0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.cZBzTiQD12 true 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 06:31:34 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.53/0.68 % Total configuration time : 828 0.53/0.68 % Estimated wc time : 1656 0.53/0.68 % Estimated cpu time (8 cpus) : 207.0 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.89 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 121.46/16.13 % Solved by lams/40_b.comb.sh. 121.46/16.13 % done 510 iterations in 15.290s 121.46/16.13 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 121.46/16.13 % SZS output start Refutation 121.46/16.13 thf(du_type, type, du: $tType). 121.46/16.13 thf(d_type, type, d: $tType). 121.46/16.13 thf(u_type, type, u: $tType). 121.46/16.13 thf(mono_2Etyop_2Eextreal_2Eextreal_type, type, mono_2Etyop_2Eextreal_2Eextreal: 121.46/16.13 $tType). 121.46/16.13 thf(c_2Ebool_2ECOND_2E3_type, type, c_2Ebool_2ECOND_2E3: du > du > du > u). 121.46/16.13 thf('#sk4_type', type, '#sk4': mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf(tyop_2Eextreal_2Eextreal_type, type, tyop_2Eextreal_2Eextreal: d). 121.46/16.13 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_type, type, 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: 121.46/16.13 (mono_2Etyop_2Eextreal_2Eextreal > $o) > u). 121.46/16.13 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_type, type, 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: 121.46/16.13 (mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal) > u). 121.46/16.13 thf(mono_2Ec_2Eextreal_2Eextreal__max_type, type, mono_2Ec_2Eextreal_2Eextreal__max: 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf('#sk2_type', type, '#sk2': mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf(app_2E2_type, type, app_2E2: du > du > u). 121.46/16.13 thf(mono_2Ec_2Eextreal_2Eextreal__le_type, type, mono_2Ec_2Eextreal_2Eextreal__le: 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o). 121.46/16.13 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_type, type, 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: 121.46/16.13 (mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal) > u). 121.46/16.13 thf(tyop_2Emin_2Efun_type, type, tyop_2Emin_2Efun: d > d > d). 121.46/16.13 thf('#ty_enc7_type', type, '#ty_enc7': mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_type, type, 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: 121.46/16.13 (mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o) > u). 121.46/16.13 thf(s_type, type, s: d > u > du). 121.46/16.13 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_type, type, 121.46/16.13 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: 121.46/16.13 du > mono_2Etyop_2Eextreal_2Eextreal > $o). 121.46/16.13 thf(i_mono_2Etyop_2Eextreal_2Eextreal_type, type, i_mono_2Etyop_2Eextreal_2Eextreal: 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > u). 121.46/16.13 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_type, type, 121.46/16.13 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: 121.46/16.13 du > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf(i_mono_2Etyop_2Emin_2Ebool_type, type, i_mono_2Etyop_2Emin_2Ebool: $o > u). 121.46/16.13 thf(tyop_2Emin_2Ebool_type, type, tyop_2Emin_2Ebool: d). 121.46/16.13 thf(mono_2Ec_2Ebool_2ET_type, type, mono_2Ec_2Ebool_2ET: $o). 121.46/16.13 thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal_type, type, 121.46/16.13 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal: $o > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf('#sk3_type', type, '#sk3': mono_2Etyop_2Eextreal_2Eextreal). 121.46/16.13 thf(j_mono_2Etyop_2Emin_2Ebool_type, type, j_mono_2Etyop_2Emin_2Ebool: 121.46/16.13 du > $o). 121.46/16.13 thf(mono_2Ec_2Ebool_2EF_type, type, mono_2Ec_2Ebool_2EF: $o). 121.46/16.13 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 121.46/16.13 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 121.46/16.13 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 121.46/16.13 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 121.46/16.13 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 121.46/16.13 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29, axiom, 121.46/16.13 (![V0:( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal )]: 121.46/16.13 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 121.46/16.13 @ 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 121.46/16.13 @ V0 ) ) ) = 121.46/16.13 ( V0 ) ))). 121.46/16.13 thf(zip_derived_cl33, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 Y0))) = 121.46/16.13 (Y0))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29])). 121.46/16.13 thf(zip_derived_cl34, plain, 121.46/16.13 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29)))))) @ 121.46/16.13 ('#I')))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl33])). 121.46/16.13 thf(zip_derived_cl124, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 X2))) = 121.46/16.13 (X2)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 121.46/16.13 thf(zip_derived_cl125, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 X2))) 121.46/16.13 = (X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl124])). 121.46/16.13 thf(zip_derived_cl235, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X3 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 X2)) @ 121.46/16.13 X3) = (X2 @ X3))), 121.46/16.13 inference('ho_complete_eq', [status(thm)], [zip_derived_cl125])). 121.46/16.13 thf(zip_derived_cl284, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 ((('#K') @ X0)))) @ 121.46/16.13 X1) = ((('#K') @ X0 @ X1)))), 121.46/16.13 inference('narrow_applied_variable', [status(thm)], [zip_derived_cl235])). 121.46/16.13 thf(zip_derived_cl287, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 ((('#K') @ X0)))) @ 121.46/16.13 X1) = (X0))), 121.46/16.13 inference('comb-normalize', [status(thm)], [zip_derived_cl284])). 121.46/16.13 thf(zip_derived_cl6989, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 ('#ty_enc7' @ X0))) @ 121.46/16.13 X1) = (X0))), 121.46/16.13 inference('remove_ty_args', [status(thm)], [zip_derived_cl287])). 121.46/16.13 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29, axiom, 121.46/16.13 (![V0:( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal ), 121.46/16.13 V1:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 121.46/16.13 @ ( V0 @ V1 ) ) ) = 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ 121.46/16.13 ( app_2E2 @ 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 121.46/16.13 @ V0 ) ) @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ))). 121.46/16.13 thf(zip_derived_cl68, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (Y0 @ Y1))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ 121.46/16.13 Y0)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ Y1))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29])). 121.46/16.13 thf(zip_derived_cl69, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)))) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29)))))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ app_2E2 @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal))) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29)))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl68])). 121.46/16.13 thf(zip_derived_cl189, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 X2)))))) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 ((('#B') @ (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ 121.46/16.13 X2))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])). 121.46/16.13 thf(zip_derived_cl190, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (X2 @ X4))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl189])). 121.46/16.13 thf(zip_derived_cl191, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (X2 @ X4))) 121.46/16.13 = (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl190])). 121.46/16.13 thf(zip_derived_cl125, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ 121.46/16.13 X2))) 121.46/16.13 = (X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl124])). 121.46/16.13 thf(thm_2Eextreal_2Eextreal__max__def, axiom, 121.46/16.13 (![V0x:mono_2Etyop_2Eextreal_2Eextreal,V1y:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__max @ V0x @ V1y ) = 121.46/16.13 ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) @ V1y @ V0x ) ))). 121.46/16.13 thf(zip_derived_cl41, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__max @ Y0 @ 121.46/16.13 Y1) = 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ Y1) @ 121.46/16.13 Y1 @ Y0)))))))))), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Eextreal_2Eextreal__max__def])). 121.46/16.13 thf(zip_derived_cl42, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__max)))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal)) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le)))) @ 121.46/16.13 ('#I'))))) @ 121.46/16.13 ('#I')))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl41])). 121.46/16.13 thf(zip_derived_cl149, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ X2))) @ 121.46/16.13 ((('#C') @ ((('#S') @ ((('#B') @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 X2))) @ 121.46/16.13 ('#I'))) @ 121.46/16.13 X2))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 121.46/16.13 thf(zip_derived_cl150, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4) = 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) @ X4 @ X2)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl149])). 121.46/16.13 thf(zip_derived_cl151, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4) 121.46/16.13 = (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) @ X4 @ X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl150])). 121.46/16.13 thf(thm_2Ebool_2ECOND__CLAUSES, axiom, 121.46/16.13 (![A_27a:d,V0t1_2E0:u,V1t2_2E0:u]: 121.46/16.13 ( ( ( s @ 121.46/16.13 A_27a @ 121.46/16.13 ( c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ 121.46/16.13 ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) ) = 121.46/16.13 ( s @ A_27a @ V1t2_2E0 ) ) & 121.46/16.13 ( ( s @ 121.46/16.13 A_27a @ 121.46/16.13 ( c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ 121.46/16.13 ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) ) = 121.46/16.13 ( s @ A_27a @ V0t1_2E0 ) ) ))). 121.46/16.13 thf(zip_derived_cl62, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : d]: 121.46/16.13 (((!!) @ (^[Y1 : u]: 121.46/16.13 (((!!) @ (^[Y2 : u]: 121.46/16.13 (((((s @ Y0 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2EF)) @ 121.46/16.13 (s @ Y0 @ Y1) @ (s @ Y0 @ Y2))) = 121.46/16.13 (s @ Y0 @ Y2))) & 121.46/16.13 (((s @ Y0 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2ET)) @ 121.46/16.13 (s @ Y0 @ Y1) @ (s @ Y0 @ Y2))) = 121.46/16.13 (s @ Y0 @ Y1))))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Ebool_2ECOND__CLAUSES])). 121.46/16.13 thf(zip_derived_cl63, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#B') @ ((('#B') @ (!!))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#S'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (&))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#S'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ( 121.46/16.13 (('#B') @ (=))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ( 121.46/16.13 '#B') @ 121.46/16.13 ((('#B') @ ( 121.46/16.13 '#B') @ s)))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ( 121.46/16.13 '#C') @ 121.46/16.13 ( 121.46/16.13 ( 121.46/16.13 ('#B') @ ( 121.46/16.13 ( 121.46/16.13 ('#B') @ ( 121.46/16.13 '#B'))) @ 121.46/16.13 ( 121.46/16.13 ( 121.46/16.13 ('#B') @ ( 121.46/16.13 ( 121.46/16.13 ('#B') @ ( 121.46/16.13 c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ( 121.46/16.13 s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 ( 121.46/16.13 i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2EF))))) @ 121.46/16.13 s)))))) @ 121.46/16.13 s)))))))))) @ 121.46/16.13 s)))))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#C'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ ('#B') @ s)))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ ( 121.46/16.13 '#B'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ( 121.46/16.13 c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ( 121.46/16.13 s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 ( 121.46/16.13 i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2ET))))) @ 121.46/16.13 s)))))) @ 121.46/16.13 s)))))))))) @ 121.46/16.13 s))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl62])). 121.46/16.13 thf(zip_derived_cl196, plain, 121.46/16.13 (![X2 : d]: 121.46/16.13 (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (&))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ( 121.46/16.13 s @ X2))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ( 121.46/16.13 '#B') @ 121.46/16.13 ((('#B') @ ( 121.46/16.13 c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2EF))) @ 121.46/16.13 (s @ X2))))) @ 121.46/16.13 (s @ X2))))))))) @ 121.46/16.13 (s @ X2))))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ X2))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2ET))) @ 121.46/16.13 (s @ X2))))) @ 121.46/16.13 (s @ X2))))))))) @ 121.46/16.13 (s @ X2)))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 121.46/16.13 thf(zip_derived_cl197, plain, 121.46/16.13 (![X2 : d, X4 : u]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (&) @ 121.46/16.13 ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ X2) @ 121.46/16.13 ((('#B') @ (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2EF)) @ 121.46/16.13 (s @ X2 @ X4)) @ 121.46/16.13 (s @ X2))))))) @ 121.46/16.13 (s @ X2))))) @ 121.46/16.13 ((('#C') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ X2) @ 121.46/16.13 ((('#B') @ (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 mono_2Ec_2Ebool_2ET)) @ 121.46/16.13 (s @ X2 @ X4)) @ 121.46/16.13 (s @ X2))))))) @ 121.46/16.13 (s @ X2 @ X4)))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl196])). 121.46/16.13 thf(zip_derived_cl198, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 (((((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF)) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X6))) & 121.46/16.13 (((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET)) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X4)))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl197])). 121.46/16.13 thf(thm_2Ebool_2EIMP__F, axiom, 121.46/16.13 (![V0t:$o]: ( ( ( V0t ) => ( mono_2Ec_2Ebool_2EF ) ) => ( ~( V0t ) ) ))). 121.46/16.13 thf(zip_derived_cl8, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : $o]: 121.46/16.13 (((((Y0) => (mono_2Ec_2Ebool_2EF))) => (((~) @ Y0)))))))), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Ebool_2EIMP__F])). 121.46/16.13 thf(zip_derived_cl9, plain, 121.46/16.13 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 121.46/16.13 ((('#C') @ (=>) @ mono_2Ec_2Ebool_2EF)))) @ 121.46/16.13 (~)))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl8])). 121.46/16.13 thf(zip_derived_cl83, plain, 121.46/16.13 (![X2 : $o]: (((((X2) => (mono_2Ec_2Ebool_2EF))) => (((~) @ X2))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 121.46/16.13 thf(zip_derived_cl84, plain, 121.46/16.13 (![X2 : $o]: (~ (((X2) => (mono_2Ec_2Ebool_2EF))) | ~ (X2))), 121.46/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 121.46/16.13 thf(zip_derived_cl86, plain, 121.46/16.13 (![X2 : $o]: (~ (mono_2Ec_2Ebool_2EF) | ~ (X2))), 121.46/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 121.46/16.13 thf(zip_derived_cl87, plain, (~ (mono_2Ec_2Ebool_2EF)), 121.46/16.13 inference('condensation', [status(thm)], [zip_derived_cl86])). 121.46/16.13 thf(thm_2Ebool_2ETRUTH, axiom, (mono_2Ec_2Ebool_2ET)). 121.46/16.13 thf(zip_derived_cl10, plain, ( (mono_2Ec_2Ebool_2ET)), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Ebool_2ETRUTH])). 121.46/16.13 thf(zip_derived_cl199, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 (((((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($false))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X6))) & 121.46/16.13 (((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($true))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X4)))))), 121.46/16.13 inference('demod', [status(thm)], 121.46/16.13 [zip_derived_cl198, zip_derived_cl87, zip_derived_cl10])). 121.46/16.13 thf(zip_derived_cl200, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 (((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($false))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X6)))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl199])). 121.46/16.13 thf(zip_derived_cl202, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 ((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($false))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) 121.46/16.13 = (s @ X2 @ X6))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl200])). 121.46/16.13 thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal, axiom, 121.46/16.13 (![V0:$o,V1:mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 V2:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 V0 @ V1 @ V2 ) ) ) = 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ V2 ) ) ) ) ))). 121.46/16.13 thf(zip_derived_cl74, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : $o]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 Y0 @ Y1 @ Y2))) = 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 Y0)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 Y1)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 Y2)))))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal])). 121.46/16.13 thf(zip_derived_cl75, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#B') @ ((('#B') @ (!!))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#S'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ ( 121.46/16.13 s @ 121.46/16.13 tyop_2Eextreal_2Eextreal))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ i_mono_2Etyop_2Eextreal_2Eextreal)))) @ 121.46/16.13 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal)))))))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (s @ 121.46/16.13 tyop_2Eextreal_2Eextreal))))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#B'))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ c_2Ebool_2ECOND_2E3 @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Ebool)))))) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal)))))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl74])). 121.46/16.13 thf(zip_derived_cl192, plain, 121.46/16.13 (![X2 : $o]: 121.46/16.13 (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ 121.46/16.13 tyop_2Eextreal_2Eextreal))) @ 121.46/16.13 ((('#B') @ ((('#B') @ i_mono_2Etyop_2Eextreal_2Eextreal)) @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 X2))))))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ tyop_2Eextreal_2Eextreal))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 X2))) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal)))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])). 121.46/16.13 thf(zip_derived_cl193, plain, 121.46/16.13 (![X2 : $o, X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 X2 @ X4))))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 ((('#B') @ (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl192])). 121.46/16.13 thf(zip_derived_cl194, plain, 121.46/16.13 (![X2 : $o, X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ 121.46/16.13 X4 @ X6))) = 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X6))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl193])). 121.46/16.13 thf(zip_derived_cl195, plain, 121.46/16.13 (![X2 : $o, X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ 121.46/16.13 X4 @ X6))) 121.46/16.13 = (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X6)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl194])). 121.46/16.13 thf(zip_derived_cl1587, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 ($false) @ X1 @ X0))) 121.46/16.13 = (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X0)))), 121.46/16.13 inference('sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl195])). 121.46/16.13 thf(thm_2Eextreal_2Ele__total, axiom, 121.46/16.13 (![V0x:mono_2Etyop_2Eextreal_2Eextreal,V1y:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) | 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V0x ) ))). 121.46/16.13 thf(zip_derived_cl47, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ Y0 @ 121.46/16.13 Y1) | (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y1 @ Y0)))))))))), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Eextreal_2Ele__total])). 121.46/16.13 thf(zip_derived_cl48, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (|))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le)))) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl47])). 121.46/16.13 thf(zip_derived_cl126, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (|) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2))) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le @ X2))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 121.46/16.13 thf(zip_derived_cl127, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) | 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl126])). 121.46/16.13 thf(zip_derived_cl128, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2))), 121.46/16.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 121.46/16.13 thf(zip_derived_cl268, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ X0)), 121.46/16.13 inference('eq_fact', [status(thm)], [zip_derived_cl128])). 121.46/16.13 thf(thm_2Eextreal_2Emax__le, conjecture, 121.46/16.13 (![V0z:mono_2Etyop_2Eextreal_2Eextreal,V1x:mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 V2y:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__max @ V1x @ V2y ) @ V0z ) <=> 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V2y @ V0z ) & 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V1x @ V0z ) ) ))). 121.46/16.13 thf(zf_stmt_0, negated_conjecture, 121.46/16.13 (~( ![V0z:mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 V1x:mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 V2y:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__max @ V1x @ V2y ) @ V0z ) <=> 121.46/16.13 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V2y @ V0z ) & 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V1x @ V0z ) ) ) )), 121.46/16.13 inference('cnf.neg', [status(esa)], [thm_2Eextreal_2Emax__le])). 121.46/16.13 thf(zip_derived_cl78, plain, 121.46/16.13 (~ (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ 121.46/16.13 Y1 @ Y2) @ 121.46/16.13 Y0) <=> 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y2 @ Y0) & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y1 @ Y0))))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], [zf_stmt_0])). 121.46/16.13 thf(zip_derived_cl79, plain, 121.46/16.13 (~ (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#B') @ ((('#B') @ (!!))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#S'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ mono_2Ec_2Eextreal_2Eextreal__le)) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__max)))))))))))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ (&))) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le)))))))) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le))))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl78])). 121.46/16.13 thf(zip_derived_cl145, plain, 121.46/16.13 (~ (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (<=>))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ mono_2Ec_2Eextreal_2Eextreal__le)) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__max)))) @ 121.46/16.13 '#sk2')))))) @ 121.46/16.13 ((('#B') @ ((('#C') @ ((('#B') @ (&) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 '#sk2')))))) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le @ '#sk2'))))))))))), 121.46/16.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 121.46/16.13 thf(zip_derived_cl146, plain, 121.46/16.13 (~ (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 121.46/16.13 ((('#C') @ ((('#B') @ mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ 121.46/16.13 '#sk3'))) @ 121.46/16.13 '#sk2')))) @ 121.46/16.13 ((('#C') @ ((('#B') @ (&) @ 121.46/16.13 ((('#C') @ mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 '#sk2')))) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2')))))))), 121.46/16.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl145])). 121.46/16.13 thf(zip_derived_cl147, plain, 121.46/16.13 (~ (((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2') <=> 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2')))))), 121.46/16.13 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl146])). 121.46/16.13 thf(zip_derived_cl148, plain, 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2') 121.46/16.13 != (((mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2'))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl147])). 121.46/16.13 thf(thm_2Eextreal_2Ele__trans, axiom, 121.46/16.13 (![V0x:mono_2Etyop_2Eextreal_2Eextreal,V1y:mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 V2z:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V2z ) & 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) ) => 121.46/16.13 ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V2z ) ))). 121.46/16.13 thf(zip_derived_cl27, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ (^[Y2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y1 @ Y2) & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y0 @ Y1))) => 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 Y0 @ Y2))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], [thm_2Eextreal_2Ele__trans])). 121.46/16.13 thf(zip_derived_cl28, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#B') @ ((('#B') @ (!!))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ ('#S'))) @ 121.46/16.13 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 121.46/16.13 ((('#B') @ ((('#S') @ ((('#B') @ ( 121.46/16.13 '#C') @ 121.46/16.13 ((('#B') @ ( 121.46/16.13 (('#B') @ (&))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le)))))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le)))))))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl27])). 121.46/16.13 thf(zip_derived_cl152, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=>))) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#C') @ 121.46/16.13 ((('#B') @ ((('#B') @ (&))) @ 121.46/16.13 mono_2Ec_2Eextreal_2Eextreal__le)))) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2))))))) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2)))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 121.46/16.13 thf(zip_derived_cl153, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 121.46/16.13 ((('#C') @ ((('#B') @ (&) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 X4))) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4))))) @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2)))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl152])). 121.46/16.13 thf(zip_derived_cl154, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((((mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4))) => 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl153])). 121.46/16.13 thf(zip_derived_cl155, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (~ (((mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4))) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6))), 121.46/16.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 121.46/16.13 thf(zip_derived_cl156, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (~ (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 121.46/16.13 thf(zip_derived_cl128, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2))), 121.46/16.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 121.46/16.13 thf(zip_derived_cl683, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X2 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X0) 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X1) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ X1))), 121.46/16.13 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl128])). 121.46/16.13 thf(zip_derived_cl148, plain, 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2') 121.46/16.13 != (((mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2'))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl147])). 121.46/16.13 thf(zip_derived_cl211, plain, 121.46/16.13 (( (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2') 121.46/16.13 | (((mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') & 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2'))))), 121.46/16.13 inference('eq_elim', [status(thm)], [zip_derived_cl148])). 121.46/16.13 thf(zip_derived_cl2277, plain, 121.46/16.13 (( (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2') 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2'))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 121.46/16.13 thf(zip_derived_cl156, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (~ (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 121.46/16.13 thf(zip_derived_cl2351, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk3' @ '#sk2') 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2') 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4')))), 121.46/16.13 inference('sup-', [status(thm)], [zip_derived_cl2277, zip_derived_cl156])). 121.46/16.13 thf(zip_derived_cl156, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (~ (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 121.46/16.13 thf(zip_derived_cl128, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X2))), 121.46/16.13 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 121.46/16.13 thf(zip_derived_cl151, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((mono_2Ec_2Eextreal_2Eextreal__max @ X2 @ X4) 121.46/16.13 = (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) @ X4 @ X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl150])). 121.46/16.13 thf(zip_derived_cl258, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((mono_2Ec_2Eextreal_2Eextreal__max @ X0 @ X1) 121.46/16.13 = (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 ($true) @ X1 @ X0)) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X1 @ X0))), 121.46/16.13 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl151])). 121.46/16.13 thf(zip_derived_cl2276, plain, 121.46/16.13 (( (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4') @ '#sk2'))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 121.46/16.13 thf(zip_derived_cl156, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (~ (mono_2Ec_2Eextreal_2Eextreal__le @ X4 @ X6) 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X4) 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X2 @ X6))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 121.46/16.13 thf(zip_derived_cl2281, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( (mono_2Ec_2Eextreal_2Eextreal__le @ '#sk4' @ '#sk2') 121.46/16.13 | (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ '#sk2') 121.46/16.13 | ~ (mono_2Ec_2Eextreal_2Eextreal__le @ X0 @ 121.46/16.13 (mono_2Ec_2Eextreal_2Eextreal__max @ '#sk3' @ '#sk4')))), 121.46/16.13 inference('sup-', [status(thm)], [zip_derived_cl2276, zip_derived_cl156])). 121.46/16.13 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29, axiom, 121.46/16.13 (![V0:( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 $o ), 121.46/16.13 V1:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 121.46/16.13 @ ( V0 @ V1 ) ) ) = 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 ( app_2E2 @ 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 121.46/16.13 @ V0 ) ) @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ))). 121.46/16.13 thf(zip_derived_cl35, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal > 121.46/16.13 mono_2Etyop_2Eextreal_2Eextreal > $o]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (Y0 @ Y1))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ 121.46/16.13 Y0)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ Y1))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29])). 121.46/16.13 thf(zip_derived_cl36, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)))) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)))))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ app_2E2 @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool))) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29)))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl35])). 121.46/16.13 thf(zip_derived_cl179, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X2)))))) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool)) @ 121.46/16.13 ((('#B') @ (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ 121.46/16.13 X2))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])). 121.46/16.13 thf(zip_derived_cl180, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (X2 @ X4))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl179])). 121.46/16.13 thf(zip_derived_cl181, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (X2 @ X4))) 121.46/16.13 = (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl180])). 121.46/16.13 thf(ji_2Emono_2Etyop_2Emin_2Ebool, axiom, 121.46/16.13 (![V0:$o]: 121.46/16.13 ( ( j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) <=> 121.46/16.13 ( V0 ) ))). 121.46/16.13 thf(zip_derived_cl37, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : $o]: 121.46/16.13 (((j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ Y0))) <=> 121.46/16.13 (Y0))))))), 121.46/16.13 inference('cnf', [status(esa)], [ji_2Emono_2Etyop_2Emin_2Ebool])). 121.46/16.13 thf(zip_derived_cl38, plain, 121.46/16.13 ( (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 121.46/16.13 ((('#B') @ j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 ((('#B') @ (s @ tyop_2Emin_2Ebool) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Ebool)))))) @ 121.46/16.13 ('#I')))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl37])). 121.46/16.13 thf(zip_derived_cl98, plain, 121.46/16.13 (![X2 : $o]: 121.46/16.13 (((j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2))) <=> 121.46/16.13 (X2)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 121.46/16.13 thf(zip_derived_cl99, plain, 121.46/16.13 (![X2 : $o]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2))) = ( 121.46/16.13 X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl98])). 121.46/16.13 thf(zip_derived_cl201, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 (((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($true))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) = 121.46/16.13 (s @ X2 @ X4)))), 121.46/16.13 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl199])). 121.46/16.13 thf(zip_derived_cl203, plain, 121.46/16.13 (![X2 : d, X4 : u, X6 : u]: 121.46/16.13 ((s @ X2 @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ ($true))) @ 121.46/16.13 (s @ X2 @ X4) @ (s @ X2 @ X6))) 121.46/16.13 = (s @ X2 @ X4))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl201])). 121.46/16.13 thf(zip_derived_cl195, plain, 121.46/16.13 (![X2 : $o, X4 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X6 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X2 @ 121.46/16.13 X4 @ X6))) 121.46/16.13 = (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (c_2Ebool_2ECOND_2E3 @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X6)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl194])). 121.46/16.13 thf(zip_derived_cl1588, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 (mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ 121.46/16.13 ($true) @ X0 @ X1))) 121.46/16.13 = (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X0)))), 121.46/16.13 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl195])). 121.46/16.13 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool, axiom, 121.46/16.13 (![V0:( mono_2Etyop_2Eextreal_2Eextreal > $o ), 121.46/16.13 V1:mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) ) = 121.46/16.13 ( s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 ( app_2E2 @ 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 121.46/16.13 @ V0 ) ) @ 121.46/16.13 ( s @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ))). 121.46/16.13 thf(zip_derived_cl4, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : mono_2Etyop_2Eextreal_2Eextreal > $o]: 121.46/16.13 (((!!) @ (^[Y1 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ (Y0 @ Y1))) = 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 Y0)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ Y1))))))))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool])). 121.46/16.13 thf(zip_derived_cl5, plain, 121.46/16.13 ( (((!!) @ ((('#B') @ (!!) @ 121.46/16.13 ((('#S') @ ((('#B') @ ('#S') @ 121.46/16.13 ((('#B') @ ((('#B') @ (=))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ tyop_2Emin_2Ebool))) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Ebool)))))))) @ 121.46/16.13 ((('#B') @ ((('#B') @ (s @ tyop_2Emin_2Ebool))) @ 121.46/16.13 ((('#C') @ ((('#B') @ ('#B') @ 121.46/16.13 ((('#B') @ app_2E2 @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29)))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl4])). 121.46/16.13 thf(zip_derived_cl140, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > $o]: 121.46/16.13 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Emin_2Ebool) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Ebool @ X2)))))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Emin_2Ebool) @ 121.46/16.13 ((('#B') @ (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X2))) @ 121.46/16.13 ((('#B') @ (s @ tyop_2Eextreal_2Eextreal) @ 121.46/16.13 i_mono_2Etyop_2Eextreal_2Eextreal))))))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 121.46/16.13 thf(zip_derived_cl141, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > $o, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 (((s @ tyop_2Emin_2Ebool @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Ebool @ (X2 @ X4))) = (s @ 121.46/16.13 tyop_2Emin_2Ebool @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4))))))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl140])). 121.46/16.13 thf(zip_derived_cl142, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > $o, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (X2 @ X4))) 121.46/16.13 = (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl141])). 121.46/16.13 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29, axiom, 121.46/16.13 (![V0_2E0:u]: 121.46/16.13 ( ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 121.46/16.13 @ 121.46/16.13 ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 121.46/16.13 @ 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 V0_2E0 ) ) ) ) = 121.46/16.13 ( s @ 121.46/16.13 ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ 121.46/16.13 V0_2E0 ) ))). 121.46/16.13 thf(zip_derived_cl51, plain, 121.46/16.13 ( (((!!) @ (^[Y0 : u]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 Y0)))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 Y0))))))), 121.46/16.13 inference('cnf', [status(esa)], 121.46/16.13 [ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29])). 121.46/16.13 thf(zip_derived_cl52, plain, 121.46/16.13 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 121.46/16.13 ((('#B') @ (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)) @ 121.46/16.13 ((('#B') @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 ((('#B') @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ 121.46/16.13 tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool)))))))))) @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool))))))), 121.46/16.13 inference('lams2combs', [status(thm)], [zip_derived_cl51])). 121.46/16.13 thf(zip_derived_cl129, plain, 121.46/16.13 (![X2 : u]: 121.46/16.13 (((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 X2)))) = 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 X2)))), 121.46/16.13 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 121.46/16.13 thf(zip_derived_cl130, plain, 121.46/16.13 (![X2 : u]: 121.46/16.13 ((s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 X2)))) 121.46/16.13 = (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl129])). 121.46/16.13 thf(zip_derived_cl142, plain, 121.46/16.13 (![X2 : mono_2Etyop_2Eextreal_2Eextreal > $o, 121.46/16.13 X4 : mono_2Etyop_2Eextreal_2Eextreal]: 121.46/16.13 ((s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ (X2 @ X4))) 121.46/16.13 = (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X2)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X4)))))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], 121.46/16.13 [zip_derived_cl141])). 121.46/16.13 thf(zip_derived_cl99, plain, 121.46/16.13 (![X2 : $o]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ (i_mono_2Etyop_2Emin_2Ebool @ X2))) = ( 121.46/16.13 X2))), 121.46/16.13 inference('simplify nested equalities', [status(thm)], [zip_derived_cl98])). 121.46/16.13 thf(zip_derived_cl556, plain, 121.46/16.13 (![X0 : mono_2Etyop_2Eextreal_2Eextreal, 121.46/16.13 X1 : mono_2Etyop_2Eextreal_2Eextreal > $o]: 121.46/16.13 ((j_mono_2Etyop_2Emin_2Ebool @ 121.46/16.13 (s @ tyop_2Emin_2Ebool @ 121.46/16.13 (app_2E2 @ 121.46/16.13 (s @ 121.46/16.13 (tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool) @ 121.46/16.13 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ 121.46/16.13 X1)) @ 121.46/16.13 (s @ tyop_2Eextreal_2Eextreal @ 121.46/16.13 (i_mono_2Etyop_2Eextreal_2Eextreal @ X0))))) 121.46/16.13 = (X1 @ X0))), 121.46/16.13 inference('sup+', [status(thm)], [zip_derived_cl142, zip_derived_cl99])). 121.46/16.13 thf(zip_derived_cl6994, plain, ($false), 121.46/16.13 inference('eprover', [status(thm)], 121.46/16.13 [zip_derived_cl6989, zip_derived_cl191, zip_derived_cl125, 121.46/16.13 zip_derived_cl151, zip_derived_cl1587, zip_derived_cl268, 121.46/16.13 zip_derived_cl148, zip_derived_cl683, zip_derived_cl2351, 121.46/16.13 zip_derived_cl156, zip_derived_cl258, zip_derived_cl2281, 121.46/16.13 zip_derived_cl181, zip_derived_cl99, zip_derived_cl1588, 121.46/16.13 zip_derived_cl142, zip_derived_cl130, zip_derived_cl556])). 121.46/16.13 121.46/16.13 % SZS output end Refutation 121.46/16.13 121.46/16.13 121.46/16.13 % Terminating... 121.46/16.22 % Runner terminated. 121.46/16.22 % Zipperpin 1.5 exiting 121.46/16.23 EOF