TSTP Solution File: NUM790^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM790^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.07GfgXSD9o true
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:44:12 EDT 2023
% Result : Theorem 91.64s 12.33s
% Output : Refutation 91.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : NUM790^4 : TPTP v8.1.2. Released v7.1.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.07GfgXSD9o true
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 17:16:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.05/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.05/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.05/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.05/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.05/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.05/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.05/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 6.82/1.46 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 91.64/12.33 % Solved by lams/30_b.l.sh.
% 91.64/12.33 % done 166 iterations in 10.834s
% 91.64/12.33 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 91.64/12.33 % SZS output start Refutation
% 91.64/12.33 thf(rt_is_type, type, rt_is: $i > $i > $o).
% 91.64/12.33 thf(lessf_type, type, lessf: $i > $i > $o).
% 91.64/12.33 thf(inf_type, type, inf: $i > $i > $o).
% 91.64/12.33 thf('#sk13_type', type, '#sk13': $i).
% 91.64/12.33 thf(rt_less_type, type, rt_less: $i > $i > $o).
% 91.64/12.33 thf(and3_type, type, and3: $o > $o > $o > $o).
% 91.64/12.33 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 91.64/12.33 thf(in_type, type, in: $i > $i > $o).
% 91.64/12.33 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 91.64/12.33 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 91.64/12.33 thf('#sk12_type', type, '#sk12': $i).
% 91.64/12.33 thf(rt_moreis_type, type, rt_moreis: $i > $i > $o).
% 91.64/12.33 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i).
% 91.64/12.33 thf(imp_type, type, imp: $o > $o > $o).
% 91.64/12.33 thf(rat_type, type, rat: $i).
% 91.64/12.33 thf(frac_type, type, frac: $i).
% 91.64/12.33 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i).
% 91.64/12.33 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 91.64/12.33 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 91.64/12.33 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i).
% 91.64/12.33 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o).
% 91.64/12.33 thf(l_or_type, type, l_or: $o > $o > $o).
% 91.64/12.33 thf(class_type, type, class: $i > $i).
% 91.64/12.33 thf(moref_type, type, moref: $i > $i > $o).
% 91.64/12.33 thf(d_not_type, type, d_not: $o > $o).
% 91.64/12.33 thf(power_type, type, power: $i > $i).
% 91.64/12.33 thf(rt_more_type, type, rt_more: $i > $i > $o).
% 91.64/12.33 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 91.64/12.33 thf(satz81j, conjecture,
% 91.64/12.33 (all_of @
% 91.64/12.33 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 91.64/12.33 ( ^[X0:$i]:
% 91.64/12.33 ( all_of @
% 91.64/12.33 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 91.64/12.33 ( ^[X1:$i]:
% 91.64/12.33 ( ( d_not @ ( rt_moreis @ X0 @ X1 ) ) => ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 91.64/12.33 thf(zf_stmt_0, negated_conjecture,
% 91.64/12.33 (~( all_of @
% 91.64/12.33 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 91.64/12.33 ( ^[X0:$i]:
% 91.64/12.33 ( all_of @
% 91.64/12.33 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 91.64/12.33 ( ^[X1:$i]:
% 91.64/12.33 ( ( d_not @ ( rt_moreis @ X0 @ X1 ) ) => ( rt_less @ X0 @ X1 ) ) ) ) ) )),
% 91.64/12.33 inference('cnf.neg', [status(esa)], [satz81j])).
% 91.64/12.33 thf(zip_derived_cl265, plain,
% 91.64/12.33 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ Y0 @ Y1)) => (rt_less @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('cnf', [status(esa)], [zf_stmt_0])).
% 91.64/12.33 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) =
% 91.64/12.33 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))).
% 91.64/12.33 thf('0', plain,
% 91.64/12.33 (![X1:( $i > $i > $o ),X0:$i]:
% 91.64/12.33 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))).
% 91.64/12.33 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])).
% 91.64/12.33 thf(zip_derived_cl293, plain,
% 91.64/12.33 (~ (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ Y0 @ Y1)) => (rt_less @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('rw', [status(thm)], [zip_derived_cl265, '0', '1'])).
% 91.64/12.33 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 91.64/12.33 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 91.64/12.33 thf('2', plain,
% 91.64/12.33 (![X0:( $i > $o ),X1:( $i > $o )]:
% 91.64/12.33 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 91.64/12.33 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 91.64/12.33 inference('rw.lit', [status(esa)], [def_all_of])).
% 91.64/12.33 thf(zip_derived_cl294, plain,
% 91.64/12.33 (~ (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 ((^[Y1 : $i]:
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y2 : $i]:
% 91.64/12.33 (in @ Y2 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y2 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ Y1 @ Y2)) => (rt_less @
% 91.64/12.33 Y1 @ Y2)))))) @
% 91.64/12.33 Y0))))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl293, '2'])).
% 91.64/12.33 thf(zip_derived_cl295, plain,
% 91.64/12.33 (~ (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ Y0 @ Y1)) => (rt_less @ Y0 @
% 91.64/12.33 Y1))))))))))),
% 91.64/12.33 inference('ho_norm', [status(thm)], [zip_derived_cl294])).
% 91.64/12.33 thf(zip_derived_cl296, plain,
% 91.64/12.33 (~ (((is_of @ '#sk12' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ '#sk12' @ Y0)) => (rt_less @ '#sk12' @
% 91.64/12.33 Y0)))))))),
% 91.64/12.33 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl295])).
% 91.64/12.33 thf(zip_derived_cl298, plain,
% 91.64/12.33 (~ (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ '#sk12' @ Y0)) => (rt_less @ '#sk12' @ Y0)))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl296])).
% 91.64/12.33 thf(zip_derived_cl299, plain,
% 91.64/12.33 (~ (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 ((^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_moreis @ '#sk12' @ Y1)) =>
% 91.64/12.33 (rt_less @ '#sk12' @ Y1)))) @
% 91.64/12.33 Y0))))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl298, '2'])).
% 91.64/12.33 thf(zip_derived_cl300, plain,
% 91.64/12.33 (~ (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((d_not @ (rt_moreis @ '#sk12' @ Y0)) => (rt_less @
% 91.64/12.33 '#sk12' @ Y0))))))))),
% 91.64/12.33 inference('ho_norm', [status(thm)], [zip_derived_cl299])).
% 91.64/12.33 thf(zip_derived_cl301, plain,
% 91.64/12.33 (~ (((is_of @ '#sk13' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((d_not @ (rt_moreis @ '#sk12' @ '#sk13')) => (rt_less @ '#sk12' @
% 91.64/12.33 '#sk13')))))),
% 91.64/12.33 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl300])).
% 91.64/12.33 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 91.64/12.33 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 91.64/12.33 thf('4', plain,
% 91.64/12.33 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 91.64/12.33 thf('5', plain,
% 91.64/12.33 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))).
% 91.64/12.33 thf('6', plain,
% 91.64/12.33 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) =
% 91.64/12.33 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))).
% 91.64/12.33 thf('7', plain,
% 91.64/12.33 (![X2:$i,X1:( $i > $i > $o ),X0:$i]:
% 91.64/12.33 ( ( ecect @ X0 @ X1 @ X2 ) =
% 91.64/12.33 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))).
% 91.64/12.33 thf('8', plain,
% 91.64/12.33 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))).
% 91.64/12.33 thf('9', plain,
% 91.64/12.33 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) =
% 91.64/12.33 ((l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 91.64/12.33 (moref @ Y0 @ Y1))))))))).
% 91.64/12.33 thf('10', plain,
% 91.64/12.33 (![X1:$i,X0:$i]:
% 91.64/12.33 ( ( rt_more @ X0 @ X1 ) =
% 91.64/12.33 ( l_some @
% 91.64/12.33 frac @
% 91.64/12.33 ( ^[V_1:$i]:
% 91.64/12.33 ( l_some @
% 91.64/12.33 frac @
% 91.64/12.33 ( ^[V_2:$i]:
% 91.64/12.33 ( and3 @
% 91.64/12.33 ( inf @ V_1 @ ( class @ X0 ) ) @
% 91.64/12.33 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) =
% 91.64/12.33 ((l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))))).
% 91.64/12.33 thf('11', plain,
% 91.64/12.33 (![X1:$i,X0:$i]:
% 91.64/12.33 ( ( rt_less @ X0 @ X1 ) =
% 91.64/12.33 ( l_some @
% 91.64/12.33 frac @
% 91.64/12.33 ( ^[V_1:$i]:
% 91.64/12.33 ( l_some @
% 91.64/12.33 frac @
% 91.64/12.33 ( ^[V_2:$i]:
% 91.64/12.33 ( and3 @
% 91.64/12.33 ( inf @ V_1 @ ( class @ X0 ) ) @
% 91.64/12.33 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(def_rt_moreis, axiom,(( rt_moreis @ (X0)@ (X1)) =
% 91.64/12.33 ((l_or @ (rt_more @ X0 @ X1) @ (rt_is @ X0 @ X1))))).
% 91.64/12.33 thf('12', plain,
% 91.64/12.33 (![X1:$i,X0:$i]:
% 91.64/12.33 ( ( rt_moreis @ X0 @ X1 ) =
% 91.64/12.33 ( l_or @ ( rt_more @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )),
% 91.64/12.33 define([status(thm)])).
% 91.64/12.33 thf(zip_derived_cl302, plain,
% 91.64/12.33 (~ (((is_of @ '#sk13' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13')))) @
% 91.64/12.33 ($false)) => (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))))))),
% 91.64/12.33 inference('rw', [status(thm)],
% 91.64/12.33 [zip_derived_cl301, '3', '3', '4', '5', '6', '6', '0', '7',
% 91.64/12.33 '7', '1', '8', '9', '9', '10', '11', '12'])).
% 91.64/12.33 thf(zip_derived_cl304, plain,
% 91.64/12.33 (~ (((imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13')))) @
% 91.64/12.33 ($false)) => (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl302])).
% 91.64/12.33 thf(zip_derived_cl305, plain,
% 91.64/12.33 ( (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13')))) @
% 91.64/12.33 ($false))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])).
% 91.64/12.33 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 91.64/12.33 thf('13', plain,
% 91.64/12.33 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 91.64/12.33 inference('rw.lit', [status(esa)], [def_imp])).
% 91.64/12.33 thf(zip_derived_cl307, plain,
% 91.64/12.33 ( (((imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13')))) => ($false)))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl305, '13'])).
% 91.64/12.33 thf(zip_derived_cl308, plain,
% 91.64/12.33 ( (((~) @ (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @
% 91.64/12.33 (inf @ Y1 @ '#sk13') @ (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13'))))))),
% 91.64/12.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl307])).
% 91.64/12.33 thf(zip_derived_cl309, plain,
% 91.64/12.33 (~ (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 ((('#sk12') = ('#sk13'))))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl308])).
% 91.64/12.33 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 91.64/12.33 thf('14', plain,
% 91.64/12.33 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 91.64/12.33 inference('rw.lit', [status(esa)], [def_imp])).
% 91.64/12.33 thf(zip_derived_cl310, plain,
% 91.64/12.33 (~ (((imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) => ((('#sk12') = ('#sk13')))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl309, '14'])).
% 91.64/12.33 thf(zip_derived_cl311, plain,
% 91.64/12.33 ( (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl310])).
% 91.64/12.33 thf(zip_derived_cl313, plain,
% 91.64/12.33 ( (((l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) =>
% 91.64/12.33 ($false)))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl311, '13'])).
% 91.64/12.33 thf(zip_derived_cl315, plain,
% 91.64/12.33 ( (((~) @ (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1))))))))),
% 91.64/12.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl313])).
% 91.64/12.33 thf(zip_derived_cl316, plain,
% 91.64/12.33 (~ (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1))))))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl315])).
% 91.64/12.33 thf(zip_derived_cl306, plain,
% 91.64/12.33 (~ (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])).
% 91.64/12.33 thf(satz81f, axiom,
% 91.64/12.33 (all_of @
% 91.64/12.33 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 91.64/12.33 ( ^[X0:$i]:
% 91.64/12.33 ( all_of @
% 91.64/12.33 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 91.64/12.33 ( ^[X1:$i]:
% 91.64/12.33 ( ( d_not @ ( rt_less @ X0 @ X1 ) ) => ( rt_moreis @ X0 @ X1 ) ) ) ) ))).
% 91.64/12.33 thf(zip_derived_cl262, plain,
% 91.64/12.33 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ Y0 @ Y1)) => (rt_moreis @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('cnf', [status(esa)], [satz81f])).
% 91.64/12.33 thf(zip_derived_cl512, plain,
% 91.64/12.33 ( (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ Y0 @ Y1)) => (rt_moreis @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('rw', [status(thm)], [zip_derived_cl262, '0', '1'])).
% 91.64/12.33 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 91.64/12.33 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 91.64/12.33 thf('15', plain,
% 91.64/12.33 (![X0:( $i > $o ),X1:( $i > $o )]:
% 91.64/12.33 ( ( all_of @ X0 @ X1 ) <=>
% 91.64/12.33 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 91.64/12.33 inference('rw.lit', [status(esa)], [def_all_of])).
% 91.64/12.33 thf(zip_derived_cl513, plain,
% 91.64/12.33 ( (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 ((^[Y1 : $i]:
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y2 : $i]:
% 91.64/12.33 (in @ Y2 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y2 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ Y1 @ Y2)) => (rt_moreis @
% 91.64/12.33 Y1 @ Y2)))))) @
% 91.64/12.33 Y0))))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl512, '15'])).
% 91.64/12.33 thf(zip_derived_cl514, plain,
% 91.64/12.33 ( (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ Y0 @ Y1)) => (rt_moreis @ Y0 @
% 91.64/12.33 Y1))))))))))),
% 91.64/12.33 inference('ho_norm', [status(thm)], [zip_derived_cl513])).
% 91.64/12.33 thf(zip_derived_cl515, plain,
% 91.64/12.33 (![X2 : $i]:
% 91.64/12.33 (((is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ X2 @ Y0)) => (rt_moreis @ X2 @ Y0)))))))),
% 91.64/12.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl514])).
% 91.64/12.33 thf(zip_derived_cl516, plain,
% 91.64/12.33 (![X2 : $i]:
% 91.64/12.33 (~ (is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (all_of @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ X2 @ Y0)) => (rt_moreis @ X2 @ Y0))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])).
% 91.64/12.33 thf(zip_derived_cl517, plain,
% 91.64/12.33 (![X0 : $i]:
% 91.64/12.33 ( (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 ((^[Y1 : $i]:
% 91.64/12.33 (((d_not @ (rt_less @ X0 @ Y1)) => (rt_moreis @
% 91.64/12.33 X0 @ Y1)))) @
% 91.64/12.33 Y0))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl516, '15'])).
% 91.64/12.33 thf(zip_derived_cl518, plain,
% 91.64/12.33 (![X0 : $i]:
% 91.64/12.33 ( (((!!) @ (^[Y0 : $i]:
% 91.64/12.33 (((is_of @ Y0 @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (in @ Y1 @
% 91.64/12.33 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((d_not @ (rt_less @ X0 @ Y0)) => (rt_moreis @ X0 @
% 91.64/12.33 Y0))))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('ho_norm', [status(thm)], [zip_derived_cl517])).
% 91.64/12.33 thf(zip_derived_cl519, plain,
% 91.64/12.33 (![X0 : $i, X2 : $i]:
% 91.64/12.33 ( (((is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((d_not @ (rt_less @ X0 @ X2)) => (rt_moreis @ X0 @ X2)))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl518])).
% 91.64/12.33 thf(zip_derived_cl520, plain,
% 91.64/12.33 (![X0 : $i, X2 : $i]:
% 91.64/12.33 ( (((is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 91.64/12.33 (((imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (lessf @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) => (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X0) = (X2))))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('rw', [status(thm)],
% 91.64/12.33 [zip_derived_cl519, '3', '3', '4', '5', '6', '6', '0', '7',
% 91.64/12.33 '7', '1', '8', '9', '9', '10', '11', '12'])).
% 91.64/12.33 thf(zip_derived_cl521, plain,
% 91.64/12.33 (![X0 : $i, X2 : $i]:
% 91.64/12.33 (~ (is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (((imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (lessf @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) => (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X0) = (X2))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl520])).
% 91.64/12.33 thf(zip_derived_cl522, plain,
% 91.64/12.33 (![X0 : $i, X2 : $i]:
% 91.64/12.33 (~ (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (lessf @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false))
% 91.64/12.33 | (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X2) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X0) = (X2))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X2 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl521])).
% 91.64/12.33 thf(zip_derived_cl523, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (((l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (lessf @ Y0 @ Y1)))))) =>
% 91.64/12.33 ($false)))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X1) = (X0)))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl522, '14'])).
% 91.64/12.33 thf(zip_derived_cl524, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (((~) @ (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X1) = (X0)))))),
% 91.64/12.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl523])).
% 91.64/12.33 thf(zip_derived_cl525, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 ( (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (imp @
% 91.64/12.33 (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X1) @ (inf @ Y1 @ X0) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) @
% 91.64/12.33 (((X1) = (X0)))))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl524])).
% 91.64/12.33 thf(zip_derived_cl526, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 ( (((imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false)) => (((X0) = (X1)))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl525, '13'])).
% 91.64/12.33 thf(zip_derived_cl527, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false))
% 91.64/12.33 | (((X0) = (X1)))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])).
% 91.64/12.33 thf(zip_derived_cl528, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (imp @
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) @
% 91.64/12.33 ($false))
% 91.64/12.33 | ((X0) = (X1))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl527])).
% 91.64/12.33 thf(zip_derived_cl529, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (((l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1)))))) =>
% 91.64/12.33 ($false)))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ((X0) = (X1)))),
% 91.64/12.33 inference('rw_clause', [status(thm)], [zip_derived_cl528, '14'])).
% 91.64/12.33 thf(zip_derived_cl530, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 (~ (((~) @ (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1))))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ((X0) = (X1)))),
% 91.64/12.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl529])).
% 91.64/12.33 thf(zip_derived_cl531, plain,
% 91.64/12.33 (![X0 : $i, X1 : $i]:
% 91.64/12.33 ( (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (moref @ Y0 @ Y1))))))
% 91.64/12.33 | ~ (is_of @ X0 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ X1 @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ X0) @ (inf @ Y1 @ X1) @
% 91.64/12.33 (lessf @ Y0 @ Y1))))))
% 91.64/12.33 | ((X0) = (X1)))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl530])).
% 91.64/12.33 thf(zip_derived_cl11177, plain,
% 91.64/12.33 (((('#sk12') = ('#sk13'))
% 91.64/12.33 | ~ (is_of @ '#sk13' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | ~ (is_of @ '#sk12' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('sup+', [status(thm)], [zip_derived_cl306, zip_derived_cl531])).
% 91.64/12.33 thf(zip_derived_cl303, plain,
% 91.64/12.33 ( (is_of @ '#sk13' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl302])).
% 91.64/12.33 thf(zip_derived_cl297, plain,
% 91.64/12.33 ( (is_of @ '#sk12' @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (in @ Y0 @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl296])).
% 91.64/12.33 thf(zip_derived_cl11195, plain,
% 91.64/12.33 (((('#sk12') = ('#sk13'))
% 91.64/12.33 | (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1)))))))),
% 91.64/12.33 inference('demod', [status(thm)],
% 91.64/12.33 [zip_derived_cl11177, zip_derived_cl303, zip_derived_cl297])).
% 91.64/12.33 thf(zip_derived_cl312, plain, (~ ((('#sk12') = ('#sk13')))),
% 91.64/12.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl310])).
% 91.64/12.33 thf(zip_derived_cl314, plain, ((('#sk12') != ('#sk13'))),
% 91.64/12.33 inference('simplify nested equalities', [status(thm)],
% 91.64/12.33 [zip_derived_cl312])).
% 91.64/12.33 thf(zip_derived_cl11196, plain,
% 91.64/12.33 ( (l_some @ frac @
% 91.64/12.33 (^[Y0 : $i]:
% 91.64/12.33 (l_some @ frac @
% 91.64/12.33 (^[Y1 : $i]:
% 91.64/12.33 (and3 @ (inf @ Y0 @ '#sk12') @ (inf @ Y1 @ '#sk13') @
% 91.64/12.33 (moref @ Y0 @ Y1))))))),
% 91.64/12.33 inference('simplify_reflect-', [status(thm)],
% 91.64/12.33 [zip_derived_cl11195, zip_derived_cl314])).
% 91.64/12.33 thf(zip_derived_cl11337, plain, ($false),
% 91.64/12.33 inference('demod', [status(thm)],
% 91.64/12.33 [zip_derived_cl316, zip_derived_cl11196])).
% 91.64/12.33
% 91.64/12.33 % SZS output end Refutation
% 91.64/12.33
% 91.64/12.33
% 91.64/12.33 % Terminating...
% 91.64/12.39 % Runner terminated.
% 91.64/12.41 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------