TSTP Solution File: SWV196+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV196+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:20 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV196+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n019.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 01:46:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -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(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(pv5_type, type, (
% 0.19/0.44 pv5: $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(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(tptp_fun_E_14_type, type, (
% 0.19/0.44 tptp_fun_E_14: $i)).
% 0.19/0.44 tff(a_select3_type, type, (
% 0.19/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(u_defuse_type, type, (
% 0.19/0.44 u_defuse: $i)).
% 0.19/0.44 tff(z_defuse_type, type, (
% 0.19/0.44 z_defuse: $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(n0_type, type, (
% 0.19/0.44 n0: $i)).
% 0.19/0.44 tff(n1_type, type, (
% 0.19/0.44 n1: $i)).
% 0.19/0.44 tff(use_type, type, (
% 0.19/0.44 use: $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 ((~((~((~((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))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~((~((~((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))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = 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] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_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] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_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(4,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 ((~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))) <=> (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 ((~((((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_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(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(10,axiom,(~((((((((((((((((((((((((((((((((((a_select2(rho_defuse, n0) = use) & (a_select2(rho_defuse, n1) = use)) & (a_select2(rho_defuse, n2) = use)) & (a_select2(sigma_defuse, n0) = use)) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(xinit_mean_defuse, n0) = use)) & (a_select2(xinit_mean_defuse, n1) = use)) & (a_select2(xinit_mean_defuse, n2) = use)) & (a_select2(xinit_mean_defuse, n3) = use)) & (a_select2(xinit_mean_defuse, n4) = use)) & (a_select2(xinit_mean_defuse, n5) = use)) & (a_select2(xinit_noise_defuse, n0) = use)) & (a_select2(xinit_noise_defuse, n1) = use)) & (a_select2(xinit_noise_defuse, n2) = use)) & (a_select2(xinit_noise_defuse, n3) = use)) & (a_select2(xinit_noise_defuse, n4) = use)) & (a_select2(xinit_noise_defuse, n5) = use)) & leq(n0, pv5)) & leq(pv5, n0)) & leq(pv5, n998)) & gt(pv5, n0)) & ![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n2)) & leq(B, pred(pv5))) => (a_select3(u_defuse, A, B) = use))) & ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, pred(pv5))) => (a_select3(z_defuse, C, D) = use))) => ![E: $i, F: $i] : ((((leq(n0, E) & leq(n0, F)) & leq(E, n2)) & leq(F, pv5)) => ((((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F)))) & (~((n2 = E) & (pv5 = F)))) => (a_select3(z_defuse, E, F) = use))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quaternion_ds1_inuse_0007')).
% 0.19/0.45 tff(11,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(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.45 inference(or_elim,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = use) | (~((~((n0 = E) & (pv5 = F))) & (~((n1 = E) & (pv5 = F))) & (~((n2 = E) & (pv5 = F))))) | (~(leq(n0, E) & leq(n0, F) & leq(E, n2) & leq(F, pv5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((a_select3(z_defuse, E, F) = a_select2(rho_defuse, succ(tptp_minus_1))) | (~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_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, 3])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_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, 2])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_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, 2])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (~![E: $i, F: $i] : ((~((~((succ(tptp_minus_1) = E) & (pv5 = F))) & (~((succ(succ(tptp_minus_1)) = E) & (pv5 = F))) & (~((succ(succ(succ(tptp_minus_1))) = E) & (pv5 = F))))) | (~(leq(succ(tptp_minus_1), E) & leq(succ(tptp_minus_1), F) & leq(E, succ(succ(succ(tptp_minus_1)))) & leq(F, pv5))) | (a_select3(z_defuse, E, F) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 2])).
% 0.19/0.45 tff(24,plain,(
% 0.19/0.45 ~((~((~((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))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_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)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (~((~((~((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))))) | (~(leq(succ(tptp_minus_1), E!14) & leq(succ(tptp_minus_1), F!13) & leq(E!14, succ(succ(succ(tptp_minus_1)))) & leq(F!13, pv5))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 1])).
% 0.19/0.45 tff(26,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, pv5)),
% 0.19/0.45 inference(or_elim,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (leq(F!13, pv5)),
% 0.19/0.45 inference(and_elim,[status(thm)],[26])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (leq(pv5, n0) <=> leq(pv5, succ(tptp_minus_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (leq(pv5, n0) <=> leq(pv5, n0)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(30,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))),
% 0.19/0.45 inference(or_elim,[status(thm)],[11])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (leq(pv5, n0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[30])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (leq(pv5, n0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (leq(pv5, succ(tptp_minus_1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.45 tff(40,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','transitivity_leq')).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.45 tff(43,plain,(
% 0.19/0.45 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.19/0.45 inference(skolemize,[status(sab)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 ((leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5))) <=> ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(F!13, succ(tptp_minus_1)) | (~leq(pv5, succ(tptp_minus_1))) | (~leq(F!13, pv5)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(pv5, succ(tptp_minus_1))) | leq(F!13, succ(tptp_minus_1)) | (~leq(F!13, pv5))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (leq(F!13, succ(tptp_minus_1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[51, 45, 33, 27])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (leq(succ(tptp_minus_1), F!13)),
% 0.19/0.46 inference(and_elim,[status(thm)],[26])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (^[X: $i] : refl(((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1))) <=> (~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> (~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> (((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))), rewrite((((~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))), (((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))) <=> ![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (^[X: $i] : rewrite(((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (^[X: $i] : rewrite(((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ((~(leq(n0, X) & leq(X, n0))) | (X = n0)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0)) <=> ![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.46 tff(63,axiom,(![X: $i] : ((leq(n0, X) & leq(X, n0)) => (X = n0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','finite_domain_0')).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(n0, X) & leq(X, n0))) | (X = n0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.19/0.46 tff(67,plain,(
% 0.19/0.46 ![X: $i] : ((~(leq(succ(tptp_minus_1), X) & leq(X, succ(tptp_minus_1)))) | (X = succ(tptp_minus_1)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[66])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[68, 55])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))) <=> ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[72, 70])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | ((F!13 = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(F!13, succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 ((~![X: $i] : ((X = succ(tptp_minus_1)) | (~leq(succ(tptp_minus_1), X)) | (~leq(X, succ(tptp_minus_1))))) | (~leq(succ(tptp_minus_1), F!13)) | (F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((F!13 = succ(tptp_minus_1)) | (~leq(F!13, succ(tptp_minus_1)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[75, 69, 53])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (F!13 = succ(tptp_minus_1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 52])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (leq(F!13, pred(pv5)) <=> leq(succ(tptp_minus_1), pred(pv5))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (leq(succ(tptp_minus_1), pred(pv5)) <=> leq(F!13, pred(pv5))),
% 0.19/0.46 inference(symmetry,[status(thm)],[78])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (^[X: $i, Y: $i] : refl((leq(X, pred(Y)) <=> gt(Y, X)) <=> (leq(X, pred(Y)) <=> gt(Y, X)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X)) <=> ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(83,axiom,(![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax','leq_gt_pred')).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.46 tff(85,plain,(
% 0.19/0.46 ![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.46 inference(skolemize,[status(sab)],[84])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : (leq(X, pred(Y)) <=> gt(Y, X))) | (leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (gt(pv5, n0) <=> gt(pv5, succ(tptp_minus_1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (gt(pv5, n0) <=> gt(pv5, n0)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (gt(pv5, n0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[30])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (gt(pv5, n0)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (gt(pv5, succ(tptp_minus_1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 ((~(leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(pv5)) | (~gt(pv5, succ(tptp_minus_1)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~(leq(succ(tptp_minus_1), pred(pv5)) <=> gt(pv5, succ(tptp_minus_1)))) | leq(succ(tptp_minus_1), pred(pv5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (leq(succ(tptp_minus_1), pred(pv5))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[95, 88])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (leq(F!13, pred(pv5))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 79])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (~(a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[25])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (leq(E!14, succ(succ(succ(tptp_minus_1))))),
% 0.19/0.46 inference(and_elim,[status(thm)],[26])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (leq(succ(tptp_minus_1), E!14)),
% 0.19/0.46 inference(and_elim,[status(thm)],[26])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (^[C: $i, D: $i] : refl(((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) <=> ![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5))) <=> (~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) <=> (~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))))), rewrite((~(~((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))), ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) <=> ((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> (((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))))), rewrite((((~leq(succ(tptp_minus_1), C)) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))), (((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1)))) <=> ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (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)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (^[C: $i, D: $i] : rewrite(((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = 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(106,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (^[C: $i, D: $i] : rewrite(((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.46 tff(109,plain,
% 0.19/0.46 (^[C: $i, D: $i] : rewrite(((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = use)) <=> ((~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 (![C: $i, D: $i] : ((~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, pred(pv5)))) | (a_select3(z_defuse, C, D) = 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(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (![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(and_elim,[status(thm)],[30])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (![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(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(rho_defuse, succ(tptp_minus_1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select2(sigma_defuse, succ(tptp_minus_1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[114, 108])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 (![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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[115, 106])).
% 0.19/0.46 tff(117,plain,(
% 0.19/0.46 ![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, pred(pv5)))) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[116])).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[117, 104])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[118, 102])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((a_select3(z_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))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_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(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_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(z_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(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_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))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((a_select3(z_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)],[121])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_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))))) <=> ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_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)],[122, 120])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | ((~leq(succ(tptp_minus_1), E!14)) | (a_select3(z_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(125,plain,
% 0.19/0.47 ((~![C: $i, D: $i] : ((~leq(succ(tptp_minus_1), C)) | (a_select3(z_defuse, C, D) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), D)) | (~leq(C, succ(succ(succ(tptp_minus_1))))) | (~leq(D, pred(pv5))))) | (a_select3(z_defuse, E!14, F!13) = a_select3(u_defuse, succ(tptp_minus_1), succ(tptp_minus_1))) | (~leq(succ(tptp_minus_1), E!14)) | (~leq(succ(tptp_minus_1), F!13)) | (~leq(E!14, succ(succ(succ(tptp_minus_1))))) | (~leq(F!13, pred(pv5)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 (~leq(F!13, pred(pv5))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[125, 119, 100, 53, 99, 98])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 97])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------