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