0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.cstHJ5Xa8S 0.15/0.36 % Computer : n005.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % DateTime : Thu Jul 2 09:04:36 EDT 2020 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 120 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.53/0.61 % Estimated wc time : 1286 0.53/0.61 % Estimated cpu time (7 cpus) : 183.71428571428572 0.53/0.66 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.53/0.66 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.53/0.67 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 71.14/10.74 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 105.15/15.71 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.15/15.75 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 146.37/21.69 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 146.37/21.74 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 185.23/27.53 % /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s 187.23/27.77 % /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s 195.08/28.88 % /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s 262.13/38.49 % Solved by lams/b.rw.sh. 262.13/38.49 % Running : timeout 17 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.cstHJ5Xa8S/e_input35e0cf --cpu-limit=15 --auto -s -p. 262.13/38.49 % done 1159 iterations in 10.656s 262.13/38.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 262.13/38.49 % SZS output start Refutation 262.13/38.49 tff(mbox_s4, axiom, mbox_s4() = 262.13/38.49 ^[Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~rel_s4(W,V))))). 262.13/38.49 tff('0', plain, 262.13/38.49 mbox_s4 = (^[Phi:(($i > $o)),W]: (![V]: (Phi(V) | (~rel_s4(W,V))))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 262.13/38.49 tff('1', plain, 262.13/38.49 mbox_s4 = 262.13/38.49 (^[V_1:(($i > $o)),V_2]: (![X4]: (V_1(X4) | (~rel_s4(V_2,X4))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(mvalid, axiom, mvalid() = ^[Phi:(($i > $o))]: (![W]: Phi(W))). 262.13/38.49 tff('2', plain, mvalid = (^[Phi:(($i > $o))]: (![W]: Phi(W))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mvalid])). 262.13/38.49 tff('3', plain, mvalid = (^[V_1:(($i > $o))]: (![X4]: V_1(X4))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(mand, axiom, mand() = 262.13/38.49 ^[Phi:(($i > $o)),Psi:(($i > $o))]: mnot(mor(mnot(Phi),mnot(Psi)))). 262.13/38.49 tff(mor, axiom, mor() = 262.13/38.49 ^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))). 262.13/38.49 tff('4', plain, 262.13/38.49 mor = (^[Phi:(($i > $o)),Psi:(($i > $o)),W]: (Phi(W) | Psi(W))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mor])). 262.13/38.49 tff('5', plain, 262.13/38.49 mor = (^[V_1:(($i > $o)),V_2:(($i > $o)),V_3]: (V_1(V_3) | V_2(V_3))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(mnot, axiom, mnot() = ^[Phi:(($i > $o)),W]: (~Phi(W))). 262.13/38.49 tff('6', plain, mnot = (^[Phi:(($i > $o)),W]: (~Phi(W))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mnot])). 262.13/38.49 tff('7', plain, mnot = (^[V_1:(($i > $o)),V_2]: (~V_1(V_2))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('8', plain, 262.13/38.49 mand = 262.13/38.49 (^[Phi:(($i > $o)),Psi:(($i > $o))]: mnot(mor(mnot(Phi),mnot(Psi)))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mand, '5', '7'])). 262.13/38.49 tff('9', plain, 262.13/38.49 mand = 262.13/38.49 (^[V_1:(($i > $o)),V_2:(($i > $o))]: mnot(mor(mnot(V_1),mnot(V_2)))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(co1, conjecture, 262.13/38.49 (mvalid(mbox_s4(mnot(mand(mor(mand(mbox_s4(qmltpeq(op(e0,e0),e0)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e1,e1),e0)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e2,e2),e0)), 262.13/38.49 mbox_s4(qmltpeq(op(e3,e3),e0))))), 262.13/38.49 mor(mand(mbox_s4(qmltpeq(op(e0,e0),e1)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e1,e1),e1)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e2,e2), 262.13/38.49 e1)), 262.13/38.49 mbox_s4(qmltpeq(op(e3,e3), 262.13/38.49 e1))))), 262.13/38.49 mor(mand(mbox_s4(qmltpeq(op(e0,e0),e2)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e1,e1), 262.13/38.49 e2)), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e2,e2),e2)), 262.13/38.49 mbox_s4(qmltpeq( 262.13/38.49 op(e3,e3),e2))))), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e0,e0),e3)), 262.13/38.49 mand(mbox_s4(qmltpeq(op(e1,e1), 262.13/38.49 e3)), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e2,e2),e3)), 262.13/38.49 mbox_s4(qmltpeq( 262.13/38.49 op(e3,e3),e3)))))))), 262.13/38.49 mbox_s4(mnot(mor(mand(mbox_s4(qmltpeq(op(e0,e0), 262.13/38.49 e0)), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e1,e1),e0)), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e2,e2), 262.13/38.49 e0)), 262.13/38.49 mbox_s4(qmltpeq( 262.13/38.49 op(e3,e3), 262.13/38.49 e0))))), 262.13/38.49 mor(mand(mbox_s4(qmltpeq( 262.13/38.49 op(e0,e0),e1)), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e1,e1), 262.13/38.49 e1)), 262.13/38.49 mand(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e2),e1)), 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e3),e1))))), 262.13/38.49 mor(mand(mbox_s4(qmltpeq( 262.13/38.49 op(e0,e0), 262.13/38.49 e2)), 262.13/38.49 mand(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1),e2)), 262.13/38.49 mand(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e2), 262.13/38.49 e2)), 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e3), 262.13/38.49 e2))))), 262.13/38.49 mand(mbox_s4(qmltpeq( 262.13/38.49 op(e0,e0), 262.13/38.49 e3)), 262.13/38.49 mand(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1),e3)), 262.13/38.49 mand(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e2), 262.13/38.49 e3)), 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e3), 262.13/38.49 e3)))))))))))))))). 262.13/38.49 tff(zf_stmt_0, conjecture, 262.13/38.49 (![X4,X6]: 262.13/38.49 ((~rel_s4(X4,X6)) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 ((~(![X18]: ((~rel_s4(X6,X18)) | qmltpeq(op(e1,e1),e1,X18)))) | 262.13/38.49 (~(![X22]: ((~rel_s4(X6,X22)) | qmltpeq(op(e3,e3),e1,X22)))) | 262.13/38.49 (~(![X20]: ((~rel_s4(X6,X20)) | qmltpeq(op(e2,e2),e1,X20)))) | 262.13/38.49 (~(![X16]: ((~rel_s4(X6,X16)) | qmltpeq(op(e0,e0),e1,X16)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X34]: ((~rel_s4(X6,X34)) | qmltpeq(op(e1,e1),e3,X34)))) | 262.13/38.49 (~(![X38]: ((~rel_s4(X6,X38)) | qmltpeq(op(e3,e3),e3,X38)))) | 262.13/38.49 (~(![X36]: ((~rel_s4(X6,X36)) | qmltpeq(op(e2,e2),e3,X36)))) | 262.13/38.49 (~(![X32]: ((~rel_s4(X6,X32)) | qmltpeq(op(e0,e0),e3,X32)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X26]: ((~rel_s4(X6,X26)) | qmltpeq(op(e1,e1),e2,X26)))) | 262.13/38.49 (~(![X30]: ((~rel_s4(X6,X30)) | qmltpeq(op(e3,e3),e2,X30)))) | 262.13/38.49 (~(![X28]: ((~rel_s4(X6,X28)) | qmltpeq(op(e2,e2),e2,X28)))) | 262.13/38.49 (~(![X24]: ((~rel_s4(X6,X24)) | qmltpeq(op(e0,e0),e2,X24)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X10]: ((~rel_s4(X6,X10)) | qmltpeq(op(e1,e1),e0,X10)))) | 262.13/38.49 (~(![X14]: ((~rel_s4(X6,X14)) | qmltpeq(op(e3,e3),e0,X14)))) | 262.13/38.49 (~(![X12]: ((~rel_s4(X6,X12)) | qmltpeq(op(e2,e2),e0,X12)))) | 262.13/38.49 (~(![X8]: ((~rel_s4(X6,X8)) | qmltpeq(op(e0,e0),e0,X8)))))))) | 262.13/38.49 (~ 262.13/38.49 (![X40]: 262.13/38.49 ((~rel_s4(X6,X40)) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 ((~ 262.13/38.49 (![X52]: ((~rel_s4(X40,X52)) | qmltpeq(op(e1,e1),e1,X52)))) | 262.13/38.49 (~ 262.13/38.49 (![X56]: ((~rel_s4(X40,X56)) | qmltpeq(op(e3,e3),e1,X56)))) | 262.13/38.49 (~ 262.13/38.49 (![X54]: ((~rel_s4(X40,X54)) | qmltpeq(op(e2,e2),e1,X54)))) | 262.13/38.49 (~ 262.13/38.49 (![X50]: ((~rel_s4(X40,X50)) | qmltpeq(op(e0,e0),e1,X50)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X68]: ((~rel_s4(X40,X68)) | qmltpeq(op(e1,e1),e3,X68)))) | 262.13/38.49 (~ 262.13/38.49 (![X72]: ((~rel_s4(X40,X72)) | qmltpeq(op(e3,e3),e3,X72)))) | 262.13/38.49 (~ 262.13/38.49 (![X70]: ((~rel_s4(X40,X70)) | qmltpeq(op(e2,e2),e3,X70)))) | 262.13/38.49 (~ 262.13/38.49 (![X66]: ((~rel_s4(X40,X66)) | qmltpeq(op(e0,e0),e3,X66)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X60]: ((~rel_s4(X40,X60)) | qmltpeq(op(e1,e1),e2,X60)))) | 262.13/38.49 (~ 262.13/38.49 (![X64]: ((~rel_s4(X40,X64)) | qmltpeq(op(e3,e3),e2,X64)))) | 262.13/38.49 (~ 262.13/38.49 (![X62]: ((~rel_s4(X40,X62)) | qmltpeq(op(e2,e2),e2,X62)))) | 262.13/38.49 (~ 262.13/38.49 (![X58]: ((~rel_s4(X40,X58)) | qmltpeq(op(e0,e0),e2,X58)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X44]: ((~rel_s4(X40,X44)) | qmltpeq(op(e1,e1),e0,X44)))) | 262.13/38.49 (~ 262.13/38.49 (![X48]: ((~rel_s4(X40,X48)) | qmltpeq(op(e3,e3),e0,X48)))) | 262.13/38.49 (~ 262.13/38.49 (![X46]: ((~rel_s4(X40,X46)) | qmltpeq(op(e2,e2),e0,X46)))) | 262.13/38.49 (~ 262.13/38.49 (![X42]: ((~rel_s4(X40,X42)) | qmltpeq(op(e0,e0),e0,X42)))))))))))))). 262.13/38.49 tff(zf_stmt_1, negated_conjecture, 262.13/38.49 (~ 262.13/38.49 (![X4,X6]: 262.13/38.49 ((~rel_s4(X4,X6)) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 ((~(![X18]: ((~rel_s4(X6,X18)) | qmltpeq(op(e1,e1),e1,X18)))) | 262.13/38.49 (~(![X22]: ((~rel_s4(X6,X22)) | qmltpeq(op(e3,e3),e1,X22)))) | 262.13/38.49 (~(![X20]: ((~rel_s4(X6,X20)) | qmltpeq(op(e2,e2),e1,X20)))) | 262.13/38.49 (~(![X16]: ((~rel_s4(X6,X16)) | qmltpeq(op(e0,e0),e1,X16)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X34]: ((~rel_s4(X6,X34)) | qmltpeq(op(e1,e1),e3,X34)))) | 262.13/38.49 (~(![X38]: ((~rel_s4(X6,X38)) | qmltpeq(op(e3,e3),e3,X38)))) | 262.13/38.49 (~(![X36]: ((~rel_s4(X6,X36)) | qmltpeq(op(e2,e2),e3,X36)))) | 262.13/38.49 (~(![X32]: ((~rel_s4(X6,X32)) | qmltpeq(op(e0,e0),e3,X32)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X26]: ((~rel_s4(X6,X26)) | qmltpeq(op(e1,e1),e2,X26)))) | 262.13/38.49 (~(![X30]: ((~rel_s4(X6,X30)) | qmltpeq(op(e3,e3),e2,X30)))) | 262.13/38.49 (~(![X28]: ((~rel_s4(X6,X28)) | qmltpeq(op(e2,e2),e2,X28)))) | 262.13/38.49 (~(![X24]: ((~rel_s4(X6,X24)) | qmltpeq(op(e0,e0),e2,X24)))))) | 262.13/38.49 (~ 262.13/38.49 ((~(![X10]: ((~rel_s4(X6,X10)) | qmltpeq(op(e1,e1),e0,X10)))) | 262.13/38.49 (~(![X14]: ((~rel_s4(X6,X14)) | qmltpeq(op(e3,e3),e0,X14)))) | 262.13/38.49 (~(![X12]: ((~rel_s4(X6,X12)) | qmltpeq(op(e2,e2),e0,X12)))) | 262.13/38.49 (~(![X8]: ((~rel_s4(X6,X8)) | qmltpeq(op(e0,e0),e0,X8)))))))) | 262.13/38.49 (~ 262.13/38.49 (![X40]: 262.13/38.49 ((~rel_s4(X6,X40)) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 ((~ 262.13/38.49 (![X52]: 262.13/38.49 ((~rel_s4(X40,X52)) | qmltpeq(op(e1,e1),e1,X52)))) | 262.13/38.49 (~ 262.13/38.49 (![X56]: 262.13/38.49 ((~rel_s4(X40,X56)) | qmltpeq(op(e3,e3),e1,X56)))) | 262.13/38.49 (~ 262.13/38.49 (![X54]: 262.13/38.49 ((~rel_s4(X40,X54)) | qmltpeq(op(e2,e2),e1,X54)))) | 262.13/38.49 (~ 262.13/38.49 (![X50]: 262.13/38.49 ((~rel_s4(X40,X50)) | qmltpeq(op(e0,e0),e1,X50)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X68]: 262.13/38.49 ((~rel_s4(X40,X68)) | qmltpeq(op(e1,e1),e3,X68)))) | 262.13/38.49 (~ 262.13/38.49 (![X72]: 262.13/38.49 ((~rel_s4(X40,X72)) | qmltpeq(op(e3,e3),e3,X72)))) | 262.13/38.49 (~ 262.13/38.49 (![X70]: 262.13/38.49 ((~rel_s4(X40,X70)) | qmltpeq(op(e2,e2),e3,X70)))) | 262.13/38.49 (~ 262.13/38.49 (![X66]: 262.13/38.49 ((~rel_s4(X40,X66)) | qmltpeq(op(e0,e0),e3,X66)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X60]: 262.13/38.49 ((~rel_s4(X40,X60)) | qmltpeq(op(e1,e1),e2,X60)))) | 262.13/38.49 (~ 262.13/38.49 (![X64]: 262.13/38.49 ((~rel_s4(X40,X64)) | qmltpeq(op(e3,e3),e2,X64)))) | 262.13/38.49 (~ 262.13/38.49 (![X62]: 262.13/38.49 ((~rel_s4(X40,X62)) | qmltpeq(op(e2,e2),e2,X62)))) | 262.13/38.49 (~ 262.13/38.49 (![X58]: 262.13/38.49 ((~rel_s4(X40,X58)) | qmltpeq(op(e0,e0),e2,X58)))))) | 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X44]: 262.13/38.49 ((~rel_s4(X40,X44)) | qmltpeq(op(e1,e1),e0,X44)))) | 262.13/38.49 (~ 262.13/38.49 (![X48]: 262.13/38.49 ((~rel_s4(X40,X48)) | qmltpeq(op(e3,e3),e0,X48)))) | 262.13/38.49 (~ 262.13/38.49 (![X46]: 262.13/38.49 ((~rel_s4(X40,X46)) | qmltpeq(op(e2,e2),e0,X46)))) | 262.13/38.49 (~ 262.13/38.49 (![X42]: 262.13/38.49 ((~rel_s4(X40,X42)) | qmltpeq(op(e0,e0),e0,X42))))))))))))))). 262.13/38.49 tff('10', plain, 262.13/38.49 ~ (!!((^[Y0 : $i]: 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1)))| 262.13/38.49 (~(((~(((~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e1, e1), e1, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e3, e3), e1, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e2, e2), e1, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e0, e0), e1, Y2))))))))))| 262.13/38.49 (~(((~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e1, e1), e3, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(op(e3, e3), e3, Y2)))))))| 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qmltpeq(op(e2, e2), e1, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e1, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e3, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e2, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e0, Y1)))))))))))))))))))), 262.13/38.49 inference('lazy_cnf_exists', [status(thm)], ['11'])). 262.13/38.49 tff('13', plain, 262.13/38.49 ((~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e1, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['12'])). 262.13/38.49 tff('14', plain, 262.13/38.49 (~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e1, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['13'])). 262.13/38.49 tff('15', plain, 262.13/38.49 ( (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e1, Y0))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['14'])). 262.13/38.49 tff(mforall_ind, axiom, mforall_ind() = 262.13/38.49 ^[Phi:((mu * $i) > $o),W]: (![X:mu]: (exists_in_world(X,W) => Phi(X,W)))). 262.13/38.49 tff('16', plain, 262.13/38.49 mforall_ind = 262.13/38.49 (^[Phi:((mu * $i) > $o),W]: (![X:mu]: (exists_in_world(X,W) => Phi(X,W)))), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 262.13/38.49 tff('17', plain, 262.13/38.49 mforall_ind = 262.13/38.49 (^[V_1:((mu * $i) > $o),V_2]: 262.13/38.49 (![X4:mu]: (exists_in_world(X4,V_2) => V_1(X4,V_2)))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(mimplies, axiom, mimplies() = 262.13/38.49 ^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)). 262.13/38.49 tff('18', plain, 262.13/38.49 mimplies = (^[Phi:(($i > $o)),Psi:(($i > $o))]: mor(mnot(Phi),Psi)), 262.13/38.49 inference('simplify_rw_rule', [status(thm)], [mimplies, '5', '7'])). 262.13/38.49 tff('19', plain, 262.13/38.49 mimplies = (^[V_1:(($i > $o)),V_2:(($i > $o))]: mor(mnot(V_1),V_2)), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff(transitivity, axiom, 262.13/38.49 (mvalid(mbox_s4(mforall_ind(^[X:mu]: 262.13/38.49 mbox_s4(mforall_ind(^[Y:mu]: 262.13/38.49 mbox_s4(mforall_ind( 262.13/38.49 ^[Z:mu]: 262.13/38.49 mbox_s4( 262.13/38.49 mimplies( 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq(X,Y)), 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq(Y,Z))), 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq(X,Z))))))))))))). 262.13/38.49 tff(zf_stmt_2, axiom, 262.13/38.49 (![X4,X6]: 262.13/38.49 ((~rel_s4(X4,X6)) | 262.13/38.49 (![X8:mu]: 262.13/38.49 (exists_in_world(X8,X6) => 262.13/38.49 (![X10]: 262.13/38.49 ((~rel_s4(X6,X10)) | 262.13/38.49 (![X12:mu]: 262.13/38.49 (exists_in_world(X12,X10) => 262.13/38.49 (![X14]: 262.13/38.49 ((~rel_s4(X10,X14)) | 262.13/38.49 (![X16:mu]: 262.13/38.49 (exists_in_world(X16,X14) => 262.13/38.49 (![X18]: 262.13/38.49 ((~rel_s4(X14,X18)) | 262.13/38.49 (~ 262.13/38.49 (![X22]: 262.13/38.49 ((~rel_s4(X18,X22)) | qmltpeq(X12,X16,X22)))) | 262.13/38.49 (~ 262.13/38.49 (![X20]: 262.13/38.49 ((~rel_s4(X18,X20)) | qmltpeq(X8,X12,X20)))) | 262.13/38.49 (![X24]: 262.13/38.49 ((~rel_s4(X18,X24)) | qmltpeq(X8,X16,X24)))))))))))))))))). 262.13/38.49 tff('20', plain, 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 (!!((^[Y2 : mu]: 262.13/38.49 (exists_in_world(Y2, Y1) => 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y3))) | 262.13/38.49 (!!((^[Y4 : mu]: 262.13/38.49 (exists_in_world(Y4, Y3) => 262.13/38.49 (!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y5))) | 262.13/38.49 (!!((^[Y6 : mu]: 262.13/38.49 (exists_in_world( 262.13/38.49 Y6, Y5) => 262.13/38.49 (!!((^[Y7 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y7)))| 262.13/38.49 ( 262.13/38.49 ~(( 262.13/38.49 !!(( 262.13/38.49 ^[Y8 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y7, Y8))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y4, Y6, 262.13/38.49 Y8)))))))| 262.13/38.49 ( 262.13/38.49 ~(( 262.13/38.49 !!(( 262.13/38.49 ^[Y8 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y7, Y8))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y2, Y4, 262.13/38.49 Y8)))))))| 262.13/38.49 ( 262.13/38.49 !!(( 262.13/38.49 ^[Y8 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y7, Y8))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y2, Y6, 262.13/38.49 Y8)))))))))))))))))))))))))))))))))))), 262.13/38.49 inference('cnf', [status(esa)], [zf_stmt_2])). 262.13/38.49 tff('21', plain, 262.13/38.49 ![X1]: 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | 262.13/38.49 (!!((^[Y1 : mu]: 262.13/38.49 (exists_in_world(Y1, Y0) => 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y2))) | 262.13/38.49 (!!((^[Y3 : mu]: 262.13/38.49 (exists_in_world(Y3, Y2) => 262.13/38.49 (!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y4))) | 262.13/38.49 (!!((^[Y5 : mu]: 262.13/38.49 (exists_in_world(Y5, 262.13/38.49 Y4) => 262.13/38.49 (!!((^[Y6 : $i]: 262.13/38.49 ((~(rel_s4(Y4, 262.13/38.49 Y6)))| 262.13/38.49 (~((!!(( 262.13/38.49 ^[Y7 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y6, Y7))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y3, Y5, 262.13/38.49 Y7)))))))| 262.13/38.49 (~((!!(( 262.13/38.49 ^[Y7 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y6, Y7))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y1, Y3, 262.13/38.49 Y7)))))))| 262.13/38.49 (!!((^[Y7 : $i]: 262.13/38.49 (( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y6, Y7))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y1, Y5, 262.13/38.49 Y7))))))))))))))))))))))))))))))))), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['20'])). 262.13/38.49 tff('22', plain, 262.13/38.49 ![X1, X2]: 262.13/38.49 ((~(rel_s4(X1, X2))) | 262.13/38.49 (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X2) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X2, Y1))) | 262.13/38.49 (!!((^[Y2 : mu]: 262.13/38.49 (exists_in_world(Y2, Y1) => 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y3))) | 262.13/38.49 (!!((^[Y4 : mu]: 262.13/38.49 (exists_in_world(Y4, Y3) => 262.13/38.49 (!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y5)))| 262.13/38.49 (~((!!((^[Y6 : $i]: 262.13/38.49 ((~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y2, Y4, 262.13/38.49 Y6)))))))| 262.13/38.49 (~((!!((^[Y6 : $i]: 262.13/38.49 ((~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y0, Y2, 262.13/38.49 Y6)))))))| 262.13/38.49 (!!((^[Y6 : $i]: 262.13/38.49 ((~(rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq(Y0, 262.13/38.49 Y4, Y6)))))))))))))))))))))))))))))), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['21'])). 262.13/38.49 tff('23', plain, 262.13/38.49 ![X1, X2]: 262.13/38.49 (~ rel_s4(X1, X2) 262.13/38.49 | (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X2) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X2, Y1))) | 262.13/38.49 (!!((^[Y2 : mu]: 262.13/38.49 (exists_in_world(Y2, Y1) => 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y3))) | 262.13/38.49 (!!((^[Y4 : mu]: 262.13/38.49 (exists_in_world(Y4, Y3) => 262.13/38.49 (!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y5)))| 262.13/38.49 (~((!!((^[Y6 : $i]: 262.13/38.49 ( 262.13/38.49 ( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y2, Y4, 262.13/38.49 Y6)))))))| 262.13/38.49 (~((!!((^[Y6 : $i]: 262.13/38.49 ( 262.13/38.49 ( 262.13/38.49 ~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y0, Y2, 262.13/38.49 Y6)))))))| 262.13/38.49 (!!((^[Y6 : $i]: 262.13/38.49 ((~( 262.13/38.49 rel_s4( 262.13/38.49 Y5, Y6))) | 262.13/38.49 qmltpeq( 262.13/38.49 Y0, Y4, 262.13/38.49 Y6)))))))))))))))))))))))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['22'])). 262.13/38.49 tff('24', plain, 262.13/38.49 ![X1, X2, X3 : mu]: 262.13/38.49 ( (exists_in_world(X3, X2) => 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X2, Y0))) | 262.13/38.49 (!!((^[Y1 : mu]: 262.13/38.49 (exists_in_world(Y1, Y0) => 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y2))) | 262.13/38.49 (!!((^[Y3 : mu]: 262.13/38.49 (exists_in_world(Y3, Y2) => 262.13/38.49 (!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y4)))| 262.13/38.49 (~((!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, Y5))) | 262.13/38.49 qmltpeq(Y1, Y3, 262.13/38.49 Y5)))))))| 262.13/38.49 (~((!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, Y5))) | 262.13/38.49 qmltpeq(X3, Y1, 262.13/38.49 Y5)))))))| 262.13/38.49 (!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, Y5))) | 262.13/38.49 qmltpeq(X3, Y3, Y5)))))))))))))))))))))))))) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['23'])). 262.13/38.49 tff('25', plain, 262.13/38.49 ![X1, X2, X3 : mu]: 262.13/38.49 (~ exists_in_world(X3, X2) 262.13/38.49 | (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X2, Y0))) | 262.13/38.49 (!!((^[Y1 : mu]: 262.13/38.49 (exists_in_world(Y1, Y0) => 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y2))) | 262.13/38.49 (!!((^[Y3 : mu]: 262.13/38.49 (exists_in_world(Y3, Y2) => 262.13/38.49 (!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y4)))| 262.13/38.49 (~((!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, 262.13/38.49 Y5))) | 262.13/38.49 qmltpeq(Y1, Y3, 262.13/38.49 Y5)))))))| 262.13/38.49 (~((!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, 262.13/38.49 Y5))) | 262.13/38.49 qmltpeq(X3, Y1, 262.13/38.49 Y5)))))))| 262.13/38.49 (!!((^[Y5 : $i]: 262.13/38.49 ((~(rel_s4(Y4, Y5))) | 262.13/38.49 qmltpeq(X3, Y3, Y5))))))))))))))))))))))))) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_imply', [status(thm)], ['24'])). 262.13/38.49 tff('26', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4]: 262.13/38.49 ( ((~(rel_s4(X2, X4))) | 262.13/38.49 (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X4) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X4, Y1))) | 262.13/38.49 (!!((^[Y2 : mu]: 262.13/38.49 (exists_in_world(Y2, Y1) => 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y3)))| 262.13/38.49 (~((!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(Y0, Y2, Y4)))))))| 262.13/38.49 (~((!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(X3, Y0, Y4)))))))| 262.13/38.49 (!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(X3, Y2, Y4)))))))))))))))))))))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['25'])). 262.13/38.49 tff('27', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4]: 262.13/38.49 (~ rel_s4(X2, X4) 262.13/38.49 | (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X4) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X4, Y1))) | 262.13/38.49 (!!((^[Y2 : mu]: 262.13/38.49 (exists_in_world(Y2, Y1) => 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y3)))| 262.13/38.49 (~((!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(Y0, Y2, Y4)))))))| 262.13/38.49 (~((!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(X3, Y0, Y4)))))))| 262.13/38.49 (!!((^[Y4 : $i]: 262.13/38.49 ((~(rel_s4(Y3, Y4))) | 262.13/38.49 qmltpeq(X3, Y2, Y4))))))))))))))))))))) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['26'])). 262.13/38.49 tff('28', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu]: 262.13/38.49 ( (exists_in_world(X5, X4) => 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X4, Y0))) | 262.13/38.49 (!!((^[Y1 : mu]: 262.13/38.49 (exists_in_world(Y1, Y0) => 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y2)))| 262.13/38.49 (~((!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X5, Y1, Y3)))))))| 262.13/38.49 (~((!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X3, X5, Y3)))))))| 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X3, Y1, Y3)))))))))))))))))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['27'])). 262.13/38.49 tff('29', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu]: 262.13/38.49 (~ exists_in_world(X5, X4) 262.13/38.49 | (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X4, Y0))) | 262.13/38.49 (!!((^[Y1 : mu]: 262.13/38.49 (exists_in_world(Y1, Y0) => 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y2)))| 262.13/38.49 (~((!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X5, Y1, Y3)))))))| 262.13/38.49 (~((!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X3, X5, Y3)))))))| 262.13/38.49 (!!((^[Y3 : $i]: 262.13/38.49 ((~(rel_s4(Y2, Y3))) | 262.13/38.49 qmltpeq(X3, Y1, Y3))))))))))))))))) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_imply', [status(thm)], ['28'])). 262.13/38.49 tff('30', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6]: 262.13/38.49 ( ((~(rel_s4(X4, X6))) | 262.13/38.49 (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X6) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X6, Y1)))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | qmltpeq(X5, Y0, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | qmltpeq(X3, X5, Y2)))))))| 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | qmltpeq(X3, Y0, Y2)))))))))))))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X5, X4)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['29'])). 262.13/38.49 tff('31', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6]: 262.13/38.49 (~ rel_s4(X4, X6) 262.13/38.49 | (!!((^[Y0 : mu]: 262.13/38.49 (exists_in_world(Y0, X6) => 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(X6, Y1)))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(X5, Y0, Y2)))))))| 262.13/38.49 (~((!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | 262.13/38.49 qmltpeq(X3, X5, Y2)))))))| 262.13/38.49 (!!((^[Y2 : $i]: 262.13/38.49 ((~(rel_s4(Y1, Y2))) | qmltpeq(X3, Y0, Y2))))))))))))) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['30'])). 262.13/38.49 tff('32', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu]: 262.13/38.49 ( (exists_in_world(X7, X6) => 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X6, Y0)))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | qmltpeq(X5, X7, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | qmltpeq(X3, X5, Y1)))))))| 262.13/38.49 (!!((^[Y1 : $i]: ((~(rel_s4(Y0, Y1))) | qmltpeq(X3, X7, Y1)))))))))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X4, X6)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['31'])). 262.13/38.49 tff('33', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu]: 262.13/38.49 (~ exists_in_world(X7, X6) 262.13/38.49 | (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X6, Y0)))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | qmltpeq(X5, X7, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | qmltpeq(X3, X5, Y1)))))))| 262.13/38.49 (!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | qmltpeq(X3, X7, Y1))))))))) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_imply', [status(thm)], ['32'])). 262.13/38.49 tff('34', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu, X8]: 262.13/38.49 ( ((~(rel_s4(X6, X8)))| 262.13/38.49 (~((!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X5, X7, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X5, Y0)))))))| 262.13/38.49 (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X7, X6)), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['33'])). 262.13/38.49 tff('35', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu, X8]: 262.13/38.49 (~ rel_s4(X6, X8) 262.13/38.49 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X5, X7, Y0))))) 262.13/38.49 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X5, Y0))))) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0))))) 262.13/38.49 | ~ exists_in_world(X7, X6) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['34'])). 262.13/38.49 tff('36', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu, X8]: 262.13/38.49 (~ ((~(rel_s4(X8, '#sk14'(X5, X7, X8)))) | 262.13/38.49 qmltpeq(X5, X7, '#sk14'(X5, X7, X8))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X7, X6) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0))))) 262.13/38.49 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X5, Y0))))) 262.13/38.49 | ~ rel_s4(X6, X8)), 262.13/38.49 inference('lazy_cnf_exists', [status(thm)], ['35'])). 262.13/38.49 tff('37', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu, X8]: 262.13/38.49 (~ qmltpeq(X5, X7, '#sk14'(X5, X7, X8)) 262.13/38.49 | ~ rel_s4(X6, X8) 262.13/38.49 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X5, Y0))))) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0))))) 262.13/38.49 | ~ exists_in_world(X7, X6) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X1, X2)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['36'])). 262.13/38.49 tff('38', plain, 262.13/38.49 ![X1, X2, X3 : mu, X4, X5 : mu, X6, X7 : mu, X8]: 262.13/38.49 (~ ((~(rel_s4(X8, '#sk14'(X3, X5, X8)))) | 262.13/38.49 qmltpeq(X3, X5, '#sk14'(X3, X5, X8))) 262.13/38.49 | ~ rel_s4(X1, X2) 262.13/38.49 | ~ exists_in_world(X3, X2) 262.13/38.49 | ~ rel_s4(X2, X4) 262.13/38.49 | ~ exists_in_world(X5, X4) 262.13/38.49 | ~ rel_s4(X4, X6) 262.13/38.49 | ~ exists_in_world(X7, X6) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0))))) 262.13/38.49 | ~ rel_s4(X6, X8) 262.13/38.49 | ~ qmltpeq(X5, X7, '#sk14'(X5, X7, X8))), 262.13/38.49 inference('lazy_cnf_exists', [status(thm)], ['37'])). 262.13/38.49 tff('39', plain, 262.13/38.49 ![X3 : mu, X7 : mu, X8]: 262.13/38.49 (~ '#form15'(X3, X7, X8) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('40', plain, 262.13/38.49 ( '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 inference('renaming', [status(thm)], ['15', '39'])). 262.13/38.49 tff('41', plain, 262.13/38.49 ( (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e1, Y0))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['14'])). 262.13/38.49 tff('42', plain, 262.13/38.49 ![X3 : mu, X7 : mu, X8]: 262.13/38.49 (~ '#form15'(X3, X7, X8) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('43', plain, 262.13/38.49 ( '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 inference('renaming', [status(thm)], ['41', '42'])). 262.13/38.49 tff('44', plain, 262.13/38.49 ( '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('45', plain, 262.13/38.49 (~ '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | '#form15'(op(e2, e2), e1, '#sk17')), 262.13/38.49 inference('renaming', [status(thm)], ['40', '44'])). 262.13/38.49 tff('46', plain, 262.13/38.49 ( '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 inference('renaming', [status(thm)], ['41', '42'])). 262.13/38.49 tff('47', plain, 262.13/38.49 ( '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('48', plain, 262.13/38.49 (~ '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | '#form15'(op(e3, e3), e1, '#sk17')), 262.13/38.49 inference('renaming', [status(thm)], ['46', '47'])). 262.13/38.49 tff('49', plain, 262.13/38.49 ( '#form19' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('50', plain, 262.13/38.49 (~ '#form19' 262.13/38.49 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ '#form18'), 262.13/38.49 inference('renaming', [status(thm)], ['45', '49'])). 262.13/38.49 tff('51', plain, 262.13/38.49 ( (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.49 | ~ '#form18' 262.13/38.49 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.49 | ~ '#form19'), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['50'])). 262.13/38.49 tff('52', plain, 262.13/38.49 ![X3 : mu, X7 : mu, X8]: 262.13/38.49 (~ '#form15'(X3, X7, X8) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('53', plain, 262.13/38.49 ( '#form15'(op(e0, e0), e3, '#sk17') 262.13/38.49 | ~ '#form19' 262.13/38.49 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.49 | ~ '#form18'), 262.13/38.49 inference('renaming', [status(thm)], ['51', '52'])). 262.13/38.49 tff('54', plain, 262.13/38.49 ( (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e1, Y0))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['14'])). 262.13/38.49 tff('55', plain, 262.13/38.49 ![X3 : mu, X7 : mu, X8]: 262.13/38.49 (~ '#form15'(X3, X7, X8) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('56', plain, 262.13/38.49 ( '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 inference('renaming', [status(thm)], ['54', '55'])). 262.13/38.49 tff('57', plain, 262.13/38.49 ( '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('58', plain, 262.13/38.49 (~ '#form18' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | '#form15'(op(e0, e0), e1, '#sk17')), 262.13/38.49 inference('renaming', [status(thm)], ['56', '57'])). 262.13/38.49 tff('59', plain, 262.13/38.49 ( '#form19' 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('60', plain, 262.13/38.49 (~ '#form19' 262.13/38.49 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.49 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ '#form18'), 262.13/38.49 inference('renaming', [status(thm)], ['58', '59'])). 262.13/38.49 tff('61', plain, 262.13/38.49 ( (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.49 | ~ '#form18' 262.13/38.49 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.49 | ~ '#form19'), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['60'])). 262.13/38.49 tff('62', plain, 262.13/38.49 ![X3 : mu, X7 : mu, X8]: 262.13/38.49 (~ '#form15'(X3, X7, X8) 262.13/38.49 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.49 define([status(thm)])). 262.13/38.49 tff('63', plain, 262.13/38.49 ( '#form15'(op(e0, e0), e3, '#sk17') 262.13/38.49 | ~ '#form19' 262.13/38.49 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.49 | ~ '#form18'), 262.13/38.49 inference('renaming', [status(thm)], ['61', '62'])). 262.13/38.49 tff('64', plain, 262.13/38.49 (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4('#sk17', Y0))) | 262.13/38.49 (~(((~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e1, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e1, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e1, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e1, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e3, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e3, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e2, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e2, Y1))))))))))| 262.13/38.49 (~(((~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e1, e1), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e3, e3), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e2, e2), e0, Y1)))))))| 262.13/38.49 (~((!!((^[Y1 : $i]: 262.13/38.49 ((~(rel_s4(Y0, Y1))) | 262.13/38.49 qmltpeq(op(e0, e0), e0, Y1))))))))))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['12'])). 262.13/38.49 tff('65', plain, 262.13/38.49 ![X1]: 262.13/38.49 ((~(rel_s4('#sk17', X1))) | 262.13/38.49 (~(((~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e1, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))))))))), 262.13/38.49 inference('lazy_cnf_forall', [status(thm)], ['64'])). 262.13/38.49 tff('66', plain, 262.13/38.49 ![X1]: 262.13/38.49 (~ rel_s4('#sk17', X1) 262.13/38.49 | ~ ((~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e1, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))))| 262.13/38.49 (~(((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))))))), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['65'])). 262.13/38.49 tff('67', plain, 262.13/38.49 ![X1]: 262.13/38.49 ( ((~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.49 (~((!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.49 | ~ rel_s4('#sk17', X1)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['66'])). 262.13/38.49 tff('68', plain, 262.13/38.49 ![X1]: 262.13/38.49 (~ (!!((^[Y0 : $i]: ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e3, Y0))))) 262.13/38.49 | ~ (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.49 | ~ (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.49 | ~ (!!((^[Y0 : $i]: 262.13/38.49 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.49 | ~ rel_s4('#sk17', X1)), 262.13/38.49 inference('lazy_cnf_or', [status(thm)], ['67'])). 262.13/38.49 tff(ax9, axiom, 262.13/38.49 (mvalid(mand(mbox_s4(mnot(mbox_s4(qmltpeq(op(e0,e0),op(e1,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq(op(e0,e0),op(e2,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq(op(e0,e0),op(e3,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq(op(e1,e0), 262.13/38.49 op(e2,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq(op(e1,e0), 262.13/38.49 op(e3,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq( 262.13/38.49 op(e2,e0), 262.13/38.49 op(e3,e0))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4(qmltpeq( 262.13/38.49 op(e0,e1), 262.13/38.49 op(e1,e1))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e1), 262.13/38.49 op(e2,e1))))), 262.13/38.49 mand(mbox_s4(mnot(mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e1), 262.13/38.49 op(e3,e1))))), 262.13/38.49 mand(mbox_s4(mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1), 262.13/38.49 op(e2,e1))))), 262.13/38.49 mand(mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1), 262.13/38.49 op(e3,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e1), 262.13/38.49 op(e3,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e2), 262.13/38.49 op(e1,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e2), 262.13/38.49 op(e2,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e2), 262.13/38.49 op(e3,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e2), 262.13/38.49 op(e2,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e2), 262.13/38.49 op(e3,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e2), 262.13/38.49 op(e3,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e3), 262.13/38.49 op(e1,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e3), 262.13/38.49 op(e2,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e3), 262.13/38.49 op(e3,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e3), 262.13/38.49 op(e2,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e3), 262.13/38.49 op(e3,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e3), 262.13/38.49 op(e3,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e0), 262.13/38.49 op(e0,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e0), 262.13/38.49 op(e0,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e0), 262.13/38.49 op(e0,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e1), 262.13/38.49 op(e0,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e1), 262.13/38.49 op(e0,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e0,e2), 262.13/38.49 op(e0,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e0), 262.13/38.49 op(e1,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e0), 262.13/38.49 op(e1,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e0), 262.13/38.49 op(e1,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1), 262.13/38.49 op(e1,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e1), 262.13/38.49 op(e1,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e1,e2), 262.13/38.49 op(e1,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e0), 262.13/38.49 op(e2,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e0), 262.13/38.49 op(e2,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e0), 262.13/38.49 op(e2,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e1), 262.13/38.49 op(e2,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e1), 262.13/38.49 op(e2,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e2,e2), 262.13/38.49 op(e2,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e0), 262.13/38.49 op(e3,e1))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e0), 262.13/38.49 op(e3,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e0), 262.13/38.49 op(e3,e3))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e1), 262.13/38.49 op(e3,e2))))), 262.13/38.49 mand( 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e1), 262.13/38.49 op(e3,e3))))), 262.13/38.49 mbox_s4( 262.13/38.49 mnot( 262.13/38.49 mbox_s4( 262.13/38.49 qmltpeq( 262.13/38.49 op(e3,e2), 262.13/38.49 op(e3,e3))))))))))))))))))))))))))))))))))))))))))))))))))))))). 262.13/38.49 tff(zf_stmt_3, axiom, 262.13/38.49 (![X4]: 262.13/38.49 (~ 262.13/38.49 ((~ 262.13/38.49 (![X10]: 262.13/38.49 ((~rel_s4(X4,X10)) | 262.13/38.49 (~ 262.13/38.49 (![X12]: 262.13/38.49 ((~rel_s4(X10,X12)) | qmltpeq(op(e0,e0),op(e2,e0),X12))))))) | 262.13/38.49 (~ 262.13/38.49 (![X18]: 262.13/38.49 ((~rel_s4(X4,X18)) | 262.13/38.49 (~ 262.13/38.49 (![X20]: 262.13/38.49 ((~rel_s4(X18,X20)) | qmltpeq(op(e1,e0),op(e2,e0),X20))))))) | 262.13/38.49 (~ 262.13/38.49 (![X26]: 262.13/38.49 ((~rel_s4(X4,X26)) | 262.13/38.49 (~ 262.13/38.49 (![X28]: 262.13/38.49 ((~rel_s4(X26,X28)) | qmltpeq(op(e2,e0),op(e3,e0),X28))))))) | 262.13/38.49 (~ 262.13/38.49 (![X34]: 262.13/38.49 ((~rel_s4(X4,X34)) | 262.13/38.49 (~ 262.13/38.49 (![X36]: 262.13/38.49 ((~rel_s4(X34,X36)) | qmltpeq(op(e0,e1),op(e2,e1),X36))))))) | 262.13/38.49 (~ 262.13/38.49 (![X42]: 262.13/38.49 ((~rel_s4(X4,X42)) | 262.13/38.49 (~ 262.13/38.49 (![X44]: 262.13/38.49 ((~rel_s4(X42,X44)) | qmltpeq(op(e1,e1),op(e2,e1),X44))))))) | 262.13/38.49 (~ 262.13/38.49 (![X50]: 262.13/38.49 ((~rel_s4(X4,X50)) | 262.13/38.49 (~ 262.13/38.49 (![X52]: 262.13/38.49 ((~rel_s4(X50,X52)) | qmltpeq(op(e2,e1),op(e3,e1),X52))))))) | 262.13/38.49 (~ 262.13/38.49 (![X58]: 262.13/38.49 ((~rel_s4(X4,X58)) | 262.13/38.49 (~ 262.13/38.49 (![X60]: 262.13/38.49 ((~rel_s4(X58,X60)) | qmltpeq(op(e0,e2),op(e2,e2),X60))))))) | 262.13/38.49 (~ 262.13/38.49 (![X66]: 262.13/38.49 ((~rel_s4(X4,X66)) | 262.13/38.49 (~ 262.13/38.49 (![X68]: 262.13/38.49 ((~rel_s4(X66,X68)) | qmltpeq(op(e1,e2),op(e2,e2),X68))))))) | 262.13/38.49 (~ 262.13/38.49 (![X74]: 262.13/38.49 ((~rel_s4(X4,X74)) | 262.13/38.49 (~ 262.13/38.49 (![X76]: 262.13/38.49 ((~rel_s4(X74,X76)) | qmltpeq(op(e2,e2),op(e3,e2),X76))))))) | 262.13/38.49 (~ 262.13/38.49 (![X82]: 262.13/38.49 ((~rel_s4(X4,X82)) | 262.13/38.49 (~ 262.13/38.49 (![X84]: 262.13/38.49 ((~rel_s4(X82,X84)) | qmltpeq(op(e0,e3),op(e2,e3),X84))))))) | 262.13/38.49 (~ 262.13/38.49 (![X90]: 262.13/38.49 ((~rel_s4(X4,X90)) | 262.13/38.49 (~ 262.13/38.49 (![X92]: 262.13/38.49 ((~rel_s4(X90,X92)) | qmltpeq(op(e1,e3),op(e2,e3),X92))))))) | 262.13/38.49 (~ 262.13/38.49 (![X98]: 262.13/38.49 ((~rel_s4(X4,X98)) | 262.13/38.49 (~ 262.13/38.49 (![X100]: 262.13/38.49 ((~rel_s4(X98,X100)) | qmltpeq(op(e2,e3),op(e3,e3),X100))))))) | 262.13/38.49 (~ 262.13/38.49 (![X106]: 262.13/38.49 ((~rel_s4(X4,X106)) | 262.13/38.49 (~ 262.13/38.49 (![X108]: 262.13/38.49 ((~rel_s4(X106,X108)) | qmltpeq(op(e0,e0),op(e0,e2),X108))))))) | 262.13/38.49 (~ 262.13/38.49 (![X114]: 262.13/38.49 ((~rel_s4(X4,X114)) | 262.13/38.49 (~ 262.13/38.49 (![X116]: 262.13/38.49 ((~rel_s4(X114,X116)) | qmltpeq(op(e0,e1),op(e0,e2),X116))))))) | 262.13/38.49 (~ 262.13/38.49 (![X122]: 262.13/38.49 ((~rel_s4(X4,X122)) | 262.13/38.49 (~ 262.13/38.49 (![X124]: 262.13/38.49 ((~rel_s4(X122,X124)) | qmltpeq(op(e0,e2),op(e0,e3),X124))))))) | 262.13/38.49 (~ 262.13/38.49 (![X130]: 262.13/38.49 ((~rel_s4(X4,X130)) | 262.13/38.49 (~ 262.13/38.49 (![X132]: 262.13/38.49 ((~rel_s4(X130,X132)) | qmltpeq(op(e1,e0),op(e1,e2),X132))))))) | 262.13/38.49 (~ 262.13/38.49 (![X138]: 262.13/38.49 ((~rel_s4(X4,X138)) | 262.13/38.49 (~ 262.13/38.49 (![X140]: 262.13/38.49 ((~rel_s4(X138,X140)) | qmltpeq(op(e1,e1),op(e1,e2),X140))))))) | 262.13/38.49 (~ 262.13/38.49 (![X146]: 262.13/38.49 ((~rel_s4(X4,X146)) | 262.13/38.49 (~ 262.13/38.49 (![X148]: 262.13/38.49 ((~rel_s4(X146,X148)) | qmltpeq(op(e1,e2),op(e1,e3),X148))))))) | 262.13/38.49 (~ 262.13/38.49 (![X154]: 262.13/38.49 ((~rel_s4(X4,X154)) | 262.13/38.49 (~ 262.13/38.49 (![X156]: 262.13/38.49 ((~rel_s4(X154,X156)) | qmltpeq(op(e2,e0),op(e2,e2),X156))))))) | 262.13/38.49 (~ 262.13/38.49 (![X162]: 262.13/38.49 ((~rel_s4(X4,X162)) | 262.13/38.49 (~ 262.13/38.49 (![X164]: 262.13/38.49 ((~rel_s4(X162,X164)) | qmltpeq(op(e2,e1),op(e2,e2),X164))))))) | 262.13/38.49 (~ 262.13/38.49 (![X170]: 262.13/38.49 ((~rel_s4(X4,X170)) | 262.13/38.49 (~ 262.13/38.49 (![X172]: 262.13/38.49 ((~rel_s4(X170,X172)) | qmltpeq(op(e2,e2),op(e2,e3),X172))))))) | 262.13/38.49 (~ 262.13/38.49 (![X178]: 262.13/38.49 ((~rel_s4(X4,X178)) | 262.13/38.49 (~ 262.13/38.49 (![X180]: 262.13/38.49 ((~rel_s4(X178,X180)) | qmltpeq(op(e3,e0),op(e3,e2),X180))))))) | 262.13/38.49 (~ 262.13/38.49 (![X186]: 262.13/38.49 ((~rel_s4(X4,X186)) | 262.13/38.49 (~ 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Y1)))))))))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | 262.13/38.50 (~((!!((^[Y1 : $i]: 262.13/38.50 ((~(rel_s4(Y0, Y1))) | 262.13/38.50 qmltpeq(op(e0, e0), op(e1, e0), Y1)))))))))))))), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['69'])). 262.13/38.50 tff('71', plain, 262.13/38.50 ![X1]: 262.13/38.50 (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | 262.13/38.50 (~((!!((^[Y1 : $i]: 262.13/38.50 ((~(rel_s4(Y0, Y1))) | 262.13/38.50 qmltpeq(op(e0, e0), op(e2, e0), Y1))))))))))), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['70'])). 262.13/38.50 tff('72', plain, 262.13/38.50 ![X1, X2]: 262.13/38.50 ((~(rel_s4(X1, X2))) | 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X2, Y0))) | qmltpeq(op(e0, e0), op(e2, e0), Y0)))))))), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['71'])). 262.13/38.50 tff('73', plain, 262.13/38.50 ![X1, X2]: 262.13/38.50 (~ rel_s4(X1, X2) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X2, Y0))) | qmltpeq(op(e0, e0), op(e2, e0), Y0)))))), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['72'])). 262.13/38.50 tff('74', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('75', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e1, e1), e3, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))), 262.13/38.50 inference('renaming', [status(thm)], ['68', '74'])). 262.13/38.50 tff('76', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('77', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e0, e0), e3, X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e3, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['75', '76'])). 262.13/38.50 tff('78', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('79', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e3, e3), e3, X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e3, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ '#form15'(op(e0, e0), e3, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['77', '78'])). 262.13/38.50 tff('80', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('81', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e2, e2), e3, X1) 262.13/38.50 | ~ '#form15'(op(e0, e0), e3, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e3, X1) 262.13/38.50 | ~ '#form15'(op(e3, e3), e3, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['79', '80'])). 262.13/38.50 tff('82', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e1, Y0))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))))))), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['14'])). 262.13/38.50 tff('83', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('84', plain, 262.13/38.50 ( '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 inference('renaming', [status(thm)], ['82', '83'])). 262.13/38.50 tff('85', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17')), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['84'])). 262.13/38.50 tff('86', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('87', plain, 262.13/38.50 ( '#form15'(op(e0, e0), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 inference('renaming', [status(thm)], ['85', '86'])). 262.13/38.50 tff('88', plain, 262.13/38.50 ( '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('89', plain, 262.13/38.50 (~ '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | '#form15'(op(e0, e0), e3, '#sk17')), 262.13/38.50 inference('renaming', [status(thm)], ['87', '88'])). 262.13/38.50 tff('90', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('91', plain, 262.13/38.50 (~ '#form19' 262.13/38.50 | '#form15'(op(e0, e0), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['89', '90'])). 262.13/38.50 tff('92', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['50'])). 262.13/38.50 tff('93', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('94', plain, 262.13/38.50 ( '#form15'(op(e1, e1), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['92', '93'])). 262.13/38.50 tff('95', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17')), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['84'])). 262.13/38.50 tff('96', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('97', plain, 262.13/38.50 ( '#form15'(op(e1, e1), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 inference('renaming', [status(thm)], ['95', '96'])). 262.13/38.50 tff('98', plain, 262.13/38.50 ( '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('99', plain, 262.13/38.50 (~ '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e3, '#sk17')), 262.13/38.50 inference('renaming', [status(thm)], ['97', '98'])). 262.13/38.50 tff('100', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('101', plain, 262.13/38.50 (~ '#form19' 262.13/38.50 | '#form15'(op(e1, e1), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['99', '100'])). 262.13/38.50 tff('102', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['60'])). 262.13/38.50 tff('103', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('104', plain, 262.13/38.50 ( '#form15'(op(e1, e1), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['102', '103'])). 262.13/38.50 tff('105', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['50'])). 262.13/38.50 tff('106', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('107', plain, 262.13/38.50 ( '#form15'(op(e3, e3), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['105', '106'])). 262.13/38.50 tff('108', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17')), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['84'])). 262.13/38.50 tff('109', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('110', plain, 262.13/38.50 ( '#form15'(op(e3, e3), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 inference('renaming', [status(thm)], ['108', '109'])). 262.13/38.50 tff('111', plain, 262.13/38.50 ( '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('112', plain, 262.13/38.50 (~ '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | '#form15'(op(e3, e3), e3, '#sk17')), 262.13/38.50 inference('renaming', [status(thm)], ['110', '111'])). 262.13/38.50 tff('113', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('114', plain, 262.13/38.50 (~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['112', '113'])). 262.13/38.50 tff('115', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e1, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e1, Y0)))))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['66'])). 262.13/38.50 tff('116', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ (!!((^[Y0 : $i]: ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e1, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['115'])). 262.13/38.50 tff('117', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('118', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e1, e1), e1, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0)))))), 262.13/38.50 inference('renaming', [status(thm)], ['116', '117'])). 262.13/38.50 tff('119', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('120', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e0, e0), e1, X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e1, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e1, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['118', '119'])). 262.13/38.50 tff('121', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('122', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e3, e3), e1, X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e1, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e1, Y0))))) 262.13/38.50 | ~ '#form15'(op(e0, e0), e1, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['120', '121'])). 262.13/38.50 tff('123', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('124', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e2, e2), e1, X1) 262.13/38.50 | ~ '#form15'(op(e0, e0), e1, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e1, X1) 262.13/38.50 | ~ '#form15'(op(e3, e3), e1, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['122', '123'])). 262.13/38.50 tff('125', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['60'])). 262.13/38.50 tff('126', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('127', plain, 262.13/38.50 ( '#form15'(op(e3, e3), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['125', '126'])). 262.13/38.50 tff('128', plain, 262.13/38.50 (~ '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17')), 262.13/38.50 inference('renaming', [status(thm)], ['46', '47'])). 262.13/38.50 tff('129', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('130', plain, 262.13/38.50 (~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0)))))))) 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['128', '129'])). 262.13/38.50 tff('131', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['130'])). 262.13/38.50 tff('132', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('133', plain, 262.13/38.50 ( '#form15'(op(e3, e3), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['131', '132'])). 262.13/38.50 tff('134', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['130'])). 262.13/38.50 tff('135', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('136', plain, 262.13/38.50 ( '#form15'(op(e1, e1), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['134', '135'])). 262.13/38.50 tff('137', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['130'])). 262.13/38.50 tff('138', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('139', plain, 262.13/38.50 ( '#form15'(op(e0, e0), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['137', '138'])). 262.13/38.50 tff('140', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['130'])). 262.13/38.50 tff('141', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('142', plain, 262.13/38.50 ( '#form15'(op(e2, e2), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e3, e3), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['140', '141'])). 262.13/38.50 tff('143', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['50'])). 262.13/38.50 tff('144', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('145', plain, 262.13/38.50 ( '#form15'(op(e2, e2), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e2, e2), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['143', '144'])). 262.13/38.50 tff('146', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17')), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['84'])). 262.13/38.50 tff('147', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('148', plain, 262.13/38.50 ( '#form15'(op(e2, e2), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 inference('renaming', [status(thm)], ['146', '147'])). 262.13/38.50 tff('149', plain, 262.13/38.50 ( '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('150', plain, 262.13/38.50 (~ '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | '#form15'(op(e2, e2), e3, '#sk17')), 262.13/38.50 inference('renaming', [status(thm)], ['148', '149'])). 262.13/38.50 tff('151', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('152', plain, 262.13/38.50 (~ '#form19' 262.13/38.50 | '#form15'(op(e2, e2), e3, '#sk17') 262.13/38.50 | '#form15'(op(e1, e1), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['150', '151'])). 262.13/38.50 tff('153', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e0, Y0)))))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['66'])). 262.13/38.50 tff('154', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ (!!((^[Y0 : $i]: ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e0, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['153'])). 262.13/38.50 tff('155', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('156', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e1, e1), e0, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))), 262.13/38.50 inference('renaming', [status(thm)], ['154', '155'])). 262.13/38.50 tff('157', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('158', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e0, e0), e0, X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e0, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e0, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['156', '157'])). 262.13/38.50 tff('159', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('160', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e3, e3), e0, X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e0, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e0, Y0))))) 262.13/38.50 | ~ '#form15'(op(e0, e0), e0, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['158', '159'])). 262.13/38.50 tff('161', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('162', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e2, e2), e0, X1) 262.13/38.50 | ~ '#form15'(op(e0, e0), e0, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e0, X1) 262.13/38.50 | ~ '#form15'(op(e3, e3), e0, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['160', '161'])). 262.13/38.50 tff('163', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e3, Y0))))) 262.13/38.50 | ~ '#form18' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['60'])). 262.13/38.50 tff('164', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ '#form15'(X3, X7, X8) 262.13/38.50 | (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('165', plain, 262.13/38.50 ( '#form15'(op(e2, e2), e3, '#sk17') 262.13/38.50 | ~ '#form19' 262.13/38.50 | '#form15'(op(e0, e0), e1, '#sk17') 262.13/38.50 | ~ '#form18'), 262.13/38.50 inference('renaming', [status(thm)], ['163', '164'])). 262.13/38.50 tff(mreflexive, axiom, mreflexive() = ^[R:(($i * $i) > $o)]: (![S]: R(S,S))). 262.13/38.50 tff('166', plain, mreflexive = (^[R:(($i * $i) > $o)]: (![S]: R(S,S))), 262.13/38.50 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 262.13/38.50 tff('167', plain, 262.13/38.50 mreflexive = (^[V_1:(($i * $i) > $o)]: (![X4]: V_1(X4,X4))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff(a1, axiom, (mreflexive(rel_s4))). 262.13/38.50 tff(zf_stmt_4, axiom, (![X4]: rel_s4(X4,X4))). 262.13/38.50 tff('168', plain, (!!((^[Y0 : $i]: rel_s4(Y0, Y0)))), 262.13/38.50 inference('cnf', [status(esa)], [zf_stmt_4])). 262.13/38.50 tff('169', plain, ![X1]: rel_s4(X1, X1), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['168'])). 262.13/38.50 tff('170', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e2, Y0)))))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['66'])). 262.13/38.50 tff('171', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ (!!((^[Y0 : $i]: ((~(rel_s4(X1, Y0))) | qmltpeq(op(e1, e1), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e2, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['170'])). 262.13/38.50 tff('172', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('173', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e1, e1), e2, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e0, e0), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))), 262.13/38.50 inference('renaming', [status(thm)], ['171', '172'])). 262.13/38.50 tff('174', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('175', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e0, e0), e2, X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e3, e3), e2, Y0))))) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0))))) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e2, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['173', '174'])). 262.13/38.50 tff('176', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('177', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e3, e3), e2, X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e2, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4(X1, Y0))) | qmltpeq(op(e2, e2), e2, Y0))))) 262.13/38.50 | ~ '#form15'(op(e0, e0), e2, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['175', '176'])). 262.13/38.50 tff('178', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('179', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ '#form15'(op(e2, e2), e2, X1) 262.13/38.50 | ~ '#form15'(op(e0, e0), e2, X1) 262.13/38.50 | ~ rel_s4('#sk17', X1) 262.13/38.50 | ~ '#form15'(op(e1, e1), e2, X1) 262.13/38.50 | ~ '#form15'(op(e3, e3), e2, X1)), 262.13/38.50 inference('renaming', [status(thm)], ['177', '178'])). 262.13/38.50 tff('180', plain, 262.13/38.50 ( '#form19' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('181', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e0, Y0))))) 262.13/38.50 | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['180'])). 262.13/38.50 tff('182', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e3, e3), e0, X1)) | '#form19'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['181'])). 262.13/38.50 tff('183', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e3, e3), e0, X1) | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['182'])). 262.13/38.50 tff('184', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e0, Y0))))) 262.13/38.50 | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['180'])). 262.13/38.50 tff('185', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e2, e2), e0, X1)) | '#form19'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['184'])). 262.13/38.50 tff('186', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e2, e2), e0, X1) | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['185'])). 262.13/38.50 tff('187', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e0, Y0))))) 262.13/38.50 | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['180'])). 262.13/38.50 tff('188', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e1, e1), e0, X1)) | '#form19'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['187'])). 262.13/38.50 tff('189', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e1, e1), e0, X1) | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['188'])). 262.13/38.50 tff('190', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e0, Y0))))) 262.13/38.50 | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['180'])). 262.13/38.50 tff('191', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e0, e0), e0, X1)) | '#form19'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['190'])). 262.13/38.50 tff('192', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e0, e0), e0, X1) | '#form19'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['191'])). 262.13/38.50 tff('193', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( '#form15'(X3, X7, X8) 262.13/38.50 | ~ (!!((^[Y0 : $i]: ((~(rel_s4(X8, Y0))) | qmltpeq(X3, X7, Y0)))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('194', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ ((~(rel_s4(X8, '#sk14'(X3, X7, X8)))) | 262.13/38.50 qmltpeq(X3, X7, '#sk14'(X3, X7, X8))) 262.13/38.50 | '#form15'(X3, X7, X8)), 262.13/38.50 inference('lazy_cnf_exists', [status(thm)], ['193'])). 262.13/38.50 tff('195', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 (~ qmltpeq(X3, X7, '#sk14'(X3, X7, X8)) | '#form15'(X3, X7, X8)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['194'])). 262.13/38.50 tff('196', plain, 262.13/38.50 ( '#form18' 262.13/38.50 | ~ ((~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0)))))))| 262.13/38.50 (~((!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))))))), 262.13/38.50 define([status(thm)])). 262.13/38.50 tff('197', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e3, e3), e2, Y0))))) 262.13/38.50 | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['196'])). 262.13/38.50 tff('198', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e3, e3), e2, X1)) | '#form18'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['197'])). 262.13/38.50 tff('199', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e3, e3), e2, X1) | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['198'])). 262.13/38.50 tff('200', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e2, e2), e2, Y0))))) 262.13/38.50 | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['196'])). 262.13/38.50 tff('201', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e2, e2), e2, X1)) | '#form18'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['200'])). 262.13/38.50 tff('202', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e2, e2), e2, X1) | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['201'])). 262.13/38.50 tff('203', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e1, e1), e2, Y0))))) 262.13/38.50 | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['196'])). 262.13/38.50 tff('204', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e1, e1), e2, X1)) | '#form18'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['203'])). 262.13/38.50 tff('205', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e1, e1), e2, X1) | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['204'])). 262.13/38.50 tff('206', plain, 262.13/38.50 ![X3 : mu, X7 : mu, X8]: 262.13/38.50 ( rel_s4(X8, '#sk14'(X3, X7, X8)) | '#form15'(X3, X7, X8)), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['194'])). 262.13/38.50 tff('207', plain, 262.13/38.50 ( (!!((^[Y0 : $i]: 262.13/38.50 ((~(rel_s4('#sk17', Y0))) | qmltpeq(op(e0, e0), e2, Y0))))) 262.13/38.50 | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['196'])). 262.13/38.50 tff('208', plain, 262.13/38.50 ![X1]: 262.13/38.50 ( ((~(rel_s4('#sk17', X1))) | qmltpeq(op(e0, e0), e2, X1)) | '#form18'), 262.13/38.50 inference('lazy_cnf_forall', [status(thm)], ['207'])). 262.13/38.50 tff('209', plain, 262.13/38.50 ![X1]: 262.13/38.50 (~ rel_s4('#sk17', X1) | qmltpeq(op(e0, e0), e2, X1) | '#form18'), 262.13/38.50 inference('lazy_cnf_or', [status(thm)], ['208'])). 262.13/38.50 tff('210', plain, $false, 262.13/38.50 inference('eprover', [status(thm)], 262.13/38.50 ['53', '63', '81', '91', '94', '101', '104', '107', '114', 262.13/38.50 '124', '127', '133', '136', '139', '142', '145', '152', 262.13/38.50 '162', '165', '169', '179', '183', '186', '189', '192', 262.13/38.50 '195', '199', '202', '205', '206', '209'])). 262.13/38.50 262.13/38.50 % SZS output end Refutation 262.13/38.50 262.13/38.50 262.13/38.50 % Terminating... 262.81/38.61 % Runner terminated. 262.81/38.62 % Zipperpin 1.5 exiting 262.81/38.63 EOF