0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rQyUoj5Jpy true 0.11/0.31 % Computer : n028.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 960 0.11/0.31 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 05:12:50 EDT 2022 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 960 s 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.45/0.61 % Total configuration time : 828 0.45/0.61 % Estimated wc time : 1656 0.45/0.61 % Estimated cpu time (8 cpus) : 207.0 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.49/0.83 % Solved by lams/35_full_unif4.sh. 0.49/0.83 % done 27 iterations in 0.089s 0.49/0.83 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.49/0.83 % SZS output start Refutation 0.49/0.83 thf(subset_type, type, subset: $i > $i > $o). 0.49/0.83 thf('#sk6_type', type, '#sk6': $i > $i > $i > $i). 0.49/0.83 thf(in_type, type, in: $i > $i > $o). 0.49/0.83 thf(funcSet_type, type, funcSet: $i > $i > $i). 0.49/0.83 thf('#sk4_type', type, '#sk4': $i). 0.49/0.83 thf(func_type, type, func: $i > $i > $i > $o). 0.49/0.83 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 0.49/0.83 thf(cartprod_type, type, cartprod: $i > $i > $i). 0.49/0.83 thf(singleton_type, type, singleton: $i > $o). 0.49/0.83 thf('#sk3_type', type, '#sk3': $i). 0.49/0.83 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 0.49/0.83 thf('#sk2_type', type, '#sk2': $i). 0.49/0.83 thf(kpair_type, type, kpair: $i > $i > $i). 0.49/0.83 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 0.49/0.83 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 0.49/0.83 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 0.49/0.83 thf(emptyset_type, type, emptyset: $i). 0.49/0.83 thf('#sk5_type', type, '#sk5': $i > $i > $i > $i). 0.49/0.83 thf('#sk1_type', type, '#sk1': $i). 0.49/0.83 thf('#sk7_type', type, '#sk7': $i). 0.49/0.83 thf(ap_type, type, ap: $i > $i > $i > $i > $i). 0.49/0.83 thf(breln_type, type, breln: $i > $i > $i > $o). 0.49/0.83 thf(funcGraphProp2, axiom, funcGraphProp2 = 0.49/0.83 (![A:$i,B:$i,Xf:$i]: 0.49/0.83 ( ( func @ A @ B @ Xf ) => 0.49/0.83 ( ![Xx:$i]: 0.49/0.83 ( ( in @ Xx @ A ) => 0.49/0.83 ( ![Xy:$i]: 0.49/0.83 ( ( in @ Xy @ B ) => 0.49/0.83 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) => 0.49/0.83 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))). 0.49/0.83 thf('0', plain, 0.49/0.83 (( funcGraphProp2 ) = 0.49/0.83 ( ![X4:$i,X6:$i,X8:$i]: 0.49/0.83 ( ( func @ X4 @ X6 @ X8 ) => 0.49/0.83 ( ![X10:$i]: 0.49/0.83 ( ( in @ X10 @ X4 ) => 0.49/0.83 ( ![X12:$i]: 0.49/0.83 ( ( in @ X12 @ X6 ) => 0.49/0.83 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) => 0.49/0.83 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf(infuncsetfunc, axiom, infuncsetfunc = 0.49/0.83 (![A:$i,B:$i,Xf:$i]: 0.49/0.83 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => ( func @ A @ B @ Xf ) ))). 0.49/0.83 thf('1', plain, 0.49/0.83 (( infuncsetfunc ) = 0.49/0.83 ( ![X4:$i,X6:$i,X8:$i]: 0.49/0.83 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => ( func @ X4 @ X6 @ X8 ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf(func, axiom,(( func ) = 0.49/0.83 (^[A:$i,B:$i,R:$i]: 0.49/0.83 ( ( breln @ A @ B @ R ) & 0.49/0.83 ( ![Xx:$i]: 0.49/0.83 ( ( in @ Xx @ A ) => 0.49/0.83 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 0.49/0.83 thf(breln, axiom,(( breln ) = 0.49/0.83 (^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) )))). 0.49/0.83 thf('2', plain, 0.49/0.83 (( breln ) = ( ^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) ) )), 0.49/0.83 inference('simplify_rw_rule', [status(thm)], [breln])). 0.49/0.83 thf('3', plain, 0.49/0.83 (( breln ) = 0.49/0.83 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf(ex1, axiom,(( ex1 ) = 0.49/0.83 (^[A:$i,Xphi:( $i > $o )]: 0.49/0.83 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))). 0.49/0.83 thf(singleton, axiom,(( singleton ) = 0.49/0.83 (^[A:$i]: 0.49/0.83 ( ?[Xx:$i]: 0.49/0.83 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 0.49/0.83 thf('4', plain, 0.49/0.83 (( singleton ) = 0.49/0.83 ( ^[A:$i]: 0.49/0.83 ( ?[Xx:$i]: 0.49/0.83 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 0.49/0.83 inference('simplify_rw_rule', [status(thm)], [singleton])). 0.49/0.83 thf('5', plain, 0.49/0.83 (( singleton ) = 0.49/0.83 ( ^[V_1:$i]: 0.49/0.83 ( ?[X4:$i]: 0.49/0.83 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf('6', plain, 0.49/0.83 (( ex1 ) = 0.49/0.83 ( ^[A:$i,Xphi:( $i > $o )]: 0.49/0.83 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )), 0.49/0.83 inference('simplify_rw_rule', [status(thm)], [ex1, '5'])). 0.49/0.83 thf('7', plain, 0.49/0.83 (( ex1 ) = 0.49/0.83 ( ^[V_1:$i,V_2:( $i > $o )]: 0.49/0.83 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf('8', plain, 0.49/0.83 (( func ) = 0.49/0.83 ( ^[A:$i,B:$i,R:$i]: 0.49/0.83 ( ( breln @ A @ B @ R ) & 0.49/0.83 ( ![Xx:$i]: 0.49/0.83 ( ( in @ Xx @ A ) => 0.49/0.83 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 0.49/0.83 inference('simplify_rw_rule', [status(thm)], [func, '3', '7', '5'])). 0.49/0.83 thf('9', plain, 0.49/0.83 (( func ) = 0.49/0.83 ( ^[V_1:$i,V_2:$i,V_3:$i]: 0.49/0.83 ( ( breln @ V_1 @ V_2 @ V_3 ) & 0.49/0.83 ( ![X4:$i]: 0.49/0.83 ( ( in @ X4 @ V_1 ) => 0.49/0.83 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 0.49/0.83 define([status(thm)])). 0.49/0.83 thf(funcGraphProp4, conjecture, 0.49/0.83 (( infuncsetfunc ) => 0.49/0.83 ( ( funcGraphProp2 ) => 0.49/0.83 ( ![A:$i,B:$i,Xf:$i]: 0.49/0.83 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => 0.49/0.83 ( ![Xx:$i]: 0.49/0.83 ( ( in @ Xx @ A ) => 0.49/0.83 ( ![Xy:$i]: 0.49/0.83 ( ( in @ Xy @ B ) => 0.49/0.83 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) => 0.49/0.83 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ) ) ))). 0.49/0.83 thf(zf_stmt_0, conjecture, 0.49/0.83 (( ![X4:$i,X6:$i,X8:$i]: 0.49/0.83 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => 0.49/0.83 ( ( ![X10:$i]: 0.49/0.83 ( ( in @ X10 @ X4 ) => 0.49/0.83 ( ?[X12:$i]: 0.49/0.83 ( ( in @ 0.49/0.83 X12 @ 0.49/0.83 ( dsetconstr @ 0.49/0.83 X6 @ ( ^[V_2:$i]: ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) & 0.49/0.83 ( ( dsetconstr @ 0.49/0.83 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) = 0.49/0.83 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) & 0.49/0.83 ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) ) ) ) => 0.49/0.83 ( ( ![X14:$i,X16:$i,X18:$i]: 0.49/0.83 ( ( ( ![X20:$i]: 0.49/0.83 ( ( in @ X20 @ X14 ) => 0.49/0.83 ( ?[X22:$i]: 0.49/0.83 ( ( in @ 0.49/0.83 X22 @ 0.49/0.83 ( dsetconstr @ 0.49/0.83 X16 @ 0.49/0.83 ( ^[V_4:$i]: ( in @ ( kpair @ X20 @ V_4 ) @ X18 ) ) ) ) & 0.49/0.83 ( ( dsetconstr @ 0.49/0.83 X16 @ 0.49/0.83 ( ^[V_3:$i]: ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) ) = 0.49/0.83 ( setadjoin @ X22 @ emptyset ) ) ) ) ) ) & 0.49/0.83 ( subset @ X18 @ ( cartprod @ X14 @ X16 ) ) ) => 0.49/0.83 ( ![X24:$i]: 0.49/0.83 ( ( in @ X24 @ X14 ) => 0.49/0.83 ( ![X26:$i]: 0.49/0.83 ( ( in @ X26 @ X16 ) => 0.49/0.83 ( ( in @ ( kpair @ X24 @ X26 ) @ X18 ) => 0.49/0.83 ( ( ap @ X14 @ X16 @ X18 @ X24 ) = ( X26 ) ) ) ) ) ) ) ) ) => 0.49/0.83 ( ![X28:$i,X30:$i,X32:$i]: 0.49/0.83 ( ( in @ X32 @ ( funcSet @ X28 @ X30 ) ) => 0.49/0.83 ( ![X34:$i]: 0.49/0.83 ( ( in @ X34 @ X28 ) => 0.49/0.83 ( ![X36:$i]: 0.49/0.83 ( ( in @ X36 @ X30 ) => 0.49/0.83 ( ( in @ ( kpair @ X34 @ X36 ) @ X32 ) => 0.49/0.83 ( ( ap @ X28 @ X30 @ X32 @ X34 ) = ( X36 ) ) ) ) ) ) ) ) ) ))). 0.49/0.83 thf(zf_stmt_1, negated_conjecture, 0.49/0.83 (~( ( ![X4:$i,X6:$i,X8:$i]: 0.49/0.83 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => 0.49/0.83 ( ( ![X10:$i]: 0.49/0.83 ( ( in @ X10 @ X4 ) => 0.49/0.83 ( ?[X12:$i]: 0.49/0.83 ( ( in @ 0.49/0.83 X12 @ 0.49/0.83 ( dsetconstr @ 0.49/0.83 X6 @ 0.49/0.83 ( ^[V_2:$i]: ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) & 0.49/0.83 ( ( dsetconstr @ 0.49/0.83 X6 @ 0.49/0.83 ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) = 0.49/0.83 ( setadjoin @ X12 @ emptyset ) ) ) ) ) ) & 0.49/0.83 ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) ) ) ) => 0.49/0.83 ( ( ![X14:$i,X16:$i,X18:$i]: 0.49/0.83 ( ( ( ![X20:$i]: 0.49/0.83 ( ( in @ X20 @ X14 ) => 0.49/0.83 ( ?[X22:$i]: 0.49/0.83 ( ( in @ 0.49/0.83 X22 @ 0.49/0.83 ( dsetconstr @ 0.49/0.83 X16 @ 0.49/0.83 ( ^[V_4:$i]: ( in @ ( kpair @ X20 @ V_4 ) @ X18 ) ) ) ) & 0.49/0.83 ( ( dsetconstr @ 0.49/0.83 X16 @ 0.49/0.83 ( ^[V_3:$i]: ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) ) = 0.49/0.83 ( setadjoin @ X22 @ emptyset ) ) ) ) ) ) & 0.49/0.83 ( subset @ X18 @ ( cartprod @ X14 @ X16 ) ) ) => 0.49/0.83 ( ![X24:$i]: 0.49/0.83 ( ( in @ X24 @ X14 ) => 0.49/0.83 ( ![X26:$i]: 0.49/0.83 ( ( in @ X26 @ X16 ) => 0.49/0.83 ( ( in @ ( kpair @ X24 @ X26 ) @ X18 ) => 0.49/0.83 ( ( ap @ X14 @ X16 @ X18 @ X24 ) = ( X26 ) ) ) ) ) ) ) ) ) => 0.49/0.83 ( ![X28:$i,X30:$i,X32:$i]: 0.49/0.83 ( ( in @ X32 @ ( funcSet @ X28 @ X30 ) ) => 0.49/0.83 ( ![X34:$i]: 0.49/0.83 ( ( in @ X34 @ X28 ) => 0.49/0.83 ( ![X36:$i]: 0.49/0.83 ( ( in @ X36 @ X30 ) => 0.49/0.83 ( ( in @ ( kpair @ X34 @ X36 ) @ X32 ) => 0.49/0.83 ( ( ap @ X28 @ X30 @ X32 @ X34 ) = ( X36 ) ) ) ) ) ) ) ) ) ) )), 0.49/0.83 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 0.49/0.83 thf(zip_derived_cl0, plain, 0.49/0.83 (~ (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (funcSet @ Y0 @ Y1)) => 0.49/0.83 (((((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((??) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 ( 0.49/0.83 dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2)))) & 0.49/0.83 (( 0.49/0.83 (dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y4 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y2 @ 0.49/0.83 (cartprod @ Y0 @ Y1))))))))))))))) => 0.49/0.83 (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((((((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((??) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 ( 0.49/0.83 dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2)))) & 0.49/0.83 (( 0.49/0.83 (dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y4 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y2 @ 0.49/0.83 (cartprod @ Y0 @ Y1)))) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((!!) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 ( 0.49/0.83 kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ 0.49/0.83 Y1 @ 0.49/0.83 Y2 @ 0.49/0.83 Y3) = 0.49/0.83 (Y4)))))))))))))))))))))))))) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (funcSet @ Y0 @ Y1)) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((!!) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 ( 0.49/0.83 kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ 0.49/0.83 Y1 @ 0.49/0.83 Y2 @ 0.49/0.83 Y3) = 0.49/0.83 (Y4))))))))))))))))))))))))))))))), 0.49/0.83 inference('cnf', [status(esa)], [zf_stmt_1])). 0.49/0.83 thf(zip_derived_cl2, plain, 0.49/0.83 (~ (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((((((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((??) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 ( 0.49/0.83 dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2)))) & 0.49/0.83 (( 0.49/0.83 (dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y4 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y2 @ 0.49/0.83 (cartprod @ Y0 @ Y1)))) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((!!) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (((in @ 0.49/0.83 Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ Y1 @ 0.49/0.83 Y2 @ Y3) = 0.49/0.83 (Y4)))))))))))))))))))))))))) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (funcSet @ Y0 @ Y1)) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((!!) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (((in @ 0.49/0.83 Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ Y1 @ 0.49/0.83 Y2 @ Y3) = 0.49/0.83 (Y4))))))))))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 0.49/0.83 thf(zip_derived_cl5, plain, 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (funcSet @ Y0 @ Y1)) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ Y0) => 0.49/0.83 (((!!) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (((in @ Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (((in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ Y1 @ 0.49/0.83 Y2 @ Y3) = 0.49/0.83 (Y4))))))))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 0.49/0.83 thf(zip_derived_cl8, plain, 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ (funcSet @ '#sk1' @ Y0)) => 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ '#sk1') => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((in @ 0.49/0.83 (kpair @ Y2 @ 0.49/0.83 Y3) @ 0.49/0.83 Y1) => 0.49/0.83 (((ap @ 0.49/0.83 '#sk1' @ 0.49/0.83 Y0 @ Y1 @ 0.49/0.83 Y2) = (Y3)))))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 0.49/0.83 thf(zip_derived_cl11, plain, 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ (funcSet @ '#sk1' @ '#sk2')) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ '#sk1') => 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ '#sk2') => 0.49/0.83 (((in @ (kpair @ Y1 @ Y2) @ 0.49/0.83 Y0) => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ 0.49/0.83 Y0 @ Y1) = (Y2))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl8])). 0.49/0.83 thf(zip_derived_cl14, plain, 0.49/0.83 (~ (((in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2')) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ '#sk1') => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ '#sk2') => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ 0.49/0.83 Y0) = (Y1)))))))))))))))))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 0.49/0.83 thf(zip_derived_cl19, plain, 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ '#sk1') => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ '#sk2') => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y0) = 0.49/0.83 (Y1)))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.49/0.83 thf(zip_derived_cl22, plain, 0.49/0.83 (~ (((in @ '#sk4' @ '#sk1') => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ '#sk2') => 0.49/0.83 (((in @ (kpair @ '#sk4' @ Y0) @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = (Y0))))))))))))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 0.49/0.83 thf(zip_derived_cl26, plain, 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ '#sk2') => 0.49/0.83 (((in @ (kpair @ '#sk4' @ Y0) @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = (Y0))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.49/0.83 thf(zip_derived_cl30, plain, 0.49/0.83 (~ (((in @ '#sk7' @ '#sk2') => 0.49/0.83 (((in @ (kpair @ '#sk4' @ '#sk7') @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))))))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 0.49/0.83 thf(zip_derived_cl36, plain, 0.49/0.83 (~ (((in @ (kpair @ '#sk4' @ '#sk7') @ '#sk3') => 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 0.49/0.83 thf(zip_derived_cl40, plain, ( (in @ (kpair @ '#sk4' @ '#sk7') @ '#sk3')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 0.49/0.83 thf(zip_derived_cl18, plain, ( (in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2'))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.49/0.83 thf(zip_derived_cl1, plain, 0.49/0.83 ( (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (funcSet @ Y0 @ Y1)) => 0.49/0.83 (((((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ Y0) => 0.49/0.83 (((??) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (((in @ Y4 @ 0.49/0.83 (dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 (^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2)))) & 0.49/0.83 (((dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y4 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y2 @ 0.49/0.83 (cartprod @ Y0 @ Y1)))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 0.49/0.83 thf(zip_derived_cl3, plain, 0.49/0.83 (![X2 : $i]: 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ (funcSet @ X2 @ Y0)) => 0.49/0.83 (((((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ X2) => 0.49/0.83 (((??) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 (dsetconstr @ 0.49/0.83 Y0 @ 0.49/0.83 (^[Y4 : $i]: 0.49/0.83 ( 0.49/0.83 in @ 0.49/0.83 ( 0.49/0.83 kpair @ 0.49/0.83 Y2 @ Y4) @ 0.49/0.83 Y1)))) & 0.49/0.83 (((dsetconstr @ 0.49/0.83 Y0 @ 0.49/0.83 (^[Y4 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y2 @ Y4) @ 0.49/0.83 Y1))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y3 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y1 @ (cartprod @ X2 @ Y0))))))))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 0.49/0.83 thf(zip_derived_cl6, plain, 0.49/0.83 (![X2 : $i, X4 : $i]: 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ (funcSet @ X2 @ X4)) => 0.49/0.83 (((((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X2) => 0.49/0.83 (((??) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y3 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ Y1 @ Y3) @ 0.49/0.83 Y0)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y3 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ Y1 @ Y3) @ 0.49/0.83 Y0))) = 0.49/0.83 (setadjoin @ Y2 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y0 @ (cartprod @ X2 @ X4)))))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 0.49/0.83 thf(zip_derived_cl9, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (((in @ X6 @ (funcSet @ X2 @ X4)) => 0.49/0.83 (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.49/0.83 (subset @ X6 @ (cartprod @ X2 @ X4))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 0.49/0.83 thf(zip_derived_cl12, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (~ (in @ X6 @ (funcSet @ X2 @ X4)) 0.49/0.83 | (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.49/0.83 (subset @ X6 @ (cartprod @ X2 @ X4)))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 0.49/0.83 thf(zip_derived_cl15, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 ( (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 0.49/0.83 thf(zip_derived_cl20, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 ( (((in @ X8 @ X2) => 0.49/0.83 (((??) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: (in @ (kpair @ X8 @ Y1) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: (in @ (kpair @ X8 @ Y1) @ X6))) = 0.49/0.83 (setadjoin @ Y0 @ emptyset)))))))))) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 0.49/0.83 thf(zip_derived_cl23, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (~ (in @ X8 @ X2) 0.49/0.83 | (((??) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: (in @ (kpair @ X8 @ Y1) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: (in @ (kpair @ X8 @ Y1) @ X6))) = 0.49/0.83 (setadjoin @ Y0 @ emptyset)))))))) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 0.49/0.83 thf(zip_derived_cl27, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 ( (((in @ ('#sk6' @ X4 @ X6 @ X8) @ 0.49/0.83 (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X8 @ Y0) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ X8 @ Y0) @ X6))) = (setadjoin @ 0.49/0.83 ('#sk6' @ X4 @ X6 @ X8) @ emptyset))))) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)) 0.49/0.83 | ~ (in @ X8 @ X2))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 0.49/0.83 thf(zip_derived_cl31, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 ( (in @ ('#sk6' @ X4 @ X6 @ X8) @ 0.49/0.83 (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X8 @ Y0) @ X6)))) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 0.49/0.83 thf(zip_derived_cl54, plain, 0.49/0.83 (![X0 : $i]: 0.49/0.83 (~ (in @ X0 @ '#sk1') 0.49/0.83 | (in @ ('#sk6' @ '#sk2' @ '#sk3' @ X0) @ 0.49/0.83 (dsetconstr @ '#sk2' @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk3')))))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl31])). 0.49/0.83 thf(zip_derived_cl4, plain, 0.49/0.83 ( (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((((((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ Y0) => 0.49/0.83 (((??) @ ( 0.49/0.83 ^[Y4 : $i]: 0.49/0.83 (((in @ Y4 @ 0.49/0.83 (dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 (^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2)))) & 0.49/0.83 (((dsetconstr @ 0.49/0.83 Y1 @ 0.49/0.83 ( 0.49/0.83 ^[Y5 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y3 @ Y5) @ 0.49/0.83 Y2))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y4 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y2 @ 0.49/0.83 (cartprod @ Y0 @ Y1)))) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ Y0) => 0.49/0.83 (((!!) @ (^[Y4 : $i]: 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 Y4 @ 0.49/0.83 Y1) => 0.49/0.83 (( 0.49/0.83 (in @ 0.49/0.83 ( 0.49/0.83 kpair @ 0.49/0.83 Y3 @ Y4) @ 0.49/0.83 Y2) => 0.49/0.83 (( 0.49/0.83 (ap @ 0.49/0.83 Y0 @ 0.49/0.83 Y1 @ 0.49/0.83 Y2 @ 0.49/0.83 Y3) = 0.49/0.83 (Y4))))))))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 0.49/0.83 thf(zip_derived_cl7, plain, 0.49/0.83 (![X2 : $i]: 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((((((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ X2) => 0.49/0.83 (((??) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 (dsetconstr @ 0.49/0.83 Y0 @ 0.49/0.83 (^[Y4 : $i]: 0.49/0.83 ( 0.49/0.83 in @ 0.49/0.83 ( 0.49/0.83 kpair @ 0.49/0.83 Y2 @ Y4) @ 0.49/0.83 Y1)))) & 0.49/0.83 (((dsetconstr @ 0.49/0.83 Y0 @ 0.49/0.83 (^[Y4 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ 0.49/0.83 Y2 @ Y4) @ 0.49/0.83 Y1))) = 0.49/0.83 (setadjoin @ 0.49/0.83 Y3 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y1 @ (cartprod @ X2 @ Y0)))) => 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ X2) => 0.49/0.83 (((!!) @ (^[Y3 : $i]: 0.49/0.83 (((in @ Y3 @ 0.49/0.83 Y0) => 0.49/0.83 (((in @ 0.49/0.83 (kpair @ 0.49/0.83 Y2 @ Y3) @ 0.49/0.83 Y1) => 0.49/0.83 (((ap @ X2 @ 0.49/0.83 Y0 @ Y1 @ 0.49/0.83 Y2) = (Y3)))))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 0.49/0.83 thf(zip_derived_cl10, plain, 0.49/0.83 (![X2 : $i, X4 : $i]: 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((((((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X2) => 0.49/0.83 (((??) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y3 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ Y1 @ Y3) @ 0.49/0.83 Y0)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y3 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ Y1 @ Y3) @ 0.49/0.83 Y0))) = 0.49/0.83 (setadjoin @ Y2 @ 0.49/0.83 emptyset))))))))))))) & 0.49/0.83 (subset @ Y0 @ (cartprod @ X2 @ X4)))) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X2) => 0.49/0.83 (((!!) @ (^[Y2 : $i]: 0.49/0.83 (((in @ Y2 @ X4) => 0.49/0.83 (((in @ 0.49/0.83 (kpair @ Y1 @ Y2) @ 0.49/0.83 Y0) => 0.49/0.83 (((ap @ X2 @ X4 @ Y0 @ 0.49/0.83 Y1) = (Y2))))))))))))))))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 0.49/0.83 thf(zip_derived_cl13, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (((((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.49/0.83 (subset @ X6 @ (cartprod @ X2 @ X4)))) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1)))))))))))))))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 0.49/0.83 thf(zip_derived_cl17, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (~ (((((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.49/0.83 (subset @ X6 @ (cartprod @ X2 @ X4)))) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 0.49/0.83 thf(zip_derived_cl21, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (~ (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((??) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y2 : $i]: 0.49/0.83 (in @ (kpair @ Y0 @ Y2) @ X6))) = 0.49/0.83 (setadjoin @ Y1 @ emptyset))))))))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl17])). 0.49/0.83 thf(zip_derived_cl24, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (~ (((in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) => 0.49/0.83 (((??) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: 0.49/0.83 (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y1) @ 0.49/0.83 X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: 0.49/0.83 (in @ 0.49/0.83 (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y1) @ X6))) = 0.49/0.83 (setadjoin @ Y0 @ emptyset)))))))))) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 0.49/0.83 thf(zip_derived_cl29, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 (~ (((??) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: 0.49/0.83 (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y1) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y1 : $i]: 0.49/0.83 (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y1) @ 0.49/0.83 X6))) = 0.49/0.83 (setadjoin @ Y0 @ emptyset)))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 0.49/0.83 thf(zip_derived_cl34, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (~ (((in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) & 0.49/0.83 (((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.49/0.83 (setadjoin @ X8 @ emptyset))))) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 0.49/0.83 thf(zip_derived_cl39, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ~ (((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) = 0.49/0.83 (setadjoin @ X8 @ emptyset))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 0.49/0.83 thf(zip_derived_cl43, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl39])). 0.49/0.83 thf(zip_derived_cl44, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 ( (((in @ X10 @ X2) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X4) => 0.49/0.83 (((in @ (kpair @ X10 @ Y0) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X10) = (Y0)))))))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 0.49/0.83 thf(zip_derived_cl47, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 (~ (in @ X10 @ X2) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X4) => 0.49/0.83 (((in @ (kpair @ X10 @ Y0) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X10) = (Y0)))))))))) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 0.49/0.83 thf(zip_derived_cl49, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 0.49/0.83 ( (((in @ X12 @ X4) => 0.49/0.83 (((in @ (kpair @ X10 @ X12) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X10) = (X12))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ~ (in @ X10 @ X2))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 0.49/0.83 thf(zip_derived_cl51, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 0.49/0.83 (~ (in @ X12 @ X4) 0.49/0.83 | (((in @ (kpair @ X10 @ X12) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X10) = (X12))))) 0.49/0.83 | ~ (in @ X10 @ X2) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 0.49/0.83 thf(zip_derived_cl52, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 0.49/0.83 (~ (in @ (kpair @ X10 @ X12) @ X6) 0.49/0.83 | (((ap @ X2 @ X4 @ X6 @ X10) = (X12))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ~ (in @ X10 @ X2) 0.49/0.83 | ~ (in @ X12 @ X4))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 0.49/0.83 thf(zip_derived_cl53, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 0.49/0.83 (~ (in @ (kpair @ X10 @ X12) @ X6) 0.49/0.83 | ((ap @ X2 @ X4 @ X6 @ X10) = (X12)) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ((dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6))) 0.49/0.83 != (setadjoin @ X8 @ emptyset)) 0.49/0.83 | ~ (in @ X8 @ 0.49/0.83 (dsetconstr @ X4 @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ ('#sk5' @ X2 @ X4 @ X6) @ Y0) @ X6)))) 0.49/0.83 | ~ (in @ X10 @ X2) 0.49/0.83 | ~ (in @ X12 @ X4))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl52])). 0.49/0.83 thf(zip_derived_cl75, plain, 0.49/0.83 (![X0 : $i, X1 : $i, X2 : $i]: 0.49/0.83 (~ (in @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ~ (in @ X1 @ '#sk2') 0.49/0.83 | ~ (in @ X2 @ X0) 0.49/0.83 | ((dsetconstr @ '#sk2' @ 0.49/0.83 (^[Y0 : $i]: 0.49/0.83 (in @ (kpair @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ Y0) @ '#sk3'))) 0.49/0.83 != (setadjoin @ 0.49/0.83 ('#sk6' @ '#sk2' @ '#sk3' @ ('#sk5' @ X0 @ '#sk2' @ '#sk3')) @ 0.49/0.83 emptyset)) 0.49/0.83 | ~ (subset @ '#sk3' @ (cartprod @ X0 @ '#sk2')) 0.49/0.83 | ((ap @ X0 @ '#sk2' @ '#sk3' @ X2) = (X1)) 0.49/0.83 | ~ (in @ (kpair @ X2 @ X1) @ '#sk3'))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl53])). 0.49/0.83 thf(zip_derived_cl18, plain, ( (in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2'))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.49/0.83 thf(zip_derived_cl32, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 ( (((dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X8 @ Y0) @ X6))) = 0.49/0.83 (setadjoin @ ('#sk6' @ X4 @ X6 @ X8) @ emptyset))) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl27])). 0.49/0.83 thf(zip_derived_cl37, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (((dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X8 @ Y0) @ X6))) 0.49/0.83 = (setadjoin @ ('#sk6' @ X4 @ X6 @ X8) @ emptyset)) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl32])). 0.49/0.83 thf(zip_derived_cl56, plain, 0.49/0.83 (![X0 : $i]: 0.49/0.83 (~ (in @ X0 @ '#sk1') 0.49/0.83 | ((dsetconstr @ '#sk2' @ 0.49/0.83 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk3'))) 0.49/0.83 = (setadjoin @ ('#sk6' @ '#sk2' @ '#sk3' @ X0) @ emptyset)))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl37])). 0.49/0.83 thf(zip_derived_cl76, plain, 0.49/0.83 (![X0 : $i, X1 : $i, X2 : $i]: 0.49/0.83 (~ (in @ (kpair @ X2 @ X1) @ '#sk3') 0.49/0.83 | ((ap @ X0 @ '#sk2' @ '#sk3' @ X2) = (X1)) 0.49/0.83 | ~ (subset @ '#sk3' @ (cartprod @ X0 @ '#sk2')) 0.49/0.83 | ~ (in @ X2 @ X0) 0.49/0.83 | ~ (in @ X1 @ '#sk2') 0.49/0.83 | ~ (in @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ '#sk1'))), 0.49/0.83 inference('clc', [status(thm)], [zip_derived_cl75, zip_derived_cl56])). 0.49/0.83 thf(zip_derived_cl77, plain, 0.49/0.83 (![X0 : $i]: 0.49/0.83 (~ (in @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ~ (in @ '#sk7' @ '#sk2') 0.49/0.83 | ~ (in @ '#sk4' @ X0) 0.49/0.83 | ~ (subset @ '#sk3' @ (cartprod @ X0 @ '#sk2')) 0.49/0.83 | ((ap @ X0 @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl76])). 0.49/0.83 thf(zip_derived_cl35, plain, ( (in @ '#sk7' @ '#sk2')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 0.49/0.83 thf(zip_derived_cl79, plain, 0.49/0.83 (![X0 : $i]: 0.49/0.83 (~ (in @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ~ (in @ '#sk4' @ X0) 0.49/0.83 | ~ (subset @ '#sk3' @ (cartprod @ X0 @ '#sk2')) 0.49/0.83 | ((ap @ X0 @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))), 0.49/0.83 inference('demod', [status(thm)], [zip_derived_cl77, zip_derived_cl35])). 0.49/0.83 thf(zip_derived_cl16, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 ( (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 0.49/0.83 thf(zip_derived_cl81, plain, 0.49/0.83 (![X0 : $i]: 0.49/0.83 (((ap @ X0 @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')) 0.49/0.83 | ~ (in @ '#sk4' @ X0) 0.49/0.83 | ~ (in @ ('#sk5' @ X0 @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ~ (in @ '#sk3' @ (funcSet @ X0 @ '#sk2')))), 0.49/0.83 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl16])). 0.49/0.83 thf(zip_derived_cl41, plain, 0.49/0.83 (~ (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 0.49/0.83 thf(zip_derived_cl45, plain, 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') != ('#sk7'))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl41])). 0.49/0.83 thf(zip_derived_cl87, plain, 0.49/0.83 (((('#sk7') != ('#sk7')) 0.49/0.83 | ~ (in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2')) 0.49/0.83 | ~ (in @ ('#sk5' @ '#sk1' @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ~ (in @ '#sk4' @ '#sk1'))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl81, zip_derived_cl45])). 0.49/0.83 thf(zip_derived_cl18, plain, ( (in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2'))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.49/0.83 thf(zip_derived_cl18, plain, ( (in @ '#sk3' @ (funcSet @ '#sk1' @ '#sk2'))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.49/0.83 thf(zip_derived_cl40, plain, ( (in @ (kpair @ '#sk4' @ '#sk7') @ '#sk3')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 0.49/0.83 thf(zip_derived_cl16, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 ( (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | ~ (in @ X6 @ (funcSet @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 0.49/0.83 thf(zip_derived_cl28, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i]: 0.49/0.83 ( (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X2) => 0.49/0.83 (((!!) @ (^[Y1 : $i]: 0.49/0.83 (((in @ Y1 @ X4) => 0.49/0.83 (((in @ (kpair @ Y0 @ Y1) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ Y0) = (Y1))))))))))))))))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 0.49/0.83 thf(zip_derived_cl33, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 ( (((in @ X8 @ X2) => 0.49/0.83 (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X4) => 0.49/0.83 (((in @ (kpair @ X8 @ Y0) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X8) = (Y0)))))))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 0.49/0.83 thf(zip_derived_cl38, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.49/0.83 (~ (in @ X8 @ X2) 0.49/0.83 | (((!!) @ (^[Y0 : $i]: 0.49/0.83 (((in @ Y0 @ X4) => 0.49/0.83 (((in @ (kpair @ X8 @ Y0) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X8) = (Y0)))))))))) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 0.49/0.83 thf(zip_derived_cl42, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 ( (((in @ X10 @ X4) => 0.49/0.83 (((in @ (kpair @ X8 @ X10) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X8) = (X10))))))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (in @ X8 @ X2))), 0.49/0.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 0.49/0.83 thf(zip_derived_cl46, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 (~ (in @ X10 @ X4) 0.49/0.83 | (((in @ (kpair @ X8 @ X10) @ X6) => 0.49/0.83 (((ap @ X2 @ X4 @ X6 @ X8) = (X10))))) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 0.49/0.83 thf(zip_derived_cl48, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 (~ (in @ (kpair @ X8 @ X10) @ X6) 0.49/0.83 | (((ap @ X2 @ X4 @ X6 @ X8) = (X10))) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | ~ (in @ X10 @ X4))), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 0.49/0.83 thf(zip_derived_cl50, plain, 0.49/0.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 0.49/0.83 (~ (in @ (kpair @ X8 @ X10) @ X6) 0.49/0.83 | ((ap @ X2 @ X4 @ X6 @ X8) = (X10)) 0.49/0.83 | ~ (subset @ X6 @ (cartprod @ X2 @ X4)) 0.49/0.83 | (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 0.49/0.83 | ~ (in @ X8 @ X2) 0.49/0.83 | ~ (in @ X10 @ X4))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl48])). 0.49/0.83 thf(zip_derived_cl60, plain, 0.49/0.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]: 0.49/0.83 (~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.49/0.83 | ~ (in @ X3 @ X0) 0.49/0.83 | ~ (in @ X4 @ X1) 0.49/0.83 | (in @ ('#sk5' @ X1 @ X0 @ X2) @ X1) 0.49/0.83 | ((ap @ X1 @ X0 @ X2 @ X4) = (X3)) 0.49/0.83 | ~ (in @ (kpair @ X4 @ X3) @ X2))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl16, zip_derived_cl50])). 0.49/0.83 thf(zip_derived_cl66, plain, 0.49/0.83 (![X0 : $i, X1 : $i]: 0.49/0.83 (((ap @ X1 @ X0 @ '#sk3' @ '#sk4') = ('#sk7')) 0.49/0.83 | (in @ ('#sk5' @ X1 @ X0 @ '#sk3') @ X1) 0.49/0.83 | ~ (in @ '#sk4' @ X1) 0.49/0.83 | ~ (in @ '#sk7' @ X0) 0.49/0.83 | ~ (in @ '#sk3' @ (funcSet @ X1 @ X0)))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl60])). 0.49/0.83 thf(zip_derived_cl68, plain, 0.49/0.83 ((~ (in @ '#sk7' @ '#sk2') 0.49/0.83 | ~ (in @ '#sk4' @ '#sk1') 0.49/0.83 | (in @ ('#sk5' @ '#sk1' @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))), 0.49/0.83 inference('sup-', [status(thm)], [zip_derived_cl18, zip_derived_cl66])). 0.49/0.83 thf(zip_derived_cl35, plain, ( (in @ '#sk7' @ '#sk2')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl30])). 0.49/0.83 thf(zip_derived_cl25, plain, ( (in @ '#sk4' @ '#sk1')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.49/0.83 thf(zip_derived_cl70, plain, 0.49/0.83 (( (in @ ('#sk5' @ '#sk1' @ '#sk2' @ '#sk3') @ '#sk1') 0.49/0.83 | ((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') = ('#sk7')))), 0.49/0.83 inference('demod', [status(thm)], 0.49/0.83 [zip_derived_cl68, zip_derived_cl35, zip_derived_cl25])). 0.49/0.83 thf(zip_derived_cl45, plain, 0.49/0.83 (((ap @ '#sk1' @ '#sk2' @ '#sk3' @ '#sk4') != ('#sk7'))), 0.49/0.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl41])). 0.49/0.83 thf(zip_derived_cl71, plain, 0.49/0.83 ( (in @ ('#sk5' @ '#sk1' @ '#sk2' @ '#sk3') @ '#sk1')), 0.49/0.83 inference('simplify_reflect-', [status(thm)], 0.49/0.83 [zip_derived_cl70, zip_derived_cl45])). 0.49/0.83 thf(zip_derived_cl25, plain, ( (in @ '#sk4' @ '#sk1')), 0.49/0.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.49/0.83 thf(zip_derived_cl89, plain, ((('#sk7') != ('#sk7'))), 0.49/0.83 inference('demod', [status(thm)], 0.49/0.83 [zip_derived_cl87, zip_derived_cl18, zip_derived_cl71, 0.49/0.83 zip_derived_cl25])). 0.49/0.83 thf(zip_derived_cl90, plain, ($false), 0.49/0.83 inference('simplify', [status(thm)], [zip_derived_cl89])). 0.49/0.83 0.49/0.83 % SZS output end Refutation 0.49/0.83 0.49/0.83 0.49/0.83 % Terminating... 0.52/0.92 % Runner terminated. 2.48/0.93 % Zipperpin 1.5 exiting 2.48/0.93 EOF