0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.K3hd7UOJbL true 0.14/0.35 % Computer : n013.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Mon Jul 3 10:26:47 EDT 2023 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 1440 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.52/0.69 % Total configuration time : 828 0.52/0.69 % Estimated wc time : 1656 0.52/0.69 % Estimated cpu time (8 cpus) : 207.0 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 6.11/1.40 % Solved by lams/20_acsne_simpl.sh. 6.11/1.40 % done 173 iterations in 0.575s 6.11/1.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 6.11/1.40 % SZS output start Refutation 6.11/1.40 thf(setukpairinjR_type, type, setukpairinjR: $o). 6.11/1.40 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 6.11/1.40 thf(in_type, type, in: $i > $i > $o). 6.11/1.40 thf('#sk5_type', type, '#sk5': $i). 6.11/1.40 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 6.11/1.40 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 6.11/1.40 thf(kpair_type, type, kpair: $i > $i > $i). 6.11/1.40 thf(ex1I_type, type, ex1I: $o). 6.11/1.40 thf('#sk20_type', type, '#sk20': $i). 6.11/1.40 thf('#sk12_type', type, '#sk12': $i). 6.11/1.40 thf(iskpair_type, type, iskpair: $i > $o). 6.11/1.40 thf(setunion_type, type, setunion: $i > $i). 6.11/1.40 thf(kfstpairEq_type, type, kfstpairEq: $o). 6.11/1.40 thf(emptyset_type, type, emptyset: $i). 6.11/1.40 thf('#sk103_type', type, '#sk103': $i > $i > $i). 6.11/1.40 thf(kfst_type, type, kfst: $i > $i). 6.11/1.40 thf('#sk104_type', type, '#sk104': $i > $i). 6.11/1.40 thf(singleton_type, type, singleton: $i > $o). 6.11/1.40 thf(setukpairinjR, axiom, setukpairinjR = 6.11/1.40 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 6.11/1.40 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))). 6.11/1.40 thf('0', plain, 6.11/1.40 (( setukpairinjR ) = 6.11/1.40 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 6.11/1.40 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 6.11/1.40 ( ( X6 ) = ( X10 ) ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(kfstpairEq, axiom, kfstpairEq = 6.11/1.40 (![Xx:$i,Xy:$i]: ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ))). 6.11/1.40 thf('1', plain, 6.11/1.40 (( kfstpairEq ) = 6.11/1.40 ( ![X4:$i,X6:$i]: ( ( kfst @ ( kpair @ X4 @ X6 ) ) = ( X4 ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(ex1I, axiom, ex1I = 6.11/1.40 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 6.11/1.40 ( ( in @ Xx @ A ) => 6.11/1.40 ( ( Xphi @ Xx ) => 6.11/1.40 ( ( ![Xy:$i]: 6.11/1.40 ( ( in @ Xy @ A ) => ( ( Xphi @ Xy ) => ( ( Xy ) = ( Xx ) ) ) ) ) => 6.11/1.40 ( ex1 @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 6.11/1.40 thf('2', plain, 6.11/1.40 (( ex1I ) = 6.11/1.40 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 6.11/1.40 ( ( in @ X8 @ X4 ) => 6.11/1.40 ( ( X6 @ X8 ) => 6.11/1.40 ( ( ![X10:$i]: 6.11/1.40 ( ( in @ X10 @ X4 ) => 6.11/1.40 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 6.11/1.40 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(ex1, axiom,(( ex1 ) = 6.11/1.40 (^[A:$i,Xphi:( $i > $o )]: 6.11/1.40 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))). 6.11/1.40 thf(singleton, axiom,(( singleton ) = 6.11/1.40 (^[A:$i]: 6.11/1.40 ( ?[Xx:$i]: 6.11/1.40 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 6.11/1.40 thf('3', plain, 6.11/1.40 (( singleton ) = 6.11/1.40 ( ^[A:$i]: 6.11/1.40 ( ?[Xx:$i]: 6.11/1.40 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 6.11/1.40 inference('simplify_rw_rule', [status(thm)], [singleton])). 6.11/1.40 thf('4', plain, 6.11/1.40 (( singleton ) = 6.11/1.40 ( ^[V_1:$i]: 6.11/1.40 ( ?[X4:$i]: 6.11/1.40 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf('5', plain, 6.11/1.40 (( ex1 ) = 6.11/1.40 ( ^[A:$i,Xphi:( $i > $o )]: 6.11/1.40 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )), 6.11/1.40 inference('simplify_rw_rule', [status(thm)], [ex1, '4'])). 6.11/1.40 thf('6', plain, 6.11/1.40 (( ex1 ) = 6.11/1.40 ( ^[V_1:$i,V_2:( $i > $o )]: 6.11/1.40 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(kpair, axiom,(( kpair ) = 6.11/1.40 (^[Xx:$i,Xy:$i]: 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )))). 6.11/1.40 thf('7', plain, 6.11/1.40 (( kpair ) = 6.11/1.40 ( ^[Xx:$i,Xy:$i]: 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )), 6.11/1.40 inference('simplify_rw_rule', [status(thm)], [kpair])). 6.11/1.40 thf('8', plain, 6.11/1.40 (( kpair ) = 6.11/1.40 ( ^[V_1:$i,V_2:$i]: 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ V_1 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(iskpair, axiom,(( iskpair ) = 6.11/1.40 (^[A:$i]: 6.11/1.40 ( ?[Xx:$i]: 6.11/1.40 ( ( ?[Xy:$i]: 6.11/1.40 ( ( ( A ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) & 6.11/1.40 ( in @ Xy @ ( setunion @ A ) ) ) ) & 6.11/1.40 ( in @ Xx @ ( setunion @ A ) ) ) )))). 6.11/1.40 thf('9', plain, 6.11/1.40 (( iskpair ) = 6.11/1.40 ( ^[A:$i]: 6.11/1.40 ( ?[Xx:$i]: 6.11/1.40 ( ( ?[Xy:$i]: 6.11/1.40 ( ( ( A ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) & 6.11/1.40 ( in @ Xy @ ( setunion @ A ) ) ) ) & 6.11/1.40 ( in @ Xx @ ( setunion @ A ) ) ) ) )), 6.11/1.40 inference('simplify_rw_rule', [status(thm)], [iskpair])). 6.11/1.40 thf('10', plain, 6.11/1.40 (( iskpair ) = 6.11/1.40 ( ^[V_1:$i]: 6.11/1.40 ( ?[X4:$i]: 6.11/1.40 ( ( ?[X6:$i]: 6.11/1.40 ( ( ( V_1 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X4 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) & 6.11/1.40 ( in @ X6 @ ( setunion @ V_1 ) ) ) ) & 6.11/1.40 ( in @ X4 @ ( setunion @ V_1 ) ) ) ) )), 6.11/1.40 define([status(thm)])). 6.11/1.40 thf(ksndsingleton, conjecture, 6.11/1.40 (( ex1I ) => 6.11/1.40 ( ( kfstpairEq ) => 6.11/1.40 ( ( setukpairinjR ) => 6.11/1.40 ( ![Xu:$i]: 6.11/1.40 ( ( iskpair @ Xu ) => 6.11/1.40 ( singleton @ 6.11/1.40 ( dsetconstr @ 6.11/1.40 ( setunion @ Xu ) @ 6.11/1.40 ( ^[Xx:$i]: ( ( Xu ) = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ) ))). 6.11/1.40 thf(zf_stmt_0, conjecture, 6.11/1.40 (( ![X4:$i,X6:( $i > $o ),X8:$i]: 6.11/1.40 ( ( in @ X8 @ X4 ) => 6.11/1.40 ( ( X6 @ X8 ) => 6.11/1.40 ( ( ![X10:$i]: 6.11/1.40 ( ( in @ X10 @ X4 ) => ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 6.11/1.40 ( ?[X12:$i]: 6.11/1.40 ( ( in @ X12 @ ( dsetconstr @ X4 @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) & 6.11/1.40 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = 6.11/1.40 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) ) ) => 6.11/1.40 ( ( ![X14:$i,X16:$i]: 6.11/1.40 ( ( kfst @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X14 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) = 6.11/1.40 ( X14 ) ) ) => 6.11/1.40 ( ( ![X18:$i,X20:$i,X22:$i,X24:$i]: 6.11/1.40 ( ( ( setadjoin @ 6.11/1.40 ( setadjoin @ X18 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X22 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) => 6.11/1.40 ( ( X20 ) = ( X24 ) ) ) ) => 6.11/1.40 ( ![X26:$i]: 6.11/1.40 ( ( ?[X28:$i]: 6.11/1.40 ( ( in @ X28 @ ( setunion @ X26 ) ) & 6.11/1.40 ( ?[X30:$i]: 6.11/1.40 ( ( in @ X30 @ ( setunion @ X26 ) ) & 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X28 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X28 @ ( setadjoin @ X30 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) ) ) => 6.11/1.40 ( ?[X32:$i]: 6.11/1.40 ( ( in @ 6.11/1.40 X32 @ 6.11/1.40 ( dsetconstr @ 6.11/1.40 ( setunion @ X26 ) @ 6.11/1.40 ( ^[V_4:$i]: 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( kfst @ X26 ) @ ( setadjoin @ V_4 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) ) & 6.11/1.40 ( ( dsetconstr @ 6.11/1.40 ( setunion @ X26 ) @ 6.11/1.40 ( ^[V_3:$i]: 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( kfst @ X26 ) @ ( setadjoin @ V_3 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) = 6.11/1.40 ( setadjoin @ X32 @ emptyset ) ) ) ) ) ) ) ))). 6.11/1.40 thf(zf_stmt_1, negated_conjecture, 6.11/1.40 (~( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 6.11/1.40 ( ( in @ X8 @ X4 ) => 6.11/1.40 ( ( X6 @ X8 ) => 6.11/1.40 ( ( ![X10:$i]: 6.11/1.40 ( ( in @ X10 @ X4 ) => 6.11/1.40 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) => 6.11/1.40 ( ?[X12:$i]: 6.11/1.40 ( ( in @ 6.11/1.40 X12 @ ( dsetconstr @ X4 @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) & 6.11/1.40 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = 6.11/1.40 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) ) ) => 6.11/1.40 ( ( ![X14:$i,X16:$i]: 6.11/1.40 ( ( kfst @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X14 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) = 6.11/1.40 ( X14 ) ) ) => 6.11/1.40 ( ( ![X18:$i,X20:$i,X22:$i,X24:$i]: 6.11/1.40 ( ( ( setadjoin @ 6.11/1.40 ( setadjoin @ X18 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X22 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) => 6.11/1.40 ( ( X20 ) = ( X24 ) ) ) ) => 6.11/1.40 ( ![X26:$i]: 6.11/1.40 ( ( ?[X28:$i]: 6.11/1.40 ( ( in @ X28 @ ( setunion @ X26 ) ) & 6.11/1.40 ( ?[X30:$i]: 6.11/1.40 ( ( in @ X30 @ ( setunion @ X26 ) ) & 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ X28 @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ 6.11/1.40 X28 @ ( setadjoin @ X30 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) ) ) => 6.11/1.40 ( ?[X32:$i]: 6.11/1.40 ( ( in @ 6.11/1.40 X32 @ 6.11/1.40 ( dsetconstr @ 6.11/1.40 ( setunion @ X26 ) @ 6.11/1.40 ( ^[V_4:$i]: 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( kfst @ X26 ) @ 6.11/1.40 ( setadjoin @ V_4 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) ) & 6.11/1.40 ( ( dsetconstr @ 6.11/1.40 ( setunion @ X26 ) @ 6.11/1.40 ( ^[V_3:$i]: 6.11/1.40 ( ( X26 ) = 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( setadjoin @ 6.11/1.40 ( kfst @ X26 ) @ 6.11/1.40 ( setadjoin @ V_3 @ emptyset ) ) @ 6.11/1.40 emptyset ) ) ) ) ) = 6.11/1.40 ( setadjoin @ X32 @ emptyset ) ) ) ) ) ) ) ) )), 6.11/1.40 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 6.11/1.40 thf(zip_derived_cl0, plain, 6.11/1.40 (~ (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i > $o]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ Y0) => 6.11/1.40 (((Y1 @ Y2) => 6.11/1.40 (((((!!) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 Y0) => 6.11/1.40 (((Y1 @ 6.11/1.40 Y3) => 6.11/1.40 (( 6.11/1.40 (Y3) = 6.11/1.40 (Y2)))))))))) => 6.11/1.40 (((??) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 (dsetconstr @ 6.11/1.40 Y0 @ 6.11/1.40 (^[Y4 : $i]: 6.11/1.40 (Y1 @ Y4)))) & 6.11/1.40 (((dsetconstr @ 6.11/1.40 Y0 @ 6.11/1.40 (^[Y4 : $i]: 6.11/1.40 (Y1 @ Y4))) = 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset))))))))))))))))))))))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (Y0))))))))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((!!) @ (^[Y3 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y1 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y3))))))))))))))))) => 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ Y0)) & 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (setunion @ Y0)) & 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))))))), 6.11/1.40 inference('cnf', [status(esa)], [zf_stmt_1])). 6.11/1.40 thf(zip_derived_cl1, plain, 6.11/1.40 (~ (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i > $o]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ Y0) => 6.11/1.40 (((Y1 @ Y2) => 6.11/1.40 (((((!!) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 Y0) => 6.11/1.40 (((Y1 @ 6.11/1.40 Y3) => 6.11/1.40 (( 6.11/1.40 (Y3) = 6.11/1.40 (Y2)))))))))) => 6.11/1.40 (((??) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 (dsetconstr @ 6.11/1.40 Y0 @ Y1)) & 6.11/1.40 (((dsetconstr @ 6.11/1.40 Y0 @ Y1) = 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset))))))))))))))))))))))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (Y0))))))))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((!!) @ (^[Y3 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y1 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y3))))))))))))))))) => 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ Y0)) & 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (setunion @ Y0)) & 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))))))), 6.11/1.40 inference('ho_norm', [status(thm)], [zip_derived_cl0])). 6.11/1.40 thf(zip_derived_cl3, plain, 6.11/1.40 (~ (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (Y0))))))))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((!!) @ (^[Y3 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y1 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y3))))))))))))))))) => 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ Y0)) & 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (setunion @ Y0)) & 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 6.11/1.40 thf(zip_derived_cl6, plain, 6.11/1.40 (~ (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((!!) @ (^[Y3 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y0 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y1 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y2 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y3))))))))))))))))) => 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ Y0)) & 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (setunion @ Y0)) & 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 6.11/1.40 thf(zip_derived_cl10, plain, 6.11/1.40 (~ (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ Y0)) & 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (setunion @ Y0)) & 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ Y0) @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 (((Y0) = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ Y0) @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 6.11/1.40 thf(zip_derived_cl14, plain, 6.11/1.40 (~ (((((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ (setunion @ '#sk5')) & 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ '#sk5')) & 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))))))))))) => 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset))))))))))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 6.11/1.40 thf(zip_derived_cl18, plain, 6.11/1.40 ( (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ (setunion @ '#sk5')) & 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (setunion @ '#sk5')) & 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 6.11/1.40 thf(zip_derived_cl22, plain, 6.11/1.40 ( (((in @ '#sk12' @ (setunion @ '#sk5')) & 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ (setunion @ '#sk5')) & 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))))))))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 6.11/1.40 thf(zip_derived_cl27, plain, 6.11/1.40 ( (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ (setunion @ '#sk5')) & 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))))))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 6.11/1.40 thf(zip_derived_cl31, plain, 6.11/1.40 ( (((in @ '#sk20' @ (setunion @ '#sk5')) & 6.11/1.40 ((('#sk5') = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset))))))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 6.11/1.40 thf(zip_derived_cl37, plain, 6.11/1.40 ( ((('#sk5') = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ emptyset))))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl2, plain, 6.11/1.40 ( (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i > $o]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ Y0) => 6.11/1.40 (((Y1 @ Y2) => 6.11/1.40 (((((!!) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 Y0) => 6.11/1.40 (((Y1 @ Y3) => 6.11/1.40 (((Y3) = (Y2)))))))))) => 6.11/1.40 (((??) @ (^[Y3 : $i]: 6.11/1.40 (((in @ Y3 @ 6.11/1.40 (dsetconstr @ 6.11/1.40 Y0 @ Y1)) & 6.11/1.40 (((dsetconstr @ 6.11/1.40 Y0 @ Y1) = 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ 6.11/1.40 emptyset)))))))))))))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 6.11/1.40 thf(zip_derived_cl4, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i > $o]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ X2) => 6.11/1.40 (((Y0 @ Y1) => 6.11/1.40 (((((!!) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ X2) => 6.11/1.40 (((Y0 @ Y2) => 6.11/1.40 (((Y2) = (Y1)))))))))) => 6.11/1.40 (((??) @ (^[Y2 : $i]: 6.11/1.40 (((in @ Y2 @ 6.11/1.40 (dsetconstr @ X2 @ Y0)) & 6.11/1.40 (((dsetconstr @ X2 @ 6.11/1.40 Y0) = (setadjoin @ 6.11/1.40 Y2 @ emptyset))))))))))))))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 6.11/1.40 thf(zip_derived_cl7, plain, 6.11/1.40 (![X2 : $i, X4 : $i > $o]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X2) => 6.11/1.40 (((X4 @ Y0) => 6.11/1.40 (((((!!) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ X2) => 6.11/1.40 (((X4 @ Y1) => (((Y1) = (Y0)))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ (dsetconstr @ X2 @ X4)) & 6.11/1.40 (((dsetconstr @ X2 @ X4) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 6.11/1.40 thf(zip_derived_cl54, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((((!!) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y0)))))))))) => 6.11/1.40 (((??) @ (^[Y1 : $i]: 6.11/1.40 (((in @ Y1 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y2 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ 6.11/1.40 (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y1 @ emptyset)))))))))))))))))), 6.11/1.40 inference('triggered_bool_instantiation', [status(thm)], 6.11/1.40 [zip_derived_cl7])). 6.11/1.40 thf(zip_derived_cl55, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (((in @ X2 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (X2)))))))))) => 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset))))))))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 6.11/1.40 thf(zip_derived_cl56, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ (in @ X2 @ X0) 6.11/1.40 | ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (X2)))))))))) => 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 6.11/1.40 thf(zip_derived_cl57, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset)))) 6.11/1.40 | (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (X2)))))))))) => 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 6.11/1.40 thf(zip_derived_cl58, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ((('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (((((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (X2)))))))))) => 6.11/1.40 (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl57])). 6.11/1.40 thf(zip_derived_cl59, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (X2)))))))))) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 6.11/1.40 thf(zip_derived_cl60, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ (((in @ ('#sk103' @ X0 @ X2) @ X0) => 6.11/1.40 ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 ((('#sk103' @ X0 @ X2) = (X2))))))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 6.11/1.40 thf(zip_derived_cl62, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ ((((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 ((('#sk103' @ X0 @ X2) = (X2))))) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 6.11/1.40 thf(zip_derived_cl65, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (~ ((('#sk103' @ X0 @ X2) = (X2))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 6.11/1.40 thf(zip_derived_cl70, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ((('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl65])). 6.11/1.40 thf(zip_derived_cl71, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (((in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ ('#sk104' @ X0) @ emptyset))))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 6.11/1.40 thf(zip_derived_cl76, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ ('#sk104' @ X0) @ emptyset))) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 6.11/1.40 thf(zip_derived_cl78, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl76])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl5, plain, 6.11/1.40 ( (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (Y0)))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])). 6.11/1.40 thf(zip_derived_cl8, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (X2))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 6.11/1.40 thf(zip_derived_cl12, plain, 6.11/1.40 (![X2 : $i, X4 : $i]: 6.11/1.40 (((kfst @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset))) = 6.11/1.40 (X2)))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 6.11/1.40 thf(zip_derived_cl16, plain, 6.11/1.40 (![X2 : $i, X4 : $i]: 6.11/1.40 ((kfst @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 = (X2))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl839, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('demod', [status(thm)], 6.11/1.40 [zip_derived_cl78, zip_derived_cl79, zip_derived_cl79])). 6.11/1.40 thf(zip_derived_cl846, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ((('#sk5') != ('#sk5')) 6.11/1.40 | ~ (in @ '#sk20' @ X0) 6.11/1.40 | (('#sk103' @ X0 @ '#sk20') != ('#sk20')) 6.11/1.40 | ((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl839])). 6.11/1.40 thf(zip_derived_cl850, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk103' @ X0 @ '#sk20') != ('#sk20')) 6.11/1.40 | ~ (in @ '#sk20' @ X0))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl846])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl75, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl705, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk103' @ X0 @ X2) != (X2)) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('demod', [status(thm)], 6.11/1.40 [zip_derived_cl75, zip_derived_cl79, zip_derived_cl79])). 6.11/1.40 thf(zip_derived_cl712, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ((('#sk5') != ('#sk5')) 6.11/1.40 | ~ (in @ '#sk20' @ X0) 6.11/1.40 | (('#sk103' @ X0 @ '#sk20') != ('#sk20')) 6.11/1.40 | (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl705])). 6.11/1.40 thf(zip_derived_cl716, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk103' @ X0 @ '#sk20') != ('#sk20')) 6.11/1.40 | ~ (in @ '#sk20' @ X0))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl712])). 6.11/1.40 thf(zip_derived_cl19, plain, 6.11/1.40 (~ (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 6.11/1.40 thf(zip_derived_cl23, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 ~ (((in @ X2 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ X2 @ emptyset)))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 6.11/1.40 thf(zip_derived_cl28, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (~ (in @ X2 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | ~ (((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ X2 @ emptyset))))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 6.11/1.40 thf(zip_derived_cl32, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (~ (in @ X2 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ X2 @ emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl28])). 6.11/1.40 thf(zip_derived_cl734, plain, 6.11/1.40 ((~ (in @ '#sk20' @ (setunion @ '#sk5')) 6.11/1.40 | (('#sk103' @ (setunion @ '#sk5') @ '#sk20') != ('#sk20')) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl716, zip_derived_cl32])). 6.11/1.40 thf(zip_derived_cl36, plain, ( (in @ '#sk20' @ (setunion @ '#sk5'))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 6.11/1.40 thf(zip_derived_cl744, plain, 6.11/1.40 (((('#sk103' @ (setunion @ '#sk5') @ '#sk20') != ('#sk20')) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)))), 6.11/1.40 inference('demod', [status(thm)], [zip_derived_cl734, zip_derived_cl36])). 6.11/1.40 thf(zip_derived_cl36, plain, ( (in @ '#sk20' @ (setunion @ '#sk5'))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl64, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset)))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 6.11/1.40 thf(zip_derived_cl68, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (((??) @ (^[Y0 : $i]: 6.11/1.40 (((in @ Y0 @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y1 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ Y0 @ emptyset)))))))))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl64])). 6.11/1.40 thf(zip_derived_cl69, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (((in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) & 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ ('#sk104' @ X0) @ emptyset))))) 6.11/1.40 | ~ (in @ X2 @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))))), 6.11/1.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 6.11/1.40 thf(zip_derived_cl74, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) = 6.11/1.40 (setadjoin @ ('#sk104' @ X0) @ emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 6.11/1.40 thf(zip_derived_cl77, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl74])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl854, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('demod', [status(thm)], 6.11/1.40 [zip_derived_cl77, zip_derived_cl79, zip_derived_cl79, 6.11/1.40 zip_derived_cl79, zip_derived_cl79])). 6.11/1.40 thf(zip_derived_cl861, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ((('#sk5') != ('#sk5')) 6.11/1.40 | ~ (in @ '#sk20' @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ '#sk20') @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl854])). 6.11/1.40 thf(zip_derived_cl865, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 (((dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ X0) @ emptyset)) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ '#sk20') @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ '#sk20' @ X0))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl861])). 6.11/1.40 thf(zip_derived_cl869, plain, 6.11/1.40 (((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ (setunion @ '#sk5') @ '#sk20') @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 = (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl865])). 6.11/1.40 thf(zip_derived_cl36, plain, ( (in @ '#sk20' @ (setunion @ '#sk5'))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl73, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl79, plain, (((kfst @ '#sk5') = ('#sk12'))), 6.11/1.40 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl16])). 6.11/1.40 thf(zip_derived_cl602, plain, 6.11/1.40 (![X0 : $i, X2 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ X2) @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (('#sk5') 6.11/1.40 != (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ X2 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ X2 @ X0))), 6.11/1.40 inference('demod', [status(thm)], 6.11/1.40 [zip_derived_cl73, zip_derived_cl79, zip_derived_cl79, 6.11/1.40 zip_derived_cl79, zip_derived_cl79])). 6.11/1.40 thf(zip_derived_cl609, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ((('#sk5') != ('#sk5')) 6.11/1.40 | ~ (in @ '#sk20' @ X0) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ '#sk20') @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl602])). 6.11/1.40 thf(zip_derived_cl613, plain, 6.11/1.40 (![X0 : $i]: 6.11/1.40 ( (in @ ('#sk104' @ X0) @ 6.11/1.40 (dsetconstr @ X0 @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | (('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ X0 @ '#sk20') @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ~ (in @ '#sk20' @ X0))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl609])). 6.11/1.40 thf(zip_derived_cl619, plain, 6.11/1.40 (((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ (setunion @ '#sk5') @ '#sk20') @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | (in @ ('#sk104' @ (setunion @ '#sk5')) @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl36, zip_derived_cl613])). 6.11/1.40 thf(zip_derived_cl32, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (~ (in @ X2 @ 6.11/1.40 (dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset))))))) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ X2 @ emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl28])). 6.11/1.40 thf(zip_derived_cl720, plain, 6.11/1.40 (((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ (setunion @ '#sk5') @ '#sk20') @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl619, zip_derived_cl32])). 6.11/1.40 thf(zip_derived_cl871, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ 6.11/1.40 (setadjoin @ ('#sk103' @ (setunion @ '#sk5') @ '#sk20') @ 6.11/1.40 emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('clc', [status(thm)], [zip_derived_cl869, zip_derived_cl720])). 6.11/1.40 thf(zip_derived_cl41, plain, 6.11/1.40 ((('#sk5') 6.11/1.40 = (setadjoin @ (setadjoin @ '#sk12' @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ '#sk12' @ (setadjoin @ '#sk20' @ emptyset)) @ 6.11/1.40 emptyset)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 6.11/1.40 thf(zip_derived_cl9, plain, 6.11/1.40 ( (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((!!) @ (^[Y3 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y1 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y2 @ 6.11/1.40 (setadjoin @ 6.11/1.40 Y3 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y1) = (Y3)))))))))))))))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 6.11/1.40 thf(zip_derived_cl13, plain, 6.11/1.40 (![X2 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((!!) @ (^[Y2 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ X2 @ 6.11/1.40 (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y1 @ 6.11/1.40 (setadjoin @ Y2 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((Y0) = (Y2))))))))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 6.11/1.40 thf(zip_derived_cl17, plain, 6.11/1.40 (![X2 : $i, X4 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((!!) @ (^[Y1 : $i]: 6.11/1.40 (((((setadjoin @ 6.11/1.40 (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ X2 @ 6.11/1.40 (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ Y0 @ 6.11/1.40 (setadjoin @ Y1 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((X4) = (Y1)))))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 6.11/1.40 thf(zip_derived_cl21, plain, 6.11/1.40 (![X2 : $i, X4 : $i, X6 : $i]: 6.11/1.40 (((!!) @ (^[Y0 : $i]: 6.11/1.40 (((((setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ X6 @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((X4) = (Y0))))))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 6.11/1.40 thf(zip_derived_cl25, plain, 6.11/1.40 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 6.11/1.40 (((((setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X8 @ emptyset)) @ 6.11/1.40 emptyset)))) => 6.11/1.40 (((X4) = (X8)))))), 6.11/1.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 6.11/1.40 thf(zip_derived_cl30, plain, 6.11/1.40 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 6.11/1.40 (~ (((setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset)) = 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X8 @ emptyset)) @ 6.11/1.40 emptyset)))) 6.11/1.40 | (((X4) = (X8))))), 6.11/1.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 6.11/1.40 thf(zip_derived_cl35, plain, 6.11/1.40 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 6.11/1.40 (((setadjoin @ (setadjoin @ X2 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ 6.11/1.40 emptyset)) 6.11/1.40 != (setadjoin @ (setadjoin @ X6 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X8 @ emptyset)) @ 6.11/1.40 emptyset))) 6.11/1.40 | ((X4) = (X8)))), 6.11/1.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl30])). 6.11/1.40 thf(zip_derived_cl148, plain, 6.11/1.40 (![X0 : $i, X1 : $i]: 6.11/1.40 (((setadjoin @ (setadjoin @ X1 @ emptyset) @ 6.11/1.40 (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ 6.11/1.40 emptyset)) 6.11/1.40 != ('#sk5')) 6.11/1.40 | ((X0) = ('#sk20')))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl35])). 6.11/1.40 thf(zip_derived_cl883, plain, 6.11/1.40 (((('#sk5') != ('#sk5')) 6.11/1.40 | (('#sk103' @ (setunion @ '#sk5') @ '#sk20') = ('#sk20')))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl871, zip_derived_cl148])). 6.11/1.40 thf(zip_derived_cl946, plain, 6.11/1.40 ((('#sk103' @ (setunion @ '#sk5') @ '#sk20') = ('#sk20'))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl883])). 6.11/1.40 thf(zip_derived_cl974, plain, 6.11/1.40 (((('#sk20') != ('#sk20')) 6.11/1.40 | ((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)))), 6.11/1.40 inference('demod', [status(thm)], [zip_derived_cl744, zip_derived_cl946])). 6.11/1.40 thf(zip_derived_cl975, plain, 6.11/1.40 (((dsetconstr @ (setunion @ '#sk5') @ 6.11/1.40 (^[Y0 : $i]: 6.11/1.40 ((('#sk5') = (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ emptyset) @ 6.11/1.40 (setadjoin @ 6.11/1.40 (setadjoin @ (kfst @ '#sk5') @ (setadjoin @ Y0 @ emptyset)) @ 6.11/1.40 emptyset)))))) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl974])). 6.11/1.40 thf(zip_derived_cl1273, plain, 6.11/1.40 ((((setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)) 6.11/1.40 | ~ (in @ '#sk20' @ (setunion @ '#sk5')) 6.11/1.40 | (('#sk103' @ (setunion @ '#sk5') @ '#sk20') != ('#sk20')))), 6.11/1.40 inference('sup-', [status(thm)], [zip_derived_cl850, zip_derived_cl975])). 6.11/1.40 thf(zip_derived_cl36, plain, ( (in @ '#sk20' @ (setunion @ '#sk5'))), 6.11/1.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl31])). 6.11/1.40 thf(zip_derived_cl946, plain, 6.11/1.40 ((('#sk103' @ (setunion @ '#sk5') @ '#sk20') = ('#sk20'))), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl883])). 6.11/1.40 thf(zip_derived_cl1278, plain, 6.11/1.40 ((((setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset) 6.11/1.40 != (setadjoin @ ('#sk104' @ (setunion @ '#sk5')) @ emptyset)) 6.11/1.40 | (('#sk20') != ('#sk20')))), 6.11/1.40 inference('demod', [status(thm)], 6.11/1.40 [zip_derived_cl1273, zip_derived_cl36, zip_derived_cl946])). 6.11/1.40 thf(zip_derived_cl1279, plain, ($false), 6.11/1.40 inference('simplify', [status(thm)], [zip_derived_cl1278])). 6.11/1.40 6.11/1.40 % SZS output end Refutation 6.11/1.40 6.11/1.40 6.11/1.40 % Terminating... 6.81/1.49 % Runner terminated. 6.81/1.51 % Zipperpin 1.5 exiting 6.81/1.51 EOF