TSTP Solution File: SWV194+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV194+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:19 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV194+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Sep 4 01:43:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 tff(leq_type, type, (
% 0.18/0.41 leq: ( $i * $i ) > $o)).
% 0.18/0.41 tff(pred_type, type, (
% 0.18/0.41 pred: $i > $i)).
% 0.18/0.41 tff(pv5_type, type, (
% 0.18/0.41 pv5: $i)).
% 0.18/0.41 tff(tptp_fun_F_13_type, type, (
% 0.18/0.41 tptp_fun_F_13: $i)).
% 0.18/0.41 tff(succ_type, type, (
% 0.18/0.41 succ: $i > $i)).
% 0.18/0.41 tff(tptp_minus_1_type, type, (
% 0.18/0.41 tptp_minus_1: $i)).
% 0.18/0.41 tff(tptp_fun_E_14_type, type, (
% 0.18/0.41 tptp_fun_E_14: $i)).
% 0.18/0.41 tff(a_select3_type, type, (
% 0.18/0.41 a_select3: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(u_defuse_type, type, (
% 0.18/0.41 u_defuse: $i)).
% 0.18/0.41 tff(a_select2_type, type, (
% 0.18/0.41 a_select2: ( $i * $i ) > $i)).
% 0.18/0.41 tff(sigma_defuse_type, type, (
% 0.18/0.41 sigma_defuse: $i)).
% 0.18/0.41 tff(rho_defuse_type, type, (
% 0.18/0.41 rho_defuse: $i)).
% 0.18/0.41 tff(use_type, type, (
% 0.18/0.41 use: $i)).
% 0.18/0.41 tff(n2_type, type, (
% 0.18/0.41 n2: $i)).
% 0.18/0.41 tff(n0_type, type, (
% 0.18/0.41 n0: $i)).
% 0.18/0.41 tff(z_defuse_type, type, (
% 0.18/0.41 z_defuse: $i)).
% 0.18/0.41 tff(gt_type, type, (
% 0.18/0.41 gt: ( $i * $i ) > $o)).
% 0.18/0.41 tff(n998_type, type, (
% 0.18/0.41 n998: $i)).
% 0.18/0.41 tff(n5_type, type, (
% 0.18/0.41 n5: $i)).
% 0.18/0.41 tff(xinit_noise_defuse_type, type, (
% 0.18/0.41 xinit_noise_defuse: $i)).
% 0.18/0.41 tff(n4_type, type, (
% 0.18/0.41 n4: $i)).
% 0.18/0.41 tff(n3_type, type, (
% 0.18/0.41 n3: $i)).
% 0.18/0.41 tff(n1_type, type, (
% 0.18/0.41 n1: $i)).
% 0.18/0.41 tff(xinit_mean_defuse_type, type, (
% 0.18/0.41 xinit_mean_defuse: $i)).
% 0.18/0.41 tff(xinit_defuse_type, type, (
% 0.18/0.41 xinit_defuse: $i)).
% 0.18/0.41 tff(1,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(2,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(3,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(4,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(6,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(7,plain,
% 0.18/0.41 ((~![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(8,plain,
% 0.18/0.41 ((~((((((((((((((((((((((((((((((((((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)) & gt(pv5, n0)) & ![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) & gt(pv5, n0) & ![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(9,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)) & gt(pv5, n0)) & ![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/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0005')).
% 0.18/0.42 tff(10,plain,
% 0.18/0.42 (~((~((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) & gt(pv5, n0) & ![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.42 tff(11,plain,
% 0.18/0.42 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.18/0.42 inference(or_elim,[status(thm)],[10])).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.18/0.42 tff(13,plain,
% 0.18/0.42 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.18/0.42 tff(14,plain,
% 0.18/0.42 (~![E: $i, F: $i] : ((~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))) | (a_select3(u_defuse, E, F) = use))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[19, 1])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[20, 1])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (~![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))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[21, 1])).
% 0.18/0.42 tff(23,plain,(
% 0.18/0.42 ~((~(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))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[22])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 (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)),
% 0.18/0.42 inference(or_elim,[status(thm)],[23])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (leq(F!13, pv5)),
% 0.18/0.42 inference(and_elim,[status(thm)],[24])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (leq(pv5, n0) <=> leq(pv5, succ(tptp_minus_1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 ((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) & gt(pv5, n0) & ![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))),
% 0.18/0.42 inference(or_elim,[status(thm)],[10])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (leq(pv5, n0)),
% 0.18/0.42 inference(and_elim,[status(thm)],[28])).
% 0.18/0.42 tff(30,plain,
% 0.18/0.42 (leq(pv5, n0)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 (leq(pv5, succ(tptp_minus_1))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.42 tff(32,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 (![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))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(36,plain,
% 0.18/0.42 (^[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)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(37,plain,
% 0.18/0.42 (![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))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.42 tff(38,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.18/0.42 tff(39,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.42 tff(40,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.18/0.42 tff(41,plain,(
% 0.18/0.42 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.18/0.42 inference(skolemize,[status(sab)],[40])).
% 0.18/0.42 tff(42,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.18/0.42 tff(43,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.18/0.42 tff(44,plain,
% 0.18/0.42 (((~![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(45,plain,
% 0.18/0.42 ((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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(46,plain,
% 0.18/0.42 (((~![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))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.18/0.42 tff(47,plain,
% 0.18/0.42 (((~![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)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[46, 44])).
% 0.18/0.42 tff(48,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(49,plain,
% 0.18/0.42 ((~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.42 tff(50,plain,
% 0.18/0.42 (leq(F!13, succ(tptp_minus_1))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[49, 43, 31, 25])).
% 0.18/0.42 tff(51,plain,
% 0.18/0.42 (leq(succ(tptp_minus_1), F!13)),
% 0.18/0.42 inference(and_elim,[status(thm)],[24])).
% 0.18/0.42 tff(52,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(53,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.42 tff(54,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(55,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.42 tff(56,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(57,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.42 tff(58,plain,
% 0.18/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(59,plain,
% 0.18/0.42 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(60,plain,
% 0.18/0.42 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.42 tff(61,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','finite_domain_0')).
% 0.18/0.42 tff(62,plain,
% 0.18/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.42 tff(63,plain,
% 0.18/0.42 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.42 tff(64,plain,
% 0.18/0.42 (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.18/0.42 tff(65,plain,(
% 0.18/0.42 ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[64])).
% 0.18/0.42 tff(66,plain,
% 0.18/0.42 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.18/0.42 tff(67,plain,
% 0.18/0.42 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[66, 53])).
% 0.18/0.42 tff(68,plain,
% 0.18/0.42 (((~![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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(69,plain,
% 0.18/0.42 (((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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(70,plain,
% 0.18/0.42 (((~![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)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.42 tff(71,plain,
% 0.18/0.42 (((~![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))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[70, 68])).
% 0.18/0.42 tff(72,plain,
% 0.18/0.42 ((~![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))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(73,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.42 tff(74,plain,
% 0.18/0.42 ((F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[73, 67, 51])).
% 0.18/0.42 tff(75,plain,
% 0.18/0.42 (F!13 = succ(tptp_minus_1)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[74, 50])).
% 0.18/0.42 tff(76,plain,
% 0.18/0.42 (leq(F!13, pred(pv5)) <=> leq(succ(tptp_minus_1), pred(pv5))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.18/0.42 tff(77,plain,
% 0.18/0.42 (leq(succ(tptp_minus_1), pred(pv5)) <=> leq(F!13, pred(pv5))),
% 0.18/0.42 inference(symmetry,[status(thm)],[76])).
% 0.18/0.42 tff(78,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(81,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.43 tff(83,plain,(
% 0.18/0.43 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.18/0.43 inference(skolemize,[status(sab)],[82])).
% 0.18/0.43 tff(84,plain,
% 0.18/0.43 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.18/0.43 tff(85,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(86,plain,
% 0.18/0.43 (leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.18/0.43 tff(87,plain,
% 0.18/0.43 (gt(pv5, n0) <=> gt(pv5, succ(tptp_minus_1))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(88,plain,
% 0.18/0.43 (gt(pv5, n0) <=> gt(pv5, n0)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(89,plain,
% 0.18/0.43 (gt(pv5, n0)),
% 0.18/0.43 inference(and_elim,[status(thm)],[28])).
% 0.18/0.43 tff(90,plain,
% 0.18/0.43 (gt(pv5, n0)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.43 tff(91,plain,
% 0.18/0.43 (gt(pv5, succ(tptp_minus_1))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.18/0.43 tff(92,plain,
% 0.18/0.43 ((~(leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(pv5)) | (~gt(pv5, succ(tptp_minus_1)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(93,plain,
% 0.18/0.43 ((~(leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(pv5))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.18/0.43 tff(94,plain,
% 0.18/0.43 (leq(succ(tptp_minus_1), pred(pv5))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[93, 86])).
% 0.18/0.43 tff(95,plain,
% 0.18/0.43 (leq(F!13, pred(pv5))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[94, 77])).
% 0.18/0.43 tff(96,plain,
% 0.18/0.43 (~(a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.18/0.43 inference(or_elim,[status(thm)],[23])).
% 0.18/0.43 tff(97,plain,
% 0.18/0.43 (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.18/0.43 inference(and_elim,[status(thm)],[24])).
% 0.18/0.43 tff(98,plain,
% 0.18/0.43 (leq(succ(tptp_minus_1), E!14)),
% 0.18/0.43 inference(and_elim,[status(thm)],[24])).
% 0.18/0.43 tff(99,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(100,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.43 tff(101,plain,
% 0.18/0.43 (^[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))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(102,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.43 tff(103,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(104,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.43 tff(105,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(106,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.43 tff(107,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(108,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.18/0.43 tff(109,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(110,plain,
% 0.18/0.43 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.18/0.43 inference(and_elim,[status(thm)],[28])).
% 0.18/0.43 tff(111,plain,
% 0.18/0.43 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.43 tff(112,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.18/0.43 tff(113,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[112, 106])).
% 0.18/0.43 tff(114,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[113, 104])).
% 0.18/0.43 tff(115,plain,(
% 0.18/0.43 ![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))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[114])).
% 0.18/0.43 tff(116,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[115, 102])).
% 0.18/0.43 tff(117,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[116, 100])).
% 0.18/0.43 tff(118,plain,
% 0.18/0.43 (((~![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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(119,plain,
% 0.18/0.43 (((~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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(120,plain,
% 0.18/0.43 (((~![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)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[119])).
% 0.18/0.43 tff(121,plain,
% 0.18/0.43 (((~![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))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[120, 118])).
% 0.18/0.43 tff(122,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(123,plain,
% 0.18/0.43 ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.43 tff(124,plain,
% 0.18/0.44 (~leq(F!13, pred(pv5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[123, 117, 98, 51, 97, 96])).
% 0.18/0.44 tff(125,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[124, 95])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------