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.5LEAis2mkL true 0.13/0.34 % Computer : n020.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 06:22:50 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.48/0.63 % Total configuration time : 828 0.48/0.63 % Estimated wc time : 1656 0.48/0.63 % Estimated cpu time (8 cpus) : 207.0 0.50/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.50/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 50.80/7.01 % Solved by lams/20_acsne_simpl.sh. 50.80/7.01 % done 3606 iterations in 6.181s 50.80/7.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.80/7.01 % SZS output start Refutation 50.80/7.01 thf('#sk5_type', type, '#sk5': $i > $i > $i > $i). 50.80/7.01 thf(in_type, type, in: $i > $i > $o). 50.80/7.01 thf(subbreln1_type, type, subbreln1: $o). 50.80/7.01 thf('#sk3_type', type, '#sk3': $i > $i > $i > $i). 50.80/7.01 thf(breln1unionIR_type, type, breln1unionIR: $o). 50.80/7.01 thf(breln1unionIL_type, type, breln1unionIL: $o). 50.80/7.01 thf(setextsub_type, type, setextsub: $o). 50.80/7.01 thf(kpair_type, type, kpair: $i > $i > $i). 50.80/7.01 thf(breln1_type, type, breln1: $i > $i > $o). 50.80/7.01 thf(breln1unionE_type, type, breln1unionE: $o). 50.80/7.01 thf('#sk1_type', type, '#sk1': $i). 50.80/7.01 thf(binunion_type, type, binunion: $i > $i > $i). 50.80/7.01 thf('#sk2_type', type, '#sk2': $i). 50.80/7.01 thf(subset_type, type, subset: $i > $i > $o). 50.80/7.01 thf('#sk4_type', type, '#sk4': $i). 50.80/7.01 thf(breln1unionprop_type, type, breln1unionprop: $o). 50.80/7.01 thf(breln1unionE, axiom, breln1unionE = 50.80/7.01 (![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => 50.80/7.01 ( ![Xx:$i]: 50.80/7.01 ( ( in @ Xx @ A ) => 50.80/7.01 ( ![Xy:$i]: 50.80/7.01 ( ( in @ Xy @ A ) => 50.80/7.01 ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) => 50.80/7.01 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) | 50.80/7.01 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ))). 50.80/7.01 thf('0', plain, 50.80/7.01 (( breln1unionE ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X6 ) => 50.80/7.01 ( ![X8:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X8 ) => 50.80/7.01 ( ![X10:$i]: 50.80/7.01 ( ( in @ X10 @ X4 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( in @ X12 @ X4 ) => 50.80/7.01 ( ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) => 50.80/7.01 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) | 50.80/7.01 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(breln1unionIR, axiom, breln1unionIR = 50.80/7.01 (![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => 50.80/7.01 ( ![Xx:$i]: 50.80/7.01 ( ( in @ Xx @ A ) => 50.80/7.01 ( ![Xy:$i]: 50.80/7.01 ( ( in @ Xy @ A ) => 50.80/7.01 ( ( in @ ( kpair @ Xx @ Xy ) @ S ) => 50.80/7.01 ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ))). 50.80/7.01 thf('1', plain, 50.80/7.01 (( breln1unionIR ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X6 ) => 50.80/7.01 ( ![X8:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X8 ) => 50.80/7.01 ( ![X10:$i]: 50.80/7.01 ( ( in @ X10 @ X4 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( in @ X12 @ X4 ) => 50.80/7.01 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) => 50.80/7.01 ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(breln1unionIL, axiom, breln1unionIL = 50.80/7.01 (![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => 50.80/7.01 ( ![Xx:$i]: 50.80/7.01 ( ( in @ Xx @ A ) => 50.80/7.01 ( ![Xy:$i]: 50.80/7.01 ( ( in @ Xy @ A ) => 50.80/7.01 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) => 50.80/7.01 ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ))). 50.80/7.01 thf('2', plain, 50.80/7.01 (( breln1unionIL ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X6 ) => 50.80/7.01 ( ![X8:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X8 ) => 50.80/7.01 ( ![X10:$i]: 50.80/7.01 ( ( in @ X10 @ X4 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( in @ X12 @ X4 ) => 50.80/7.01 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) => 50.80/7.01 ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(breln1unionprop, axiom, breln1unionprop = 50.80/7.01 (![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ))). 50.80/7.01 thf('3', plain, 50.80/7.01 (( breln1unionprop ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X6 ) => 50.80/7.01 ( ![X8:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X8 ) => ( breln1 @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(subbreln1, axiom, subbreln1 = 50.80/7.01 (![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => 50.80/7.01 ( ( ![Xx:$i]: 50.80/7.01 ( ( in @ Xx @ A ) => 50.80/7.01 ( ![Xy:$i]: 50.80/7.01 ( ( in @ Xy @ A ) => 50.80/7.01 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) => 50.80/7.01 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) => 50.80/7.01 ( subset @ R @ S ) ) ) ) ))). 50.80/7.01 thf('4', plain, 50.80/7.01 (( subbreln1 ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X6 ) => 50.80/7.01 ( ![X8:$i]: 50.80/7.01 ( ( breln1 @ X4 @ X8 ) => 50.80/7.01 ( ( ![X10:$i]: 50.80/7.01 ( ( in @ X10 @ X4 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( in @ X12 @ X4 ) => 50.80/7.01 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) => 50.80/7.01 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) => 50.80/7.01 ( subset @ X6 @ X8 ) ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(setextsub, axiom, setextsub = 50.80/7.01 (![A:$i,B:$i]: 50.80/7.01 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))). 50.80/7.01 thf('5', plain, 50.80/7.01 (( setextsub ) = 50.80/7.01 ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( subset @ X4 @ X6 ) => 50.80/7.01 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )), 50.80/7.01 define([status(thm)])). 50.80/7.01 thf(breln1unionCommutes, conjecture, 50.80/7.01 (( setextsub ) => 50.80/7.01 ( ( subbreln1 ) => 50.80/7.01 ( ( breln1unionprop ) => 50.80/7.01 ( ( breln1unionIL ) => 50.80/7.01 ( ( breln1unionIR ) => 50.80/7.01 ( ( breln1unionE ) => 50.80/7.01 ( ![A:$i,R:$i]: 50.80/7.01 ( ( breln1 @ A @ R ) => 50.80/7.01 ( ![S:$i]: 50.80/7.01 ( ( breln1 @ A @ S ) => 50.80/7.01 ( ( binunion @ R @ S ) = ( binunion @ S @ R ) ) ) ) ) ) ) ) ) ) ))). 50.80/7.01 thf(zf_stmt_0, conjecture, 50.80/7.01 (( ![X4:$i,X6:$i]: 50.80/7.01 ( ( subset @ X4 @ X6 ) => 50.80/7.01 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) ) => 50.80/7.01 ( ( ![X8:$i,X10:$i]: 50.80/7.01 ( ( breln1 @ X8 @ X10 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( breln1 @ X8 @ X12 ) => 50.80/7.01 ( ( ![X14:$i]: 50.80/7.01 ( ( in @ X14 @ X8 ) => 50.80/7.01 ( ![X16:$i]: 50.80/7.01 ( ( in @ X16 @ X8 ) => 50.80/7.01 ( ( in @ ( kpair @ X14 @ X16 ) @ X10 ) => 50.80/7.01 ( in @ ( kpair @ X14 @ X16 ) @ X12 ) ) ) ) ) ) => 50.80/7.01 ( subset @ X10 @ X12 ) ) ) ) ) ) => 50.80/7.01 ( ( ![X18:$i,X20:$i]: 50.80/7.01 ( ( breln1 @ X18 @ X20 ) => 50.80/7.01 ( ![X22:$i]: 50.80/7.01 ( ( breln1 @ X18 @ X22 ) => 50.80/7.01 ( breln1 @ X18 @ ( binunion @ X20 @ X22 ) ) ) ) ) ) => 50.80/7.01 ( ( ![X24:$i,X26:$i]: 50.80/7.01 ( ( breln1 @ X24 @ X26 ) => 50.80/7.01 ( ![X28:$i]: 50.80/7.01 ( ( breln1 @ X24 @ X28 ) => 50.80/7.01 ( ![X30:$i]: 50.80/7.01 ( ( in @ X30 @ X24 ) => 50.80/7.01 ( ![X32:$i]: 50.80/7.01 ( ( in @ X32 @ X24 ) => 50.80/7.01 ( ( in @ ( kpair @ X30 @ X32 ) @ X26 ) => 50.80/7.01 ( in @ 50.80/7.01 ( kpair @ X30 @ X32 ) @ ( binunion @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ( ![X34:$i,X36:$i]: 50.80/7.01 ( ( breln1 @ X34 @ X36 ) => 50.80/7.01 ( ![X38:$i]: 50.80/7.01 ( ( breln1 @ X34 @ X38 ) => 50.80/7.01 ( ![X40:$i]: 50.80/7.01 ( ( in @ X40 @ X34 ) => 50.80/7.01 ( ![X42:$i]: 50.80/7.01 ( ( in @ X42 @ X34 ) => 50.80/7.01 ( ( in @ ( kpair @ X40 @ X42 ) @ X38 ) => 50.80/7.01 ( in @ 50.80/7.01 ( kpair @ X40 @ X42 ) @ 50.80/7.01 ( binunion @ X36 @ X38 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ( ![X44:$i,X46:$i]: 50.80/7.01 ( ( breln1 @ X44 @ X46 ) => 50.80/7.01 ( ![X48:$i]: 50.80/7.01 ( ( breln1 @ X44 @ X48 ) => 50.80/7.01 ( ![X50:$i]: 50.80/7.01 ( ( in @ X50 @ X44 ) => 50.80/7.01 ( ![X52:$i]: 50.80/7.01 ( ( in @ X52 @ X44 ) => 50.80/7.01 ( ( in @ 50.80/7.01 ( kpair @ X50 @ X52 ) @ 50.80/7.01 ( binunion @ X46 @ X48 ) ) => 50.80/7.01 ( ( in @ ( kpair @ X50 @ X52 ) @ X48 ) | 50.80/7.01 ( in @ ( kpair @ X50 @ X52 ) @ X46 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ![X54:$i,X56:$i]: 50.80/7.01 ( ( breln1 @ X54 @ X56 ) => 50.80/7.01 ( ![X58:$i]: 50.80/7.01 ( ( breln1 @ X54 @ X58 ) => 50.80/7.01 ( ( binunion @ X56 @ X58 ) = ( binunion @ X58 @ X56 ) ) ) ) ) ) ) ) ) ) ))). 50.80/7.01 thf(zf_stmt_1, negated_conjecture, 50.80/7.01 (~( ( ![X4:$i,X6:$i]: 50.80/7.01 ( ( subset @ X4 @ X6 ) => 50.80/7.01 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) ) => 50.80/7.01 ( ( ![X8:$i,X10:$i]: 50.80/7.01 ( ( breln1 @ X8 @ X10 ) => 50.80/7.01 ( ![X12:$i]: 50.80/7.01 ( ( breln1 @ X8 @ X12 ) => 50.80/7.01 ( ( ![X14:$i]: 50.80/7.01 ( ( in @ X14 @ X8 ) => 50.80/7.01 ( ![X16:$i]: 50.80/7.01 ( ( in @ X16 @ X8 ) => 50.80/7.01 ( ( in @ ( kpair @ X14 @ X16 ) @ X10 ) => 50.80/7.01 ( in @ ( kpair @ X14 @ X16 ) @ X12 ) ) ) ) ) ) => 50.80/7.01 ( subset @ X10 @ X12 ) ) ) ) ) ) => 50.80/7.01 ( ( ![X18:$i,X20:$i]: 50.80/7.01 ( ( breln1 @ X18 @ X20 ) => 50.80/7.01 ( ![X22:$i]: 50.80/7.01 ( ( breln1 @ X18 @ X22 ) => 50.80/7.01 ( breln1 @ X18 @ ( binunion @ X20 @ X22 ) ) ) ) ) ) => 50.80/7.01 ( ( ![X24:$i,X26:$i]: 50.80/7.01 ( ( breln1 @ X24 @ X26 ) => 50.80/7.01 ( ![X28:$i]: 50.80/7.01 ( ( breln1 @ X24 @ X28 ) => 50.80/7.01 ( ![X30:$i]: 50.80/7.01 ( ( in @ X30 @ X24 ) => 50.80/7.01 ( ![X32:$i]: 50.80/7.01 ( ( in @ X32 @ X24 ) => 50.80/7.01 ( ( in @ ( kpair @ X30 @ X32 ) @ X26 ) => 50.80/7.01 ( in @ 50.80/7.01 ( kpair @ X30 @ X32 ) @ 50.80/7.01 ( binunion @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ( ![X34:$i,X36:$i]: 50.80/7.01 ( ( breln1 @ X34 @ X36 ) => 50.80/7.01 ( ![X38:$i]: 50.80/7.01 ( ( breln1 @ X34 @ X38 ) => 50.80/7.01 ( ![X40:$i]: 50.80/7.01 ( ( in @ X40 @ X34 ) => 50.80/7.01 ( ![X42:$i]: 50.80/7.01 ( ( in @ X42 @ X34 ) => 50.80/7.01 ( ( in @ ( kpair @ X40 @ X42 ) @ X38 ) => 50.80/7.01 ( in @ 50.80/7.01 ( kpair @ X40 @ X42 ) @ 50.80/7.01 ( binunion @ X36 @ X38 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ( ![X44:$i,X46:$i]: 50.80/7.01 ( ( breln1 @ X44 @ X46 ) => 50.80/7.01 ( ![X48:$i]: 50.80/7.01 ( ( breln1 @ X44 @ X48 ) => 50.80/7.01 ( ![X50:$i]: 50.80/7.01 ( ( in @ X50 @ X44 ) => 50.80/7.01 ( ![X52:$i]: 50.80/7.01 ( ( in @ X52 @ X44 ) => 50.80/7.01 ( ( in @ 50.80/7.01 ( kpair @ X50 @ X52 ) @ 50.80/7.01 ( binunion @ X46 @ X48 ) ) => 50.80/7.01 ( ( in @ ( kpair @ X50 @ X52 ) @ X48 ) | 50.80/7.01 ( in @ ( kpair @ X50 @ X52 ) @ X46 ) ) ) ) ) ) ) ) ) ) ) => 50.80/7.01 ( ![X54:$i,X56:$i]: 50.80/7.01 ( ( breln1 @ X54 @ X56 ) => 50.80/7.01 ( ![X58:$i]: 50.80/7.01 ( ( breln1 @ X54 @ X58 ) => 50.80/7.01 ( ( binunion @ X56 @ X58 ) = ( binunion @ X58 @ X56 ) ) ) ) ) ) ) ) ) ) ) )), 50.80/7.01 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 50.80/7.01 thf(zip_derived_cl0, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((subset @ Y0 @ Y1) => 50.80/7.01 (((subset @ Y1 @ Y0) => (((Y0) = (Y1))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2))))))))))))) => 50.80/7.01 (subset @ Y1 @ Y2)))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (breln1 @ Y0 @ 50.80/7.01 (binunion @ Y1 @ Y2))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ 50.80/7.01 Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ 50.80/7.01 Y2) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ 50.80/7.01 Y2) => 50.80/7.01 (((binunion @ 50.80/7.01 Y1 @ Y2) = 50.80/7.01 (binunion @ 50.80/7.01 Y2 @ Y1))))))))))))))))))))))))))))), 50.80/7.01 inference('cnf', [status(esa)], [zf_stmt_1])). 50.80/7.01 thf(zip_derived_cl2, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2))))))))))))) => 50.80/7.01 (subset @ Y1 @ Y2)))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (breln1 @ Y0 @ 50.80/7.01 (binunion @ Y1 @ Y2))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ 50.80/7.01 Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ 50.80/7.01 Y2) => 50.80/7.01 (((binunion @ Y1 @ 50.80/7.01 Y2) = (binunion @ 50.80/7.01 Y2 @ Y1))))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 50.80/7.01 thf(zip_derived_cl5, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (breln1 @ Y0 @ 50.80/7.01 (binunion @ Y1 @ Y2))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((binunion @ Y1 @ 50.80/7.01 Y2) = (binunion @ 50.80/7.01 Y2 @ Y1))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 50.80/7.01 thf(zip_derived_cl9, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ 50.80/7.01 Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((binunion @ Y1 @ Y2) = 50.80/7.01 (binunion @ Y2 @ Y1))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 50.80/7.01 thf(zip_derived_cl14, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2))))))))))))))))))))))))))) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((binunion @ Y1 @ Y2) = 50.80/7.01 (binunion @ Y2 @ Y1))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 50.80/7.01 thf(zip_derived_cl20, plain, 50.80/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1)))))))))))))))))))))))))))) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((binunion @ Y1 @ Y2) = 50.80/7.01 (binunion @ Y2 @ Y1))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 50.80/7.01 thf(zip_derived_cl27, plain, 50.80/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((binunion @ Y1 @ Y2) = 50.80/7.01 (binunion @ Y2 @ Y1))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.80/7.01 thf(zip_derived_cl33, plain, 50.80/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ '#sk1' @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ '#sk1' @ Y1) => 50.80/7.01 (((binunion @ Y0 @ Y1) = (binunion @ Y1 @ 50.80/7.01 Y0)))))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 50.80/7.01 thf(zip_derived_cl39, plain, 50.80/7.01 (~ (((breln1 @ '#sk1' @ '#sk2') => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ '#sk1' @ Y0) => 50.80/7.01 (((binunion @ '#sk2' @ Y0) = (binunion @ Y0 @ '#sk2'))))))))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 50.80/7.01 thf(zip_derived_cl45, plain, 50.80/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ '#sk1' @ Y0) => 50.80/7.01 (((binunion @ '#sk2' @ Y0) = (binunion @ Y0 @ '#sk2'))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 50.80/7.01 thf(zip_derived_cl51, plain, 50.80/7.01 (~ (((breln1 @ '#sk1' @ '#sk4') => 50.80/7.01 (((binunion @ '#sk2' @ '#sk4') = (binunion @ '#sk4' @ '#sk2')))))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 50.80/7.01 thf(zip_derived_cl57, plain, 50.80/7.01 (~ (((binunion @ '#sk2' @ '#sk4') = (binunion @ '#sk4' @ '#sk2')))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 50.80/7.01 thf(zip_derived_cl63, plain, 50.80/7.01 (((binunion @ '#sk2' @ '#sk4') != (binunion @ '#sk4' @ '#sk2'))), 50.80/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl57])). 50.80/7.01 thf(zip_derived_cl1, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((subset @ Y0 @ Y1) => 50.80/7.01 (((subset @ Y1 @ Y0) => (((Y0) = (Y1)))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 50.80/7.01 thf(zip_derived_cl3, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((subset @ X2 @ Y0) => 50.80/7.01 (((subset @ Y0 @ X2) => (((X2) = (Y0))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 50.80/7.01 thf(zip_derived_cl6, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((subset @ X2 @ X4) => (((subset @ X4 @ X2) => (((X2) = (X4)))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 50.80/7.01 thf(zip_derived_cl10, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (subset @ X2 @ X4) | (((subset @ X4 @ X2) => (((X2) = (X4))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 50.80/7.01 thf(zip_derived_cl15, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (subset @ X4 @ X2) | (((X2) = (X4))) | ~ (subset @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 50.80/7.01 thf(zip_derived_cl21, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (subset @ X4 @ X2) | ((X2) = (X4)) | ~ (subset @ X2 @ X4))), 50.80/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl15])). 50.80/7.01 thf(zip_derived_cl4, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (((in @ 50.80/7.01 Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2))))))))))))) => 50.80/7.01 (subset @ Y1 @ Y2))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 50.80/7.01 thf(zip_derived_cl7, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y1) => 50.80/7.01 (((((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 X2) => 50.80/7.01 (((in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y0) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y1))))))))))))) => 50.80/7.01 (subset @ Y0 @ Y1)))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 50.80/7.01 thf(zip_derived_cl11, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((breln1 @ X2 @ X4) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0))))))))))))) => 50.80/7.01 (subset @ X4 @ Y0))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 50.80/7.01 thf(zip_derived_cl16, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X4) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0))))))))))))) => 50.80/7.01 (subset @ X4 @ Y0)))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 50.80/7.01 thf(zip_derived_cl22, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (((breln1 @ X2 @ X6) => 50.80/7.01 (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X4) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ X6))))))))))))) => 50.80/7.01 (subset @ X4 @ X6))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.80/7.01 thf(zip_derived_cl28, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (((((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X4) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ X6))))))))))))) => 50.80/7.01 (subset @ X4 @ X6))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 50.80/7.01 thf(zip_derived_cl34, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X4) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ X6))))))))))))) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 50.80/7.01 thf(zip_derived_cl40, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (((in @ ('#sk3' @ X2 @ X4 @ X6) @ X2) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ Y0) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ Y0) @ X6)))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | (subset @ X4 @ X6))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 50.80/7.01 thf(zip_derived_cl46, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (in @ ('#sk3' @ X2 @ X4 @ X6) @ X2) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 50.80/7.01 thf(zip_derived_cl56, plain, ( (breln1 @ '#sk1' @ '#sk4')), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 50.80/7.01 thf(zip_derived_cl44, plain, ( (breln1 @ '#sk1' @ '#sk2')), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 50.80/7.01 thf(zip_derived_cl47, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ Y0) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ Y0) @ X6)))))))) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 50.80/7.01 thf(zip_derived_cl52, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (((in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ 50.80/7.01 X6))))) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | (subset @ X4 @ X6))), 50.80/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 50.80/7.01 thf(zip_derived_cl59, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (((in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ X6))) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 50.80/7.01 thf(zip_derived_cl65, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (in @ 50.80/7.01 (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | (subset @ X4 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 50.80/7.01 thf(zip_derived_cl13, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (((in @ Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (((in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)))))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 50.80/7.01 thf(zip_derived_cl18, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y0) => 50.80/7.01 (in @ 50.80/7.01 (kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 (binunion @ 50.80/7.01 Y0 @ Y1))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 50.80/7.01 thf(zip_derived_cl24, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((breln1 @ X2 @ X4) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0)))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 50.80/7.01 thf(zip_derived_cl30, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X4) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 50.80/7.01 thf(zip_derived_cl36, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (((breln1 @ X2 @ X6) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X4) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)))))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 50.80/7.01 thf(zip_derived_cl41, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X4) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 50.80/7.01 thf(zip_derived_cl48, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 ( (((in @ X8 @ X2) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X4) => (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 50.80/7.01 thf(zip_derived_cl53, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 (~ (in @ X8 @ X2) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X4) => (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 50.80/7.01 thf(zip_derived_cl60, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 ( (((in @ X10 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ X10) @ X4) => (in @ (kpair @ X8 @ X10) @ 50.80/7.01 (binunion @ X4 @ X6)))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 50.80/7.01 thf(zip_derived_cl66, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ X10 @ X2) 50.80/7.01 | (((in @ (kpair @ X8 @ X10) @ X4) => (in @ (kpair @ X8 @ X10) @ 50.80/7.01 (binunion @ X4 @ X6)))) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 50.80/7.01 thf(zip_derived_cl69, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ (kpair @ X8 @ X10) @ X4) 50.80/7.01 | (in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (in @ X10 @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 50.80/7.01 thf(zip_derived_cl19, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (((in @ Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (((in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) => 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)))))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 50.80/7.01 thf(zip_derived_cl25, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y1) => 50.80/7.01 (in @ 50.80/7.01 (kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 (binunion @ 50.80/7.01 Y0 @ Y1))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 50.80/7.01 thf(zip_derived_cl31, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((breln1 @ X2 @ X4) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0)))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 50.80/7.01 thf(zip_derived_cl37, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X4) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0) => (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl31])). 50.80/7.01 thf(zip_derived_cl42, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (((breln1 @ X2 @ X6) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X6) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)))))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 50.80/7.01 thf(zip_derived_cl49, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X6) => 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 50.80/7.01 thf(zip_derived_cl54, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 ( (((in @ X8 @ X2) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X6) => (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 50.80/7.01 thf(zip_derived_cl61, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 (~ (in @ X8 @ X2) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X6) => (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 50.80/7.01 thf(zip_derived_cl67, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 ( (((in @ X10 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ X10) @ X6) => (in @ (kpair @ X8 @ X10) @ 50.80/7.01 (binunion @ X4 @ X6)))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 50.80/7.01 thf(zip_derived_cl70, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ X10 @ X2) 50.80/7.01 | (((in @ (kpair @ X8 @ X10) @ X6) => (in @ (kpair @ X8 @ X10) @ 50.80/7.01 (binunion @ X4 @ X6)))) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 50.80/7.01 thf(zip_derived_cl72, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ (kpair @ X8 @ X10) @ X6) 50.80/7.01 | (in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (in @ X10 @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 50.80/7.01 thf(zip_derived_cl8, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (breln1 @ Y0 @ 50.80/7.01 (binunion @ Y1 @ Y2)))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 50.80/7.01 thf(zip_derived_cl12, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y1) => (breln1 @ X2 @ 50.80/7.01 (binunion @ Y0 @ Y1))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 50.80/7.01 thf(zip_derived_cl17, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((breln1 @ X2 @ X4) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => (breln1 @ X2 @ 50.80/7.01 (binunion @ X4 @ Y0)))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 50.80/7.01 thf(zip_derived_cl23, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X4) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => (breln1 @ X2 @ 50.80/7.01 (binunion @ X4 @ Y0))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 50.80/7.01 thf(zip_derived_cl29, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (((breln1 @ X2 @ X6) => (breln1 @ X2 @ (binunion @ X4 @ X6)))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl23])). 50.80/7.01 thf(zip_derived_cl35, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (breln1 @ X2 @ (binunion @ X4 @ X6)) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 50.80/7.01 thf(zip_derived_cl46, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (in @ ('#sk3' @ X2 @ X4 @ X6) @ X2) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 50.80/7.01 thf(zip_derived_cl80, plain, 50.80/7.01 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X1) 50.80/7.01 | ~ (breln1 @ X2 @ X0) 50.80/7.01 | ~ (breln1 @ X2 @ X3) 50.80/7.01 | (subset @ (binunion @ X1 @ X0) @ X3) 50.80/7.01 | (in @ ('#sk3' @ X2 @ (binunion @ X1 @ X0) @ X3) @ X2))), 50.80/7.01 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl46])). 50.80/7.01 thf(zip_derived_cl35, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (breln1 @ X2 @ (binunion @ X4 @ X6)) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 50.80/7.01 thf(zip_derived_cl58, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (in @ ('#sk5' @ X2 @ X4 @ X6) @ X2) 50.80/7.01 | (subset @ X4 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 50.80/7.01 thf(zip_derived_cl64, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (in @ (kpair @ ('#sk3' @ X2 @ X4 @ X6) @ ('#sk5' @ X2 @ X4 @ X6)) @ 50.80/7.01 X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | (subset @ X4 @ X6))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 50.80/7.01 thf(zip_derived_cl26, plain, 50.80/7.01 ( (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((breln1 @ Y0 @ Y2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ Y0) => 50.80/7.01 (((!!) @ ( 50.80/7.01 ^[Y4 : $i]: 50.80/7.01 (((in @ Y4 @ 50.80/7.01 Y0) => 50.80/7.01 (((in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 ( 50.80/7.01 binunion @ 50.80/7.01 Y1 @ Y2)) => 50.80/7.01 (( 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y2) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y3 @ Y4) @ 50.80/7.01 Y1))))))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 50.80/7.01 thf(zip_derived_cl32, plain, 50.80/7.01 (![X2 : $i]: 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y1) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((!!) @ (^[Y3 : $i]: 50.80/7.01 (((in @ Y3 @ 50.80/7.01 X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 (binunion @ 50.80/7.01 Y0 @ Y1)) => 50.80/7.01 (((in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y1) | 50.80/7.01 (in @ 50.80/7.01 ( 50.80/7.01 kpair @ 50.80/7.01 Y2 @ Y3) @ 50.80/7.01 Y0)))))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 50.80/7.01 thf(zip_derived_cl38, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (((breln1 @ X2 @ X4) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0)) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0) | (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4))))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 50.80/7.01 thf(zip_derived_cl43, plain, 50.80/7.01 (![X2 : $i, X4 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X4) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((breln1 @ X2 @ Y0) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((!!) @ (^[Y2 : $i]: 50.80/7.01 (((in @ Y2 @ X2) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 (binunion @ X4 @ Y0)) => 50.80/7.01 (((in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 Y0) | (in @ 50.80/7.01 (kpair @ Y1 @ Y2) @ 50.80/7.01 X4)))))))))))))))))))))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 50.80/7.01 thf(zip_derived_cl50, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 ( (((breln1 @ X2 @ X6) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X6) | 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ X4))))))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 50.80/7.01 thf(zip_derived_cl55, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.80/7.01 (~ (breln1 @ X2 @ X6) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((!!) @ (^[Y1 : $i]: 50.80/7.01 (((in @ Y1 @ X2) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ 50.80/7.01 (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ Y0 @ Y1) @ X6) | 50.80/7.01 (in @ (kpair @ Y0 @ Y1) @ X4))))))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 50.80/7.01 thf(zip_derived_cl62, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 ( (((in @ X8 @ X2) => 50.80/7.01 (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X6) | (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ X4)))))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 50.80/7.01 thf(zip_derived_cl68, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.80/7.01 (~ (in @ X8 @ X2) 50.80/7.01 | (((!!) @ (^[Y0 : $i]: 50.80/7.01 (((in @ Y0 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ X8 @ Y0) @ X6) | (in @ 50.80/7.01 (kpair @ X8 @ Y0) @ X4)))))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 50.80/7.01 thf(zip_derived_cl71, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 ( (((in @ X10 @ X2) => 50.80/7.01 (((in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ X8 @ X10) @ X6) | (in @ (kpair @ X8 @ X10) @ 50.80/7.01 X4))))))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2))), 50.80/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl68])). 50.80/7.01 thf(zip_derived_cl73, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ X10 @ X2) 50.80/7.01 | (((in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)) => 50.80/7.01 (((in @ (kpair @ X8 @ X10) @ X6) | (in @ (kpair @ X8 @ X10) @ 50.80/7.01 X4))))) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 50.80/7.01 thf(zip_derived_cl74, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 (~ (in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)) 50.80/7.01 | (((in @ (kpair @ X8 @ X10) @ X6) | (in @ (kpair @ X8 @ X10) @ X4))) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (in @ X10 @ X2))), 50.80/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 50.80/7.01 thf(zip_derived_cl75, plain, 50.80/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 50.80/7.01 ( (in @ (kpair @ X8 @ X10) @ X6) 50.80/7.01 | (in @ (kpair @ X8 @ X10) @ X4) 50.80/7.01 | ~ (in @ X10 @ X2) 50.80/7.01 | ~ (in @ X8 @ X2) 50.80/7.01 | ~ (breln1 @ X2 @ X6) 50.80/7.01 | ~ (breln1 @ X2 @ X4) 50.80/7.01 | ~ (in @ (kpair @ X8 @ X10) @ (binunion @ X4 @ X6)))), 50.80/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 50.80/7.01 thf(zip_derived_cl5864, plain, ($false), 50.80/7.01 inference('eprover', [status(thm)], 50.80/7.01 [zip_derived_cl63, zip_derived_cl21, zip_derived_cl46, 50.80/7.01 zip_derived_cl56, zip_derived_cl44, zip_derived_cl65, 50.80/7.01 zip_derived_cl69, zip_derived_cl72, zip_derived_cl80, 50.80/7.01 zip_derived_cl35, zip_derived_cl58, zip_derived_cl64, 50.80/7.01 zip_derived_cl75])). 50.80/7.01 50.80/7.01 % SZS output end Refutation 50.80/7.01 50.80/7.01 50.80/7.01 % Terminating... 51.08/7.09 % Runner terminated. 51.08/7.11 % Zipperpin 1.5 exiting 51.08/7.12 EOF