% 0.62/0.66      (((pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1)))) <=> ((~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.66      inference(rewrite,[status(thm)],[])).
% 0.62/0.66  tff(291,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14)))))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[290])).
% 0.62/0.66  tff(292,plain,
% 0.62/0.66      (((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))))),
% 0.62/0.66      inference(transitivity,[status(thm)],[291, 289])).
% 0.62/0.66  tff(293,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | ((pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))))),
% 0.62/0.66      inference(quant_inst,[status(thm)],[])).
% 0.62/0.66  tff(294,plain,
% 0.62/0.66      ((~![X: $i, Y: $i] : ((X = Y) | gt(Y, X) | (~leq(X, Y)))) | (~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14)))),
% 0.62/0.66      inference(modus_ponens,[status(thm)],[293, 292])).
% 0.62/0.66  tff(295,plain,
% 0.62/0.66      ((~leq(pred(pred(E!14)), succ(tptp_minus_1))) | (pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[294, 181])).
% 0.62/0.66  tff(296,plain,
% 0.62/0.66      ((pred(pred(E!14)) = succ(tptp_minus_1)) | gt(succ(tptp_minus_1), pred(pred(E!14)))),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[295, 288])).
% 0.62/0.66  tff(297,plain,
% 0.62/0.66      (pred(pred(E!14)) = succ(tptp_minus_1)),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[296, 274])).
% 0.62/0.66  tff(298,plain,
% 0.62/0.66      (plus(pred(pred(E!14)), succ(succ(succ(tptp_minus_1)))) = plus(succ(tptp_minus_1), succ(succ(succ(tptp_minus_1))))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[297])).
% 0.62/0.66  tff(299,plain,
% 0.62/0.66      (E!14 = succ(succ(succ(tptp_minus_1)))),
% 0.62/0.66      inference(transitivity,[status(thm)],[134, 131, 121, 298, 96])).
% 0.62/0.66  tff(300,plain,
% 0.62/0.66      (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(succ(succ(tptp_minus_1))), succ(tptp_minus_1))),
% 0.62/0.66      inference(monotonicity,[status(thm)],[299, 84])).
% 0.62/0.66  tff(301,plain,
% 0.62/0.66      (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.62/0.66      inference(transitivity,[status(thm)],[300, 13])).
% 0.62/0.66  tff(302,plain,
% 0.62/0.66      ($false),
% 0.62/0.66      inference(unit_resolution,[status(thm)],[138, 301])).
% 0.62/0.66  % SZS output end Proof
%------------------------------------------------------------------------------