0.04/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.17 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.Wh3YmRGxx1 0.17/0.39 % Computer : n029.cluster.edu 0.17/0.39 % Model : x86_64 x86_64 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.39 % Memory : 8042.1875MB 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.39 % CPULimit : 1200 0.17/0.39 % DateTime : Tue Jul 13 12:41:55 EDT 2021 0.17/0.39 % CPUTime : 0.17/0.39 % Running portfolio for 120 s 0.17/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.17/0.39 % Number of cores: 8 0.17/0.40 % Python version: Python 3.6.8 0.17/0.40 % Running in HO mode 0.58/0.71 % Estimated wc time : 1286 0.58/0.71 % Estimated cpu time (7 cpus) : 183.71428571428572 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.59/0.83 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.59/0.83 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.59/0.83 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 70.69/10.92 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 105.20/16.05 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.20/16.06 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 145.02/21.84 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 148.15/22.45 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 184.30/27.80 % /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s 186.31/28.18 % /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s 261.02/38.86 % /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s 287.15/42.72 % /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s 287.59/42.82 % /export/starexec/sandbox2/solver/bin/lams/c.preprocess2.sh running for 21s 317.87/47.20 % /export/starexec/sandbox2/solver/bin/lams/sh.or.sh running for 26s 366.21/54.21 % /export/starexec/sandbox2/solver/bin/lams/new.cs3.comb.sh running for 18s 389.33/58.08 % /export/starexec/sandbox2/solver/bin/lams/old_b2.sh running for 31s 389.33/58.09 % /export/starexec/sandbox2/solver/bin/lams/sp5.sh running for 36s 432.03/64.36 % /export/starexec/sandbox2/solver/bin/lams/b2.sh running for 15s 474.80/70.78 % /export/starexec/sandbox2/solver/bin/lams/b.lcnf.od.sh running for 26s 483.58/72.03 % Solved by lams/b.lcnf.od.sh. 483.58/72.03 % done 1905 iterations in 1.144s 483.58/72.03 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 483.58/72.03 % SZS output start Refutation 483.58/72.03 tff(mor, axiom, mor() = 483.58/72.03 ^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))). 483.58/72.03 tff('0', plain, 483.58/72.03 mor = (^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mor])). 483.58/72.03 tff('1', plain, 483.58/72.03 mor = (^[V_1:(($i > $o)),V_2:(($i > $o)),V_3]: (V_1(V_3) | V_2(V_3))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mimplies, axiom, mimplies() = 483.58/72.03 ^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)). 483.58/72.03 tff('2', plain, 483.58/72.03 mimplies = (^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mimplies])). 483.58/72.03 tff('3', plain, 483.58/72.03 mimplies = (^[V_1:(($i > $o)),V_2:(($i > $o))]: mor(mnot(V_1),V_2)), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mand, axiom, mand() = 483.58/72.03 ^[Phi:(($i > $o)),Psi:(($i > $o))]: mnot(mor(mnot(Phi),mnot(Psi)))). 483.58/72.03 tff('4', plain, 483.58/72.03 mand = 483.58/72.03 (^[Phi:(($i > $o)),Psi:(($i > $o))]: mnot(mor(mnot(Phi),mnot(Psi)))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mand])). 483.58/72.03 tff('5', plain, 483.58/72.03 mand = 483.58/72.03 (^[V_1:(($i > $o)),V_2:(($i > $o))]: mnot(mor(mnot(V_1),mnot(V_2)))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mforall_ind, axiom, mforall_ind() = 483.58/72.03 ^[Phi:((mu * $i) > $o),W]: (![X:mu]: (exists_in_world(X,W) => Phi(X,W)))). 483.58/72.03 tff('6', plain, 483.58/72.03 mforall_ind = 483.58/72.03 (^[Phi:((mu * $i) > $o),W]: (![X:mu]: (exists_in_world(X,W) => Phi(X,W)))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 483.58/72.03 tff('7', plain, 483.58/72.03 mforall_ind = 483.58/72.03 (^[V_1:((mu * $i) > $o),V_2]: 483.58/72.03 (![X4:mu]: (exists_in_world(X4,V_2) => V_1(X4,V_2)))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mvalid, axiom, mvalid() = ^[Phi:(($i > $o))]: (![W]: Phi(W))). 483.58/72.03 tff('8', plain, mvalid = (^[Phi:(($i > $o))]: (![W]: Phi(W))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mvalid])). 483.58/72.03 tff('9', plain, mvalid = (^[V_1:(($i > $o))]: (![X4]: V_1(X4))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mbox_s4, axiom, mbox_s4() = 483.58/72.03 ^[Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~rel_s4(W,V))))). 483.58/72.03 tff('10', plain, 483.58/72.03 mbox_s4 = (^[Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~rel_s4(W,V))))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 483.58/72.03 tff('11', plain, 483.58/72.03 mbox_s4 = 483.58/72.03 (^[V_1:(($i > $o)),V_2]: (![X4]: (V_1(X4) | (~rel_s4(V_2,X4))))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(mnot, axiom, mnot() = ^[Phi:(($i > $o)),W]: (~Phi(W))). 483.58/72.03 tff('12', plain, mnot = (^[Phi:(($i > $o)),W]: (~Phi(W))), 483.58/72.03 inference('simplify_rw_rule', [status(thm)], [mnot])). 483.58/72.03 tff('13', plain, mnot = (^[V_1:(($i > $o)),V_2]: (~V_1(V_2))), 483.58/72.03 define([status(thm)])). 483.58/72.03 tff(quaternion_ds1_inuse_0009, conjecture, 483.58/72.03 (mvalid(mbox_s4(mimplies(mand(mbox_s4(qmltpeq(a_select2(rho_defuse,n0),use)), 483.58/72.03 mand(mbox_s4(qmltpeq(a_select2(rho_defuse,n1), 483.58/72.03 use)), 483.58/72.03 mand(mbox_s4(qmltpeq(a_select2(rho_defuse, 483.58/72.03 n2), 483.58/72.03 use)), 483.58/72.03 mand(mbox_s4(qmltpeq(a_select2( 483.58/72.03 sigma_defuse, 483.58/72.03 n0),use)), 483.58/72.03 mand(mbox_s4(qmltpeq(a_select2( 483.58/72.03 sigma_defuse, 483.58/72.03 n1),use)), 483.58/72.03 mand(mbox_s4(qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 sigma_defuse, 483.58/72.03 n2),use)), 483.58/72.03 mand(mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 sigma_defuse,n3), 483.58/72.03 use)), 483.58/72.03 mand(mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 sigma_defuse, 483.58/72.03 n4),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 sigma_defuse, 483.58/72.03 n5),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select3( 483.58/72.03 u_defuse, 483.58/72.03 n0,n0),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select3( 483.58/72.03 u_defuse, 483.58/72.03 n1,n0),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select3( 483.58/72.03 u_defuse, 483.58/72.03 n2,n0),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 xinit_defuse, 483.58/72.03 n3),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 xinit_defuse, 483.58/72.03 n4),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 xinit_defuse, 483.58/72.03 n5),use)), 483.58/72.03 mand( 483.58/72.03 mbox_s4( 483.58/72.03 qmltpeq( 483.58/72.03 a_select2( 483.58/72.03 xinit_mean_defuse, 483.58/72.04 n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n1),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n2),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n3),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n1),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n2),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n3),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 n0,pv5)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 pv5, 483.58/72.04 minus( 483.58/72.04 n999,n1))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[A:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[B:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mimplies( 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,A)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,B)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(A,n2)), 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 B,pv5))))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 A,B),use)), 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 A,B),use))))))))), 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[C:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[D:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mimplies( 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,C)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,D)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(C,n2)), 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 D, 483.58/72.04 minus( 483.58/72.04 pv5,n1)))))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 C,D),use)), 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 C,D),use))))))))))))))))))))))))))))))))))))))), 483.58/72.04 mand(mbox_s4(qmltpeq(a_select2(rho_defuse,n0),use)), 483.58/72.04 mand(mbox_s4(qmltpeq(a_select2(rho_defuse,n1), 483.58/72.04 use)), 483.58/72.04 mand(mbox_s4(qmltpeq(a_select2(rho_defuse, 483.58/72.04 n2), 483.58/72.04 use)), 483.58/72.04 mand(mbox_s4(qmltpeq(a_select2( 483.58/72.04 sigma_defuse, 483.58/72.04 n0),use)), 483.58/72.04 mand(mbox_s4(qmltpeq(a_select2( 483.58/72.04 sigma_defuse, 483.58/72.04 n1),use)), 483.58/72.04 mand(mbox_s4(qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 sigma_defuse, 483.58/72.04 n2),use)), 483.58/72.04 mand(mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 sigma_defuse,n3), 483.58/72.04 use)), 483.58/72.04 mand(mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 sigma_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 sigma_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 n0,n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 n1,n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 n2,n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_defuse, 483.58/72.04 n3),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n1),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n2),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n3),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_mean_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n0),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n1),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n2),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n3),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n4),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select2( 483.58/72.04 xinit_noise_defuse, 483.58/72.04 n5),use)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 n0,pv5)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 pv5, 483.58/72.04 minus( 483.58/72.04 n999,n1))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[E:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[F:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mimplies( 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,E)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,F)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(E,n2)), 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 F,pv5))))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 E,F),use)), 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 E,F),use))))))))), 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[G:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mforall_ind( 483.58/72.04 ^[H:mu]: 483.58/72.04 mbox_s4( 483.58/72.04 mimplies( 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,G)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(n0,H)), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 leq(G,n2)), 483.58/72.04 mbox_s4( 483.58/72.04 leq( 483.58/72.04 H, 483.58/72.04 minus( 483.58/72.04 pv5,n1)))))), 483.58/72.04 mand( 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 G,H),use)), 483.58/72.04 mbox_s4( 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 G,H),use)))))))))))))))))))))))))))))))))))))))))))). 483.58/72.04 tff(zf_stmt_0, conjecture, 483.58/72.04 (![X4,X6]: 483.58/72.04 ((~rel_s4(X4,X6)) | 483.58/72.04 (~ 483.58/72.04 (![X10]: 483.58/72.04 ((~rel_s4(X6,X10)) | qmltpeq(a_select2(rho_defuse,n1),use,X10)))) | 483.58/72.04 (~ 483.58/72.04 (![X14]: 483.58/72.04 ((~rel_s4(X6,X14)) | qmltpeq(a_select2(sigma_defuse,n0),use,X14)))) | 483.58/72.04 (~ 483.58/72.04 (![X18]: 483.58/72.04 ((~rel_s4(X6,X18)) | qmltpeq(a_select2(sigma_defuse,n2),use,X18)))) | 483.58/72.04 (~ 483.58/72.04 (![X22]: 483.58/72.04 ((~rel_s4(X6,X22)) | qmltpeq(a_select2(sigma_defuse,n4),use,X22)))) | 483.58/72.04 (~ 483.58/72.04 (![X26]: 483.58/72.04 ((~rel_s4(X6,X26)) | qmltpeq(a_select3(u_defuse,n0,n0),use,X26)))) | 483.58/72.04 (~ 483.58/72.04 (![X30]: 483.58/72.04 ((~rel_s4(X6,X30)) | qmltpeq(a_select3(u_defuse,n2,n0),use,X30)))) | 483.58/72.04 (~ 483.58/72.04 (![X34]: 483.58/72.04 ((~rel_s4(X6,X34)) | qmltpeq(a_select2(xinit_defuse,n4),use,X34)))) | 483.58/72.04 (~ 483.58/72.04 (![X38]: 483.58/72.04 ((~rel_s4(X6,X38)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n0),use,X38)))) | 483.58/72.04 (~ 483.58/72.04 (![X42]: 483.58/72.04 ((~rel_s4(X6,X42)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n2),use,X42)))) | 483.58/72.04 (~ 483.58/72.04 (![X46]: 483.58/72.04 ((~rel_s4(X6,X46)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n4),use,X46)))) | 483.58/72.04 (~ 483.58/72.04 (![X50]: 483.58/72.04 ((~rel_s4(X6,X50)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n0),use,X50)))) | 483.58/72.04 (~ 483.58/72.04 (![X54]: 483.58/72.04 ((~rel_s4(X6,X54)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n2),use,X54)))) | 483.58/72.04 (~ 483.58/72.04 (![X58]: 483.58/72.04 ((~rel_s4(X6,X58)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n4),use,X58)))) | 483.58/72.04 (~(![X62]: ((~rel_s4(X6,X62)) | leq(n0,pv5,X62)))) | 483.58/72.04 (~ 483.58/72.04 (![X66]: 483.58/72.04 ((~rel_s4(X6,X66)) | 483.58/72.04 (![X68:mu]: 483.58/72.04 (exists_in_world(X68,X66) => 483.58/72.04 (![X70]: 483.58/72.04 ((~rel_s4(X66,X70)) | 483.58/72.04 (![X72:mu]: 483.58/72.04 (exists_in_world(X72,X70) => 483.58/72.04 (![X74]: 483.58/72.04 ((~rel_s4(X70,X74)) | 483.58/72.04 (~ 483.58/72.04 (![X78]: ((~rel_s4(X74,X78)) | leq(n0,X72,X78)))) | 483.58/72.04 (~ 483.58/72.04 (![X82]: 483.58/72.04 ((~rel_s4(X74,X82)) | leq(X72,pv5,X82)))) | 483.58/72.04 (~ 483.58/72.04 (![X80]: ((~rel_s4(X74,X80)) | leq(X68,n2,X80)))) | 483.58/72.04 (~ 483.58/72.04 (![X76]: ((~rel_s4(X74,X76)) | leq(n0,X68,X76)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X86]: 483.58/72.04 ((~rel_s4(X74,X86)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X68,X72),use, 483.58/72.04 X86)))) | 483.58/72.04 (~ 483.58/72.04 (![X84]: 483.58/72.04 ((~rel_s4(X74,X84)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X68,X72),use, 483.58/72.04 X84))))))))))))))))) | 483.58/72.04 (~ 483.58/72.04 (![X88]: 483.58/72.04 ((~rel_s4(X6,X88)) | 483.58/72.04 (![X90:mu]: 483.58/72.04 (exists_in_world(X90,X88) => 483.58/72.04 (![X92]: 483.58/72.04 ((~rel_s4(X88,X92)) | 483.58/72.04 (![X94:mu]: 483.58/72.04 (exists_in_world(X94,X92) => 483.58/72.04 (![X96]: 483.58/72.04 ((~rel_s4(X92,X96)) | 483.58/72.04 (~ 483.58/72.04 (![X100]: 483.58/72.04 ((~rel_s4(X96,X100)) | leq(n0,X94,X100)))) | 483.58/72.04 (~ 483.58/72.04 (![X104]: 483.58/72.04 ((~rel_s4(X96,X104)) | 483.58/72.04 leq(X94,minus(pv5,n1),X104)))) | 483.58/72.04 (~ 483.58/72.04 (![X102]: 483.58/72.04 ((~rel_s4(X96,X102)) | leq(X90,n2,X102)))) | 483.58/72.04 (~ 483.58/72.04 (![X98]: ((~rel_s4(X96,X98)) | leq(n0,X90,X98)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X108]: 483.58/72.04 ((~rel_s4(X96,X108)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X90,X94),use, 483.58/72.04 X108)))) | 483.58/72.04 (~ 483.58/72.04 (![X106]: 483.58/72.04 ((~rel_s4(X96,X106)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X90,X94),use, 483.58/72.04 X106))))))))))))))))) | 483.58/72.04 (~(![X64]: ((~rel_s4(X6,X64)) | leq(pv5,minus(n999,n1),X64)))) | 483.58/72.04 (~ 483.58/72.04 (![X60]: 483.58/72.04 ((~rel_s4(X6,X60)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n5),use,X60)))) | 483.58/72.04 (~ 483.58/72.04 (![X56]: 483.58/72.04 ((~rel_s4(X6,X56)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n3),use,X56)))) | 483.58/72.04 (~ 483.58/72.04 (![X52]: 483.58/72.04 ((~rel_s4(X6,X52)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n1),use,X52)))) | 483.58/72.04 (~ 483.58/72.04 (![X48]: 483.58/72.04 ((~rel_s4(X6,X48)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n5),use,X48)))) | 483.58/72.04 (~ 483.58/72.04 (![X44]: 483.58/72.04 ((~rel_s4(X6,X44)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n3),use,X44)))) | 483.58/72.04 (~ 483.58/72.04 (![X40]: 483.58/72.04 ((~rel_s4(X6,X40)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n1),use,X40)))) | 483.58/72.04 (~ 483.58/72.04 (![X36]: 483.58/72.04 ((~rel_s4(X6,X36)) | qmltpeq(a_select2(xinit_defuse,n5),use,X36)))) | 483.58/72.04 (~ 483.58/72.04 (![X32]: 483.58/72.04 ((~rel_s4(X6,X32)) | qmltpeq(a_select2(xinit_defuse,n3),use,X32)))) | 483.58/72.04 (~ 483.58/72.04 (![X28]: 483.58/72.04 ((~rel_s4(X6,X28)) | qmltpeq(a_select3(u_defuse,n1,n0),use,X28)))) | 483.58/72.04 (~ 483.58/72.04 (![X24]: 483.58/72.04 ((~rel_s4(X6,X24)) | qmltpeq(a_select2(sigma_defuse,n5),use,X24)))) | 483.58/72.04 (~ 483.58/72.04 (![X20]: 483.58/72.04 ((~rel_s4(X6,X20)) | qmltpeq(a_select2(sigma_defuse,n3),use,X20)))) | 483.58/72.04 (~ 483.58/72.04 (![X16]: 483.58/72.04 ((~rel_s4(X6,X16)) | qmltpeq(a_select2(sigma_defuse,n1),use,X16)))) | 483.58/72.04 (~ 483.58/72.04 (![X12]: 483.58/72.04 ((~rel_s4(X6,X12)) | qmltpeq(a_select2(rho_defuse,n2),use,X12)))) | 483.58/72.04 (~ 483.58/72.04 (![X8]: ((~rel_s4(X6,X8)) | qmltpeq(a_select2(rho_defuse,n0),use,X8)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X112]: 483.58/72.04 ((~rel_s4(X6,X112)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n1),use,X112)))) | 483.58/72.04 (~ 483.58/72.04 (![X116]: 483.58/72.04 ((~rel_s4(X6,X116)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n0),use,X116)))) | 483.58/72.04 (~ 483.58/72.04 (![X120]: 483.58/72.04 ((~rel_s4(X6,X120)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n2),use,X120)))) | 483.58/72.04 (~ 483.58/72.04 (![X124]: 483.58/72.04 ((~rel_s4(X6,X124)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n4),use,X124)))) | 483.58/72.04 (~ 483.58/72.04 (![X128]: 483.58/72.04 ((~rel_s4(X6,X128)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n0,n0),use,X128)))) | 483.58/72.04 (~ 483.58/72.04 (![X132]: 483.58/72.04 ((~rel_s4(X6,X132)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n2,n0),use,X132)))) | 483.58/72.04 (~ 483.58/72.04 (![X136]: 483.58/72.04 ((~rel_s4(X6,X136)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n4),use,X136)))) | 483.58/72.04 (~ 483.58/72.04 (![X140]: 483.58/72.04 ((~rel_s4(X6,X140)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n0),use,X140)))) | 483.58/72.04 (~ 483.58/72.04 (![X144]: 483.58/72.04 ((~rel_s4(X6,X144)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n2),use,X144)))) | 483.58/72.04 (~ 483.58/72.04 (![X148]: 483.58/72.04 ((~rel_s4(X6,X148)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n4),use,X148)))) | 483.58/72.04 (~ 483.58/72.04 (![X152]: 483.58/72.04 ((~rel_s4(X6,X152)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n0),use,X152)))) | 483.58/72.04 (~ 483.58/72.04 (![X156]: 483.58/72.04 ((~rel_s4(X6,X156)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n2),use,X156)))) | 483.58/72.04 (~ 483.58/72.04 (![X160]: 483.58/72.04 ((~rel_s4(X6,X160)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n4),use,X160)))) | 483.58/72.04 (~(![X164]: ((~rel_s4(X6,X164)) | leq(n0,pv5,X164)))) | 483.58/72.04 (~ 483.58/72.04 (![X168]: 483.58/72.04 ((~rel_s4(X6,X168)) | 483.58/72.04 (![X170:mu]: 483.58/72.04 (exists_in_world(X170,X168) => 483.58/72.04 (![X172]: 483.58/72.04 ((~rel_s4(X168,X172)) | 483.58/72.04 (![X174:mu]: 483.58/72.04 (exists_in_world(X174,X172) => 483.58/72.04 (![X176]: 483.58/72.04 ((~rel_s4(X172,X176)) | 483.58/72.04 (~ 483.58/72.04 (![X180]: 483.58/72.04 ((~rel_s4(X176,X180)) | leq(n0,X174,X180)))) | 483.58/72.04 (~ 483.58/72.04 (![X184]: 483.58/72.04 ((~rel_s4(X176,X184)) | 483.58/72.04 leq(X174,pv5,X184)))) | 483.58/72.04 (~ 483.58/72.04 (![X182]: 483.58/72.04 ((~rel_s4(X176,X182)) | leq(X170,n2,X182)))) | 483.58/72.04 (~ 483.58/72.04 (![X178]: 483.58/72.04 ((~rel_s4(X176,X178)) | leq(n0,X170,X178)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X188]: 483.58/72.04 ((~rel_s4(X176,X188)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X170,X174), 483.58/72.04 use,X188)))) | 483.58/72.04 (~ 483.58/72.04 (![X186]: 483.58/72.04 ((~rel_s4(X176,X186)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X170,X174), 483.58/72.04 use,X186))))))))))))))))) | 483.58/72.04 (~ 483.58/72.04 (![X190]: 483.58/72.04 ((~rel_s4(X6,X190)) | 483.58/72.04 (![X192:mu]: 483.58/72.04 (exists_in_world(X192,X190) => 483.58/72.04 (![X194]: 483.58/72.04 ((~rel_s4(X190,X194)) | 483.58/72.04 (![X196:mu]: 483.58/72.04 (exists_in_world(X196,X194) => 483.58/72.04 (![X198]: 483.58/72.04 ((~rel_s4(X194,X198)) | 483.58/72.04 (~ 483.58/72.04 (![X202]: 483.58/72.04 ((~rel_s4(X198,X202)) | leq(n0,X196,X202)))) | 483.58/72.04 (~ 483.58/72.04 (![X206]: 483.58/72.04 ((~rel_s4(X198,X206)) | 483.58/72.04 leq(X196,minus(pv5,n1),X206)))) | 483.58/72.04 (~ 483.58/72.04 (![X204]: 483.58/72.04 ((~rel_s4(X198,X204)) | leq(X192,n2,X204)))) | 483.58/72.04 (~ 483.58/72.04 (![X200]: 483.58/72.04 ((~rel_s4(X198,X200)) | leq(n0,X192,X200)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X210]: 483.58/72.04 ((~rel_s4(X198,X210)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X192,X196), 483.58/72.04 use,X210)))) | 483.58/72.04 (~ 483.58/72.04 (![X208]: 483.58/72.04 ((~rel_s4(X198,X208)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X192,X196), 483.58/72.04 use,X208))))))))))))))))) | 483.58/72.04 (~(![X166]: ((~rel_s4(X6,X166)) | leq(pv5,minus(n999,n1),X166)))) | 483.58/72.04 (~ 483.58/72.04 (![X162]: 483.58/72.04 ((~rel_s4(X6,X162)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n5),use,X162)))) | 483.58/72.04 (~ 483.58/72.04 (![X158]: 483.58/72.04 ((~rel_s4(X6,X158)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n3),use,X158)))) | 483.58/72.04 (~ 483.58/72.04 (![X154]: 483.58/72.04 ((~rel_s4(X6,X154)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n1),use,X154)))) | 483.58/72.04 (~ 483.58/72.04 (![X150]: 483.58/72.04 ((~rel_s4(X6,X150)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n5),use,X150)))) | 483.58/72.04 (~ 483.58/72.04 (![X146]: 483.58/72.04 ((~rel_s4(X6,X146)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n3),use,X146)))) | 483.58/72.04 (~ 483.58/72.04 (![X142]: 483.58/72.04 ((~rel_s4(X6,X142)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n1),use,X142)))) | 483.58/72.04 (~ 483.58/72.04 (![X138]: 483.58/72.04 ((~rel_s4(X6,X138)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n5),use,X138)))) | 483.58/72.04 (~ 483.58/72.04 (![X134]: 483.58/72.04 ((~rel_s4(X6,X134)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n3),use,X134)))) | 483.58/72.04 (~ 483.58/72.04 (![X130]: 483.58/72.04 ((~rel_s4(X6,X130)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n1,n0),use,X130)))) | 483.58/72.04 (~ 483.58/72.04 (![X126]: 483.58/72.04 ((~rel_s4(X6,X126)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n5),use,X126)))) | 483.58/72.04 (~ 483.58/72.04 (![X122]: 483.58/72.04 ((~rel_s4(X6,X122)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n3),use,X122)))) | 483.58/72.04 (~ 483.58/72.04 (![X118]: 483.58/72.04 ((~rel_s4(X6,X118)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n1),use,X118)))) | 483.58/72.04 (~ 483.58/72.04 (![X114]: 483.58/72.04 ((~rel_s4(X6,X114)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n2),use,X114)))) | 483.58/72.04 (~ 483.58/72.04 (![X110]: 483.58/72.04 ((~rel_s4(X6,X110)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n0),use,X110))))))))). 483.58/72.04 tff(zf_stmt_1, negated_conjecture, 483.58/72.04 (~ 483.58/72.04 (![X4,X6]: 483.58/72.04 ((~rel_s4(X4,X6)) | 483.58/72.04 (~ 483.58/72.04 (![X10]: 483.58/72.04 ((~rel_s4(X6,X10)) | qmltpeq(a_select2(rho_defuse,n1),use,X10)))) | 483.58/72.04 (~ 483.58/72.04 (![X14]: 483.58/72.04 ((~rel_s4(X6,X14)) | qmltpeq(a_select2(sigma_defuse,n0),use,X14)))) | 483.58/72.04 (~ 483.58/72.04 (![X18]: 483.58/72.04 ((~rel_s4(X6,X18)) | qmltpeq(a_select2(sigma_defuse,n2),use,X18)))) | 483.58/72.04 (~ 483.58/72.04 (![X22]: 483.58/72.04 ((~rel_s4(X6,X22)) | qmltpeq(a_select2(sigma_defuse,n4),use,X22)))) | 483.58/72.04 (~ 483.58/72.04 (![X26]: 483.58/72.04 ((~rel_s4(X6,X26)) | qmltpeq(a_select3(u_defuse,n0,n0),use,X26)))) | 483.58/72.04 (~ 483.58/72.04 (![X30]: 483.58/72.04 ((~rel_s4(X6,X30)) | qmltpeq(a_select3(u_defuse,n2,n0),use,X30)))) | 483.58/72.04 (~ 483.58/72.04 (![X34]: 483.58/72.04 ((~rel_s4(X6,X34)) | qmltpeq(a_select2(xinit_defuse,n4),use,X34)))) | 483.58/72.04 (~ 483.58/72.04 (![X38]: 483.58/72.04 ((~rel_s4(X6,X38)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n0),use,X38)))) | 483.58/72.04 (~ 483.58/72.04 (![X42]: 483.58/72.04 ((~rel_s4(X6,X42)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n2),use,X42)))) | 483.58/72.04 (~ 483.58/72.04 (![X46]: 483.58/72.04 ((~rel_s4(X6,X46)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n4),use,X46)))) | 483.58/72.04 (~ 483.58/72.04 (![X50]: 483.58/72.04 ((~rel_s4(X6,X50)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n0),use,X50)))) | 483.58/72.04 (~ 483.58/72.04 (![X54]: 483.58/72.04 ((~rel_s4(X6,X54)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n2),use,X54)))) | 483.58/72.04 (~ 483.58/72.04 (![X58]: 483.58/72.04 ((~rel_s4(X6,X58)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n4),use,X58)))) | 483.58/72.04 (~(![X62]: ((~rel_s4(X6,X62)) | leq(n0,pv5,X62)))) | 483.58/72.04 (~ 483.58/72.04 (![X66]: 483.58/72.04 ((~rel_s4(X6,X66)) | 483.58/72.04 (![X68:mu]: 483.58/72.04 (exists_in_world(X68,X66) => 483.58/72.04 (![X70]: 483.58/72.04 ((~rel_s4(X66,X70)) | 483.58/72.04 (![X72:mu]: 483.58/72.04 (exists_in_world(X72,X70) => 483.58/72.04 (![X74]: 483.58/72.04 ((~rel_s4(X70,X74)) | 483.58/72.04 (~ 483.58/72.04 (![X78]: 483.58/72.04 ((~rel_s4(X74,X78)) | leq(n0,X72,X78)))) | 483.58/72.04 (~ 483.58/72.04 (![X82]: 483.58/72.04 ((~rel_s4(X74,X82)) | leq(X72,pv5,X82)))) | 483.58/72.04 (~ 483.58/72.04 (![X80]: 483.58/72.04 ((~rel_s4(X74,X80)) | leq(X68,n2,X80)))) | 483.58/72.04 (~ 483.58/72.04 (![X76]: 483.58/72.04 ((~rel_s4(X74,X76)) | leq(n0,X68,X76)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X86]: 483.58/72.04 ((~rel_s4(X74,X86)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X68,X72), 483.58/72.04 use,X86)))) | 483.58/72.04 (~ 483.58/72.04 (![X84]: 483.58/72.04 ((~rel_s4(X74,X84)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X68,X72), 483.58/72.04 use,X84))))))))))))))))) | 483.58/72.04 (~ 483.58/72.04 (![X88]: 483.58/72.04 ((~rel_s4(X6,X88)) | 483.58/72.04 (![X90:mu]: 483.58/72.04 (exists_in_world(X90,X88) => 483.58/72.04 (![X92]: 483.58/72.04 ((~rel_s4(X88,X92)) | 483.58/72.04 (![X94:mu]: 483.58/72.04 (exists_in_world(X94,X92) => 483.58/72.04 (![X96]: 483.58/72.04 ((~rel_s4(X92,X96)) | 483.58/72.04 (~ 483.58/72.04 (![X100]: 483.58/72.04 ((~rel_s4(X96,X100)) | leq(n0,X94,X100)))) | 483.58/72.04 (~ 483.58/72.04 (![X104]: 483.58/72.04 ((~rel_s4(X96,X104)) | 483.58/72.04 leq(X94,minus(pv5,n1),X104)))) | 483.58/72.04 (~ 483.58/72.04 (![X102]: 483.58/72.04 ((~rel_s4(X96,X102)) | leq(X90,n2,X102)))) | 483.58/72.04 (~ 483.58/72.04 (![X98]: 483.58/72.04 ((~rel_s4(X96,X98)) | leq(n0,X90,X98)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X108]: 483.58/72.04 ((~rel_s4(X96,X108)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X90,X94), 483.58/72.04 use,X108)))) | 483.58/72.04 (~ 483.58/72.04 (![X106]: 483.58/72.04 ((~rel_s4(X96,X106)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X90,X94), 483.58/72.04 use,X106))))))))))))))))) | 483.58/72.04 (~(![X64]: ((~rel_s4(X6,X64)) | leq(pv5,minus(n999,n1),X64)))) | 483.58/72.04 (~ 483.58/72.04 (![X60]: 483.58/72.04 ((~rel_s4(X6,X60)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n5),use,X60)))) | 483.58/72.04 (~ 483.58/72.04 (![X56]: 483.58/72.04 ((~rel_s4(X6,X56)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n3),use,X56)))) | 483.58/72.04 (~ 483.58/72.04 (![X52]: 483.58/72.04 ((~rel_s4(X6,X52)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n1),use,X52)))) | 483.58/72.04 (~ 483.58/72.04 (![X48]: 483.58/72.04 ((~rel_s4(X6,X48)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n5),use,X48)))) | 483.58/72.04 (~ 483.58/72.04 (![X44]: 483.58/72.04 ((~rel_s4(X6,X44)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n3),use,X44)))) | 483.58/72.04 (~ 483.58/72.04 (![X40]: 483.58/72.04 ((~rel_s4(X6,X40)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n1),use,X40)))) | 483.58/72.04 (~ 483.58/72.04 (![X36]: 483.58/72.04 ((~rel_s4(X6,X36)) | qmltpeq(a_select2(xinit_defuse,n5),use,X36)))) | 483.58/72.04 (~ 483.58/72.04 (![X32]: 483.58/72.04 ((~rel_s4(X6,X32)) | qmltpeq(a_select2(xinit_defuse,n3),use,X32)))) | 483.58/72.04 (~ 483.58/72.04 (![X28]: 483.58/72.04 ((~rel_s4(X6,X28)) | qmltpeq(a_select3(u_defuse,n1,n0),use,X28)))) | 483.58/72.04 (~ 483.58/72.04 (![X24]: 483.58/72.04 ((~rel_s4(X6,X24)) | qmltpeq(a_select2(sigma_defuse,n5),use,X24)))) | 483.58/72.04 (~ 483.58/72.04 (![X20]: 483.58/72.04 ((~rel_s4(X6,X20)) | qmltpeq(a_select2(sigma_defuse,n3),use,X20)))) | 483.58/72.04 (~ 483.58/72.04 (![X16]: 483.58/72.04 ((~rel_s4(X6,X16)) | qmltpeq(a_select2(sigma_defuse,n1),use,X16)))) | 483.58/72.04 (~ 483.58/72.04 (![X12]: 483.58/72.04 ((~rel_s4(X6,X12)) | qmltpeq(a_select2(rho_defuse,n2),use,X12)))) | 483.58/72.04 (~ 483.58/72.04 (![X8]: 483.58/72.04 ((~rel_s4(X6,X8)) | qmltpeq(a_select2(rho_defuse,n0),use,X8)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X112]: 483.58/72.04 ((~rel_s4(X6,X112)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n1),use,X112)))) | 483.58/72.04 (~ 483.58/72.04 (![X116]: 483.58/72.04 ((~rel_s4(X6,X116)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n0),use,X116)))) | 483.58/72.04 (~ 483.58/72.04 (![X120]: 483.58/72.04 ((~rel_s4(X6,X120)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n2),use,X120)))) | 483.58/72.04 (~ 483.58/72.04 (![X124]: 483.58/72.04 ((~rel_s4(X6,X124)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n4),use,X124)))) | 483.58/72.04 (~ 483.58/72.04 (![X128]: 483.58/72.04 ((~rel_s4(X6,X128)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n0,n0),use,X128)))) | 483.58/72.04 (~ 483.58/72.04 (![X132]: 483.58/72.04 ((~rel_s4(X6,X132)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n2,n0),use,X132)))) | 483.58/72.04 (~ 483.58/72.04 (![X136]: 483.58/72.04 ((~rel_s4(X6,X136)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n4),use,X136)))) | 483.58/72.04 (~ 483.58/72.04 (![X140]: 483.58/72.04 ((~rel_s4(X6,X140)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n0),use,X140)))) | 483.58/72.04 (~ 483.58/72.04 (![X144]: 483.58/72.04 ((~rel_s4(X6,X144)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n2),use,X144)))) | 483.58/72.04 (~ 483.58/72.04 (![X148]: 483.58/72.04 ((~rel_s4(X6,X148)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n4),use,X148)))) | 483.58/72.04 (~ 483.58/72.04 (![X152]: 483.58/72.04 ((~rel_s4(X6,X152)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n0),use,X152)))) | 483.58/72.04 (~ 483.58/72.04 (![X156]: 483.58/72.04 ((~rel_s4(X6,X156)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n2),use,X156)))) | 483.58/72.04 (~ 483.58/72.04 (![X160]: 483.58/72.04 ((~rel_s4(X6,X160)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n4),use,X160)))) | 483.58/72.04 (~(![X164]: ((~rel_s4(X6,X164)) | leq(n0,pv5,X164)))) | 483.58/72.04 (~ 483.58/72.04 (![X168]: 483.58/72.04 ((~rel_s4(X6,X168)) | 483.58/72.04 (![X170:mu]: 483.58/72.04 (exists_in_world(X170,X168) => 483.58/72.04 (![X172]: 483.58/72.04 ((~rel_s4(X168,X172)) | 483.58/72.04 (![X174:mu]: 483.58/72.04 (exists_in_world(X174,X172) => 483.58/72.04 (![X176]: 483.58/72.04 ((~rel_s4(X172,X176)) | 483.58/72.04 (~ 483.58/72.04 (![X180]: 483.58/72.04 ((~rel_s4(X176,X180)) | 483.58/72.04 leq(n0,X174,X180)))) | 483.58/72.04 (~ 483.58/72.04 (![X184]: 483.58/72.04 ((~rel_s4(X176,X184)) | 483.58/72.04 leq(X174,pv5,X184)))) | 483.58/72.04 (~ 483.58/72.04 (![X182]: 483.58/72.04 ((~rel_s4(X176,X182)) | 483.58/72.04 leq(X170,n2,X182)))) | 483.58/72.04 (~ 483.58/72.04 (![X178]: 483.58/72.04 ((~rel_s4(X176,X178)) | 483.58/72.04 leq(n0,X170,X178)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X188]: 483.58/72.04 ((~rel_s4(X176,X188)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X170, 483.58/72.04 X174), 483.58/72.04 use,X188)))) | 483.58/72.04 (~ 483.58/72.04 (![X186]: 483.58/72.04 ((~rel_s4(X176,X186)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X170, 483.58/72.04 X174), 483.58/72.04 use,X186))))))))))))))))) | 483.58/72.04 (~ 483.58/72.04 (![X190]: 483.58/72.04 ((~rel_s4(X6,X190)) | 483.58/72.04 (![X192:mu]: 483.58/72.04 (exists_in_world(X192,X190) => 483.58/72.04 (![X194]: 483.58/72.04 ((~rel_s4(X190,X194)) | 483.58/72.04 (![X196:mu]: 483.58/72.04 (exists_in_world(X196,X194) => 483.58/72.04 (![X198]: 483.58/72.04 ((~rel_s4(X194,X198)) | 483.58/72.04 (~ 483.58/72.04 (![X202]: 483.58/72.04 ((~rel_s4(X198,X202)) | 483.58/72.04 leq(n0,X196,X202)))) | 483.58/72.04 (~ 483.58/72.04 (![X206]: 483.58/72.04 ((~rel_s4(X198,X206)) | 483.58/72.04 leq(X196,minus(pv5,n1),X206)))) | 483.58/72.04 (~ 483.58/72.04 (![X204]: 483.58/72.04 ((~rel_s4(X198,X204)) | 483.58/72.04 leq(X192,n2,X204)))) | 483.58/72.04 (~ 483.58/72.04 (![X200]: 483.58/72.04 ((~rel_s4(X198,X200)) | 483.58/72.04 leq(n0,X192,X200)))) | 483.58/72.04 (~ 483.58/72.04 ((~ 483.58/72.04 (![X210]: 483.58/72.04 ((~rel_s4(X198,X210)) | 483.58/72.04 qmltpeq(a_select3(z_defuse,X192, 483.58/72.04 X196), 483.58/72.04 use,X210)))) | 483.58/72.04 (~ 483.58/72.04 (![X208]: 483.58/72.04 ((~rel_s4(X198,X208)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,X192, 483.58/72.04 X196), 483.58/72.04 use,X208))))))))))))))))) | 483.58/72.04 (~(![X166]: ((~rel_s4(X6,X166)) | leq(pv5,minus(n999,n1),X166)))) | 483.58/72.04 (~ 483.58/72.04 (![X162]: 483.58/72.04 ((~rel_s4(X6,X162)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n5),use,X162)))) | 483.58/72.04 (~ 483.58/72.04 (![X158]: 483.58/72.04 ((~rel_s4(X6,X158)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n3),use,X158)))) | 483.58/72.04 (~ 483.58/72.04 (![X154]: 483.58/72.04 ((~rel_s4(X6,X154)) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse,n1),use,X154)))) | 483.58/72.04 (~ 483.58/72.04 (![X150]: 483.58/72.04 ((~rel_s4(X6,X150)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n5),use,X150)))) | 483.58/72.04 (~ 483.58/72.04 (![X146]: 483.58/72.04 ((~rel_s4(X6,X146)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n3),use,X146)))) | 483.58/72.04 (~ 483.58/72.04 (![X142]: 483.58/72.04 ((~rel_s4(X6,X142)) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse,n1),use,X142)))) | 483.58/72.04 (~ 483.58/72.04 (![X138]: 483.58/72.04 ((~rel_s4(X6,X138)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n5),use,X138)))) | 483.58/72.04 (~ 483.58/72.04 (![X134]: 483.58/72.04 ((~rel_s4(X6,X134)) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse,n3),use,X134)))) | 483.58/72.04 (~ 483.58/72.04 (![X130]: 483.58/72.04 ((~rel_s4(X6,X130)) | 483.58/72.04 qmltpeq(a_select3(u_defuse,n1,n0),use,X130)))) | 483.58/72.04 (~ 483.58/72.04 (![X126]: 483.58/72.04 ((~rel_s4(X6,X126)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n5),use,X126)))) | 483.58/72.04 (~ 483.58/72.04 (![X122]: 483.58/72.04 ((~rel_s4(X6,X122)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n3),use,X122)))) | 483.58/72.04 (~ 483.58/72.04 (![X118]: 483.58/72.04 ((~rel_s4(X6,X118)) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse,n1),use,X118)))) | 483.58/72.04 (~ 483.58/72.04 (![X114]: 483.58/72.04 ((~rel_s4(X6,X114)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n2),use,X114)))) | 483.58/72.04 (~ 483.58/72.04 (![X110]: 483.58/72.04 ((~rel_s4(X6,X110)) | 483.58/72.04 qmltpeq(a_select2(rho_defuse,n0),use,X110)))))))))). 483.58/72.04 tff('14', plain, 483.58/72.04 ~ (!!((^[Y0 : $i]: 483.58/72.04 (!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1)))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n2, n0), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n4), use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n0), 483.58/72.04 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483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select2(xinit_mean_defuse, n3), use, 483.58/72.04 Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select2(xinit_mean_defuse, n1), use, 483.58/72.04 Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), 483.58/72.04 use, Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, 483.58/72.04 Y2)))))))| 483.58/72.04 (~((!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y2))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, 483.58/72.04 Y2))))))))))))))))), 483.58/72.04 inference('cnf', [status(esa)], [zf_stmt_1])). 483.58/72.04 tff('15', plain, 483.58/72.04 ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk1', Y0)))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n2, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, pv5, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 (!!((^[Y2 : mu]: 483.58/72.04 (exists_in_world(Y2, Y1) => 483.58/72.04 (!!((^[Y3 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y3))) | 483.58/72.04 (!!((^[Y4 : mu]: 483.58/72.04 (exists_in_world(Y4, Y3) => 483.58/72.04 (!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y3, Y5)))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y4, Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y4, 483.58/72.04 pv5, Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y2, 483.58/72.04 n2, Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y2, Y6)))))))| 483.58/72.04 (~(((~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))) | 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 (!!((^[Y2 : mu]: 483.58/72.04 (exists_in_world(Y2, Y1) => 483.58/72.04 (!!((^[Y3 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y3))) | 483.58/72.04 (!!((^[Y4 : mu]: 483.58/72.04 (exists_in_world(Y4, Y3) => 483.58/72.04 (!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y3, Y5)))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y4, Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y4, 483.58/72.04 minus( 483.58/72.04 pv5, n1), 483.58/72.04 Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y2, 483.58/72.04 n2, Y6)))))))| 483.58/72.04 (~((!!((^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 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Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y1)))))))| 483.58/72.04 (~(((~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n2, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n4), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n0), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n2), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n4), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n0), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n2), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n4), use, 483.58/72.04 Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | leq(n0, pv5, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 (!!((^[Y2 : mu]: 483.58/72.04 (exists_in_world(Y2, Y1) => 483.58/72.04 (!!((^[Y3 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y3))) | 483.58/72.04 (!!((^[Y4 : mu]: 483.58/72.04 (exists_in_world(Y4, Y3) => 483.58/72.04 (!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y3, 483.58/72.04 Y5)))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y4, Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y4, 483.58/72.04 pv5, Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y2, 483.58/72.04 n2, Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y2, Y6)))))))| 483.58/72.04 (~(((~(( 483.58/72.04 !!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))) | 483.58/72.04 (~(( 483.58/72.04 !!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 (!!((^[Y2 : mu]: 483.58/72.04 (exists_in_world(Y2, Y1) => 483.58/72.04 (!!((^[Y3 : $i]: 483.58/72.04 ((~(rel_s4(Y1, Y3))) | 483.58/72.04 (!!((^[Y4 : mu]: 483.58/72.04 (exists_in_world(Y4, Y3) => 483.58/72.04 (!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y3, 483.58/72.04 Y5)))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y4, Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y4, 483.58/72.04 minus( 483.58/72.04 pv5, n1), 483.58/72.04 Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(Y2, 483.58/72.04 n2, Y6)))))))| 483.58/72.04 (~((!!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 (( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 leq(n0, 483.58/72.04 Y2, Y6)))))))| 483.58/72.04 (~(((~(( 483.58/72.04 !!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))) | 483.58/72.04 (~(( 483.58/72.04 !!(( 483.58/72.04 ^[Y6 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y5, Y6))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y2, Y4), 483.58/72.04 use, Y6))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, 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(~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y1)))))))| 483.58/72.04 (~((!!((^[Y1 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y1))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y1)))))))))))))), 483.58/72.04 inference('lazy_cnf_exists', [status(thm)], ['14'])). 483.58/72.04 tff('16', plain, 483.58/72.04 ~ ((~(rel_s4('#sk1', '#sk2')))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 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qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y2))) | 483.58/72.04 (!!((^[Y3 : mu]: 483.58/72.04 (exists_in_world(Y3, Y2) => 483.58/72.04 (!!((^[Y4 : $i]: 483.58/72.04 ((~(rel_s4(Y2, Y4)))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, 483.58/72.04 Y5))) | 483.58/72.04 leq(n0, Y3, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, 483.58/72.04 Y5))) | 483.58/72.04 leq(Y3, pv5, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, 483.58/72.04 Y5))) | 483.58/72.04 leq(Y1, n2, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, 483.58/72.04 Y5))) | 483.58/72.04 leq(n0, Y1, Y5)))))))| 483.58/72.04 (~(((~((!!((^[Y5 : $i]: 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((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))))| 483.58/72.04 (~(((~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 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qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y2))) | 483.58/72.04 (!!((^[Y3 : mu]: 483.58/72.04 (exists_in_world(Y3, Y2) => 483.58/72.04 (!!((^[Y4 : $i]: 483.58/72.04 ((~(rel_s4(Y2, Y4)))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(n0, Y3, 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(Y3, 483.58/72.04 pv5, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(Y1, n2, 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(n0, Y1, 483.58/72.04 Y5)))))))| 483.58/72.04 (~(((~((!!((^[Y5 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))) | 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y2))) | 483.58/72.04 (!!((^[Y3 : mu]: 483.58/72.04 (exists_in_world(Y3, Y2) => 483.58/72.04 (!!((^[Y4 : $i]: 483.58/72.04 ((~(rel_s4(Y2, Y4)))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(n0, Y3, 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(Y3, 483.58/72.04 minus( 483.58/72.04 pv5, n1), 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(Y1, n2, 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 leq(n0, Y1, 483.58/72.04 Y5)))))))| 483.58/72.04 (~(((~((!!((^[Y5 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))) | 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ( 483.58/72.04 ( 483.58/72.04 ~( 483.58/72.04 rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))))))), 483.58/72.04 inference('lazy_cnf_exists', [status(thm)], ['15'])). 483.58/72.04 tff('17', plain, 483.58/72.04 ((~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y2))) | 483.58/72.04 (!!((^[Y3 : mu]: 483.58/72.04 (exists_in_world(Y3, Y2) => 483.58/72.04 (!!((^[Y4 : $i]: 483.58/72.04 ((~(rel_s4(Y2, Y4)))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(n0, Y3, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(Y3, pv5, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(Y1, n2, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(n0, Y1, Y5)))))))| 483.58/72.04 (~(((~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))) | 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.58/72.04 ((~(rel_s4(Y0, Y2))) | 483.58/72.04 (!!((^[Y3 : mu]: 483.58/72.04 (exists_in_world(Y3, Y2) => 483.58/72.04 (!!((^[Y4 : $i]: 483.58/72.04 ((~(rel_s4(Y2, Y4)))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(n0, Y3, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(Y3, 483.58/72.04 minus(pv5, n1), 483.58/72.04 Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(Y1, n2, Y5)))))))| 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4(Y4, Y5))) | 483.58/72.04 leq(n0, Y1, Y5)))))))| 483.58/72.04 (~(((~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 z_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))) | 483.58/72.04 (~((!!((^[Y5 : $i]: 483.58/72.04 ((~(rel_s4( 483.58/72.04 Y4, Y5))) | 483.58/72.04 qmltpeq( 483.58/72.04 a_select3( 483.58/72.04 u_defuse, 483.58/72.04 Y1, Y3), 483.58/72.04 use, Y5))))))))))))))))))))))))))))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))))| 483.58/72.04 (~((!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))))), 483.58/72.04 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.58/72.04 tff('18', plain, 483.58/72.04 (~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))) 483.58/72.04 | ~ (!!((^[Y0 : $i]: 483.58/72.04 ((~(rel_s4('#sk2', Y0))) | 483.58/72.04 (!!((^[Y1 : mu]: 483.58/72.04 (exists_in_world(Y1, Y0) => 483.58/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y3, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y3, pv5, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y1, n2, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y1, Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y3, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, n1), 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y1, n2, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y1, Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['17'])). 483.84/72.04 tff('19', plain, 483.84/72.04 (~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y3, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, n1), 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y1, n2, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y1, Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))))))))))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('split', [status(esa)], ['18'])). 483.84/72.04 tff('20', plain, 483.84/72.04 (~ ((~(rel_s4('#sk2', '#sk18'))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, '#sk18') => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4('#sk18', Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y2, minus(pv5, n1), 483.84/72.04 Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y0, n2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y0, Y4)))))))| 483.84/72.04 (~(((~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))) | 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, 483.84/72.04 Y0, Y2), use, Y4)))))))))))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['19'])). 483.84/72.04 tff('21', plain, 483.84/72.04 (~ (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, '#sk18') => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4('#sk18', Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y2, minus(pv5, n1), Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y0, n2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y0, Y4)))))))| 483.84/72.04 (~(((~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))) | 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))))))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.04 tff('22', plain, 483.84/72.04 (~ (exists_in_world('#sk34', '#sk18') => 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk18', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, minus(pv5, n1), Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq('#sk34', n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, '#sk34', Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, 483.84/72.04 '#sk34', Y1), use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, 483.84/72.04 '#sk34', Y1), use, Y3)))))))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['21'])). 483.84/72.04 tff('23', plain, 483.84/72.04 (~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk18', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, minus(pv5, n1), Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq('#sk34', n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, '#sk34', Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, '#sk34', 483.84/72.04 Y1), use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, '#sk34', 483.84/72.04 Y1), use, Y3))))))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.04 tff('24', plain, 483.84/72.04 (~ ((~(rel_s4('#sk18', '#sk36'))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, '#sk36') => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4('#sk36', Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 leq(Y0, minus(pv5, n1), Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq('#sk34', n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, '#sk34', Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, '#sk34', Y0), 483.84/72.04 use, Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, '#sk34', Y0), 483.84/72.04 use, Y2)))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['23'])). 483.84/72.04 tff('25', plain, 483.84/72.04 (~ (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, '#sk36') => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4('#sk36', Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 leq(Y0, minus(pv5, n1), Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq('#sk34', n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, '#sk34', Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, '#sk34', Y0), 483.84/72.04 use, Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, '#sk34', Y0), 483.84/72.04 use, Y2))))))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.04 tff('26', plain, 483.84/72.04 (~ (exists_in_world('#sk38', '#sk36') => 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk36', Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk38', Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 leq('#sk38', minus(pv5, n1), Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq('#sk34', n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk34', Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, '#sk34', '#sk38'), use, 483.84/72.04 Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, '#sk34', '#sk38'), use, 483.84/72.04 Y1)))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['25'])). 483.84/72.04 tff('27', plain, 483.84/72.04 ( exists_in_world('#sk38', '#sk36')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.04 tff('28', plain, 483.84/72.04 ( rel_s4('#sk2', '#sk18')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.04 tff('29', plain, 483.84/72.04 (~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk36', Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk38', Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 leq('#sk38', minus(pv5, n1), Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq('#sk34', n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk34', Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), 483.84/72.04 use, Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), 483.84/72.04 use, Y1))))))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.04 tff('30', plain, 483.84/72.04 (~ ((~(rel_s4('#sk36', '#sk41')))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq(n0, '#sk38', Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk41', Y0))) | 483.84/72.04 leq('#sk38', minus(pv5, n1), Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq('#sk34', n2, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq(n0, '#sk34', Y0)))))))| 483.84/72.04 (~(((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk41', Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, 483.84/72.04 Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk41', Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, 483.84/72.04 Y0)))))))))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['29'])). 483.84/72.04 tff('31', plain, 483.84/72.04 ( rel_s4('#sk36', '#sk41')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.04 tff('32', plain, 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y3, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y3, pv5, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y1, n2, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y1, Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.04 tff('33', plain, 483.84/72.04 ![X1]: 483.84/72.04 ((~(rel_s4('#sk2', X1))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X1) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y2, pv5, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y0, n2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y0, Y4)))))))| 483.84/72.04 (~(((~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))) | 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['32'])). 483.84/72.04 tff('34', plain, 483.84/72.04 ![X1]: 483.84/72.04 (~ rel_s4('#sk2', X1) 483.84/72.04 | (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X1) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 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483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, pv5, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(X2, n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, X2, Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, Y1), 483.84/72.04 use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, Y1), 483.84/72.04 use, Y3))))))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['34'])). 483.84/72.04 tff('36', plain, 483.84/72.04 ![X1, X2 : mu]: 483.84/72.04 (~ exists_in_world(X2, X1) 483.84/72.04 | (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, pv5, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(X2, n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, X2, Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, 483.84/72.04 Y1), use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, 483.84/72.04 Y1), use, Y3)))))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['35'])). 483.84/72.04 tff('37', plain, 483.84/72.04 ![X1, X2 : mu, X3]: 483.84/72.04 ( ((~(rel_s4(X1, X3))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X3) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(Y0, pv5, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(X2, n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, X2, Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, Y0), 483.84/72.04 use, Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, Y0), 483.84/72.04 use, Y2))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['36'])). 483.84/72.04 tff('38', plain, 483.84/72.04 ![X1, X2 : mu, X3]: 483.84/72.04 (~ rel_s4(X1, X3) 483.84/72.04 | (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X3) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(Y0, pv5, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(X2, n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, X2, Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, Y0), use, 483.84/72.04 Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, Y0), use, 483.84/72.04 Y2)))))))))))))))))) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['37'])). 483.84/72.04 tff('39', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu]: 483.84/72.04 ( (exists_in_world(X4, X3) => 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X4, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(X4, pv5, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(X2, n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X2, Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y1))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['38'])). 483.84/72.04 tff('40', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu]: 483.84/72.04 (~ exists_in_world(X4, X3) 483.84/72.04 | (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X4, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(X4, pv5, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(X2, n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X2, Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, 483.84/72.04 Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, 483.84/72.04 Y1)))))))))))))) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['39'])). 483.84/72.04 tff('41', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 ( ((~(rel_s4(X3, X5)))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X4, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))))| 483.84/72.04 (~(((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['40'])). 483.84/72.04 tff('42', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X4, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['41'])). 483.84/72.04 tff('43', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ ((~(rel_s4(X5, '#sk40'(X4, X5)))) | leq(n0, X4, '#sk40'(X4, X5))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5)), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['42'])). 483.84/72.04 tff('44', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 ( rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['43'])). 483.84/72.04 tff('45', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 ( rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['43'])). 483.84/72.04 tff('46', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 ( '#form43'(X2, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('47', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form43'(X2, X5) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | rel_s4(X5, '#sk40'(X4, X5))), 483.84/72.04 inference('renaming', [status(thm)], ['44', '46'])). 483.84/72.04 tff('48', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form43'(X2, X5) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | rel_s4(X5, '#sk40'(X4, X5))), 483.84/72.04 inference('renaming', [status(thm)], ['44', '46'])). 483.84/72.04 tff('49', plain, 483.84/72.04 ![X2 : mu, X4 : mu, X5]: 483.84/72.04 ( '#form44'(X2, X4, X5) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('50', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form44'(X2, X4, X5) 483.84/72.04 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ '#form43'(X2, X5)), 483.84/72.04 inference('renaming', [status(thm)], ['47', '49'])). 483.84/72.04 tff('51', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 ( '#form46'(X2, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('52', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 (~ ((~(rel_s4(X5, '#sk40'(X2, X5)))) | leq(n0, X2, '#sk40'(X2, X5))) 483.84/72.04 | '#form46'(X2, X5)), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['51'])). 483.84/72.04 tff('53', plain, 483.84/72.04 ![X2 : mu, X5]: ( rel_s4(X5, '#sk40'(X2, X5)) | '#form46'(X2, X5)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['52'])). 483.84/72.04 tff('54', plain, 483.84/72.04 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq(n0, '#sk34', Y0)))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.04 tff('55', plain, 483.84/72.04 (![X1]: ((~(rel_s4('#sk41', X1))) | leq(n0, '#sk34', X1))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['54'])). 483.84/72.04 tff('56', plain, 483.84/72.04 (![X1]: (~ rel_s4('#sk41', X1) | leq(n0, '#sk34', X1))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['55'])). 483.84/72.04 tff('57', plain, 483.84/72.04 (![X0 : mu]: 483.84/72.04 ( '#form46'(X0, '#sk41') | leq(n0, '#sk34', '#sk40'(X0, '#sk41')))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('sup-', [status(thm)], ['53', '56'])). 483.84/72.04 tff('58', plain, 483.84/72.04 ![X2 : mu, X5]: (~ leq(n0, X2, '#sk40'(X2, X5)) | '#form46'(X2, X5)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['52'])). 483.84/72.04 tff('59', plain, 483.84/72.04 (( '#form46'('#sk34', '#sk41') | '#form46'('#sk34', '#sk41'))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('sup-', [status(thm)], ['57', '58'])). 483.84/72.04 tff('60', plain, 483.84/72.04 ( '#form46'('#sk34', '#sk41')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('simplify', [status(thm)], ['59'])). 483.84/72.04 tff('61', plain, 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y3, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(Y1, n2, Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 leq(n0, Y1, Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.04 tff('62', plain, 483.84/72.04 ![X1]: 483.84/72.04 ((~(rel_s4('#sk2', X1))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X1) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y2, minus(pv5, n1), 483.84/72.04 Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y0, n2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y0, Y4)))))))| 483.84/72.04 (~(((~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))) | 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, 483.84/72.04 Y0, Y2), use, Y4))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['61'])). 483.84/72.04 tff('63', plain, 483.84/72.04 ![X1]: 483.84/72.04 (~ rel_s4('#sk2', X1) 483.84/72.04 | (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X1) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y1))) | 483.84/72.04 (!!((^[Y2 : mu]: 483.84/72.04 (exists_in_world(Y2, Y1) => 483.84/72.04 (!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y3)))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y2, minus(pv5, n1), 483.84/72.04 Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(Y0, n2, Y4)))))))| 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 leq(n0, Y0, Y4)))))))| 483.84/72.04 (~(((~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, Y0, 483.84/72.04 Y2), use, Y4))))))) | 483.84/72.04 (~((!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y3, Y4))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, Y0, 483.84/72.04 Y2), use, Y4))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['62'])). 483.84/72.04 tff('64', plain, 483.84/72.04 ![X1, X2 : mu]: 483.84/72.04 ( (exists_in_world(X2, X1) => 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, minus(pv5, n1), Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(X2, n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, X2, Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, Y1), 483.84/72.04 use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, Y1), 483.84/72.04 use, Y3))))))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['63'])). 483.84/72.04 tff('65', plain, 483.84/72.04 ![X1, X2 : mu]: 483.84/72.04 (~ exists_in_world(X2, X1) 483.84/72.04 | (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X1, Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2)))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, Y1, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(Y1, minus(pv5, n1), Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(X2, n2, Y3)))))))| 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 leq(n0, X2, Y3)))))))| 483.84/72.04 (~(((~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, 483.84/72.04 Y1), use, Y3))))))) | 483.84/72.04 (~((!!((^[Y3 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y3))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, 483.84/72.04 Y1), use, Y3)))))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['64'])). 483.84/72.04 tff('66', plain, 483.84/72.04 ![X1, X2 : mu, X3]: 483.84/72.04 ( ((~(rel_s4(X1, X3))) | 483.84/72.04 (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X3) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 leq(Y0, minus(pv5, n1), Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(X2, n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, X2, Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, Y0), 483.84/72.04 use, Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, Y0), 483.84/72.04 use, Y2))))))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['65'])). 483.84/72.04 tff('67', plain, 483.84/72.04 ![X1, X2 : mu, X3]: 483.84/72.04 (~ rel_s4(X1, X3) 483.84/72.04 | (!!((^[Y0 : mu]: 483.84/72.04 (exists_in_world(Y0, X3) => 483.84/72.04 (!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y1)))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 leq(Y0, minus(pv5, n1), Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(X2, n2, Y2)))))))| 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | leq(n0, X2, Y2)))))))| 483.84/72.04 (~(((~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(z_defuse, X2, Y0), use, 483.84/72.04 Y2))))))) | 483.84/72.04 (~((!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y1, Y2))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3(u_defuse, X2, Y0), use, 483.84/72.04 Y2)))))))))))))))))) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['66'])). 483.84/72.04 tff('68', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu]: 483.84/72.04 ( (exists_in_world(X4, X3) => 483.84/72.04 (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X4, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | leq(X4, minus(pv5, n1), Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(X2, n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X2, Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y1))))))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['67'])). 483.84/72.04 tff('69', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu]: 483.84/72.04 (~ exists_in_world(X4, X3) 483.84/72.04 | (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X3, Y0)))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X4, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 leq(X4, minus(pv5, n1), Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(X2, n2, Y1)))))))| 483.84/72.04 (~((!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | leq(n0, X2, Y1)))))))| 483.84/72.04 (~(((~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, 483.84/72.04 Y1))))))) | 483.84/72.04 (~((!!((^[Y1 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y1))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, 483.84/72.04 Y1)))))))))))))) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['68'])). 483.84/72.04 tff('70', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 ( ((~(rel_s4(X3, X5)))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X4, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))))| 483.84/72.04 (~((!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))))| 483.84/72.04 (~(((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3)), 483.84/72.04 inference('lazy_cnf_forall', [status(thm)], ['69'])). 483.84/72.04 tff('71', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X4, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['70'])). 483.84/72.04 tff('72', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ ((~(rel_s4(X5, '#sk40'(X4, X5)))) | leq(n0, X4, '#sk40'(X4, X5))) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5)), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['71'])). 483.84/72.04 tff('73', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['72'])). 483.84/72.04 tff('74', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 ( '#form43'(X2, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('75', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form43'(X2, X5) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ leq(n0, X4, '#sk40'(X4, X5))), 483.84/72.04 inference('renaming', [status(thm)], ['73', '74'])). 483.84/72.04 tff('76', plain, 483.84/72.04 ![X2 : mu, X4 : mu, X5]: 483.84/72.04 ( '#form44'(X2, X4, X5) 483.84/72.04 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.04 (~((!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | 483.84/72.04 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('77', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form44'(X2, X4, X5) 483.84/72.04 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ '#form43'(X2, X5)), 483.84/72.04 inference('renaming', [status(thm)], ['75', '76'])). 483.84/72.04 tff('78', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 ( '#form46'(X2, X5) 483.84/72.04 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('79', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ '#form46'(X2, X5) 483.84/72.04 | ~ '#form43'(X2, X5) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.04 | ~ '#form44'(X2, X4, X5)), 483.84/72.04 inference('renaming', [status(thm)], ['77', '78'])). 483.84/72.04 tff('80', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 (~ ((~(rel_s4(X5, '#sk52'(X4, X5)))) | 483.84/72.04 leq(X4, minus(pv5, n1), '#sk52'(X4, X5))) 483.84/72.04 | ~ '#form44'(X2, X4, X5) 483.84/72.04 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ '#form43'(X2, X5) 483.84/72.04 | ~ '#form46'(X2, X5)), 483.84/72.04 inference('lazy_cnf_exists', [status(thm)], ['79'])). 483.84/72.04 tff('81', plain, 483.84/72.04 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.04 ( rel_s4(X5, '#sk52'(X4, X5)) 483.84/72.04 | ~ '#form46'(X2, X5) 483.84/72.04 | ~ '#form43'(X2, X5) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world(X2, X1) 483.84/72.04 | ~ rel_s4(X1, X3) 483.84/72.04 | ~ exists_in_world(X4, X3) 483.84/72.04 | ~ rel_s4(X3, X5) 483.84/72.04 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.04 | ~ '#form44'(X2, X4, X5)), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['80'])). 483.84/72.04 tff('82', plain, 483.84/72.04 (![X0 : mu, X1, X2]: 483.84/72.04 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.04 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.04 | ~ rel_s4(X1, '#sk41') 483.84/72.04 | ~ exists_in_world(X0, X1) 483.84/72.04 | ~ rel_s4(X2, X1) 483.84/72.04 | ~ exists_in_world('#sk34', X2) 483.84/72.04 | ~ rel_s4('#sk2', X2) 483.84/72.04 | ~ '#form43'('#sk34', '#sk41') 483.84/72.04 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('sup-', [status(thm)], ['60', '81'])). 483.84/72.04 tff('83', plain, 483.84/72.04 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq('#sk34', n2, Y0)))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.04 tff('84', plain, 483.84/72.04 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq('#sk34', n2, Y0)))))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.04 tff('85', plain, 483.84/72.04 ![X2 : mu, X5]: 483.84/72.04 (~ '#form43'(X2, X5) 483.84/72.04 | (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.04 define([status(thm)])). 483.84/72.04 tff('86', plain, 483.84/72.04 ( '#form43'('#sk34', '#sk41')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('renaming', [status(thm)], ['83', '85'])). 483.84/72.04 tff('87', plain, 483.84/72.04 (![X0 : mu, X1, X2]: 483.84/72.04 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.04 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.04 | ~ rel_s4(X1, '#sk41') 483.84/72.04 | ~ exists_in_world(X0, X1) 483.84/72.04 | ~ rel_s4(X2, X1) 483.84/72.04 | ~ exists_in_world('#sk34', X2) 483.84/72.04 | ~ rel_s4('#sk2', X2) 483.84/72.04 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('demod', [status(thm)], ['82', '86'])). 483.84/72.04 tff('88', plain, 483.84/72.04 (![X0 : mu, X1]: 483.84/72.04 ( rel_s4('#sk41', '#sk52'(X0, '#sk41')) 483.84/72.04 | ~ rel_s4('#sk2', X1) 483.84/72.04 | ~ exists_in_world('#sk34', X1) 483.84/72.04 | ~ rel_s4(X1, '#sk36') 483.84/72.04 | ~ exists_in_world(X0, '#sk36') 483.84/72.04 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.04 | ~ '#form44'('#sk34', X0, '#sk41'))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('sup-', [status(thm)], ['31', '87'])). 483.84/72.04 tff('89', plain, 483.84/72.04 (![X0 : mu]: 483.84/72.04 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.04 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.04 | ~ exists_in_world(X0, '#sk36') 483.84/72.04 | ~ rel_s4('#sk18', '#sk36') 483.84/72.04 | ~ exists_in_world('#sk34', '#sk18') 483.84/72.04 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('sup-', [status(thm)], ['28', '88'])). 483.84/72.04 tff('90', plain, 483.84/72.04 ( rel_s4('#sk18', '#sk36')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.04 tff('91', plain, 483.84/72.04 ( exists_in_world('#sk34', '#sk18')) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.04 (!!((^[Y2 : $i]: 483.84/72.04 ((~(rel_s4(Y0, Y2))) | 483.84/72.04 (!!((^[Y3 : mu]: 483.84/72.04 (exists_in_world(Y3, Y2) => 483.84/72.04 (!!((^[Y4 : $i]: 483.84/72.04 ((~(rel_s4(Y2, Y4)))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y3, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y3, 483.84/72.04 minus(pv5, 483.84/72.04 n1), Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(Y1, n2, 483.84/72.04 Y5)))))))| 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~(rel_s4(Y4, 483.84/72.04 Y5))) | 483.84/72.04 leq(n0, Y1, 483.84/72.04 Y5)))))))| 483.84/72.04 (~(((~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 z_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5))))))) | 483.84/72.04 (~((!!((^[Y5 : $i]: 483.84/72.04 ((~( 483.84/72.04 rel_s4( 483.84/72.04 Y4, Y5))) | 483.84/72.04 qmltpeq( 483.84/72.04 a_select3( 483.84/72.04 u_defuse, 483.84/72.04 Y1, Y3), 483.84/72.04 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.04 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.04 tff('92', plain, 483.84/72.04 (![X0 : mu]: 483.84/72.04 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.04 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.04 | ~ exists_in_world(X0, '#sk36') 483.84/72.04 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.04 <= (~ 483.84/72.04 ( (!!((^[Y0 : $i]: 483.84/72.04 ((~(rel_s4('#sk2', Y0))) | 483.84/72.04 (!!((^[Y1 : mu]: 483.84/72.04 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['89', '90', '91'])). 483.84/72.05 tff('93', plain, 483.84/72.05 (( rel_s4('#sk41', '#sk52'('#sk38', '#sk41')) 483.84/72.05 | ~ leq(n0, '#sk38', '#sk40'('#sk38', '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', '#sk38', '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['27', '92'])). 483.84/72.05 tff('94', plain, 483.84/72.05 ~ ( leq(n0, '#sk38', '#sk40'('#sk38', '#sk41'))) | 483.84/72.05 ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41'))) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, n1), 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.05 ~ ( '#form44'('#sk34', '#sk38', '#sk41')), 483.84/72.05 inference('split', [status(esa)], ['93'])). 483.84/72.05 tff('95', plain, 483.84/72.05 ( ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.05 tff('96', plain, 483.84/72.05 ((~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['95'])). 483.84/72.05 tff('97', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['96'])). 483.84/72.05 tff('98', plain, 483.84/72.05 (~ ((~(rel_s4('#sk41', '#sk48'))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, '#sk48'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['97'])). 483.84/72.05 tff('99', plain, 483.84/72.05 ( rel_s4('#sk41', '#sk48')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['98'])). 483.84/72.05 tff('100', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5]: 483.84/72.05 ( '#form44'(X2, X4, X5) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('101', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5]: 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['100'])). 483.84/72.05 tff('102', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.05 ( ((~(rel_s4(X5, X6))) | qmltpeq(a_select3(z_defuse, X2, X4), use, X6)) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['101'])). 483.84/72.05 tff('103', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.05 (~ rel_s4(X5, X6) 483.84/72.05 | qmltpeq(a_select3(z_defuse, X2, X4), use, X6) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['102'])). 483.84/72.05 tff('104', plain, 483.84/72.05 (![X0 : mu, X1 : mu]: 483.84/72.05 ( '#form44'(X1, X0, '#sk41') 483.84/72.05 | qmltpeq(a_select3(z_defuse, X1, X0), use, '#sk48'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['99', '103'])). 483.84/72.05 tff('105', plain, 483.84/72.05 (~ qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, '#sk48')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['98'])). 483.84/72.05 tff('106', plain, 483.84/72.05 ( '#form44'('#sk34', '#sk38', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['104', '105'])). 483.84/72.05 tff('107', plain, 483.84/72.05 ( exists_in_world('#sk38', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.05 tff('108', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.05 tff('109', plain, 483.84/72.05 ( rel_s4('#sk36', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.05 tff('110', plain, 483.84/72.05 ( '#form46'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('simplify', [status(thm)], ['59'])). 483.84/72.05 tff('111', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['43'])). 483.84/72.05 tff('112', plain, 483.84/72.05 ![X2 : mu, X5]: 483.84/72.05 ( '#form43'(X2, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('113', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5))), 483.84/72.05 inference('renaming', [status(thm)], ['111', '112'])). 483.84/72.05 tff('114', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5]: 483.84/72.05 ( '#form44'(X2, X4, X5) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('115', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form44'(X2, X4, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ '#form43'(X2, X5)), 483.84/72.05 inference('renaming', [status(thm)], ['113', '114'])). 483.84/72.05 tff('116', plain, 483.84/72.05 ![X2 : mu, X5]: 483.84/72.05 ( '#form46'(X2, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('117', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form46'(X2, X5) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ '#form44'(X2, X4, X5)), 483.84/72.05 inference('renaming', [status(thm)], ['115', '116'])). 483.84/72.05 tff('118', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ ((~(rel_s4(X5, '#sk51'(X4, X5)))) | leq(X4, pv5, '#sk51'(X4, X5))) 483.84/72.05 | ~ '#form44'(X2, X4, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ '#form46'(X2, X5)), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['117'])). 483.84/72.05 tff('119', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ leq(X4, pv5, '#sk51'(X4, X5)) 483.84/72.05 | ~ '#form46'(X2, X5) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['118'])). 483.84/72.05 tff('120', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ '#form43'('#sk34', '#sk41') 483.84/72.05 | ~ leq(X0, pv5, '#sk51'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['110', '119'])). 483.84/72.05 tff('121', plain, 483.84/72.05 ( '#form43'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('renaming', [status(thm)], ['83', '85'])). 483.84/72.05 tff('122', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ leq(X0, pv5, '#sk51'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['120', '121'])). 483.84/72.05 tff('123', plain, 483.84/72.05 (![X0 : mu, X1]: 483.84/72.05 (~ leq(X0, pv5, '#sk51'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world('#sk34', X1) 483.84/72.05 | ~ rel_s4(X1, '#sk36') 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', X0, '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['109', '122'])). 483.84/72.05 tff('124', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ rel_s4('#sk18', '#sk36') 483.84/72.05 | ~ exists_in_world('#sk34', '#sk18') 483.84/72.05 | ~ leq(X0, pv5, '#sk51'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['108', '123'])). 483.84/72.05 tff('125', plain, 483.84/72.05 ( rel_s4('#sk18', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.05 tff('126', plain, 483.84/72.05 ( exists_in_world('#sk34', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.05 tff('127', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ leq(X0, pv5, '#sk51'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['124', '125', '126'])). 483.84/72.05 tff('128', plain, 483.84/72.05 ((~ leq('#sk38', pv5, '#sk51'('#sk38', '#sk41')) 483.84/72.05 | ~ leq(n0, '#sk38', '#sk40'('#sk38', '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', '#sk38', '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['107', '127'])). 483.84/72.05 tff('129', plain, 483.84/72.05 (~ '#form44'('#sk34', '#sk38', '#sk41')) 483.84/72.05 <= (~ ( '#form44'('#sk34', '#sk38', '#sk41'))), 483.84/72.05 inference('split', [status(esa)], ['128'])). 483.84/72.05 tff('130', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0)))))) | 483.84/72.05 ( '#form44'('#sk34', '#sk38', '#sk41')), 483.84/72.05 inference('sup-', [status(thm)], ['106', '129'])). 483.84/72.05 tff('131', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['96'])). 483.84/72.05 tff('132', plain, 483.84/72.05 (~ ((~(rel_s4('#sk41', '#sk47'))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, '#sk47'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['131'])). 483.84/72.05 tff('133', plain, 483.84/72.05 ( rel_s4('#sk41', '#sk47')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['132'])). 483.84/72.05 tff('134', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5]: 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['100'])). 483.84/72.05 tff('135', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.05 ( ((~(rel_s4(X5, X6))) | qmltpeq(a_select3(u_defuse, X2, X4), use, X6)) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['134'])). 483.84/72.05 tff('136', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.05 (~ rel_s4(X5, X6) 483.84/72.05 | qmltpeq(a_select3(u_defuse, X2, X4), use, X6) 483.84/72.05 | '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['135'])). 483.84/72.05 tff('137', plain, 483.84/72.05 (![X0 : mu, X1 : mu]: 483.84/72.05 ( '#form44'(X1, X0, '#sk41') 483.84/72.05 | qmltpeq(a_select3(u_defuse, X1, X0), use, '#sk47'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['133', '136'])). 483.84/72.05 tff('138', plain, 483.84/72.05 (~ qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, '#sk47')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['132'])). 483.84/72.05 tff('139', plain, 483.84/72.05 ( '#form44'('#sk34', '#sk38', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['137', '138'])). 483.84/72.05 tff('140', plain, 483.84/72.05 (~ '#form44'('#sk34', '#sk38', '#sk41')) 483.84/72.05 <= (~ ( '#form44'('#sk34', '#sk38', '#sk41'))), 483.84/72.05 inference('split', [status(esa)], ['128'])). 483.84/72.05 tff('141', plain, 483.84/72.05 ( '#form44'('#sk34', '#sk38', '#sk41')) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0)))))), 483.84/72.05 inference('sup-', [status(thm)], ['139', '140'])). 483.84/72.05 tff('142', plain, 483.84/72.05 ~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, '#sk34', '#sk38'), use, Y0)))))) | 483.84/72.05 ~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk41', Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, '#sk34', '#sk38'), use, Y0)))))) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, n1), 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))), 483.84/72.05 inference('split', [status(esa)], ['96'])). 483.84/72.05 tff('143', plain, 483.84/72.05 ( exists_in_world('#sk38', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.05 tff('144', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.05 tff('145', plain, 483.84/72.05 ( rel_s4('#sk36', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.05 tff('146', plain, 483.84/72.05 ( '#form46'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('simplify', [status(thm)], ['59'])). 483.84/72.05 tff('147', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ leq(X4, minus(pv5, n1), '#sk52'(X4, X5)) 483.84/72.05 | ~ '#form46'(X2, X5) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.05 | ~ '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['80'])). 483.84/72.05 tff('148', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ '#form43'('#sk34', '#sk41') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['146', '147'])). 483.84/72.05 tff('149', plain, 483.84/72.05 ( '#form43'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('renaming', [status(thm)], ['83', '85'])). 483.84/72.05 tff('150', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['148', '149'])). 483.84/72.05 tff('151', plain, 483.84/72.05 (![X0 : mu, X1]: 483.84/72.05 (~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world('#sk34', X1) 483.84/72.05 | ~ rel_s4(X1, '#sk36') 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', X0, '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['145', '150'])). 483.84/72.05 tff('152', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ rel_s4('#sk18', '#sk36') 483.84/72.05 | ~ exists_in_world('#sk34', '#sk18') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['144', '151'])). 483.84/72.05 tff('153', plain, 483.84/72.05 ( rel_s4('#sk18', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.05 tff('154', plain, 483.84/72.05 ( exists_in_world('#sk34', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.05 tff('155', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | ~ leq(n0, X0, '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['152', '153', '154'])). 483.84/72.05 tff('156', plain, 483.84/72.05 ((~ leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41')) 483.84/72.05 | ~ leq(n0, '#sk38', '#sk40'('#sk38', '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', '#sk38', '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['143', '155'])). 483.84/72.05 tff('157', plain, 483.84/72.05 ~ ( leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41'))) | 483.84/72.05 ~ ( leq(n0, '#sk38', '#sk40'('#sk38', '#sk41'))) | 483.84/72.05 ~ ( '#form44'('#sk34', '#sk38', '#sk41')) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, n1), 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))), 483.84/72.05 inference('split', [status(esa)], ['156'])). 483.84/72.05 tff('158', plain, 483.84/72.05 ( exists_in_world('#sk38', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.05 tff('159', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.05 tff('160', plain, 483.84/72.05 ( rel_s4('#sk36', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.05 tff('161', plain, 483.84/72.05 ( '#form46'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('simplify', [status(thm)], ['59'])). 483.84/72.05 tff('162', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 ( rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['72'])). 483.84/72.05 tff('163', plain, 483.84/72.05 ![X2 : mu, X5]: 483.84/72.05 ( '#form43'(X2, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('164', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0)))))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | rel_s4(X5, '#sk40'(X4, X5))), 483.84/72.05 inference('renaming', [status(thm)], ['162', '163'])). 483.84/72.05 tff('165', plain, 483.84/72.05 ![X2 : mu, X4 : mu, X5]: 483.84/72.05 ( '#form44'(X2, X4, X5) 483.84/72.05 | ~ ((~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(z_defuse, X2, X4), use, Y0))))))) | 483.84/72.05 (~((!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, X2, X4), use, Y0))))))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('166', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form44'(X2, X4, X5) 483.84/72.05 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ '#form43'(X2, X5)), 483.84/72.05 inference('renaming', [status(thm)], ['164', '165'])). 483.84/72.05 tff('167', plain, 483.84/72.05 ![X2 : mu, X5]: 483.84/72.05 ( '#form46'(X2, X5) 483.84/72.05 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))), 483.84/72.05 define([status(thm)])). 483.84/72.05 tff('168', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ '#form46'(X2, X5) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4(X5, Y0))) | leq(X4, minus(pv5, n1), Y0))))) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.05 | ~ '#form44'(X2, X4, X5)), 483.84/72.05 inference('renaming', [status(thm)], ['166', '167'])). 483.84/72.05 tff('169', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ ((~(rel_s4(X5, '#sk52'(X4, X5)))) | 483.84/72.05 leq(X4, minus(pv5, n1), '#sk52'(X4, X5))) 483.84/72.05 | ~ '#form44'(X2, X4, X5) 483.84/72.05 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ '#form46'(X2, X5)), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['168'])). 483.84/72.05 tff('170', plain, 483.84/72.05 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.05 (~ leq(X4, minus(pv5, n1), '#sk52'(X4, X5)) 483.84/72.05 | ~ '#form46'(X2, X5) 483.84/72.05 | ~ '#form43'(X2, X5) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world(X2, X1) 483.84/72.05 | ~ rel_s4(X1, X3) 483.84/72.05 | ~ exists_in_world(X4, X3) 483.84/72.05 | ~ rel_s4(X3, X5) 483.84/72.05 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.05 | ~ '#form44'(X2, X4, X5)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['169'])). 483.84/72.05 tff('171', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ '#form43'('#sk34', '#sk41') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['161', '170'])). 483.84/72.05 tff('172', plain, 483.84/72.05 ( '#form43'('#sk34', '#sk41')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('renaming', [status(thm)], ['83', '85'])). 483.84/72.05 tff('173', plain, 483.84/72.05 (![X0 : mu, X1, X2]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4(X1, '#sk41') 483.84/72.05 | ~ exists_in_world(X0, X1) 483.84/72.05 | ~ rel_s4(X2, X1) 483.84/72.05 | ~ exists_in_world('#sk34', X2) 483.84/72.05 | ~ rel_s4('#sk2', X2) 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['171', '172'])). 483.84/72.05 tff('174', plain, 483.84/72.05 (![X0 : mu, X1]: 483.84/72.05 (~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')) 483.84/72.05 | ~ rel_s4('#sk2', X1) 483.84/72.05 | ~ exists_in_world('#sk34', X1) 483.84/72.05 | ~ rel_s4(X1, '#sk36') 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', X0, '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['160', '173'])). 483.84/72.05 tff('175', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ rel_s4('#sk18', '#sk36') 483.84/72.05 | ~ exists_in_world('#sk34', '#sk18') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['159', '174'])). 483.84/72.05 tff('176', plain, 483.84/72.05 ( rel_s4('#sk18', '#sk36')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.05 tff('177', plain, 483.84/72.05 ( exists_in_world('#sk34', '#sk18')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.05 tff('178', plain, 483.84/72.05 (![X0 : mu]: 483.84/72.05 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.05 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.05 | ~ exists_in_world(X0, '#sk36') 483.84/72.05 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk41')))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('demod', [status(thm)], ['175', '176', '177'])). 483.84/72.05 tff('179', plain, 483.84/72.05 ((~ leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41')) 483.84/72.05 | rel_s4('#sk41', '#sk40'('#sk38', '#sk41')) 483.84/72.05 | ~ '#form44'('#sk34', '#sk38', '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['158', '178'])). 483.84/72.05 tff('180', plain, 483.84/72.05 ~ ( leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41'))) | 483.84/72.05 ( rel_s4('#sk41', '#sk40'('#sk38', '#sk41'))) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, n1), 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.05 ~ ( '#form44'('#sk34', '#sk38', '#sk41')), 483.84/72.05 inference('split', [status(esa)], ['179'])). 483.84/72.05 tff('181', plain, 483.84/72.05 ( rel_s4('#sk41', '#sk40'('#sk38', '#sk41'))) 483.84/72.05 <= (( rel_s4('#sk41', '#sk40'('#sk38', '#sk41')))), 483.84/72.05 inference('split', [status(esa)], ['179'])). 483.84/72.05 tff('182', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk41', Y0))) | leq(n0, '#sk38', Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.05 tff('183', plain, 483.84/72.05 (![X1]: ((~(rel_s4('#sk41', X1))) | leq(n0, '#sk38', X1))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['182'])). 483.84/72.05 tff('184', plain, 483.84/72.05 (![X1]: (~ rel_s4('#sk41', X1) | leq(n0, '#sk38', X1))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['183'])). 483.84/72.05 tff('185', plain, 483.84/72.05 ( leq(n0, '#sk38', '#sk40'('#sk38', '#sk41'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, 483.84/72.05 n1), Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))) & 483.84/72.05 ( rel_s4('#sk41', '#sk40'('#sk38', '#sk41')))), 483.84/72.05 inference('sup-', [status(thm)], ['181', '184'])). 483.84/72.05 tff('186', plain, 483.84/72.05 (~ leq(n0, '#sk38', '#sk40'('#sk38', '#sk41'))) 483.84/72.05 <= (~ ( leq(n0, '#sk38', '#sk40'('#sk38', '#sk41')))), 483.84/72.05 inference('split', [status(esa)], ['128'])). 483.84/72.05 tff('187', plain, 483.84/72.05 ~ ( rel_s4('#sk41', '#sk40'('#sk38', '#sk41'))) | 483.84/72.05 ( leq(n0, '#sk38', '#sk40'('#sk38', '#sk41'))) | 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, 483.84/72.05 minus(pv5, n1), 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))), 483.84/72.05 inference('sup-', [status(thm)], ['185', '186'])). 483.84/72.05 tff('188', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('189', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk8'))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, '#sk8'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['188'])). 483.84/72.05 tff('190', plain, 483.84/72.05 (~ qmltpeq(a_select3(u_defuse, n1, n0), use, '#sk8')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['189'])). 483.84/72.05 tff('191', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk8')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['189'])). 483.84/72.05 tff('192', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('193', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['192'])). 483.84/72.05 tff('194', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select3(u_defuse, n1, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['193'])). 483.84/72.05 tff('195', plain, 483.84/72.05 ( qmltpeq(a_select3(u_defuse, n1, n0), use, '#sk8')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['191', '194'])). 483.84/72.05 tff('196', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['190', '195'])). 483.84/72.05 tff('197', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('198', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk6'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, '#sk6'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['197'])). 483.84/72.05 tff('199', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n3), use, '#sk6')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['198'])). 483.84/72.05 tff('200', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk6')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['198'])). 483.84/72.05 tff('201', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('202', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['201'])). 483.84/72.05 tff('203', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['202'])). 483.84/72.05 tff('204', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n3), use, '#sk6')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['200', '203'])). 483.84/72.05 tff('205', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['199', '204'])). 483.84/72.05 tff('206', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('207', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk4'))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, '#sk4'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['206'])). 483.84/72.05 tff('208', plain, 483.84/72.05 (~ qmltpeq(a_select2(rho_defuse, n2), use, '#sk4')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['207'])). 483.84/72.05 tff('209', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk4')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['207'])). 483.84/72.05 tff('210', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('211', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | qmltpeq(a_select2(rho_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['210'])). 483.84/72.05 tff('212', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(rho_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['211'])). 483.84/72.05 tff('213', plain, 483.84/72.05 ( qmltpeq(a_select2(rho_defuse, n2), use, '#sk4')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['209', '212'])). 483.84/72.05 tff('214', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['208', '213'])). 483.84/72.05 tff('215', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('216', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk3'))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, '#sk3'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['215'])). 483.84/72.05 tff('217', plain, 483.84/72.05 (~ qmltpeq(a_select2(rho_defuse, n0), use, '#sk3')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['216'])). 483.84/72.05 tff('218', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk3')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['216'])). 483.84/72.05 tff('219', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('220', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | qmltpeq(a_select2(rho_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['219'])). 483.84/72.05 tff('221', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(rho_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['220'])). 483.84/72.05 tff('222', plain, 483.84/72.05 ( qmltpeq(a_select2(rho_defuse, n0), use, '#sk3')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['218', '221'])). 483.84/72.05 tff('223', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['217', '222'])). 483.84/72.05 tff('224', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('225', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk5'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, '#sk5'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['224'])). 483.84/72.05 tff('226', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n1), use, '#sk5')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['225'])). 483.84/72.05 tff('227', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk5')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['225'])). 483.84/72.05 tff('228', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('229', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['228'])). 483.84/72.05 tff('230', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['229'])). 483.84/72.05 tff('231', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n1), use, '#sk5')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['227', '230'])). 483.84/72.05 tff('232', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['226', '231'])). 483.84/72.05 tff('233', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('234', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk7'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, '#sk7'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['233'])). 483.84/72.05 tff('235', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n5), use, '#sk7')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['234'])). 483.84/72.05 tff('236', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk7')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['234'])). 483.84/72.05 tff('237', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('238', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['237'])). 483.84/72.05 tff('239', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['238'])). 483.84/72.05 tff('240', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n5), use, '#sk7')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['236', '239'])). 483.84/72.05 tff('241', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['235', '240'])). 483.84/72.05 tff('242', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('243', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk9'))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, '#sk9'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['242'])). 483.84/72.05 tff('244', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_defuse, n3), use, '#sk9')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['243'])). 483.84/72.05 tff('245', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk9')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['243'])). 483.84/72.05 tff('246', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('247', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['246'])). 483.84/72.05 tff('248', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(xinit_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['247'])). 483.84/72.05 tff('249', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_defuse, n3), use, '#sk9')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['245', '248'])). 483.84/72.05 tff('250', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['244', '249'])). 483.84/72.05 tff('251', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('252', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk10'))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, '#sk10'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['251'])). 483.84/72.05 tff('253', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_defuse, n5), use, '#sk10')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['252'])). 483.84/72.05 tff('254', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk10')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['252'])). 483.84/72.05 tff('255', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('256', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['255'])). 483.84/72.05 tff('257', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(xinit_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['256'])). 483.84/72.05 tff('258', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_defuse, n5), use, '#sk10')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['254', '257'])). 483.84/72.05 tff('259', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['253', '258'])). 483.84/72.05 tff('260', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('261', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk11'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, '#sk11'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['260'])). 483.84/72.05 tff('262', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n1), use, '#sk11')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['261'])). 483.84/72.05 tff('263', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk11')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['261'])). 483.84/72.05 tff('264', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('265', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['264'])). 483.84/72.05 tff('266', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['265'])). 483.84/72.05 tff('267', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n1), use, '#sk11')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['263', '266'])). 483.84/72.05 tff('268', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['262', '267'])). 483.84/72.05 tff('269', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('270', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk12'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, '#sk12'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['269'])). 483.84/72.05 tff('271', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n3), use, '#sk12')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['270'])). 483.84/72.05 tff('272', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk12')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['270'])). 483.84/72.05 tff('273', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('274', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['273'])). 483.84/72.05 tff('275', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['274'])). 483.84/72.05 tff('276', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n3), use, '#sk12')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['272', '275'])). 483.84/72.05 tff('277', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['271', '276'])). 483.84/72.05 tff('278', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('279', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk28'))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, '#sk28'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['278'])). 483.84/72.05 tff('280', plain, 483.84/72.05 (~ qmltpeq(a_select3(u_defuse, n2, n0), use, '#sk28')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['279'])). 483.84/72.05 tff('281', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk28')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['279'])). 483.84/72.05 tff('282', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('283', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['282'])). 483.84/72.05 tff('284', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select3(u_defuse, n2, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['283'])). 483.84/72.05 tff('285', plain, 483.84/72.05 ( qmltpeq(a_select3(u_defuse, n2, n0), use, '#sk28')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['281', '284'])). 483.84/72.05 tff('286', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['280', '285'])). 483.84/72.05 tff('287', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('288', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk13'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, '#sk13'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['287'])). 483.84/72.05 tff('289', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n5), use, '#sk13')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['288'])). 483.84/72.05 tff('290', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk13')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['288'])). 483.84/72.05 tff('291', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('292', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['291'])). 483.84/72.05 tff('293', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['292'])). 483.84/72.05 tff('294', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n5), use, '#sk13')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['290', '293'])). 483.84/72.05 tff('295', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['289', '294'])). 483.84/72.05 tff('296', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('297', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk14'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, '#sk14'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['296'])). 483.84/72.05 tff('298', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n1), use, '#sk14')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['297'])). 483.84/72.05 tff('299', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk14')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['297'])). 483.84/72.05 tff('300', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('301', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['300'])). 483.84/72.05 tff('302', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['301'])). 483.84/72.05 tff('303', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n1), use, '#sk14')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['299', '302'])). 483.84/72.05 tff('304', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['298', '303'])). 483.84/72.05 tff('305', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('306', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk15'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, '#sk15'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['305'])). 483.84/72.05 tff('307', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n3), use, '#sk15')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['306'])). 483.84/72.05 tff('308', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk15')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['306'])). 483.84/72.05 tff('309', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('310', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['309'])). 483.84/72.05 tff('311', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n3), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['310'])). 483.84/72.05 tff('312', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n3), use, '#sk15')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['308', '311'])). 483.84/72.05 tff('313', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['307', '312'])). 483.84/72.05 tff('314', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('315', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk16'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, '#sk16'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['314'])). 483.84/72.05 tff('316', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n5), use, '#sk16')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['315'])). 483.84/72.05 tff('317', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk16')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['315'])). 483.84/72.05 tff('318', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('319', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['318'])). 483.84/72.05 tff('320', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n5), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['319'])). 483.84/72.05 tff('321', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n5), use, '#sk16')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['317', '320'])). 483.84/72.05 tff('322', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['316', '321'])). 483.84/72.05 tff('323', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('324', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk20'))) | leq(n0, pv5, '#sk20'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['323'])). 483.84/72.05 tff('325', plain, 483.84/72.05 (~ leq(n0, pv5, '#sk20')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['324'])). 483.84/72.05 tff('326', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk20')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['324'])). 483.84/72.05 tff('327', plain, 483.84/72.05 (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('328', plain, ![X1]: ((~(rel_s4('#sk2', X1))) | leq(n0, pv5, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['327'])). 483.84/72.05 tff('329', plain, ![X1]: (~ rel_s4('#sk2', X1) | leq(n0, pv5, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['328'])). 483.84/72.05 tff('330', plain, 483.84/72.05 ( leq(n0, pv5, '#sk20')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['326', '329'])). 483.84/72.05 tff('331', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['325', '330'])). 483.84/72.05 tff('332', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('333', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk17'))) | leq(pv5, minus(n999, n1), '#sk17'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['332'])). 483.84/72.05 tff('334', plain, 483.84/72.05 (~ leq(pv5, minus(n999, n1), '#sk17')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['333'])). 483.84/72.05 tff('335', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk17')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['333'])). 483.84/72.05 tff('336', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('337', plain, 483.84/72.05 ![X1]: ((~(rel_s4('#sk2', X1))) | leq(pv5, minus(n999, n1), X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['336'])). 483.84/72.05 tff('338', plain, 483.84/72.05 ![X1]: (~ rel_s4('#sk2', X1) | leq(pv5, minus(n999, n1), X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['337'])). 483.84/72.05 tff('339', plain, 483.84/72.05 ( leq(pv5, minus(n999, n1), '#sk17')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['335', '338'])). 483.84/72.05 tff('340', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['334', '339'])). 483.84/72.05 tff('341', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('342', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk21'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, '#sk21'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['341'])). 483.84/72.05 tff('343', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n4), use, '#sk21')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['342'])). 483.84/72.05 tff('344', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk21')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['342'])). 483.84/72.05 tff('345', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('346', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['345'])). 483.84/72.05 tff('347', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['346'])). 483.84/72.05 tff('348', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n4), use, '#sk21')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['344', '347'])). 483.84/72.05 tff('349', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['343', '348'])). 483.84/72.05 tff('350', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('351', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk23'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, '#sk23'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['350'])). 483.84/72.05 tff('352', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n0), use, '#sk23')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['351'])). 483.84/72.05 tff('353', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk23')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['351'])). 483.84/72.05 tff('354', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('355', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['354'])). 483.84/72.05 tff('356', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['355'])). 483.84/72.05 tff('357', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n0), use, '#sk23')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['353', '356'])). 483.84/72.05 tff('358', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['352', '357'])). 483.84/72.05 tff('359', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('360', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk22'))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, '#sk22'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['359'])). 483.84/72.05 tff('361', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_noise_defuse, n2), use, '#sk22')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['360'])). 483.84/72.05 tff('362', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk22')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['360'])). 483.84/72.05 tff('363', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('364', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['363'])). 483.84/72.05 tff('365', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_noise_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['364'])). 483.84/72.05 tff('366', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_noise_defuse, n2), use, '#sk22')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['362', '365'])). 483.84/72.05 tff('367', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['361', '366'])). 483.84/72.05 tff('368', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('369', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk25'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, '#sk25'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['368'])). 483.84/72.05 tff('370', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n2), use, '#sk25')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['369'])). 483.84/72.05 tff('371', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk25')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['369'])). 483.84/72.05 tff('372', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('373', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['372'])). 483.84/72.05 tff('374', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['373'])). 483.84/72.05 tff('375', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n2), use, '#sk25')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['371', '374'])). 483.84/72.05 tff('376', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['370', '375'])). 483.84/72.05 tff('377', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('378', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk24'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, '#sk24'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['377'])). 483.84/72.05 tff('379', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n4), use, '#sk24')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['378'])). 483.84/72.05 tff('380', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk24')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['378'])). 483.84/72.05 tff('381', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('382', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['381'])). 483.84/72.05 tff('383', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['382'])). 483.84/72.05 tff('384', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n4), use, '#sk24')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['380', '383'])). 483.84/72.05 tff('385', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['379', '384'])). 483.84/72.05 tff('386', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('387', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk27'))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, '#sk27'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['386'])). 483.84/72.05 tff('388', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_defuse, n4), use, '#sk27')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['387'])). 483.84/72.05 tff('389', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk27')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['387'])). 483.84/72.05 tff('390', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('391', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['390'])). 483.84/72.05 tff('392', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(xinit_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['391'])). 483.84/72.05 tff('393', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_defuse, n4), use, '#sk27')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['389', '392'])). 483.84/72.05 tff('394', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_defuse, n4), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['388', '393'])). 483.84/72.05 tff('395', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('396', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk26'))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, '#sk26'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['395'])). 483.84/72.05 tff('397', plain, 483.84/72.05 (~ qmltpeq(a_select2(xinit_mean_defuse, n0), use, '#sk26')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['396'])). 483.84/72.05 tff('398', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk26')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['396'])). 483.84/72.05 tff('399', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('400', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['399'])). 483.84/72.05 tff('401', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) 483.84/72.05 | qmltpeq(a_select2(xinit_mean_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['400'])). 483.84/72.05 tff('402', plain, 483.84/72.05 ( qmltpeq(a_select2(xinit_mean_defuse, n0), use, '#sk26')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['398', '401'])). 483.84/72.05 tff('403', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['397', '402'])). 483.84/72.05 tff('404', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('405', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk29'))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, '#sk29'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['404'])). 483.84/72.05 tff('406', plain, 483.84/72.05 (~ qmltpeq(a_select3(u_defuse, n0, n0), use, '#sk29')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['405'])). 483.84/72.05 tff('407', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk29')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['405'])). 483.84/72.05 tff('408', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('409', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['408'])). 483.84/72.05 tff('410', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select3(u_defuse, n0, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['409'])). 483.84/72.05 tff('411', plain, 483.84/72.05 ( qmltpeq(a_select3(u_defuse, n0, n0), use, '#sk29')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['407', '410'])). 483.84/72.05 tff('412', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['406', '411'])). 483.84/72.05 tff('413', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('414', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk30'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, '#sk30'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['413'])). 483.84/72.05 tff('415', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n4), use, '#sk30')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['414'])). 483.84/72.05 tff('416', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk30')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['414'])). 483.84/72.05 tff('417', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('418', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['417'])). 483.84/72.05 tff('419', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n4), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['418'])). 483.84/72.05 tff('420', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n4), use, '#sk30')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['416', '419'])). 483.84/72.05 tff('421', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n4), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['415', '420'])). 483.84/72.05 tff('422', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('423', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk33'))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, '#sk33'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['422'])). 483.84/72.05 tff('424', plain, 483.84/72.05 (~ qmltpeq(a_select2(rho_defuse, n1), use, '#sk33')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['423'])). 483.84/72.05 tff('425', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk33')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['423'])). 483.84/72.05 tff('426', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('427', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | qmltpeq(a_select2(rho_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['426'])). 483.84/72.05 tff('428', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(rho_defuse, n1), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['427'])). 483.84/72.05 tff('429', plain, 483.84/72.05 ( qmltpeq(a_select2(rho_defuse, n1), use, '#sk33')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['425', '428'])). 483.84/72.05 tff('430', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['424', '429'])). 483.84/72.05 tff('431', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('432', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk31'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, '#sk31'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['431'])). 483.84/72.05 tff('433', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n2), use, '#sk31')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['432'])). 483.84/72.05 tff('434', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk31')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['432'])). 483.84/72.05 tff('435', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('436', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['435'])). 483.84/72.05 tff('437', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n2), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['436'])). 483.84/72.05 tff('438', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n2), use, '#sk31')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['434', '437'])). 483.84/72.05 tff('439', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n2), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['433', '438'])). 483.84/72.05 tff('440', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0)))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('441', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk32'))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, '#sk32'))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['440'])). 483.84/72.05 tff('442', plain, 483.84/72.05 (~ qmltpeq(a_select2(sigma_defuse, n0), use, '#sk32')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['441'])). 483.84/72.05 tff('443', plain, 483.84/72.05 ( rel_s4('#sk2', '#sk32')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['441'])). 483.84/72.05 tff('444', plain, 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['16'])). 483.84/72.05 tff('445', plain, 483.84/72.05 ![X1]: 483.84/72.05 ((~(rel_s4('#sk2', X1))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_forall', [status(thm)], ['444'])). 483.84/72.05 tff('446', plain, 483.84/72.05 ![X1]: 483.84/72.05 (~ rel_s4('#sk2', X1) | qmltpeq(a_select2(sigma_defuse, n0), use, X1)), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['445'])). 483.84/72.05 tff('447', plain, 483.84/72.05 ( qmltpeq(a_select2(sigma_defuse, n0), use, '#sk32')) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0))))))), 483.84/72.05 inference('sup-', [status(thm)], ['443', '446'])). 483.84/72.05 tff('448', plain, 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 qmltpeq(a_select2(sigma_defuse, n0), use, Y0)))))), 483.84/72.05 inference('demod', [status(thm)], ['442', '447'])). 483.84/72.05 tff('449', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y3, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y3, pv5, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(Y1, n2, Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, Y5))) | 483.84/72.05 leq(n0, Y1, Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))))))))))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('split', [status(esa)], ['18'])). 483.84/72.05 tff('450', plain, 483.84/72.05 (~ ((~(rel_s4('#sk2', '#sk19'))) | 483.84/72.05 (!!((^[Y0 : mu]: 483.84/72.05 (exists_in_world(Y0, '#sk19') => 483.84/72.05 (!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4('#sk19', Y1))) | 483.84/72.05 (!!((^[Y2 : mu]: 483.84/72.05 (exists_in_world(Y2, Y1) => 483.84/72.05 (!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y3)))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(n0, Y2, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(Y2, pv5, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(Y0, n2, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(n0, Y0, Y4)))))))| 483.84/72.05 (~(((~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, 483.84/72.05 Y0, Y2), use, Y4))))))) | 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, 483.84/72.05 Y0, Y2), use, Y4)))))))))))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['449'])). 483.84/72.05 tff('451', plain, 483.84/72.05 (~ (!!((^[Y0 : mu]: 483.84/72.05 (exists_in_world(Y0, '#sk19') => 483.84/72.05 (!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4('#sk19', Y1))) | 483.84/72.05 (!!((^[Y2 : mu]: 483.84/72.05 (exists_in_world(Y2, Y1) => 483.84/72.05 (!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y3)))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(n0, Y2, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(Y2, pv5, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(Y0, n2, Y4)))))))| 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 leq(n0, Y0, Y4)))))))| 483.84/72.05 (~(((~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, 483.84/72.05 Y0, Y2), use, Y4))))))) | 483.84/72.05 (~((!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y3, Y4))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, 483.84/72.05 Y0, Y2), use, Y4))))))))))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.05 tff('452', plain, 483.84/72.05 (~ (exists_in_world('#sk35', '#sk19') => 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk19', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2)))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(n0, Y1, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(Y1, pv5, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq('#sk35', n2, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(n0, '#sk35', Y3)))))))| 483.84/72.05 (~(((~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, 483.84/72.05 '#sk35', Y1), use, Y3))))))) | 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, 483.84/72.05 '#sk35', Y1), use, Y3)))))))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['451'])). 483.84/72.05 tff('453', plain, 483.84/72.05 (~ (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk19', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2)))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(n0, Y1, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(Y1, pv5, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq('#sk35', n2, Y3)))))))| 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 leq(n0, '#sk35', Y3)))))))| 483.84/72.05 (~(((~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, '#sk35', 483.84/72.05 Y1), use, Y3))))))) | 483.84/72.05 (~((!!((^[Y3 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y3))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, '#sk35', 483.84/72.05 Y1), use, Y3))))))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.05 tff('454', plain, 483.84/72.05 (~ ((~(rel_s4('#sk19', '#sk37'))) | 483.84/72.05 (!!((^[Y0 : mu]: 483.84/72.05 (exists_in_world(Y0, '#sk37') => 483.84/72.05 (!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4('#sk37', Y1)))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(Y0, pv5, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq('#sk35', n2, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(n0, '#sk35', Y2)))))))| 483.84/72.05 (~(((~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, '#sk35', Y0), 483.84/72.05 use, Y2))))))) | 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, '#sk35', Y0), 483.84/72.05 use, Y2)))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_exists', [status(thm)], ['453'])). 483.84/72.05 tff('455', plain, 483.84/72.05 (~ (!!((^[Y0 : mu]: 483.84/72.05 (exists_in_world(Y0, '#sk37') => 483.84/72.05 (!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4('#sk37', Y1)))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(n0, Y0, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(Y0, pv5, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq('#sk35', n2, Y2)))))))| 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | leq(n0, '#sk35', Y2)))))))| 483.84/72.05 (~(((~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, '#sk35', Y0), 483.84/72.05 use, Y2))))))) | 483.84/72.05 (~((!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y1, Y2))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, '#sk35', Y0), 483.84/72.05 use, Y2))))))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y3, pv5, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(Y1, n2, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y1, 483.84/72.05 Y5)))))))| 483.84/72.05 (~(((~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 z_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5))))))) | 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~( 483.84/72.05 rel_s4( 483.84/72.05 Y4, Y5))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3( 483.84/72.05 u_defuse, 483.84/72.05 Y1, Y3), 483.84/72.05 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.05 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.05 tff('456', plain, 483.84/72.05 (~ (exists_in_world('#sk39', '#sk37') => 483.84/72.05 (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk37', Y0)))| 483.84/72.05 (~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk39', Y1)))))))| 483.84/72.05 (~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | leq('#sk39', pv5, Y1)))))))| 483.84/72.05 (~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | leq('#sk35', n2, Y1)))))))| 483.84/72.05 (~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk35', Y1)))))))| 483.84/72.05 (~(((~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(z_defuse, '#sk35', '#sk39'), use, 483.84/72.05 Y1))))))) | 483.84/72.05 (~((!!((^[Y1 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y1))) | 483.84/72.05 qmltpeq( 483.84/72.05 a_select3(u_defuse, '#sk35', '#sk39'), use, 483.84/72.05 Y1)))))))))))))))) 483.84/72.05 <= (~ 483.84/72.05 ( (!!((^[Y0 : $i]: 483.84/72.05 ((~(rel_s4('#sk2', Y0))) | 483.84/72.05 (!!((^[Y1 : mu]: 483.84/72.05 (exists_in_world(Y1, Y0) => 483.84/72.05 (!!((^[Y2 : $i]: 483.84/72.05 ((~(rel_s4(Y0, Y2))) | 483.84/72.05 (!!((^[Y3 : mu]: 483.84/72.05 (exists_in_world(Y3, Y2) => 483.84/72.05 (!!((^[Y4 : $i]: 483.84/72.05 ((~(rel_s4(Y2, Y4)))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.05 ((~(rel_s4(Y4, 483.84/72.05 Y5))) | 483.84/72.05 leq(n0, Y3, 483.84/72.05 Y5)))))))| 483.84/72.05 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_exists', [status(thm)], ['455'])). 483.84/72.06 tff('457', plain, 483.84/72.06 ( exists_in_world('#sk39', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('458', plain, 483.84/72.06 ( rel_s4('#sk2', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.06 tff('459', plain, 483.84/72.06 (~ (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk37', Y0)))| 483.84/72.06 (~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk39', Y1)))))))| 483.84/72.06 (~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | leq('#sk39', pv5, Y1)))))))| 483.84/72.06 (~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | leq('#sk35', n2, Y1)))))))| 483.84/72.06 (~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | leq(n0, '#sk35', Y1)))))))| 483.84/72.06 (~(((~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), 483.84/72.06 use, Y1))))))) | 483.84/72.06 (~((!!((^[Y1 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y1))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), 483.84/72.06 use, Y1))))))))))))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('460', plain, 483.84/72.06 (~ ((~(rel_s4('#sk37', '#sk42')))| 483.84/72.06 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq(n0, '#sk39', Y0)))))))| 483.84/72.06 (~((!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | leq('#sk39', pv5, Y0)))))))| 483.84/72.06 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq('#sk35', n2, Y0)))))))| 483.84/72.06 (~((!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq(n0, '#sk35', Y0)))))))| 483.84/72.06 (~(((~((!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, 483.84/72.06 Y0))))))) | 483.84/72.06 (~((!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, 483.84/72.06 Y0)))))))))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_exists', [status(thm)], ['459'])). 483.84/72.06 tff('461', plain, 483.84/72.06 ( rel_s4('#sk37', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('462', plain, 483.84/72.06 ![X2 : mu, X5]: ( rel_s4(X5, '#sk40'(X2, X5)) | '#form46'(X2, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['52'])). 483.84/72.06 tff('463', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq(n0, '#sk35', Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('464', plain, 483.84/72.06 (![X1]: ((~(rel_s4('#sk42', X1))) | leq(n0, '#sk35', X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_forall', [status(thm)], ['463'])). 483.84/72.06 tff('465', plain, 483.84/72.06 (![X1]: (~ rel_s4('#sk42', X1) | leq(n0, '#sk35', X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['464'])). 483.84/72.06 tff('466', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 ( '#form46'(X0, '#sk42') | leq(n0, '#sk35', '#sk40'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['462', '465'])). 483.84/72.06 tff('467', plain, 483.84/72.06 ![X2 : mu, X5]: (~ leq(n0, X2, '#sk40'(X2, X5)) | '#form46'(X2, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['52'])). 483.84/72.06 tff('468', plain, 483.84/72.06 (( '#form46'('#sk35', '#sk42') | '#form46'('#sk35', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['466', '467'])). 483.84/72.06 tff('469', plain, 483.84/72.06 ( '#form46'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('simplify', [status(thm)], ['468'])). 483.84/72.06 tff('470', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ '#form44'(X2, X4, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.06 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0))))) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ '#form43'(X2, X5)), 483.84/72.06 inference('renaming', [status(thm)], ['47', '49'])). 483.84/72.06 tff('471', plain, 483.84/72.06 ![X2 : mu, X5]: 483.84/72.06 ( '#form46'(X2, X5) 483.84/72.06 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(n0, X2, Y0)))))), 483.84/72.06 define([status(thm)])). 483.84/72.06 tff('472', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X4, pv5, Y0))))) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('renaming', [status(thm)], ['470', '471'])). 483.84/72.06 tff('473', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ ((~(rel_s4(X5, '#sk51'(X4, X5)))) | leq(X4, pv5, '#sk51'(X4, X5))) 483.84/72.06 | ~ '#form44'(X2, X4, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ '#form46'(X2, X5)), 483.84/72.06 inference('lazy_cnf_exists', [status(thm)], ['472'])). 483.84/72.06 tff('474', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 ( rel_s4(X5, '#sk51'(X4, X5)) 483.84/72.06 | ~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['473'])). 483.84/72.06 tff('475', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ '#form43'('#sk35', '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['469', '474'])). 483.84/72.06 tff('476', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq('#sk35', n2, Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('477', plain, 483.84/72.06 ![X2 : mu, X5]: 483.84/72.06 (~ '#form43'(X2, X5) 483.84/72.06 | (!!((^[Y0 : $i]: ((~(rel_s4(X5, Y0))) | leq(X2, n2, Y0)))))), 483.84/72.06 define([status(thm)])). 483.84/72.06 tff('478', plain, 483.84/72.06 ( '#form43'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('renaming', [status(thm)], ['476', '477'])). 483.84/72.06 tff('479', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['475', '478'])). 483.84/72.06 tff('480', plain, 483.84/72.06 (![X0 : mu, X1]: 483.84/72.06 ( rel_s4('#sk42', '#sk51'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world('#sk35', X1) 483.84/72.06 | ~ rel_s4(X1, '#sk37') 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', X0, '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['461', '479'])). 483.84/72.06 tff('481', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ rel_s4('#sk19', '#sk37') 483.84/72.06 | ~ exists_in_world('#sk35', '#sk19') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['458', '480'])). 483.84/72.06 tff('482', plain, 483.84/72.06 ( rel_s4('#sk19', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.06 tff('483', plain, 483.84/72.06 ( exists_in_world('#sk35', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.06 tff('484', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['481', '482', '483'])). 483.84/72.06 tff('485', plain, 483.84/72.06 (( rel_s4('#sk42', '#sk51'('#sk39', '#sk42')) 483.84/72.06 | rel_s4('#sk42', '#sk40'('#sk39', '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', '#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['457', '484'])). 483.84/72.06 tff('486', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ( rel_s4('#sk42', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('split', [status(esa)], ['485'])). 483.84/72.06 tff('487', plain, 483.84/72.06 ( exists_in_world('#sk39', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('488', plain, 483.84/72.06 ( rel_s4('#sk2', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.06 tff('489', plain, 483.84/72.06 ( rel_s4('#sk37', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('490', plain, 483.84/72.06 ( '#form46'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('simplify', [status(thm)], ['468'])). 483.84/72.06 tff('491', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ leq(X4, pv5, '#sk51'(X4, X5)) 483.84/72.06 | ~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['473'])). 483.84/72.06 tff('492', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ '#form43'('#sk35', '#sk42') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['490', '491'])). 483.84/72.06 tff('493', plain, 483.84/72.06 ( '#form43'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('renaming', [status(thm)], ['476', '477'])). 483.84/72.06 tff('494', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['492', '493'])). 483.84/72.06 tff('495', plain, 483.84/72.06 (![X0 : mu, X1]: 483.84/72.06 (~ leq(X0, pv5, '#sk51'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world('#sk35', X1) 483.84/72.06 | ~ rel_s4(X1, '#sk37') 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', X0, '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['489', '494'])). 483.84/72.06 tff('496', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ rel_s4('#sk19', '#sk37') 483.84/72.06 | ~ exists_in_world('#sk35', '#sk19') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['488', '495'])). 483.84/72.06 tff('497', plain, 483.84/72.06 ( rel_s4('#sk19', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.06 tff('498', plain, 483.84/72.06 ( exists_in_world('#sk35', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.06 tff('499', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['496', '497', '498'])). 483.84/72.06 tff('500', plain, 483.84/72.06 ((~ leq('#sk39', pv5, '#sk51'('#sk39', '#sk42')) 483.84/72.06 | rel_s4('#sk42', '#sk40'('#sk39', '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', '#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['487', '499'])). 483.84/72.06 tff('501', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ ( leq('#sk39', pv5, '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('split', [status(esa)], ['500'])). 483.84/72.06 tff('502', plain, 483.84/72.06 ( exists_in_world('#sk39', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('503', plain, 483.84/72.06 ( rel_s4('#sk2', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.06 tff('504', plain, 483.84/72.06 ( rel_s4('#sk37', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('505', plain, 483.84/72.06 ( '#form46'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('simplify', [status(thm)], ['468'])). 483.84/72.06 tff('506', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ leq(X4, minus(pv5, n1), '#sk52'(X4, X5)) 483.84/72.06 | ~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['169'])). 483.84/72.06 tff('507', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ '#form43'('#sk35', '#sk42') 483.84/72.06 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['505', '506'])). 483.84/72.06 tff('508', plain, 483.84/72.06 ( '#form43'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('renaming', [status(thm)], ['476', '477'])). 483.84/72.06 tff('509', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['507', '508'])). 483.84/72.06 tff('510', plain, 483.84/72.06 (![X0 : mu, X1]: 483.84/72.06 (~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world('#sk35', X1) 483.84/72.06 | ~ rel_s4(X1, '#sk37') 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', X0, '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['504', '509'])). 483.84/72.06 tff('511', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ rel_s4('#sk19', '#sk37') 483.84/72.06 | ~ exists_in_world('#sk35', '#sk19') 483.84/72.06 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['503', '510'])). 483.84/72.06 tff('512', plain, 483.84/72.06 ( rel_s4('#sk19', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.06 tff('513', plain, 483.84/72.06 ( exists_in_world('#sk35', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.06 tff('514', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ leq(X0, minus(pv5, n1), '#sk52'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['511', '512', '513'])). 483.84/72.06 tff('515', plain, 483.84/72.06 ((~ leq('#sk39', minus(pv5, n1), '#sk52'('#sk39', '#sk42')) 483.84/72.06 | rel_s4('#sk42', '#sk40'('#sk39', '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', '#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['502', '514'])). 483.84/72.06 tff('516', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk40'('#sk39', '#sk42'))) 483.84/72.06 <= (( rel_s4('#sk42', '#sk40'('#sk39', '#sk42')))), 483.84/72.06 inference('split', [status(esa)], ['515'])). 483.84/72.06 tff('517', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq(n0, '#sk39', Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('518', plain, 483.84/72.06 (![X1]: ((~(rel_s4('#sk42', X1))) | leq(n0, '#sk39', X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_forall', [status(thm)], ['517'])). 483.84/72.06 tff('519', plain, 483.84/72.06 (![X1]: (~ rel_s4('#sk42', X1) | leq(n0, '#sk39', X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['518'])). 483.84/72.06 tff('520', plain, 483.84/72.06 ( leq(n0, '#sk39', '#sk40'('#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) & 483.84/72.06 ( rel_s4('#sk42', '#sk40'('#sk39', '#sk42')))), 483.84/72.06 inference('sup-', [status(thm)], ['516', '519'])). 483.84/72.06 tff('521', plain, 483.84/72.06 ( exists_in_world('#sk39', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('522', plain, 483.84/72.06 ( rel_s4('#sk2', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.06 tff('523', plain, 483.84/72.06 ( rel_s4('#sk37', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('524', plain, 483.84/72.06 ( '#form46'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('simplify', [status(thm)], ['468'])). 483.84/72.06 tff('525', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 (~ leq(X4, pv5, '#sk51'(X4, X5)) 483.84/72.06 | ~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['118'])). 483.84/72.06 tff('526', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ '#form43'('#sk35', '#sk42') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['524', '525'])). 483.84/72.06 tff('527', plain, 483.84/72.06 ( '#form43'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('renaming', [status(thm)], ['476', '477'])). 483.84/72.06 tff('528', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['526', '527'])). 483.84/72.06 tff('529', plain, 483.84/72.06 (![X0 : mu, X1]: 483.84/72.06 (~ leq(X0, pv5, '#sk51'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world('#sk35', X1) 483.84/72.06 | ~ rel_s4(X1, '#sk37') 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', X0, '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['523', '528'])). 483.84/72.06 tff('530', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ rel_s4('#sk19', '#sk37') 483.84/72.06 | ~ exists_in_world('#sk35', '#sk19') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['522', '529'])). 483.84/72.06 tff('531', plain, 483.84/72.06 ( rel_s4('#sk19', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.06 tff('532', plain, 483.84/72.06 ( exists_in_world('#sk35', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.06 tff('533', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ leq(X0, pv5, '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['530', '531', '532'])). 483.84/72.06 tff('534', plain, 483.84/72.06 ((~ leq('#sk39', pv5, '#sk51'('#sk39', '#sk42')) 483.84/72.06 | ~ leq(n0, '#sk39', '#sk40'('#sk39', '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', '#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['521', '533'])). 483.84/72.06 tff('535', plain, 483.84/72.06 (~ leq(n0, '#sk39', '#sk40'('#sk39', '#sk42'))) 483.84/72.06 <= (~ ( leq(n0, '#sk39', '#sk40'('#sk39', '#sk42')))), 483.84/72.06 inference('split', [status(esa)], ['534'])). 483.84/72.06 tff('536', plain, 483.84/72.06 ( leq(n0, '#sk39', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( rel_s4('#sk42', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['520', '535'])). 483.84/72.06 tff('537', plain, 483.84/72.06 ( exists_in_world('#sk39', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['456'])). 483.84/72.06 tff('538', plain, 483.84/72.06 ( rel_s4('#sk2', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['450'])). 483.84/72.06 tff('539', plain, 483.84/72.06 ( rel_s4('#sk37', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('540', plain, 483.84/72.06 ( '#form46'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('simplify', [status(thm)], ['468'])). 483.84/72.06 tff('541', plain, 483.84/72.06 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.06 ( rel_s4(X5, '#sk51'(X4, X5)) 483.84/72.06 | ~ '#form46'(X2, X5) 483.84/72.06 | ~ '#form43'(X2, X5) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world(X2, X1) 483.84/72.06 | ~ rel_s4(X1, X3) 483.84/72.06 | ~ exists_in_world(X4, X3) 483.84/72.06 | ~ rel_s4(X3, X5) 483.84/72.06 | ~ leq(n0, X4, '#sk40'(X4, X5)) 483.84/72.06 | ~ '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['118'])). 483.84/72.06 tff('542', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | ~ '#form43'('#sk35', '#sk42') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['540', '541'])). 483.84/72.06 tff('543', plain, 483.84/72.06 ( '#form43'('#sk35', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('renaming', [status(thm)], ['476', '477'])). 483.84/72.06 tff('544', plain, 483.84/72.06 (![X0 : mu, X1, X2]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4(X1, '#sk42') 483.84/72.06 | ~ exists_in_world(X0, X1) 483.84/72.06 | ~ rel_s4(X2, X1) 483.84/72.06 | ~ exists_in_world('#sk35', X2) 483.84/72.06 | ~ rel_s4('#sk2', X2) 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['542', '543'])). 483.84/72.06 tff('545', plain, 483.84/72.06 (![X0 : mu, X1]: 483.84/72.06 ( rel_s4('#sk42', '#sk51'(X0, '#sk42')) 483.84/72.06 | ~ rel_s4('#sk2', X1) 483.84/72.06 | ~ exists_in_world('#sk35', X1) 483.84/72.06 | ~ rel_s4(X1, '#sk37') 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', X0, '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['539', '544'])). 483.84/72.06 tff('546', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | ~ rel_s4('#sk19', '#sk37') 483.84/72.06 | ~ exists_in_world('#sk35', '#sk19') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['538', '545'])). 483.84/72.06 tff('547', plain, 483.84/72.06 ( rel_s4('#sk19', '#sk37')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['454'])). 483.84/72.06 tff('548', plain, 483.84/72.06 ( exists_in_world('#sk35', '#sk19')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_imply', [status(thm)], ['452'])). 483.84/72.06 tff('549', plain, 483.84/72.06 (![X0 : mu]: 483.84/72.06 (~ '#form44'('#sk35', X0, '#sk42') 483.84/72.06 | ~ leq(n0, X0, '#sk40'(X0, '#sk42')) 483.84/72.06 | ~ exists_in_world(X0, '#sk37') 483.84/72.06 | rel_s4('#sk42', '#sk51'(X0, '#sk42')))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('demod', [status(thm)], ['546', '547', '548'])). 483.84/72.06 tff('550', plain, 483.84/72.06 (( rel_s4('#sk42', '#sk51'('#sk39', '#sk42')) 483.84/72.06 | ~ leq(n0, '#sk39', '#sk40'('#sk39', '#sk42')) 483.84/72.06 | ~ '#form44'('#sk35', '#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['537', '549'])). 483.84/72.06 tff('551', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ ( leq(n0, '#sk39', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('split', [status(esa)], ['550'])). 483.84/72.06 tff('552', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ ( leq(n0, '#sk39', '#sk40'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( leq('#sk39', pv5, '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('split', [status(esa)], ['534'])). 483.84/72.06 tff('553', plain, 483.84/72.06 ( ((~((!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))) | 483.84/72.06 (~((!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('554', plain, 483.84/72.06 ((~ (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))) 483.84/72.06 | ~ (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['553'])). 483.84/72.06 tff('555', plain, 483.84/72.06 (~ (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('split', [status(esa)], ['554'])). 483.84/72.06 tff('556', plain, 483.84/72.06 (~ ((~(rel_s4('#sk42', '#sk50'))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, '#sk50'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_exists', [status(thm)], ['555'])). 483.84/72.06 tff('557', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk50')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['556'])). 483.84/72.06 tff('558', plain, 483.84/72.06 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.06 (~ rel_s4(X5, X6) 483.84/72.06 | qmltpeq(a_select3(z_defuse, X2, X4), use, X6) 483.84/72.06 | '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['102'])). 483.84/72.06 tff('559', plain, 483.84/72.06 (![X0 : mu, X1 : mu]: 483.84/72.06 ( '#form44'(X1, X0, '#sk42') 483.84/72.06 | qmltpeq(a_select3(z_defuse, X1, X0), use, '#sk50'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('sup-', [status(thm)], ['557', '558'])). 483.84/72.06 tff('560', plain, 483.84/72.06 (~ qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, '#sk50')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['556'])). 483.84/72.06 tff('561', plain, 483.84/72.06 ( '#form44'('#sk35', '#sk39', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('sup-', [status(thm)], ['559', '560'])). 483.84/72.06 tff('562', plain, 483.84/72.06 (~ '#form44'('#sk35', '#sk39', '#sk42')) 483.84/72.06 <= (~ ( '#form44'('#sk35', '#sk39', '#sk42'))), 483.84/72.06 inference('split', [status(esa)], ['534'])). 483.84/72.06 tff('563', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0)))))) | 483.84/72.06 ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('sup-', [status(thm)], ['561', '562'])). 483.84/72.06 tff('564', plain, 483.84/72.06 (~ (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('split', [status(esa)], ['554'])). 483.84/72.06 tff('565', plain, 483.84/72.06 (~ ((~(rel_s4('#sk42', '#sk49'))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, '#sk49'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_exists', [status(thm)], ['564'])). 483.84/72.06 tff('566', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk49')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['565'])). 483.84/72.06 tff('567', plain, 483.84/72.06 ![X2 : mu, X4 : mu, X5, X6]: 483.84/72.06 (~ rel_s4(X5, X6) 483.84/72.06 | qmltpeq(a_select3(u_defuse, X2, X4), use, X6) 483.84/72.06 | '#form44'(X2, X4, X5)), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['135'])). 483.84/72.06 tff('568', plain, 483.84/72.06 (![X0 : mu, X1 : mu]: 483.84/72.06 ( '#form44'(X1, X0, '#sk42') 483.84/72.06 | qmltpeq(a_select3(u_defuse, X1, X0), use, '#sk49'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('sup-', [status(thm)], ['566', '567'])). 483.84/72.06 tff('569', plain, 483.84/72.06 (~ qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, '#sk49')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['565'])). 483.84/72.06 tff('570', plain, 483.84/72.06 ( '#form44'('#sk35', '#sk39', '#sk42')) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0))))))), 483.84/72.06 inference('sup-', [status(thm)], ['568', '569'])). 483.84/72.06 tff('571', plain, 483.84/72.06 (~ '#form44'('#sk35', '#sk39', '#sk42')) 483.84/72.06 <= (~ ( '#form44'('#sk35', '#sk39', '#sk42'))), 483.84/72.06 inference('split', [status(esa)], ['534'])). 483.84/72.06 tff('572', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0)))))) | 483.84/72.06 ( '#form44'('#sk35', '#sk39', '#sk42')), 483.84/72.06 inference('sup-', [status(thm)], ['570', '571'])). 483.84/72.06 tff('573', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, '#sk35', '#sk39'), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk42', Y0))) | 483.84/72.06 qmltpeq(a_select3(z_defuse, '#sk35', '#sk39'), use, Y0)))))), 483.84/72.06 inference('split', [status(esa)], ['554'])). 483.84/72.06 tff('574', plain, 483.84/72.06 ( rel_s4('#sk42', '#sk51'('#sk39', '#sk42'))) 483.84/72.06 <= (( rel_s4('#sk42', '#sk51'('#sk39', '#sk42')))), 483.84/72.06 inference('split', [status(esa)], ['485'])). 483.84/72.06 tff('575', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk42', Y0))) | leq('#sk39', pv5, Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['460'])). 483.84/72.06 tff('576', plain, 483.84/72.06 (![X1]: ((~(rel_s4('#sk42', X1))) | leq('#sk39', pv5, X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_forall', [status(thm)], ['575'])). 483.84/72.06 tff('577', plain, 483.84/72.06 (![X1]: (~ rel_s4('#sk42', X1) | leq('#sk39', pv5, X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['576'])). 483.84/72.06 tff('578', plain, 483.84/72.06 ( leq('#sk39', pv5, '#sk51'('#sk39', '#sk42'))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, pv5, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) & 483.84/72.06 ( rel_s4('#sk42', '#sk51'('#sk39', '#sk42')))), 483.84/72.06 inference('sup-', [status(thm)], ['574', '577'])). 483.84/72.06 tff('579', plain, 483.84/72.06 (~ leq('#sk39', pv5, '#sk51'('#sk39', '#sk42'))) 483.84/72.06 <= (~ ( leq('#sk39', pv5, '#sk51'('#sk39', '#sk42')))), 483.84/72.06 inference('split', [status(esa)], ['534'])). 483.84/72.06 tff('580', plain, 483.84/72.06 ( leq('#sk39', pv5, '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ~ ( rel_s4('#sk42', '#sk51'('#sk39', '#sk42'))) | 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))), 483.84/72.06 inference('sup-', [status(thm)], ['578', '579'])). 483.84/72.06 tff('581', plain, 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, 483.84/72.06 minus(pv5, n1), 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y3, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y3, pv5, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(Y1, n2, Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, Y5))) | 483.84/72.06 leq(n0, Y1, Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n2), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(rho_defuse, n1), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n4), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, n0, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_defuse, n4), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n4), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n2), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n2), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n4), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | leq(pv5, minus(n999, n1), Y0)))))) | 483.84/72.06 ~ ( (!!((^[Y0 : $i]: ((~(rel_s4('#sk2', Y0))) | leq(n0, pv5, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n5), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n3), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_noise_defuse, n1), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n5), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, n2, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n3), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_mean_defuse, n1), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_defuse, n5), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(xinit_defuse, n3), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n5), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n1), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(rho_defuse, n0), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(rho_defuse, n2), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select2(sigma_defuse, n3), use, Y0)))))) | 483.84/72.06 ~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 qmltpeq(a_select3(u_defuse, n1, n0), use, Y0)))))), 483.84/72.06 inference('split', [status(esa)], ['18'])). 483.84/72.06 tff('582', plain, 483.84/72.06 ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41'))) 483.84/72.06 <= (( rel_s4('#sk41', '#sk52'('#sk38', '#sk41')))), 483.84/72.06 inference('split', [status(esa)], ['93'])). 483.84/72.06 tff('583', plain, 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk41', Y0))) | leq('#sk38', minus(pv5, n1), Y0)))))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y3, 483.84/72.06 minus(pv5, 483.84/72.06 n1), Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(Y1, n2, 483.84/72.06 Y5)))))))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y1, 483.84/72.06 Y5)))))))| 483.84/72.06 (~(((~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 z_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5))))))) | 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~( 483.84/72.06 rel_s4( 483.84/72.06 Y4, Y5))) | 483.84/72.06 qmltpeq( 483.84/72.06 a_select3( 483.84/72.06 u_defuse, 483.84/72.06 Y1, Y3), 483.84/72.06 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.06 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.06 tff('584', plain, 483.84/72.06 (![X1]: ((~(rel_s4('#sk41', X1))) | leq('#sk38', minus(pv5, n1), X1))) 483.84/72.06 <= (~ 483.84/72.06 ( (!!((^[Y0 : $i]: 483.84/72.06 ((~(rel_s4('#sk2', Y0))) | 483.84/72.06 (!!((^[Y1 : mu]: 483.84/72.06 (exists_in_world(Y1, Y0) => 483.84/72.06 (!!((^[Y2 : $i]: 483.84/72.06 ((~(rel_s4(Y0, Y2))) | 483.84/72.06 (!!((^[Y3 : mu]: 483.84/72.06 (exists_in_world(Y3, Y2) => 483.84/72.06 (!!((^[Y4 : $i]: 483.84/72.06 ((~(rel_s4(Y2, Y4)))| 483.84/72.06 (~((!!((^[Y5 : $i]: 483.84/72.06 ((~(rel_s4(Y4, 483.84/72.06 Y5))) | 483.84/72.06 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_forall', [status(thm)], ['583'])). 483.84/72.07 tff('585', plain, 483.84/72.07 (![X1]: (~ rel_s4('#sk41', X1) | leq('#sk38', minus(pv5, n1), X1))) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_or', [status(thm)], ['584'])). 483.84/72.07 tff('586', plain, 483.84/72.07 ( leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41'))) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))) & 483.84/72.07 ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41')))), 483.84/72.07 inference('sup-', [status(thm)], ['582', '585'])). 483.84/72.07 tff('587', plain, 483.84/72.07 (~ leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41'))) 483.84/72.07 <= (~ ( leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41')))), 483.84/72.07 inference('split', [status(esa)], ['156'])). 483.84/72.07 tff('588', plain, 483.84/72.07 ~ ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41'))) | 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))) | 483.84/72.07 ( leq('#sk38', minus(pv5, n1), '#sk52'('#sk38', '#sk41'))), 483.84/72.07 inference('sup-', [status(thm)], ['586', '587'])). 483.84/72.07 tff('589', plain, 483.84/72.07 ( exists_in_world('#sk38', '#sk36')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_imply', [status(thm)], ['26'])). 483.84/72.07 tff('590', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('591', plain, exists_in_world('#sk38', '#sk36'), 483.84/72.07 inference('simpl_trail', [status(thm)], ['589', '590'])). 483.84/72.07 tff('592', plain, 483.84/72.07 ( rel_s4('#sk2', '#sk18')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_or', [status(thm)], ['20'])). 483.84/72.07 tff('593', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('594', plain, rel_s4('#sk2', '#sk18'), 483.84/72.07 inference('simpl_trail', [status(thm)], ['592', '593'])). 483.84/72.07 tff('595', plain, 483.84/72.07 ( rel_s4('#sk36', '#sk41')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_or', [status(thm)], ['30'])). 483.84/72.07 tff('596', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('597', plain, rel_s4('#sk36', '#sk41'), 483.84/72.07 inference('simpl_trail', [status(thm)], ['595', '596'])). 483.84/72.07 tff('598', plain, 483.84/72.07 ( '#form46'('#sk34', '#sk41')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('simplify', [status(thm)], ['59'])). 483.84/72.07 tff('599', plain, 483.84/72.07 ![X1, X2 : mu, X3, X4 : mu, X5]: 483.84/72.07 ( rel_s4(X5, '#sk52'(X4, X5)) 483.84/72.07 | ~ '#form46'(X2, X5) 483.84/72.07 | ~ '#form43'(X2, X5) 483.84/72.07 | ~ rel_s4('#sk2', X1) 483.84/72.07 | ~ exists_in_world(X2, X1) 483.84/72.07 | ~ rel_s4(X1, X3) 483.84/72.07 | ~ exists_in_world(X4, X3) 483.84/72.07 | ~ rel_s4(X3, X5) 483.84/72.07 | rel_s4(X5, '#sk40'(X4, X5)) 483.84/72.07 | ~ '#form44'(X2, X4, X5)), 483.84/72.07 inference('lazy_cnf_or', [status(thm)], ['169'])). 483.84/72.07 tff('600', plain, 483.84/72.07 (![X0 : mu, X1, X2]: 483.84/72.07 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ rel_s4(X1, '#sk41') 483.84/72.07 | ~ exists_in_world(X0, X1) 483.84/72.07 | ~ rel_s4(X2, X1) 483.84/72.07 | ~ exists_in_world('#sk34', X2) 483.84/72.07 | ~ rel_s4('#sk2', X2) 483.84/72.07 | ~ '#form43'('#sk34', '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('sup-', [status(thm)], ['598', '599'])). 483.84/72.07 tff('601', plain, 483.84/72.07 ( '#form43'('#sk34', '#sk41')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('renaming', [status(thm)], ['83', '85'])). 483.84/72.07 tff('602', plain, 483.84/72.07 (![X0 : mu, X1, X2]: 483.84/72.07 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ rel_s4(X1, '#sk41') 483.84/72.07 | ~ exists_in_world(X0, X1) 483.84/72.07 | ~ rel_s4(X2, X1) 483.84/72.07 | ~ exists_in_world('#sk34', X2) 483.84/72.07 | ~ rel_s4('#sk2', X2) 483.84/72.07 | rel_s4('#sk41', '#sk52'(X0, '#sk41')))) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('demod', [status(thm)], ['600', '601'])). 483.84/72.07 tff('603', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('604', plain, 483.84/72.07 ![X0 : mu, X1, X2]: 483.84/72.07 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ rel_s4(X1, '#sk41') 483.84/72.07 | ~ exists_in_world(X0, X1) 483.84/72.07 | ~ rel_s4(X2, X1) 483.84/72.07 | ~ exists_in_world('#sk34', X2) 483.84/72.07 | ~ rel_s4('#sk2', X2) 483.84/72.07 | rel_s4('#sk41', '#sk52'(X0, '#sk41'))), 483.84/72.07 inference('simpl_trail', [status(thm)], ['602', '603'])). 483.84/72.07 tff('605', plain, 483.84/72.07 ![X0 : mu, X1]: 483.84/72.07 ( rel_s4('#sk41', '#sk52'(X0, '#sk41')) 483.84/72.07 | ~ rel_s4('#sk2', X1) 483.84/72.07 | ~ exists_in_world('#sk34', X1) 483.84/72.07 | ~ rel_s4(X1, '#sk36') 483.84/72.07 | ~ exists_in_world(X0, '#sk36') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ '#form44'('#sk34', X0, '#sk41')), 483.84/72.07 inference('sup-', [status(thm)], ['597', '604'])). 483.84/72.07 tff('606', plain, 483.84/72.07 ![X0 : mu]: 483.84/72.07 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ exists_in_world(X0, '#sk36') 483.84/72.07 | ~ rel_s4('#sk18', '#sk36') 483.84/72.07 | ~ exists_in_world('#sk34', '#sk18') 483.84/72.07 | rel_s4('#sk41', '#sk52'(X0, '#sk41'))), 483.84/72.07 inference('sup-', [status(thm)], ['594', '605'])). 483.84/72.07 tff('607', plain, 483.84/72.07 ( rel_s4('#sk18', '#sk36')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_or', [status(thm)], ['24'])). 483.84/72.07 tff('608', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('609', plain, rel_s4('#sk18', '#sk36'), 483.84/72.07 inference('simpl_trail', [status(thm)], ['607', '608'])). 483.84/72.07 tff('610', plain, 483.84/72.07 ( exists_in_world('#sk34', '#sk18')) 483.84/72.07 <= (~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y3, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, 483.84/72.07 n1), Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(Y1, n2, 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 leq(n0, Y1, 483.84/72.07 Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~( 483.84/72.07 rel_s4( 483.84/72.07 Y4, Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5)))))))))))))))))))))))))))))))), 483.84/72.07 inference('lazy_cnf_imply', [status(thm)], ['22'])). 483.84/72.07 tff('611', plain, 483.84/72.07 ~ 483.84/72.07 ( (!!((^[Y0 : $i]: 483.84/72.07 ((~(rel_s4('#sk2', Y0))) | 483.84/72.07 (!!((^[Y1 : mu]: 483.84/72.07 (exists_in_world(Y1, Y0) => 483.84/72.07 (!!((^[Y2 : $i]: 483.84/72.07 ((~(rel_s4(Y0, Y2))) | 483.84/72.07 (!!((^[Y3 : mu]: 483.84/72.07 (exists_in_world(Y3, Y2) => 483.84/72.07 (!!((^[Y4 : $i]: 483.84/72.07 ((~(rel_s4(Y2, Y4)))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y3, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y3, 483.84/72.07 minus(pv5, n1), 483.84/72.07 Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(Y1, n2, Y5)))))))| 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, Y5))) | 483.84/72.07 leq(n0, Y1, Y5)))))))| 483.84/72.07 (~(((~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 z_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))) | 483.84/72.07 (~((!!((^[Y5 : $i]: 483.84/72.07 ((~(rel_s4(Y4, 483.84/72.07 Y5))) | 483.84/72.07 qmltpeq( 483.84/72.07 a_select3( 483.84/72.07 u_defuse, 483.84/72.07 Y1, Y3), 483.84/72.07 use, Y5))))))))))))))))))))))))))))))), 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['196', '205', '214', '223', '232', '241', '250', '259', 483.84/72.07 '268', '277', '286', '295', '304', '313', '322', '331', 483.84/72.07 '340', '349', '358', '367', '376', '385', '394', '403', 483.84/72.07 '412', '421', '430', '439', '448', '486', '501', '536', 483.84/72.07 '551', '552', '563', '572', '573', '580', '581'])). 483.84/72.07 tff('612', plain, exists_in_world('#sk34', '#sk18'), 483.84/72.07 inference('simpl_trail', [status(thm)], ['610', '611'])). 483.84/72.07 tff('613', plain, 483.84/72.07 ![X0 : mu]: 483.84/72.07 (~ '#form44'('#sk34', X0, '#sk41') 483.84/72.07 | rel_s4('#sk41', '#sk40'(X0, '#sk41')) 483.84/72.07 | ~ exists_in_world(X0, '#sk36') 483.84/72.07 | rel_s4('#sk41', '#sk52'(X0, '#sk41'))), 483.84/72.07 inference('demod', [status(thm)], ['606', '609', '612'])). 483.84/72.07 tff('614', plain, 483.84/72.07 ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41')) 483.84/72.07 | rel_s4('#sk41', '#sk40'('#sk38', '#sk41')) 483.84/72.07 | ~ '#form44'('#sk34', '#sk38', '#sk41')), 483.84/72.07 inference('sup-', [status(thm)], ['591', '613'])). 483.84/72.07 tff('615', plain, 483.84/72.07 ( rel_s4('#sk41', '#sk52'('#sk38', '#sk41'))) | 483.84/72.07 ( rel_s4('#sk41', '#sk40'('#sk38', '#sk41'))) | 483.84/72.07 ~ ( '#form44'('#sk34', '#sk38', '#sk41')), 483.84/72.07 inference('split', [status(esa)], ['614'])). 483.84/72.07 tff('616', plain, $false, 483.84/72.07 inference('sat_resolution*', [status(thm)], 483.84/72.07 ['94', '130', '141', '142', '157', '180', '187', '196', '205', 483.84/72.07 '214', '223', '232', '241', '250', '259', '268', '277', 483.84/72.07 '286', '295', '304', '313', '322', '331', '340', '349', 483.84/72.07 '358', '367', '376', '385', '394', '403', '412', '421', 483.84/72.07 '430', '439', '448', '486', '501', '536', '551', '552', 483.84/72.07 '563', '572', '573', '580', '581', '588', '615'])). 483.84/72.07 483.84/72.07 % SZS output end Refutation 483.84/72.07 483.84/72.07 483.84/72.07 % Terminating... 484.48/72.16 % Runner terminated. 484.48/72.17 % Zipperpin 1.5 exiting 484.48/72.18 EOF