TSTP Solution File: SWV192+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV192+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:19 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV192+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 01:43:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(a_select3_type, type, (
% 0.19/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(succ_type, type, (
% 0.19/0.44 succ: $i > $i)).
% 0.19/0.44 tff(tptp_minus_1_type, type, (
% 0.19/0.44 tptp_minus_1: $i)).
% 0.19/0.44 tff(u_defuse_type, type, (
% 0.19/0.44 u_defuse: $i)).
% 0.19/0.44 tff(tptp_fun_F_13_type, type, (
% 0.19/0.44 tptp_fun_F_13: $i)).
% 0.19/0.44 tff(tptp_fun_E_14_type, type, (
% 0.19/0.44 tptp_fun_E_14: $i)).
% 0.19/0.44 tff(pv5_type, type, (
% 0.19/0.44 pv5: $i)).
% 0.19/0.44 tff(leq_type, type, (
% 0.19/0.44 leq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(pred_type, type, (
% 0.19/0.44 pred: $i > $i)).
% 0.19/0.44 tff(a_select2_type, type, (
% 0.19/0.44 a_select2: ( $i * $i ) > $i)).
% 0.19/0.44 tff(sigma_defuse_type, type, (
% 0.19/0.44 sigma_defuse: $i)).
% 0.19/0.44 tff(rho_defuse_type, type, (
% 0.19/0.44 rho_defuse: $i)).
% 0.19/0.44 tff(n2_type, type, (
% 0.19/0.44 n2: $i)).
% 0.19/0.44 tff(n1_type, type, (
% 0.19/0.44 n1: $i)).
% 0.19/0.44 tff(n0_type, type, (
% 0.19/0.44 n0: $i)).
% 0.19/0.44 tff(use_type, type, (
% 0.19/0.44 use: $i)).
% 0.19/0.44 tff(z_defuse_type, type, (
% 0.19/0.44 z_defuse: $i)).
% 0.19/0.44 tff(gt_type, type, (
% 0.19/0.44 gt: ( $i * $i ) > $o)).
% 0.19/0.44 tff(n998_type, type, (
% 0.19/0.44 n998: $i)).
% 0.19/0.44 tff(n5_type, type, (
% 0.19/0.44 n5: $i)).
% 0.19/0.44 tff(xinit_noise_defuse_type, type, (
% 0.19/0.44 xinit_noise_defuse: $i)).
% 0.19/0.44 tff(n4_type, type, (
% 0.19/0.44 n4: $i)).
% 0.19/0.44 tff(n3_type, type, (
% 0.19/0.44 n3: $i)).
% 0.19/0.44 tff(xinit_mean_defuse_type, type, (
% 0.19/0.44 xinit_mean_defuse: $i)).
% 0.19/0.44 tff(xinit_defuse_type, type, (
% 0.19/0.44 xinit_defuse: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))))) <=> (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 ((~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))))) <=> (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 ((~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))) <=> (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 ((~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))) <=> (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~((((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pred(pv5))) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(u_defuse, E, F) = use))))) <=> (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(9,axiom,(~((((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pred(pv5))) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(u_defuse, E, F) = use))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0003')).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (~((~((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)))) | ![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.19/0.45 inference(or_elim,[status(thm)],[10])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = use) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pred(pv5)))) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(u_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[19, 1])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[20, 1])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~![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, pred(pv5)))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (a_select3(u_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 1])).
% 0.19/0.45 tff(23,plain,(
% 0.19/0.45 ~((~(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)))) | (~((~((succ(tptp_minus_1) = E!14) & (pv5 = F!13))) & (~((succ(succ(tptp_minus_1)) = E!14) & (pv5 = F!13))) & (~((succ(succ(succ(tptp_minus_1))) = E!14) & (pv5 = F!13))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[22])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (~(a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.19/0.45 inference(or_elim,[status(thm)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (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))),
% 0.19/0.45 inference(or_elim,[status(thm)],[23])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (leq(F!13, pred(pv5))),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (leq(succ(tptp_minus_1), F!13)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (leq(succ(tptp_minus_1), E!14)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (^[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))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use) & (a_select2(rho_defuse, n2) = use) & (a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(xinit_mean_defuse, n0) = use) & (a_select2(xinit_mean_defuse, n1) = use) & (a_select2(xinit_mean_defuse, n2) = use) & (a_select2(xinit_mean_defuse, n3) = use) & (a_select2(xinit_mean_defuse, n4) = use) & (a_select2(xinit_mean_defuse, n5) = use) & (a_select2(xinit_noise_defuse, n0) = use) & (a_select2(xinit_noise_defuse, n1) = use) & (a_select2(xinit_noise_defuse, n2) = use) & (a_select2(xinit_noise_defuse, n3) = use) & (a_select2(xinit_noise_defuse, n4) = use) & (a_select2(xinit_noise_defuse, n5) = use) & leq(n0, pv5) & leq(pv5, n0) & leq(pv5, n998) & gt(pv5, n0) & ![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use)) & ![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use))),
% 0.19/0.46 inference(or_elim,[status(thm)],[10])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.19/0.46 inference(and_elim,[status(thm)],[41])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n2) & leq(B, pred(pv5)))) | (a_select3(u_defuse, A, B) = use))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.19/0.46 tff(47,plain,(
% 0.19/0.46 ![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))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[46])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[47, 33])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[48, 31])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 (((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (((~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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (((~![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)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : ((~leq(succ(tptp_minus_1), A)) | (a_select3(u_defuse, A, B) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), B)) | (~leq(A, succ(succ(succ(tptp_minus_1))))) | (~leq(B, pred(pv5))))) | (a_select3(u_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[55, 49, 29, 28, 27, 26, 24])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------