0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.c4F5N5xksV true 0.13/0.34 % Computer : n016.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 08:10:27 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.52/0.64 % Total configuration time : 828 0.52/0.64 % Estimated wc time : 1656 0.52/0.64 % Estimated cpu time (8 cpus) : 207.0 0.52/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 239.03/30.69 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 317.98/40.68 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 322.59/41.40 % Solved by lams/35_full_unif.sh. 322.59/41.40 % done 638 iterations in 0.691s 322.59/41.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 322.59/41.40 % SZS output start Refutation 322.59/41.40 thf(image1Ex_type, type, image1Ex: $o). 322.59/41.40 thf('#sk3_type', type, '#sk3': $i > $i). 322.59/41.40 thf(in_type, type, in: $i > $i > $o). 322.59/41.40 thf('#sk2_type', type, '#sk2': $i). 322.59/41.40 thf('#sk1_type', type, '#sk1': $i > $i > $i). 322.59/41.40 thf(subsetI1_type, type, subsetI1: $o). 322.59/41.40 thf('#sk6_type', type, '#sk6': $i > $i). 322.59/41.40 thf('#sk15_type', type, '#sk15': $i > ($i > $i) > $i). 322.59/41.40 thf('#form5_type', type, '#form5': $i > $o). 322.59/41.40 thf(subset_type, type, subset: $i > $i > $o). 322.59/41.40 thf('#sk4_type', type, '#sk4': $i > $i). 322.59/41.40 thf(setextsub_type, type, setextsub: $o). 322.59/41.40 thf(exu_type, type, exu: ($i > $o) > $o). 322.59/41.40 thf(image1Ex, axiom, image1Ex = 322.59/41.40 (![A:$i,Xf:( $i > $i )]: 322.59/41.40 ( ?[B:$i]: 322.59/41.40 ( ![Xx:$i]: 322.59/41.40 ( ( in @ Xx @ B ) <=> 322.59/41.40 ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) ) ) ))). 322.59/41.40 thf('0', plain, 322.59/41.40 (( image1Ex ) = 322.59/41.40 ( ![X4:$i,X6:( $i > $i )]: 322.59/41.40 ( ?[X8:$i]: 322.59/41.40 ( ![X10:$i]: 322.59/41.40 ( ( in @ X10 @ X8 ) <=> 322.59/41.40 ( ?[X12:$i]: ( ( ( X10 ) = ( X6 @ X12 ) ) & ( in @ X12 @ X4 ) ) ) ) ) ) )), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(setextsub, axiom, setextsub = 322.59/41.40 (![A:$i,B:$i]: 322.59/41.40 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))). 322.59/41.40 thf('1', plain, 322.59/41.40 (( setextsub ) = 322.59/41.40 ( ![X4:$i,X6:$i]: 322.59/41.40 ( ( subset @ X4 @ X6 ) => 322.59/41.40 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(subsetI1, axiom, subsetI1 = 322.59/41.40 (![A:$i,B:$i]: 322.59/41.40 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) => 322.59/41.40 ( subset @ A @ B ) ))). 322.59/41.40 thf('2', plain, 322.59/41.40 (( subsetI1 ) = 322.59/41.40 ( ![X4:$i,X6:$i]: 322.59/41.40 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 322.59/41.40 ( subset @ X4 @ X6 ) ) )), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(exu, axiom,(( exu ) = 322.59/41.40 (^[Xphi:( $i > $o )]: 322.59/41.40 ( ?[Xx:$i]: 322.59/41.40 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))). 322.59/41.40 thf('3', plain, 322.59/41.40 (( exu ) = 322.59/41.40 ( ^[Xphi:( $i > $o )]: 322.59/41.40 ( ?[Xx:$i]: 322.59/41.40 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & 322.59/41.40 ( Xphi @ Xx ) ) ) )), 322.59/41.40 inference('simplify_rw_rule', [status(thm)], [exu])). 322.59/41.40 thf('4', plain, 322.59/41.40 (( exu ) = 322.59/41.40 ( ^[V_1:( $i > $o )]: 322.59/41.40 ( ?[X4:$i]: 322.59/41.40 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) & 322.59/41.40 ( V_1 @ X4 ) ) ) )), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(image1Ex1, conjecture, 322.59/41.40 (( subsetI1 ) => 322.59/41.40 ( ( setextsub ) => 322.59/41.40 ( ( image1Ex ) => 322.59/41.40 ( ![A:$i,Xf:( $i > $i )]: 322.59/41.40 ( exu @ 322.59/41.40 ( ^[B:$i]: 322.59/41.40 ( ![Xx:$i]: 322.59/41.40 ( ( in @ Xx @ B ) <=> 322.59/41.40 ( ?[Xy:$i]: ( ( in @ Xy @ A ) & ( ( Xx ) = ( Xf @ Xy ) ) ) ) ) ) ) ) ) ) ))). 322.59/41.40 thf(zf_stmt_0, conjecture, 322.59/41.40 (( ![X4:$i,X6:$i]: 322.59/41.40 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 322.59/41.40 ( subset @ X4 @ X6 ) ) ) => 322.59/41.40 ( ( ![X10:$i,X12:$i]: 322.59/41.40 ( ( subset @ X10 @ X12 ) => 322.59/41.40 ( ( subset @ X12 @ X10 ) => ( ( X10 ) = ( X12 ) ) ) ) ) => 322.59/41.40 ( ( ![X14:$i,X16:( $i > $i )]: 322.59/41.40 ( ?[X18:$i]: 322.59/41.40 ( ![X20:$i]: 322.59/41.40 ( ( in @ X20 @ X18 ) <=> 322.59/41.40 ( ?[X22:$i]: 322.59/41.40 ( ( in @ X22 @ X14 ) & ( ( X20 ) = ( X16 @ X22 ) ) ) ) ) ) ) ) => 322.59/41.40 ( ![X24:$i,X26:( $i > $i )]: 322.59/41.40 ( ?[X28:$i]: 322.59/41.40 ( ( ![X36:$i]: 322.59/41.40 ( ( in @ X36 @ X28 ) <=> 322.59/41.40 ( ?[X38:$i]: 322.59/41.40 ( ( ( X36 ) = ( X26 @ X38 ) ) & ( in @ X38 @ X24 ) ) ) ) ) & 322.59/41.40 ( ![X30:$i]: 322.59/41.40 ( ( ![X32:$i]: 322.59/41.40 ( ( in @ X32 @ X30 ) <=> 322.59/41.40 ( ?[X34:$i]: 322.59/41.40 ( ( ( X32 ) = ( X26 @ X34 ) ) & ( in @ X34 @ X24 ) ) ) ) ) => 322.59/41.40 ( ( X28 ) = ( X30 ) ) ) ) ) ) ) ) ))). 322.59/41.40 thf(zf_stmt_1, negated_conjecture, 322.59/41.40 (~( ( ![X4:$i,X6:$i]: 322.59/41.40 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 322.59/41.40 ( subset @ X4 @ X6 ) ) ) => 322.59/41.40 ( ( ![X10:$i,X12:$i]: 322.59/41.40 ( ( subset @ X10 @ X12 ) => 322.59/41.40 ( ( subset @ X12 @ X10 ) => ( ( X10 ) = ( X12 ) ) ) ) ) => 322.59/41.40 ( ( ![X14:$i,X16:( $i > $i )]: 322.59/41.40 ( ?[X18:$i]: 322.59/41.40 ( ![X20:$i]: 322.59/41.40 ( ( in @ X20 @ X18 ) <=> 322.59/41.40 ( ?[X22:$i]: 322.59/41.40 ( ( in @ X22 @ X14 ) & ( ( X20 ) = ( X16 @ X22 ) ) ) ) ) ) ) ) => 322.59/41.40 ( ![X24:$i,X26:( $i > $i )]: 322.59/41.40 ( ?[X28:$i]: 322.59/41.40 ( ( ![X36:$i]: 322.59/41.40 ( ( in @ X36 @ X28 ) <=> 322.59/41.40 ( ?[X38:$i]: 322.59/41.40 ( ( ( X36 ) = ( X26 @ X38 ) ) & ( in @ X38 @ X24 ) ) ) ) ) & 322.59/41.40 ( ![X30:$i]: 322.59/41.40 ( ( ![X32:$i]: 322.59/41.40 ( ( in @ X32 @ X30 ) <=> 322.59/41.40 ( ?[X34:$i]: 322.59/41.40 ( ( ( X32 ) = ( X26 @ X34 ) ) & ( in @ X34 @ X24 ) ) ) ) ) => 322.59/41.40 ( ( X28 ) = ( X30 ) ) ) ) ) ) ) ) ) )), 322.59/41.40 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 322.59/41.40 thf(zip_derived_cl0, plain, 322.59/41.40 (~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((((!!) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ Y0) => (in @ 322.59/41.40 Y2 @ Y1)))))) => 322.59/41.40 (subset @ Y0 @ Y1))))))))) => 322.59/41.40 (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((subset @ Y0 @ Y1) => 322.59/41.40 (((subset @ Y1 @ Y0) => (((Y0) = (Y1))))))))))))) => 322.59/41.40 (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (( 322.59/41.40 (in @ 322.59/41.40 Y4 @ 322.59/41.40 Y0) & 322.59/41.40 (( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4)))))))))))))))))))))) => 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4))) & 322.59/41.40 (in @ 322.59/41.40 Y4 @ Y0))))))))))) & 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((((!!) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (( 322.59/41.40 (in @ 322.59/41.40 Y4 @ 322.59/41.40 Y3) <=> 322.59/41.40 (( 322.59/41.40 (??) @ ( 322.59/41.40 ^[Y5 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y4) = 322.59/41.40 (Y1 @ Y5))) & 322.59/41.40 (in @ 322.59/41.40 Y5 @ Y0))))))))))) => 322.59/41.40 (((Y2) = 322.59/41.40 (Y3)))))))))))))))))))))))))), 322.59/41.40 inference('cnf', [status(esa)], [zf_stmt_1])). 322.59/41.40 thf(zip_derived_cl2, plain, 322.59/41.40 (~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((subset @ Y0 @ Y1) => 322.59/41.40 (((subset @ Y1 @ Y0) => (((Y0) = (Y1))))))))))))) => 322.59/41.40 (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((in @ 322.59/41.40 Y4 @ Y0) & 322.59/41.40 (( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4)))))))))))))))))))))) => 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4))) & 322.59/41.40 (in @ 322.59/41.40 Y4 @ Y0))))))))))) & 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((((!!) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (( 322.59/41.40 (in @ 322.59/41.40 Y4 @ 322.59/41.40 Y3) <=> 322.59/41.40 (( 322.59/41.40 (??) @ ( 322.59/41.40 ^[Y5 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y4) = 322.59/41.40 (Y1 @ Y5))) & 322.59/41.40 (in @ 322.59/41.40 Y5 @ Y0))))))))))) => 322.59/41.40 (((Y2) = (Y3)))))))))))))))))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 322.59/41.40 thf(zip_derived_cl4, plain, 322.59/41.40 (~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((in @ Y4 @ 322.59/41.40 Y0) & 322.59/41.40 (((Y3) = 322.59/41.40 (Y1 @ Y4)))))))))))))))))))))) => 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4))) & 322.59/41.40 (in @ 322.59/41.40 Y4 @ Y0))))))))))) & 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((((!!) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((in @ 322.59/41.40 Y4 @ 322.59/41.40 Y3) <=> 322.59/41.40 (( 322.59/41.40 (??) @ ( 322.59/41.40 ^[Y5 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y4) = 322.59/41.40 (Y1 @ Y5))) & 322.59/41.40 (in @ 322.59/41.40 Y5 @ Y0))))))))))) => 322.59/41.40 (((Y2) = (Y3)))))))))))))))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 322.59/41.40 thf(zip_derived_cl5, plain, 322.59/41.40 ( (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ Y2) <=> 322.59/41.40 (((??) @ (^[Y4 : $i]: 322.59/41.40 ( 322.59/41.40 ( 322.59/41.40 (in @ 322.59/41.40 Y4 @ 322.59/41.40 Y0) & 322.59/41.40 (( 322.59/41.40 (Y3) = 322.59/41.40 (Y1 @ Y4))))))))))))))))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 322.59/41.40 thf(zip_derived_cl26, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (((!!) @ (^[Y0 : $i > $i]: 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((!!) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ Y1) <=> 322.59/41.40 (((??) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ X2) & 322.59/41.40 (((Y2) = (Y0 @ 322.59/41.40 Y3)))))))))))))))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 322.59/41.40 thf(zip_derived_cl228, plain, 322.59/41.40 (![X2 : $i, X4 : $i > $i]: 322.59/41.40 (((??) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ X2) & 322.59/41.40 (((Y1) = (X4 @ Y2))))))))))))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 322.59/41.40 thf(zip_derived_cl2348, plain, 322.59/41.40 (![X2 : $i, X4 : $i > $i]: 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ ('#sk15' @ X2 @ X4)) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ X2) & (((Y0) = (X4 @ Y1)))))))))))))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl228])). 322.59/41.40 thf(zip_derived_cl6, plain, 322.59/41.40 (~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i > $i]: 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((((Y3) = 322.59/41.40 (Y1 @ Y4))) & 322.59/41.40 (in @ Y4 @ 322.59/41.40 Y0))))))))))) & 322.59/41.40 (((!!) @ (^[Y3 : $i]: 322.59/41.40 (((((!!) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((in @ Y4 @ 322.59/41.40 Y3) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y5 : $i]: 322.59/41.40 (( 322.59/41.40 (( 322.59/41.40 (Y4) = 322.59/41.40 (Y1 @ Y5))) & 322.59/41.40 (in @ 322.59/41.40 Y5 @ Y0))))))))))) => 322.59/41.40 (((Y2) = (Y3)))))))))))))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 322.59/41.40 thf(zip_derived_cl19, plain, 322.59/41.40 (~ (((!!) @ (^[Y0 : $i > $i]: 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((!!) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ Y1) <=> 322.59/41.40 (((??) @ (^[Y3 : $i]: 322.59/41.40 (((((Y2) = (Y0 @ 322.59/41.40 Y3))) & 322.59/41.40 (in @ Y3 @ 322.59/41.40 '#sk2'))))))))))) & 322.59/41.40 (((!!) @ (^[Y2 : $i]: 322.59/41.40 (((((!!) @ (^[Y3 : $i]: 322.59/41.40 (((in @ Y3 @ 322.59/41.40 Y2) <=> 322.59/41.40 (((??) @ ( 322.59/41.40 ^[Y4 : $i]: 322.59/41.40 (((( 322.59/41.40 (Y3) = 322.59/41.40 (Y0 @ Y4))) & 322.59/41.40 (in @ 322.59/41.40 Y4 @ 322.59/41.40 '#sk2'))))))))))) => 322.59/41.40 (((Y1) = (Y2))))))))))))))))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 322.59/41.40 thf(zip_derived_cl20, plain, 322.59/41.40 (~ (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) & 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((((!!) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ Y1) <=> 322.59/41.40 (((??) @ (^[Y3 : $i]: 322.59/41.40 (((((Y2) = 322.59/41.40 ('#sk3' @ 322.59/41.40 Y3))) & 322.59/41.40 (in @ Y3 @ 322.59/41.40 '#sk2'))))))))))) => 322.59/41.40 (((Y0) = (Y1)))))))))))))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 322.59/41.40 thf(zip_derived_cl21, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ X2) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((Y0) = ('#sk3' @ Y1))) & (in @ Y1 @ 322.59/41.40 '#sk2'))))))))))) & 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0))))))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 322.59/41.40 thf(zip_derived_cl3097, plain, 322.59/41.40 (~ ((($true) & 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 ((('#sk15' @ '#sk2' @ (^[Y1 : $i]: ('#sk3' @ Y1))) = 322.59/41.40 (Y0))))))))))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl2348, zip_derived_cl21])). 322.59/41.40 thf(zip_derived_cl3100, plain, 322.59/41.40 (~ ((($true) & 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 ((('#sk15' @ '#sk2' @ '#sk3') = (Y0))))))))))), 322.59/41.40 inference('ho_norm', [status(thm)], [zip_derived_cl3097])). 322.59/41.40 thf(zip_derived_cl3101, plain, 322.59/41.40 (~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 ((('#sk15' @ '#sk2' @ '#sk3') = (Y0))))))))), 322.59/41.40 inference('simplify boolean subterms', [status(thm)], 322.59/41.40 [zip_derived_cl3100])). 322.59/41.40 thf(zip_derived_cl21, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ X2) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((Y0) = ('#sk3' @ Y1))) & (in @ Y1 @ 322.59/41.40 '#sk2'))))))))))) & 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0))))))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 322.59/41.40 thf(zip_derived_cl32, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ X2) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((Y0) = ('#sk3' @ Y1))) & (in @ Y1 @ 322.59/41.40 '#sk2'))))))))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl21])). 322.59/41.40 thf(zip_derived_cl33, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ (((in @ ('#sk4' @ X2) @ X2) <=> 322.59/41.40 (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 322.59/41.40 thf(zip_derived_cl34, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (((in @ ('#sk4' @ X2) @ X2) 322.59/41.40 != (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2'))))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl33])). 322.59/41.40 thf(zip_derived_cl36, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ (in @ ('#sk4' @ X2) @ X2) 322.59/41.40 | ~ (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl34])). 322.59/41.40 thf(zip_derived_cl37, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( ('#form5' @ X2) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(zip_derived_cl3102, plain, (~ ('#form5' @ ('#sk15' @ '#sk2' @ '#sk3'))), 322.59/41.40 inference('renaming', [status(thm)], 322.59/41.40 [zip_derived_cl3101, zip_derived_cl37])). 322.59/41.40 thf(zip_derived_cl1, plain, 322.59/41.40 ( (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((((!!) @ (^[Y2 : $i]: 322.59/41.40 (((in @ Y2 @ Y0) => (in @ Y2 @ 322.59/41.40 Y1)))))) => 322.59/41.40 (subset @ Y0 @ Y1)))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 322.59/41.40 thf(zip_derived_cl13, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ X2) => (in @ Y1 @ Y0)))))) => 322.59/41.40 (subset @ X2 @ Y0))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 322.59/41.40 thf(zip_derived_cl16, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))))) => 322.59/41.40 (subset @ X2 @ X4)))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 322.59/41.40 thf(zip_derived_cl17, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))))) 322.59/41.40 | (subset @ X2 @ X4))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 322.59/41.40 thf(zip_derived_cl18, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (((in @ ('#sk1' @ X2 @ X4) @ X2) => (in @ ('#sk1' @ X2 @ X4) @ X4))) 322.59/41.40 | (subset @ X2 @ X4))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 322.59/41.40 thf(zip_derived_cl157, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 ( (in @ ('#sk1' @ X2 @ X4) @ X2) | (subset @ X2 @ X4))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 322.59/41.40 thf(zip_derived_cl37, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( ('#form5' @ X2) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(zip_derived_cl38, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ (((((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ ('#sk6' @ X2)) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((Y0) = ('#sk3' @ Y1))) & (in @ 322.59/41.40 Y1 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = ('#sk6' @ X2))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 322.59/41.40 thf(zip_derived_cl40, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((in @ Y0 @ ('#sk6' @ X2)) <=> 322.59/41.40 (((??) @ (^[Y1 : $i]: 322.59/41.40 (((((Y0) = ('#sk3' @ Y1))) & (in @ Y1 @ 322.59/41.40 '#sk2'))))))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 322.59/41.40 thf(zip_derived_cl50, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 ( (((in @ X4 @ ('#sk6' @ X2)) <=> 322.59/41.40 (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((X4) = ('#sk3' @ Y0))) & (in @ Y0 @ '#sk2')))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 322.59/41.40 thf(zip_derived_cl51, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((in @ X4 @ ('#sk6' @ X2)) 322.59/41.40 = (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((X4) = ('#sk3' @ Y0))) & (in @ Y0 @ '#sk2'))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl50])). 322.59/41.40 thf(zip_derived_cl51, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((in @ X4 @ ('#sk6' @ X2)) 322.59/41.40 = (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((X4) = ('#sk3' @ Y0))) & (in @ Y0 @ '#sk2'))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl50])). 322.59/41.40 thf(zip_derived_cl65, plain, 322.59/41.40 (![X0 : $i, X1 : $i, X2 : $i]: 322.59/41.40 (((in @ X1 @ ('#sk6' @ X2)) = (in @ X1 @ ('#sk6' @ X0))) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl51])). 322.59/41.40 thf(zip_derived_cl175, plain, 322.59/41.40 (![X0 : $i, X1 : $i, X2 : $i]: 322.59/41.40 ( (in @ ('#sk1' @ ('#sk6' @ X2) @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | (subset @ ('#sk6' @ X2) @ X1) 322.59/41.40 | ('#form5' @ X2) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('sup+', [status(thm)], [zip_derived_cl157, zip_derived_cl65])). 322.59/41.40 thf(zip_derived_cl158, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (in @ ('#sk1' @ X2 @ X4) @ X4) | (subset @ X2 @ X4))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 322.59/41.40 thf(zip_derived_cl232, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 ( ('#form5' @ X0) 322.59/41.40 | ('#form5' @ X1) 322.59/41.40 | (subset @ ('#sk6' @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | (subset @ ('#sk6' @ X1) @ ('#sk6' @ X0)))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl175, zip_derived_cl158])). 322.59/41.40 thf(zip_derived_cl246, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 ( (subset @ ('#sk6' @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X1) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('simplify', [status(thm)], [zip_derived_cl232])). 322.59/41.40 thf(zip_derived_cl3, plain, 322.59/41.40 ( (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((!!) @ (^[Y1 : $i]: 322.59/41.40 (((subset @ Y0 @ Y1) => 322.59/41.40 (((subset @ Y1 @ Y0) => (((Y0) = (Y1)))))))))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 322.59/41.40 thf(zip_derived_cl9, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((subset @ X2 @ Y0) => 322.59/41.40 (((subset @ Y0 @ X2) => (((X2) = (Y0))))))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 322.59/41.40 thf(zip_derived_cl15, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((subset @ X2 @ X4) => (((subset @ X4 @ X2) => (((X2) = (X4)))))))), 322.59/41.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 322.59/41.40 thf(zip_derived_cl22, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (subset @ X2 @ X4) | (((subset @ X4 @ X2) => (((X2) = (X4))))))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 322.59/41.40 thf(zip_derived_cl30, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (subset @ X4 @ X2) | (((X2) = (X4))) | ~ (subset @ X2 @ X4))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 322.59/41.40 thf(zip_derived_cl31, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (~ (subset @ X4 @ X2) | ((X2) = (X4)) | ~ (subset @ X2 @ X4))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl30])). 322.59/41.40 thf(zip_derived_cl264, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 ( ('#form5' @ X0) 322.59/41.40 | ('#form5' @ X1) 322.59/41.40 | ~ (subset @ ('#sk6' @ X0) @ ('#sk6' @ X1)) 322.59/41.40 | (('#sk6' @ X0) = ('#sk6' @ X1)))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl246, zip_derived_cl31])). 322.59/41.40 thf(zip_derived_cl246, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 ( (subset @ ('#sk6' @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X1) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('simplify', [status(thm)], [zip_derived_cl232])). 322.59/41.40 thf(zip_derived_cl2412, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 ((('#sk6' @ X0) = ('#sk6' @ X1)) | ('#form5' @ X1) | ('#form5' @ X0))), 322.59/41.40 inference('clc', [status(thm)], [zip_derived_cl264, zip_derived_cl246])). 322.59/41.40 thf(zip_derived_cl41, plain, 322.59/41.40 (![X2 : $i]: (~ (((X2) = ('#sk6' @ X2))) | ('#form5' @ X2))), 322.59/41.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 322.59/41.40 thf(zip_derived_cl42, plain, 322.59/41.40 (![X2 : $i]: (((X2) != ('#sk6' @ X2)) | ('#form5' @ X2))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl41])). 322.59/41.40 thf(zip_derived_cl2504, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 (((X1) != ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X1) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ('#form5' @ X1))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl2412, zip_derived_cl42])). 322.59/41.40 thf(zip_derived_cl2726, plain, 322.59/41.40 (![X0 : $i]: ( ('#form5' @ X0) | ('#form5' @ ('#sk6' @ X0)))), 322.59/41.40 inference('simplify', [status(thm)], [zip_derived_cl2504])). 322.59/41.40 thf(zip_derived_cl34, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (((in @ ('#sk4' @ X2) @ X2) 322.59/41.40 != (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2'))))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl33])). 322.59/41.40 thf(zip_derived_cl35, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( (in @ ('#sk4' @ X2) @ X2) 322.59/41.40 | (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl34])). 322.59/41.40 thf(zip_derived_cl37, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( ('#form5' @ X2) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(zip_derived_cl280, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ ('#form5' @ X2) 322.59/41.40 | (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | (in @ ('#sk4' @ X2) @ X2))), 322.59/41.40 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl37])). 322.59/41.40 thf(zip_derived_cl51, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((in @ X4 @ ('#sk6' @ X2)) 322.59/41.40 = (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((X4) = ('#sk3' @ Y0))) & (in @ Y0 @ '#sk2'))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl50])). 322.59/41.40 thf(zip_derived_cl36, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ (in @ ('#sk4' @ X2) @ X2) 322.59/41.40 | ~ (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 inference('lazy_cnf_xor', [status(thm)], [zip_derived_cl34])). 322.59/41.40 thf(zip_derived_cl37, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 ( ('#form5' @ X2) 322.59/41.40 | ~ (((!!) @ (^[Y0 : $i]: 322.59/41.40 (((((!!) @ (^[Y1 : $i]: 322.59/41.40 (((in @ Y1 @ Y0) <=> 322.59/41.40 (((??) @ (^[Y2 : $i]: 322.59/41.40 (((((Y1) = ('#sk3' @ Y2))) & 322.59/41.40 (in @ Y2 @ '#sk2'))))))))))) => 322.59/41.40 (((X2) = (Y0)))))))))), 322.59/41.40 define([status(thm)])). 322.59/41.40 thf(zip_derived_cl39, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ ('#form5' @ X2) 322.59/41.40 | ~ (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | ~ (in @ ('#sk4' @ X2) @ X2))), 322.59/41.40 inference('renaming', [status(thm)], [zip_derived_cl36, zip_derived_cl37])). 322.59/41.40 thf(zip_derived_cl66, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 (~ (in @ ('#sk4' @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ~ (in @ ('#sk4' @ X1) @ X1) 322.59/41.40 | ~ ('#form5' @ X1))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl39])). 322.59/41.40 thf(zip_derived_cl281, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 ( (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ ('#sk6' @ X0)) = ('#sk3' @ Y0))) & (in @ 322.59/41.40 Y0 @ '#sk2')))))) 322.59/41.40 | ~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | ~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | ~ (in @ ('#sk4' @ ('#sk6' @ X0)) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl66])). 322.59/41.40 thf(zip_derived_cl298, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 ( ('#form5' @ X0) 322.59/41.40 | ~ (in @ ('#sk4' @ ('#sk6' @ X0)) @ ('#sk6' @ X0)) 322.59/41.40 | ~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ ('#sk6' @ X0)) = ('#sk3' @ Y0))) & 322.59/41.40 (in @ Y0 @ '#sk2')))))))), 322.59/41.40 inference('simplify', [status(thm)], [zip_derived_cl281])). 322.59/41.40 thf(zip_derived_cl280, plain, 322.59/41.40 (![X2 : $i]: 322.59/41.40 (~ ('#form5' @ X2) 322.59/41.40 | (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ X2) = ('#sk3' @ Y0))) & (in @ Y0 @ 322.59/41.40 '#sk2')))))) 322.59/41.40 | (in @ ('#sk4' @ X2) @ X2))), 322.59/41.40 inference('renaming', [status(thm)], [zip_derived_cl35, zip_derived_cl37])). 322.59/41.40 thf(zip_derived_cl340, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 ( (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ ('#sk6' @ X0)) = ('#sk3' @ Y0))) & (in @ 322.59/41.40 Y0 @ '#sk2')))))) 322.59/41.40 | ~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('clc', [status(thm)], [zip_derived_cl298, zip_derived_cl280])). 322.59/41.40 thf(zip_derived_cl51, plain, 322.59/41.40 (![X2 : $i, X4 : $i]: 322.59/41.40 (((in @ X4 @ ('#sk6' @ X2)) 322.59/41.40 = (((??) @ (^[Y0 : $i]: 322.59/41.40 (((((X4) = ('#sk3' @ Y0))) & (in @ Y0 @ '#sk2'))))))) 322.59/41.40 | ('#form5' @ X2))), 322.59/41.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl50])). 322.59/41.40 thf(zip_derived_cl66, plain, 322.59/41.40 (![X0 : $i, X1 : $i]: 322.59/41.40 (~ (in @ ('#sk4' @ X1) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ~ (in @ ('#sk4' @ X1) @ X1) 322.59/41.40 | ~ ('#form5' @ X1))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl39])). 322.59/41.40 thf(zip_derived_cl135, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 (~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | ~ (in @ ('#sk4' @ ('#sk6' @ X0)) @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0))), 322.59/41.40 inference('eq_fact', [status(thm)], [zip_derived_cl66])). 322.59/41.40 thf(zip_derived_cl315, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 (~ (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ ('#sk6' @ X0)) = ('#sk3' @ Y0))) & (in @ 322.59/41.40 Y0 @ '#sk2')))))) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ~ ('#form5' @ ('#sk6' @ X0)))), 322.59/41.40 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl135])). 322.59/41.40 thf(zip_derived_cl323, plain, 322.59/41.40 (![X0 : $i]: 322.59/41.40 (~ ('#form5' @ ('#sk6' @ X0)) 322.59/41.40 | ('#form5' @ X0) 322.59/41.40 | ~ (((??) @ (^[Y0 : $i]: 322.59/41.40 ((((('#sk4' @ ('#sk6' @ X0)) = ('#sk3' @ Y0))) & 322.59/41.40 (in @ Y0 @ '#sk2')))))))), 322.59/41.40 inference('simplify', [status(thm)], [zip_derived_cl315])). 322.59/41.40 thf(zip_derived_cl341, plain, 322.59/41.40 (![X0 : $i]: ( ('#form5' @ X0) | ~ ('#form5' @ ('#sk6' @ X0)))), 322.59/41.40 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl323])). 322.59/41.40 thf(zip_derived_cl2808, plain, (![X0 : $i]: ('#form5' @ X0)), 322.59/41.40 inference('clc', [status(thm)], [zip_derived_cl2726, zip_derived_cl341])). 322.59/41.40 thf(zip_derived_cl3103, plain, ($false), 322.59/41.40 inference('demod', [status(thm)], 322.59/41.40 [zip_derived_cl3102, zip_derived_cl2808])). 322.59/41.40 322.59/41.40 % SZS output end Refutation 322.59/41.40 322.59/41.40 322.59/41.40 % Terminating... 323.01/41.48 % Runner terminated. 323.01/41.48 % Zipperpin 1.5 exiting 323.01/41.48 EOF