0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ZWchboc2ae true 0.12/0.34 % Computer : n019.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 04:20:35 EDT 2023 0.12/0.34 % CPUTime : 0.12/0.34 % Running portfolio for 1440 s 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.19/0.35 % Python version: Python 3.6.8 0.19/0.35 % Running in HO mode 0.49/0.63 % Total configuration time : 828 0.49/0.63 % Estimated wc time : 1656 0.49/0.63 % Estimated cpu time (8 cpus) : 207.0 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.86 % Solved by lams/35_full_unif4.sh. 0.55/0.86 % done 26 iterations in 0.068s 0.55/0.86 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.55/0.86 % SZS output start Refutation 0.55/0.86 thf(singleton_type, type, singleton: $i > $o). 0.55/0.86 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 0.55/0.86 thf(kpair_type, type, kpair: $i > $i > $i). 0.55/0.86 thf(in_type, type, in: $i > $i > $o). 0.55/0.86 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 0.55/0.86 thf('#sk2_type', type, '#sk2': $i). 0.55/0.86 thf(func_type, type, func: $i > $i > $i > $o). 0.55/0.86 thf('#sk18_type', type, '#sk18': $i > $i > $i > $i). 0.55/0.86 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 0.55/0.86 thf(funcSet_type, type, funcSet: $i > $i > $i). 0.55/0.86 thf(dsetconstrER_type, type, dsetconstrER: $o). 0.55/0.86 thf(powerset_type, type, powerset: $i > $i). 0.55/0.86 thf('#sk1_type', type, '#sk1': $i). 0.55/0.86 thf(subset_type, type, subset: $i > $i > $o). 0.55/0.86 thf('#sk5_type', type, '#sk5': $i). 0.55/0.86 thf(emptyset_type, type, emptyset: $i). 0.55/0.86 thf('#sk8_type', type, '#sk8': $i). 0.55/0.86 thf(breln_type, type, breln: $i > $i > $i > $o). 0.55/0.86 thf(cartprod_type, type, cartprod: $i > $i > $i). 0.55/0.86 thf(func, axiom,(( func ) = 0.55/0.86 (^[A:$i,B:$i,R:$i]: 0.55/0.86 ( ( breln @ A @ B @ R ) & 0.55/0.86 ( ![Xx:$i]: 0.55/0.86 ( ( in @ Xx @ A ) => 0.55/0.86 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 0.55/0.86 thf(breln, axiom,(( breln ) = 0.55/0.86 (^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) )))). 0.55/0.86 thf('0', plain, 0.55/0.86 (( breln ) = ( ^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) ) )), 0.55/0.86 inference('simplify_rw_rule', [status(thm)], [breln])). 0.55/0.86 thf('1', plain, 0.55/0.86 (( breln ) = 0.55/0.86 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) )), 0.55/0.86 define([status(thm)])). 0.55/0.86 thf(ex1, axiom,(( ex1 ) = 0.55/0.86 (^[A:$i,Xphi:( $i > $o )]: 0.55/0.86 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))). 0.55/0.86 thf(singleton, axiom,(( singleton ) = 0.55/0.86 (^[A:$i]: 0.55/0.86 ( ?[Xx:$i]: 0.55/0.86 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 0.55/0.86 thf('2', plain, 0.55/0.86 (( singleton ) = 0.55/0.86 ( ^[A:$i]: 0.55/0.86 ( ?[Xx:$i]: 0.55/0.86 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 0.55/0.86 inference('simplify_rw_rule', [status(thm)], [singleton])). 0.55/0.86 thf('3', plain, 0.55/0.86 (( singleton ) = 0.55/0.86 ( ^[V_1:$i]: 0.55/0.86 ( ?[X4:$i]: 0.55/0.86 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 0.55/0.86 define([status(thm)])). 0.55/0.86 thf('4', plain, 0.55/0.86 (( ex1 ) = 0.55/0.86 ( ^[A:$i,Xphi:( $i > $o )]: 0.55/0.86 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )), 0.55/0.86 inference('simplify_rw_rule', [status(thm)], [ex1, '3'])). 0.55/0.86 thf('5', plain, 0.55/0.86 (( ex1 ) = 0.55/0.86 ( ^[V_1:$i,V_2:( $i > $o )]: 0.55/0.86 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )), 0.55/0.86 define([status(thm)])). 0.55/0.86 thf('6', plain, 0.55/0.86 (( func ) = 0.55/0.86 ( ^[A:$i,B:$i,R:$i]: 0.55/0.86 ( ( breln @ A @ B @ R ) & 0.55/0.86 ( ![Xx:$i]: 0.55/0.86 ( ( in @ Xx @ A ) => 0.55/0.86 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 0.55/0.86 inference('simplify_rw_rule', [status(thm)], [func, '1', '5', '3'])). 0.55/0.86 thf('7', plain, 0.55/0.86 (( func ) = 0.55/0.86 ( ^[V_1:$i,V_2:$i,V_3:$i]: 0.55/0.86 ( ( breln @ V_1 @ V_2 @ V_3 ) & 0.55/0.86 ( ![X4:$i]: 0.55/0.86 ( ( in @ X4 @ V_1 ) => 0.55/0.86 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 0.55/0.86 define([status(thm)])). 0.55/0.86 thf(funcSet, axiom, 0.55/0.86 (( funcSet ) = 0.55/0.86 ( ^[A:$i,B:$i]: 0.55/0.86 ( dsetconstr @ 0.55/0.86 ( powerset @ ( cartprod @ A @ B ) ) @ 0.55/0.86 ( ^[Xf:$i]: ( func @ A @ B @ Xf ) ) ) ))). 0.55/0.86 thf(zf_stmt_0, axiom, 0.55/0.86 (( funcSet ) = 0.55/0.86 ( ^[V_1:$i,V_2:$i]: 0.55/0.86 ( dsetconstr @ 0.55/0.86 ( powerset @ ( cartprod @ V_1 @ V_2 ) ) @ 0.55/0.86 ( ^[V_3:$i]: 0.55/0.86 ( ( ![X4:$i]: 0.55/0.86 ( ( in @ X4 @ V_1 ) => 0.55/0.86 ( ?[X6:$i]: 0.55/0.86 ( ( in @ 0.55/0.86 X6 @ 0.55/0.86 ( dsetconstr @ 0.55/0.86 V_2 @ 0.55/0.86 ( ^[V_5:$i]: ( in @ ( kpair @ X4 @ V_5 ) @ V_3 ) ) ) ) & 0.55/0.86 ( ( dsetconstr @ 0.55/0.86 V_2 @ 0.55/0.86 ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) = 0.55/0.86 ( setadjoin @ X6 @ emptyset ) ) ) ) ) ) & 0.55/0.86 ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ) ) ))). 0.55/0.86 thf(zip_derived_cl0, plain, 0.55/0.86 (((funcSet) 0.55/0.86 = ((^[Y0 : $i,Y1 : $i]: 0.55/0.86 (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (((((!!) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ Y0) => 0.55/0.86 (((??) @ (^[Y4 : $i]: 0.55/0.86 (((in @ Y4 @ 0.55/0.86 (dsetconstr @ Y1 @ 0.55/0.86 (^[Y5 : $i]: 0.55/0.86 (in @ (kpair @ Y3 @ Y5) @ 0.55/0.86 Y2)))) & 0.55/0.86 (((dsetconstr @ Y1 @ 0.55/0.86 (^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y3 @ Y5) @ Y2))) = 0.55/0.86 (setadjoin @ Y4 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y2 @ (cartprod @ Y0 @ Y1)))))))))), 0.55/0.86 inference('cnf', [status(esa)], [zf_stmt_0])). 0.55/0.86 thf(zip_derived_cl3, plain, 0.55/0.86 (![X1 : $i, X2 : $i]: 0.55/0.86 ((funcSet @ X1 @ X2) 0.55/0.86 = ((^[Y0 : $i,Y1 : $i]: 0.55/0.86 (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (((((!!) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ Y0) => 0.55/0.86 (((??) @ (^[Y4 : $i]: 0.55/0.86 (((in @ Y4 @ 0.55/0.86 (dsetconstr @ Y1 @ 0.55/0.86 (^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y3 @ Y5) @ Y2)))) & 0.55/0.86 (((dsetconstr @ Y1 @ 0.55/0.86 (^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y3 @ Y5) @ Y2))) = 0.55/0.86 (setadjoin @ Y4 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ 0.55/0.86 X1 @ X2))), 0.55/0.86 inference('ho_complete_eq', [status(thm)], [zip_derived_cl0])). 0.55/0.86 thf(zip_derived_cl5, plain, 0.55/0.86 (![X1 : $i, X2 : $i]: 0.55/0.86 ((funcSet @ X1 @ X2) 0.55/0.86 = (dsetconstr @ (powerset @ (cartprod @ X1 @ X2)) @ 0.55/0.86 (^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0)))) & 0.55/0.86 (((dsetconstr @ X2 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X2)))))))), 0.55/0.86 inference('ho_norm', [status(thm)], [zip_derived_cl3])). 0.55/0.86 thf(dsetconstrER, axiom, dsetconstrER = 0.55/0.86 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 0.55/0.86 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 0.55/0.86 ( Xphi @ Xx ) ))). 0.55/0.86 thf('8', plain, 0.55/0.86 (( dsetconstrER ) = 0.55/0.86 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.55/0.86 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.55/0.86 ( X6 @ X8 ) ) )), 0.55/0.86 define([status(thm)])). 0.55/0.86 thf(infuncsetfunc, conjecture, 0.55/0.86 (( dsetconstrER ) => 0.55/0.86 ( ![A:$i,B:$i,Xf:$i]: 0.55/0.86 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => ( func @ A @ B @ Xf ) ) ))). 0.55/0.86 thf(zf_stmt_1, conjecture, 0.55/0.86 (( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.55/0.86 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.55/0.86 ( X6 @ X8 ) ) ) => 0.55/0.86 ( ![X10:$i,X12:$i,X14:$i]: 0.55/0.86 ( ( in @ X14 @ ( funcSet @ X10 @ X12 ) ) => 0.55/0.86 ( ( ![X16:$i]: 0.55/0.86 ( ( in @ X16 @ X10 ) => 0.55/0.86 ( ?[X18:$i]: 0.55/0.86 ( ( in @ 0.55/0.86 X18 @ 0.55/0.86 ( dsetconstr @ 0.55/0.86 X12 @ 0.55/0.86 ( ^[V_3:$i]: ( in @ ( kpair @ X16 @ V_3 ) @ X14 ) ) ) ) & 0.55/0.86 ( ( dsetconstr @ 0.55/0.86 X12 @ 0.55/0.86 ( ^[V_2:$i]: ( in @ ( kpair @ X16 @ V_2 ) @ X14 ) ) ) = 0.55/0.86 ( setadjoin @ X18 @ emptyset ) ) ) ) ) ) & 0.55/0.86 ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ))). 0.55/0.86 thf(zf_stmt_2, negated_conjecture, 0.55/0.86 (~( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.55/0.86 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.55/0.86 ( X6 @ X8 ) ) ) => 0.55/0.86 ( ![X10:$i,X12:$i,X14:$i]: 0.55/0.86 ( ( in @ X14 @ ( funcSet @ X10 @ X12 ) ) => 0.55/0.86 ( ( ![X16:$i]: 0.55/0.86 ( ( in @ X16 @ X10 ) => 0.55/0.86 ( ?[X18:$i]: 0.55/0.86 ( ( in @ 0.55/0.86 X18 @ 0.55/0.86 ( dsetconstr @ 0.55/0.86 X12 @ 0.55/0.86 ( ^[V_3:$i]: ( in @ ( kpair @ X16 @ V_3 ) @ X14 ) ) ) ) & 0.55/0.86 ( ( dsetconstr @ 0.55/0.86 X12 @ 0.55/0.86 ( ^[V_2:$i]: ( in @ ( kpair @ X16 @ V_2 ) @ X14 ) ) ) = 0.55/0.86 ( setadjoin @ X18 @ emptyset ) ) ) ) ) ) & 0.55/0.86 ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ) )), 0.55/0.86 inference('cnf.neg', [status(esa)], [zf_stmt_1])). 0.55/0.86 thf(zip_derived_cl1, plain, 0.55/0.86 (~ (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ Y0 @ 0.55/0.86 (^[Y3 : $i]: (Y1 @ Y3)))) => 0.55/0.86 (Y1 @ Y2)))))))))))) => 0.55/0.86 (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (funcSet @ Y0 @ Y1)) => 0.55/0.86 (((((!!) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ 0.55/0.86 Y0) => 0.55/0.86 (((??) @ ( 0.55/0.86 ^[Y4 : $i]: 0.55/0.86 (( 0.55/0.86 (in @ 0.55/0.86 Y4 @ 0.55/0.86 ( 0.55/0.86 dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 ( 0.55/0.86 ^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2)))) & 0.55/0.86 (( 0.55/0.86 (dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 ( 0.55/0.86 ^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2))) = 0.55/0.86 (setadjoin @ 0.55/0.86 Y4 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y2 @ 0.55/0.86 (cartprod @ Y0 @ Y1)))))))))))))))))), 0.55/0.86 inference('cnf', [status(esa)], [zf_stmt_2])). 0.55/0.86 thf(zip_derived_cl8, plain, 0.55/0.86 (~ (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ Y0 @ Y1)) => 0.55/0.86 (Y1 @ Y2)))))))))))) => 0.55/0.86 (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (funcSet @ Y0 @ Y1)) => 0.55/0.86 (((((!!) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ 0.55/0.86 Y0) => 0.55/0.86 (((??) @ ( 0.55/0.86 ^[Y4 : $i]: 0.55/0.86 (( 0.55/0.86 (in @ 0.55/0.86 Y4 @ 0.55/0.86 ( 0.55/0.86 dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 ( 0.55/0.86 ^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2)))) & 0.55/0.86 (( 0.55/0.86 (dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 ( 0.55/0.86 ^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2))) = 0.55/0.86 (setadjoin @ 0.55/0.86 Y4 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y2 @ 0.55/0.86 (cartprod @ Y0 @ Y1)))))))))))))))))), 0.55/0.86 inference('ho_norm', [status(thm)], [zip_derived_cl1])). 0.55/0.86 thf(zip_derived_cl9, plain, 0.55/0.86 ( (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ Y0 @ Y1)) => (Y1 @ 0.55/0.86 Y2))))))))))))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 0.55/0.86 thf(zip_derived_cl11, plain, 0.55/0.86 (![X2 : $i]: 0.55/0.86 (((!!) @ (^[Y0 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ (dsetconstr @ X2 @ Y0)) => 0.55/0.86 (Y0 @ Y1)))))))))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 0.55/0.86 thf(zip_derived_cl13, plain, 0.55/0.86 (![X2 : $i, X4 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) => (X4 @ Y0))))))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 0.55/0.86 thf(zip_derived_cl14, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y1 : $i]: 0.55/0.86 (((((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ X1) => 0.55/0.86 (((??) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y4 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y2 @ Y4) @ 0.55/0.86 Y1)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y4 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y2 @ 0.55/0.86 Y4) @ 0.55/0.86 Y1))) = 0.55/0.86 (setadjoin @ Y3 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y1 @ (cartprod @ X1 @ X0))))))) => 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X0)))))))))), 0.55/0.86 inference('triggered_bool_instantiation', [status(thm)], 0.55/0.86 [zip_derived_cl13])). 0.55/0.86 thf(zip_derived_cl57, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 (((in @ X4 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X0))))))) => 0.55/0.86 (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ X1) => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X4)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X4))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.55/0.86 (subset @ X4 @ (cartprod @ X1 @ X0))))))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 0.55/0.86 thf(zip_derived_cl58, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 (~ (in @ X4 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X0))))))) 0.55/0.86 | (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ X1) => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X4)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X4))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.55/0.86 (subset @ X4 @ (cartprod @ X1 @ X0)))))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 0.55/0.86 thf(zip_derived_cl60, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 ( (subset @ X4 @ (cartprod @ X1 @ X0)) 0.55/0.86 | ~ (in @ X4 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y1 @ Y3) @ Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X0))))))))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl58])). 0.55/0.86 thf(zip_derived_cl67, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 (~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.55/0.86 | (subset @ X2 @ (cartprod @ X1 @ X0)))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl60])). 0.55/0.86 thf(zip_derived_cl10, plain, 0.55/0.86 (~ (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i]: 0.55/0.86 (((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (funcSet @ Y0 @ Y1)) => 0.55/0.86 (((((!!) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ 0.55/0.86 Y0) => 0.55/0.86 (((??) @ ( 0.55/0.86 ^[Y4 : $i]: 0.55/0.86 (((in @ 0.55/0.86 Y4 @ 0.55/0.86 (dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 ( 0.55/0.86 ^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2)))) & 0.55/0.86 (( 0.55/0.86 (dsetconstr @ 0.55/0.86 Y1 @ 0.55/0.86 (^[Y5 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ 0.55/0.86 Y3 @ Y5) @ 0.55/0.86 Y2))) = 0.55/0.86 (setadjoin @ 0.55/0.86 Y4 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y2 @ 0.55/0.86 (cartprod @ Y0 @ Y1)))))))))))))))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 0.55/0.86 thf(zip_derived_cl12, plain, 0.55/0.86 (~ (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ (funcSet @ '#sk1' @ Y0)) => 0.55/0.86 (((((!!) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ '#sk1') => 0.55/0.86 (((??) @ (^[Y3 : $i]: 0.55/0.86 (((in @ Y3 @ 0.55/0.86 (dsetconstr @ 0.55/0.86 Y0 @ 0.55/0.86 (^[Y4 : $i]: 0.55/0.86 (in @ 0.55/0.86 ( 0.55/0.86 kpair @ 0.55/0.86 Y2 @ Y4) @ 0.55/0.86 Y1)))) & 0.55/0.86 (((dsetconstr @ 0.55/0.86 Y0 @ 0.55/0.86 (^[Y4 : $i]: 0.55/0.86 ( 0.55/0.86 in @ 0.55/0.86 ( 0.55/0.86 kpair @ 0.55/0.86 Y2 @ Y4) @ 0.55/0.86 Y1))) = 0.55/0.86 (setadjoin @ 0.55/0.86 Y3 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y1 @ (cartprod @ '#sk1' @ Y0))))))))))))), 0.55/0.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 0.55/0.86 thf(zip_derived_cl15, plain, 0.55/0.86 (~ (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ (funcSet @ '#sk1' @ '#sk2')) => 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ '#sk1') => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0)))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ 0.55/0.86 (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ 0.55/0.86 emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ '#sk1' @ '#sk2')))))))))), 0.55/0.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 0.55/0.86 thf(zip_derived_cl17, plain, 0.55/0.86 (~ (((in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2')) => 0.55/0.86 (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ '#sk1') => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5'))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.55/0.86 (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2'))))))), 0.55/0.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 0.55/0.86 thf(zip_derived_cl19, plain, ( (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 0.55/0.86 thf(zip_derived_cl5, plain, 0.55/0.86 (![X1 : $i, X2 : $i]: 0.55/0.86 ((funcSet @ X1 @ X2) 0.55/0.86 = (dsetconstr @ (powerset @ (cartprod @ X1 @ X2)) @ 0.55/0.86 (^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X2 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0)))) & 0.55/0.86 (((dsetconstr @ X2 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X2)))))))), 0.55/0.86 inference('ho_norm', [status(thm)], [zip_derived_cl3])). 0.55/0.86 thf(zip_derived_cl13, plain, 0.55/0.86 (![X2 : $i, X4 : $i > $o]: 0.55/0.86 (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) => (X4 @ Y0))))))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 0.55/0.86 thf(zip_derived_cl16, plain, 0.55/0.86 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.55/0.86 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (X4 @ X6)))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 0.55/0.86 thf(zip_derived_cl18, plain, 0.55/0.86 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.55/0.86 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (X4 @ X6))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 0.55/0.86 thf(zip_derived_cl28, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 (~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.55/0.86 | ((^[Y0 : $i]: 0.55/0.86 (((((!!) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ X1) => 0.55/0.86 (((??) @ (^[Y2 : $i]: 0.55/0.86 (((in @ Y2 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ Y0)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y3 : $i]: 0.55/0.86 (in @ (kpair @ Y1 @ Y3) @ 0.55/0.86 Y0))) = 0.55/0.86 (setadjoin @ Y2 @ emptyset))))))))))))) & 0.55/0.86 (subset @ Y0 @ (cartprod @ X1 @ X0))))) @ 0.55/0.86 X2))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl18])). 0.55/0.86 thf(zip_derived_cl37, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 (~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.55/0.86 | (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ X1) => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X2)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X2))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.55/0.86 (subset @ X2 @ (cartprod @ X1 @ X0)))))), 0.55/0.86 inference('ho_norm', [status(thm)], [zip_derived_cl28])). 0.55/0.86 thf(zip_derived_cl76, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 ( (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ X1) => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X2)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ X2))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 0.55/0.86 thf(zip_derived_cl78, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 ( (((in @ X4 @ X1) => 0.55/0.86 (((??) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X2)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X2))) = 0.55/0.86 (setadjoin @ Y0 @ emptyset)))))))))) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])). 0.55/0.86 thf(zip_derived_cl79, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 (~ (in @ X4 @ X1) 0.55/0.86 | (((??) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ 0.55/0.86 (dsetconstr @ X0 @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X2)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X2))) = 0.55/0.86 (setadjoin @ Y0 @ emptyset)))))))) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 0.55/0.86 thf(zip_derived_cl80, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 ( (((in @ ('#sk18' @ X0 @ X2 @ X4) @ 0.55/0.86 (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X2)))) & 0.55/0.86 (((dsetconstr @ X0 @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X2))) = (setadjoin @ 0.55/0.86 ('#sk18' @ X0 @ X2 @ X4) @ emptyset))))) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.55/0.86 | ~ (in @ X4 @ X1))), 0.55/0.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl79])). 0.55/0.86 thf(zip_derived_cl82, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 ( (((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X2))) = 0.55/0.86 (setadjoin @ ('#sk18' @ X0 @ X2 @ X4) @ emptyset))) 0.55/0.86 | ~ (in @ X4 @ X1) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl80])). 0.55/0.86 thf(zip_derived_cl83, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 (((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X2))) 0.55/0.86 = (setadjoin @ ('#sk18' @ X0 @ X2 @ X4) @ emptyset)) 0.55/0.86 | ~ (in @ X4 @ X1) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('simplify nested equalities', [status(thm)], [zip_derived_cl82])). 0.55/0.86 thf(zip_derived_cl92, plain, 0.55/0.86 (![X0 : $i]: 0.55/0.86 (~ (in @ X0 @ '#sk1') 0.55/0.86 | ((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk5'))) 0.55/0.86 = (setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ X0) @ emptyset)))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl83])). 0.55/0.86 thf(zip_derived_cl20, plain, 0.55/0.86 (~ (((((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ '#sk1') => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5'))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) & 0.55/0.86 (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2'))))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 0.55/0.86 thf(zip_derived_cl21, plain, 0.55/0.86 ((~ (((!!) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ '#sk1') => 0.55/0.86 (((??) @ (^[Y1 : $i]: 0.55/0.86 (((in @ Y1 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y2 : $i]: 0.55/0.86 (in @ (kpair @ Y0 @ Y2) @ '#sk5'))) = 0.55/0.86 (setadjoin @ Y1 @ emptyset))))))))))))) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])). 0.55/0.86 thf(zip_derived_cl22, plain, 0.55/0.86 ((~ (((in @ '#sk8' @ '#sk1') => 0.55/0.86 (((??) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ '#sk8' @ Y1) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ '#sk8' @ Y1) @ '#sk5'))) = 0.55/0.86 (setadjoin @ Y0 @ emptyset)))))))))) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl21])). 0.55/0.86 thf(zip_derived_cl24, plain, 0.55/0.86 ((~ (((??) @ (^[Y0 : $i]: 0.55/0.86 (((in @ Y0 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ '#sk8' @ Y1) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y1 : $i]: (in @ (kpair @ '#sk8' @ Y1) @ '#sk5'))) = 0.55/0.86 (setadjoin @ Y0 @ emptyset)))))))) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.55/0.86 thf(zip_derived_cl25, plain, 0.55/0.86 (![X2 : $i]: 0.55/0.86 (~ (((in @ X2 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5')))) & 0.55/0.86 (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5'))) = 0.55/0.86 (setadjoin @ X2 @ emptyset))))) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 0.55/0.86 thf(zip_derived_cl26, plain, 0.55/0.86 (![X2 : $i]: 0.55/0.86 (~ (in @ X2 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5')))) 0.55/0.86 | ~ (((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5'))) = 0.55/0.86 (setadjoin @ X2 @ emptyset))) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 0.55/0.86 thf(zip_derived_cl27, plain, 0.55/0.86 (![X2 : $i]: 0.55/0.86 (~ (in @ X2 @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5')))) 0.55/0.86 | ((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5'))) 0.55/0.86 != (setadjoin @ X2 @ emptyset)) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('simplify nested equalities', [status(thm)], [zip_derived_cl26])). 0.55/0.86 thf(zip_derived_cl19, plain, ( (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 0.55/0.86 thf(zip_derived_cl81, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 0.55/0.86 ( (in @ ('#sk18' @ X0 @ X2 @ X4) @ 0.55/0.86 (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X2)))) 0.55/0.86 | ~ (in @ X4 @ X1) 0.55/0.86 | ~ (in @ X2 @ (funcSet @ X1 @ X0)))), 0.55/0.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl80])). 0.55/0.86 thf(zip_derived_cl84, plain, 0.55/0.86 (![X0 : $i]: 0.55/0.86 (~ (in @ X0 @ '#sk1') 0.55/0.86 | (in @ ('#sk18' @ '#sk2' @ '#sk5' @ X0) @ 0.55/0.86 (dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ '#sk5')))))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl81])). 0.55/0.86 thf(zip_derived_cl88, plain, 0.55/0.86 ((~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')) 0.55/0.86 | ((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5'))) 0.55/0.86 != (setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset)) 0.55/0.86 | ~ (in @ '#sk8' @ '#sk1'))), 0.55/0.86 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl84])). 0.55/0.86 thf(zip_derived_cl23, plain, 0.55/0.86 (( (in @ '#sk8' @ '#sk1') 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 0.55/0.86 thf(zip_derived_cl67, plain, 0.55/0.86 (![X0 : $i, X1 : $i, X2 : $i]: 0.55/0.86 (~ (in @ X2 @ (funcSet @ X1 @ X0)) 0.55/0.86 | (subset @ X2 @ (cartprod @ X1 @ X0)))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl60])). 0.55/0.86 thf(zip_derived_cl69, plain, 0.55/0.86 (( (in @ '#sk8' @ '#sk1') | ~ (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl67])). 0.55/0.86 thf(zip_derived_cl19, plain, ( (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 0.55/0.86 thf(zip_derived_cl72, plain, ( (in @ '#sk8' @ '#sk1')), 0.55/0.86 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl19])). 0.55/0.86 thf(zip_derived_cl89, plain, 0.55/0.86 ((~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')) 0.55/0.86 | ((dsetconstr @ '#sk2' @ 0.55/0.86 (^[Y0 : $i]: (in @ (kpair @ '#sk8' @ Y0) @ '#sk5'))) 0.55/0.86 != (setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset)))), 0.55/0.86 inference('demod', [status(thm)], [zip_derived_cl88, zip_derived_cl72])). 0.55/0.86 thf(zip_derived_cl95, plain, 0.55/0.86 ((((setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset) 0.55/0.86 != (setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset)) 0.55/0.86 | ~ (in @ '#sk8' @ '#sk1') 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl89])). 0.55/0.86 thf(zip_derived_cl72, plain, ( (in @ '#sk8' @ '#sk1')), 0.55/0.86 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl19])). 0.55/0.86 thf(zip_derived_cl99, plain, 0.55/0.86 ((((setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset) 0.55/0.86 != (setadjoin @ ('#sk18' @ '#sk2' @ '#sk5' @ '#sk8') @ emptyset)) 0.55/0.86 | ~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2')))), 0.55/0.86 inference('demod', [status(thm)], [zip_derived_cl95, zip_derived_cl72])). 0.55/0.86 thf(zip_derived_cl100, plain, 0.55/0.86 (~ (subset @ '#sk5' @ (cartprod @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('simplify', [status(thm)], [zip_derived_cl99])). 0.55/0.86 thf(zip_derived_cl105, plain, 0.55/0.86 (~ (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl100])). 0.55/0.86 thf(zip_derived_cl19, plain, ( (in @ '#sk5' @ (funcSet @ '#sk1' @ '#sk2'))), 0.55/0.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 0.55/0.86 thf(zip_derived_cl108, plain, ($false), 0.55/0.86 inference('demod', [status(thm)], [zip_derived_cl105, zip_derived_cl19])). 0.55/0.86 0.55/0.86 % SZS output end Refutation 0.55/0.86 0.55/0.86 0.55/0.86 % Terminating... 1.34/0.94 % Runner terminated. 2.08/0.95 % Zipperpin 1.5 exiting 2.08/0.95 EOF