TSTP Solution File: SWV099+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV099+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 15:09:58 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV099+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n029.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 01:33:45 EDT 2022
% 0.12/0.32 % 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.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(a_select3_type, type, (
% 0.18/0.48 a_select3: ( $i * $i * $i ) > $i)).
% 0.18/0.48 tff(succ_type, type, (
% 0.18/0.48 succ: $i > $i)).
% 0.18/0.48 tff(tptp_minus_1_type, type, (
% 0.18/0.48 tptp_minus_1: $i)).
% 0.18/0.48 tff(u_defuse_type, type, (
% 0.18/0.48 u_defuse: $i)).
% 0.18/0.48 tff(tptp_fun_D_13_type, type, (
% 0.18/0.48 tptp_fun_D_13: $i)).
% 0.18/0.48 tff(tptp_fun_C_14_type, type, (
% 0.18/0.48 tptp_fun_C_14: $i)).
% 0.18/0.48 tff(z_defuse_type, type, (
% 0.18/0.48 z_defuse: $i)).
% 0.18/0.48 tff(leq_type, type, (
% 0.18/0.48 leq: ( $i * $i ) > $o)).
% 0.18/0.48 tff(minus_type, type, (
% 0.18/0.48 minus: ( $i * $i ) > $i)).
% 0.18/0.48 tff(pv5_type, type, (
% 0.18/0.48 pv5: $i)).
% 0.18/0.48 tff(a_select2_type, type, (
% 0.18/0.48 a_select2: ( $i * $i ) > $i)).
% 0.18/0.48 tff(sigma_defuse_type, type, (
% 0.18/0.48 sigma_defuse: $i)).
% 0.18/0.48 tff(rho_defuse_type, type, (
% 0.18/0.48 rho_defuse: $i)).
% 0.18/0.48 tff(use_type, type, (
% 0.18/0.48 use: $i)).
% 0.18/0.48 tff(n1_type, type, (
% 0.18/0.48 n1: $i)).
% 0.18/0.48 tff(n2_type, type, (
% 0.18/0.48 n2: $i)).
% 0.18/0.48 tff(n0_type, type, (
% 0.18/0.48 n0: $i)).
% 0.18/0.48 tff(n999_type, type, (
% 0.18/0.48 n999: $i)).
% 0.18/0.48 tff(n5_type, type, (
% 0.18/0.48 n5: $i)).
% 0.18/0.48 tff(xinit_noise_defuse_type, type, (
% 0.18/0.48 xinit_noise_defuse: $i)).
% 0.18/0.48 tff(n4_type, type, (
% 0.18/0.48 n4: $i)).
% 0.18/0.48 tff(n3_type, type, (
% 0.18/0.48 n3: $i)).
% 0.18/0.48 tff(xinit_mean_defuse_type, type, (
% 0.18/0.48 xinit_mean_defuse: $i)).
% 0.18/0.48 tff(xinit_defuse_type, type, (
% 0.18/0.48 xinit_defuse: $i)).
% 0.18/0.48 tff(1,assumption,((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))), introduced(assumption)).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(4,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(5,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(6,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(7,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))) <=> (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(8,plain,
% 0.18/0.48 ((~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))) <=> (~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(9,plain,
% 0.18/0.48 ((~((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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))) <=> (~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(10,plain,
% 0.18/0.48 (((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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = 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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(11,plain,
% 0.18/0.48 ((~((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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = 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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.49 tff(12,plain,
% 0.18/0.49 ((~(((((((((((((((((((((((((((((((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, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, minus(pv5, n1))) => ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = 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, minus(n999, n1))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, minus(pv5, n1))) => ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = 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, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = 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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(13,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, minus(n999, n1))) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, minus(pv5, n1))) => ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = 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, minus(n999, n1))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, minus(pv5, n1))) => ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0011')).
% 0.18/0.49 tff(14,plain,
% 0.18/0.49 (~((~((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, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = 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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.49 tff(15,plain,
% 0.18/0.49 (~((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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))),
% 0.18/0.50 inference(or_elim,[status(thm)],[14])).
% 0.18/0.50 tff(16,plain,
% 0.18/0.50 (~((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, minus(n999, n1)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.50 tff(17,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.18/0.50 tff(18,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[17, 8])).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, minus(pv5, n1)))) | ((a_select3(u_defuse, C, D) = use) & (a_select3(z_defuse, C, D) = use)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[19, 7])).
% 0.18/0.50 tff(21,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[20, 6])).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.18/0.50 tff(23,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[22, 4])).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[23, 3])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[24, 2])).
% 0.18/0.50 tff(26,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[25, 2])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 (~![C: $i, D: $i] : ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[26, 2])).
% 0.18/0.50 tff(28,plain,(
% 0.18/0.50 ~((~(leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[27])).
% 0.18/0.50 tff(29,plain,
% 0.18/0.50 (leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))),
% 0.18/0.50 inference(or_elim,[status(thm)],[28])).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))),
% 0.18/0.50 inference(and_elim,[status(thm)],[29])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.50 (leq(C!14, succ(succ(succ(tptp_minus_1))))),
% 0.18/0.50 inference(and_elim,[status(thm)],[29])).
% 0.18/0.50 tff(32,plain,
% 0.18/0.50 (leq(succ(tptp_minus_1), D!13)),
% 0.18/0.50 inference(and_elim,[status(thm)],[29])).
% 0.18/0.50 tff(33,plain,
% 0.18/0.50 (leq(succ(tptp_minus_1), C!14)),
% 0.18/0.50 inference(and_elim,[status(thm)],[29])).
% 0.18/0.50 tff(34,plain,
% 0.18/0.50 (^[A: $i, B: $i] : refl(((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(35,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.50 tff(36,plain,
% 0.18/0.50 (^[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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(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, minus(pv5, succ(succ(tptp_minus_1)))))))), rewrite(((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(37,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_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)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.50 tff(38,plain,
% 0.18/0.50 (^[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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(39,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.50 tff(40,plain,
% 0.18/0.50 (^[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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(41,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.50 tff(42,plain,
% 0.18/0.50 (^[A: $i, B: $i] : rewrite(((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(43,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.50 tff(44,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use))) <=> ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(45,plain,
% 0.18/0.50 ((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, minus(n999, n1)) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.18/0.50 inference(or_elim,[status(thm)],[14])).
% 0.18/0.50 tff(46,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.18/0.50 inference(and_elim,[status(thm)],[45])).
% 0.18/0.50 tff(47,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, minus(pv5, n1)))) | ((a_select3(u_defuse, A, B) = use) & (a_select3(z_defuse, A, B) = use)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.18/0.50 tff(48,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.50 tff(49,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.18/0.50 tff(50,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.18/0.50 tff(51,plain,(
% 0.18/0.50 ![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, minus(pv5, succ(succ(tptp_minus_1)))))) | ((a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[50])).
% 0.18/0.50 tff(52,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[51, 37])).
% 0.18/0.50 tff(53,plain,
% 0.18/0.50 (![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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[52, 35])).
% 0.18/0.50 tff(54,plain,
% 0.18/0.50 (((~![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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))) | ((~leq(succ(tptp_minus_1), C!14)) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(C!14, succ(succ(succ(tptp_minus_1))))) | (~leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), 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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))) | (~leq(succ(tptp_minus_1), C!14)) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(C!14, succ(succ(succ(tptp_minus_1))))) | (~leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(55,plain,
% 0.18/0.50 ((~![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, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))) | ((~leq(succ(tptp_minus_1), C!14)) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(C!14, succ(succ(succ(tptp_minus_1))))) | (~leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(56,plain,
% 0.18/0.50 ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))) | (~leq(succ(tptp_minus_1), C!14)) | (~leq(succ(tptp_minus_1), D!13)) | (~leq(C!14, succ(succ(succ(tptp_minus_1))))) | (~leq(D!13, minus(pv5, succ(succ(tptp_minus_1))))) | (~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[56, 53, 33, 32, 31, 30, 1])).
% 0.18/0.51 tff(58,plain,(~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(59,plain,
% 0.18/0.51 (((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) | (a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 (a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 (((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) | (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(62,plain,
% 0.18/0.51 (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 ((~(~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))) <=> ((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (((a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> (~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 ((~((a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~(~((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[64])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 ((~((a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> ((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[65, 63])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (~((a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) & (a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.18/0.51 inference(or_elim,[status(thm)],[28])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 ((~(a_select3(u_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) | (~(a_select3(z_defuse, C!14, D!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[68, 62, 60])).
% 0.18/0.51 % SZS output end Proof
%------------------------------------------------------------------------------