0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5B0y1sjXcH true 0.10/0.31 % Computer : n010.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Tue Aug 9 06:10:05 EDT 2022 0.10/0.31 % CPUTime : 0.10/0.31 % Running portfolio for 960 s 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.10/0.31 % Number of cores: 8 0.15/0.31 % Python version: Python 3.6.8 0.15/0.31 % Running in HO mode 0.45/0.59 % Total configuration time : 828 0.45/0.59 % Estimated wc time : 1656 0.45/0.59 % Estimated cpu time (8 cpus) : 207.0 0.46/0.66 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.46/0.67 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.46/0.67 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.46/0.68 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.46/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.46/0.68 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.46/0.68 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.46/0.68 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.47/0.78 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 8.20/1.59 % Solved by lams/35_full_unif4.sh. 8.20/1.59 % done 69 iterations in 0.839s 8.20/1.59 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 8.20/1.59 % SZS output start Refutation 8.20/1.59 thf('#sk56_type', type, '#sk56': ($i > $i > $o) > $i). 8.20/1.59 thf('#sk76_type', type, '#sk76': ($i > $i > $o) > $i). 8.20/1.59 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 8.20/1.59 thf(sc_type, type, sc: ($i > $i > $o) > $i > $i > $o). 8.20/1.59 thf(mono_type, type, mono: (($i > $i > $o) > $i > $i > $o) > $o). 8.20/1.59 thf('#sk5_type', type, '#sk5': $i > $i > $o). 8.20/1.59 thf('#sk223_type', type, '#sk223': ($i > $i > $o) > $i). 8.20/1.59 thf(trsc_type, type, trsc: ($i > $i > $o) > $i > $i > $o). 8.20/1.59 thf('#form126_type', type, '#form126': ($i > $i > $o) > $o). 8.20/1.59 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 8.20/1.59 thf('#sk127_type', type, '#sk127': ($i > $i > $o) > $i). 8.20/1.59 thf('#sk174_type', type, '#sk174': ($i > $i > $o) > $i). 8.20/1.59 thf(trans_type, type, trans: ($i > $i > $o) > $o). 8.20/1.59 thf('#sk3_type', type, '#sk3': $i). 8.20/1.59 thf('#sk2_type', type, '#sk2': $i > $i > $o). 8.20/1.59 thf('#sk4_type', type, '#sk4': $i). 8.20/1.59 thf('#form15_type', type, '#form15': $o). 8.20/1.59 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 8.20/1.59 thf('#sk1_type', type, '#sk1': $i > $i > $o). 8.20/1.59 thf('#sk6_type', type, '#sk6': $i > $i > $o). 8.20/1.59 thf(transitive_reflexive_symmetric_closure, axiom,(( trsc ) = 8.20/1.59 (^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) )))). 8.20/1.59 thf(transitive_closure, axiom,(( tc ) = 8.20/1.59 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 8.20/1.59 ( ![S:( $i > $i > $o )]: 8.20/1.59 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 8.20/1.59 thf(transitive, axiom,(( trans ) = 8.20/1.59 (^[R:( $i > $i > $o )]: 8.20/1.59 ( ![X:$i,Y:$i,Z:$i]: 8.20/1.59 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 8.20/1.59 thf('0', plain, 8.20/1.59 (( trans ) = 8.20/1.59 ( ^[R:( $i > $i > $o )]: 8.20/1.59 ( ![X:$i,Y:$i,Z:$i]: 8.20/1.59 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], [transitive])). 8.20/1.59 thf('1', plain, 8.20/1.59 (( trans ) = 8.20/1.59 ( ^[V_1:( $i > $i > $o )]: 8.20/1.59 ( ![X4:$i,X6:$i,X8:$i]: 8.20/1.59 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf(subrel, axiom,(( subrel ) = 8.20/1.59 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 8.20/1.59 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 8.20/1.59 thf('2', plain, 8.20/1.59 (( subrel ) = 8.20/1.59 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 8.20/1.59 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], [subrel])). 8.20/1.59 thf('3', plain, 8.20/1.59 (( subrel ) = 8.20/1.59 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 8.20/1.59 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf('4', plain, 8.20/1.59 (( tc ) = 8.20/1.59 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 8.20/1.59 ( ![S:( $i > $i > $o )]: 8.20/1.59 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], 8.20/1.59 [transitive_closure, '1', '3'])). 8.20/1.59 thf('5', plain, 8.20/1.59 (( tc ) = 8.20/1.59 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 8.20/1.59 ( ![X4:( $i > $i > $o )]: 8.20/1.59 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf(symmetric_closure, axiom,(( sc ) = 8.20/1.59 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) )))). 8.20/1.59 thf('6', plain, 8.20/1.59 (( sc ) = 8.20/1.59 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], [symmetric_closure])). 8.20/1.59 thf('7', plain, 8.20/1.59 (( sc ) = 8.20/1.59 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 8.20/1.59 ( ( V_1 @ V_3 @ V_2 ) | ( V_1 @ V_2 @ V_3 ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf(reflexive_closure, axiom,(( rc ) = 8.20/1.59 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) )))). 8.20/1.59 thf('8', plain, 8.20/1.59 (( rc ) = 8.20/1.59 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], [reflexive_closure])). 8.20/1.59 thf('9', plain, 8.20/1.59 (( rc ) = 8.20/1.59 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 8.20/1.59 ( ( ( V_2 ) = ( V_3 ) ) | ( V_1 @ V_2 @ V_3 ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf('10', plain, 8.20/1.59 (( trsc ) = ( ^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], 8.20/1.59 [transitive_reflexive_symmetric_closure, '5', '1', '7', '9', 8.20/1.59 '3'])). 8.20/1.59 thf('11', plain, 8.20/1.59 (( trsc ) = ( ^[V_1:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ V_1 ) ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf(monotonic, axiom,(( mono ) = 8.20/1.59 (^[F:( ( $i > $i > $o ) > $i > $i > $o )]: 8.20/1.59 ( ![R:( $i > $i > $o ),S:( $i > $i > $o )]: 8.20/1.59 ( ( subrel @ R @ S ) => ( subrel @ ( F @ R ) @ ( F @ S ) ) ) )))). 8.20/1.59 thf('12', plain, 8.20/1.59 (( mono ) = 8.20/1.59 ( ^[F:( ( $i > $i > $o ) > $i > $i > $o )]: 8.20/1.59 ( ![R:( $i > $i > $o ),S:( $i > $i > $o )]: 8.20/1.59 ( ( subrel @ R @ S ) => ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) )), 8.20/1.59 inference('simplify_rw_rule', [status(thm)], [monotonic, '3'])). 8.20/1.59 thf('13', plain, 8.20/1.59 (( mono ) = 8.20/1.59 ( ^[V_1:( ( $i > $i > $o ) > $i > $i > $o )]: 8.20/1.59 ( ![X4:( $i > $i > $o ),X6:( $i > $i > $o )]: 8.20/1.59 ( ( subrel @ X4 @ X6 ) => ( subrel @ ( V_1 @ X4 ) @ ( V_1 @ X6 ) ) ) ) )), 8.20/1.59 define([status(thm)])). 8.20/1.59 thf(transitive_reflexive_symmetric_closure_op_is_monotonic, conjecture, 8.20/1.59 (mono @ trsc)). 8.20/1.59 thf(zf_stmt_0, conjecture, 8.20/1.59 (![X4:( $i > $i > $o ),X6:( $i > $i > $o )]: 8.20/1.59 ( ( ![X8:$i,X10:$i]: ( ( X4 @ X8 @ X10 ) => ( X6 @ X8 @ X10 ) ) ) => 8.20/1.59 ( ![X12:$i,X14:$i]: 8.20/1.59 ( ( ( ![X28:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X36:$i,X38:$i]: 8.20/1.59 ( ( X4 @ X36 @ X38 ) => ( X28 @ X36 @ X38 ) ) ) & 8.20/1.59 ( ![X30:$i,X32:$i,X34:$i]: 8.20/1.59 ( ( ( X28 @ X32 @ X34 ) & ( X28 @ X30 @ X32 ) ) => 8.20/1.59 ( X28 @ X30 @ X34 ) ) ) ) => 8.20/1.59 ( X28 @ X12 @ X14 ) ) ) | 8.20/1.59 ( ( X12 ) = ( X14 ) ) | 8.20/1.59 ( ![X16:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X24:$i,X26:$i]: 8.20/1.59 ( ( X4 @ X24 @ X26 ) => ( X16 @ X24 @ X26 ) ) ) & 8.20/1.59 ( ![X18:$i,X20:$i,X22:$i]: 8.20/1.59 ( ( ( X16 @ X20 @ X22 ) & ( X16 @ X18 @ X20 ) ) => 8.20/1.59 ( X16 @ X18 @ X22 ) ) ) ) => 8.20/1.59 ( X16 @ X14 @ X12 ) ) ) | 8.20/1.59 ( ( X14 ) = ( X12 ) ) ) => 8.20/1.59 ( ( ![X52:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X60:$i,X62:$i]: 8.20/1.59 ( ( X6 @ X60 @ X62 ) => ( X52 @ X60 @ X62 ) ) ) & 8.20/1.59 ( ![X54:$i,X56:$i,X58:$i]: 8.20/1.59 ( ( ( X52 @ X56 @ X58 ) & ( X52 @ X54 @ X56 ) ) => 8.20/1.59 ( X52 @ X54 @ X58 ) ) ) ) => 8.20/1.59 ( X52 @ X12 @ X14 ) ) ) | 8.20/1.59 ( ( X12 ) = ( X14 ) ) | 8.20/1.59 ( ![X40:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X48:$i,X50:$i]: 8.20/1.59 ( ( X6 @ X48 @ X50 ) => ( X40 @ X48 @ X50 ) ) ) & 8.20/1.59 ( ![X42:$i,X44:$i,X46:$i]: 8.20/1.59 ( ( ( X40 @ X44 @ X46 ) & ( X40 @ X42 @ X44 ) ) => 8.20/1.59 ( X40 @ X42 @ X46 ) ) ) ) => 8.20/1.59 ( X40 @ X14 @ X12 ) ) ) | 8.20/1.59 ( ( X14 ) = ( X12 ) ) ) ) ) ))). 8.20/1.59 thf(zf_stmt_1, negated_conjecture, 8.20/1.59 (~( ![X4:( $i > $i > $o ),X6:( $i > $i > $o )]: 8.20/1.59 ( ( ![X8:$i,X10:$i]: ( ( X4 @ X8 @ X10 ) => ( X6 @ X8 @ X10 ) ) ) => 8.20/1.59 ( ![X12:$i,X14:$i]: 8.20/1.59 ( ( ( ![X28:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X36:$i,X38:$i]: 8.20/1.59 ( ( X4 @ X36 @ X38 ) => ( X28 @ X36 @ X38 ) ) ) & 8.20/1.59 ( ![X30:$i,X32:$i,X34:$i]: 8.20/1.59 ( ( ( X28 @ X32 @ X34 ) & ( X28 @ X30 @ X32 ) ) => 8.20/1.59 ( X28 @ X30 @ X34 ) ) ) ) => 8.20/1.59 ( X28 @ X12 @ X14 ) ) ) | 8.20/1.59 ( ( X12 ) = ( X14 ) ) | 8.20/1.59 ( ![X16:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X24:$i,X26:$i]: 8.20/1.59 ( ( X4 @ X24 @ X26 ) => ( X16 @ X24 @ X26 ) ) ) & 8.20/1.59 ( ![X18:$i,X20:$i,X22:$i]: 8.20/1.59 ( ( ( X16 @ X20 @ X22 ) & ( X16 @ X18 @ X20 ) ) => 8.20/1.59 ( X16 @ X18 @ X22 ) ) ) ) => 8.20/1.59 ( X16 @ X14 @ X12 ) ) ) | 8.20/1.59 ( ( X14 ) = ( X12 ) ) ) => 8.20/1.59 ( ( ![X52:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X60:$i,X62:$i]: 8.20/1.59 ( ( X6 @ X60 @ X62 ) => ( X52 @ X60 @ X62 ) ) ) & 8.20/1.59 ( ![X54:$i,X56:$i,X58:$i]: 8.20/1.59 ( ( ( X52 @ X56 @ X58 ) & ( X52 @ X54 @ X56 ) ) => 8.20/1.59 ( X52 @ X54 @ X58 ) ) ) ) => 8.20/1.59 ( X52 @ X12 @ X14 ) ) ) | 8.20/1.59 ( ( X12 ) = ( X14 ) ) | 8.20/1.59 ( ![X40:( $i > $i > $o )]: 8.20/1.59 ( ( ( ![X48:$i,X50:$i]: 8.20/1.59 ( ( X6 @ X48 @ X50 ) => ( X40 @ X48 @ X50 ) ) ) & 8.20/1.59 ( ![X42:$i,X44:$i,X46:$i]: 8.20/1.59 ( ( ( X40 @ X44 @ X46 ) & ( X40 @ X42 @ X44 ) ) => 8.20/1.59 ( X40 @ X42 @ X46 ) ) ) ) => 8.20/1.59 ( X40 @ X14 @ X12 ) ) ) | 8.20/1.59 ( ( X14 ) = ( X12 ) ) ) ) ) ) )), 8.20/1.59 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 8.20/1.59 thf(zip_derived_cl0, plain, 8.20/1.59 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.59 (((!!) @ (^[Y1 : $i > $i > $o]: 8.20/1.59 (((((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((Y0 @ Y2 @ Y3) => 8.20/1.59 (Y1 @ Y2 @ Y3))))))))) => 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((((((!!) @ ( 8.20/1.59 ^[Y4 : 8.20/1.59 $i > $i > $o]: 8.20/1.59 (((( 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (Y0 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))))))))) & 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y7 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y4 @ 8.20/1.59 Y6 @ 8.20/1.59 Y7) & 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y7)))))))))))))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y2 @ Y3)))))) | 8.20/1.59 (((Y2) = (Y3))) | 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : 8.20/1.59 $i > $i > $o]: 8.20/1.59 (((( 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (Y0 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))))))))) & 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y7 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y4 @ 8.20/1.59 Y6 @ 8.20/1.59 Y7) & 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y7)))))))))))))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y3 @ Y2)))))) | 8.20/1.59 (((Y3) = (Y2))))) => 8.20/1.59 (((((!!) @ ( 8.20/1.59 ^[Y4 : 8.20/1.59 $i > $i > $o]: 8.20/1.59 (((( 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (Y1 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))))))))) & 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y7 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y4 @ 8.20/1.59 Y6 @ 8.20/1.59 Y7) & 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y7)))))))))))))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y2 @ Y3)))))) | 8.20/1.59 (((Y2) = (Y3))) | 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : 8.20/1.59 $i > $i > $o]: 8.20/1.59 (((( 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (Y1 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))))))))) & 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y7 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y4 @ 8.20/1.59 Y6 @ 8.20/1.59 Y7) & 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y6))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y5 @ Y7)))))))))))))) => 8.20/1.59 (Y4 @ 8.20/1.59 Y3 @ Y2)))))) | 8.20/1.59 (((Y3) = (Y2)))))))))))))))))))))), 8.20/1.59 inference('cnf', [status(esa)], [zf_stmt_1])). 8.20/1.59 thf(zip_derived_cl1, plain, 8.20/1.59 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.59 (((((!!) @ (^[Y1 : $i]: 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.59 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 8.20/1.59 Y1 @ Y2))))))))) => 8.20/1.59 (((!!) @ (^[Y1 : $i]: 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))))))))) & 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y3 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) & 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y6)))))))))))))) => 8.20/1.59 (Y3 @ Y1 @ Y2)))))) | 8.20/1.59 (((Y1) = (Y2))) | 8.20/1.59 (((!!) @ (^[Y3 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))))))))) & 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y3 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) & 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y6)))))))))))))) => 8.20/1.59 (Y3 @ Y2 @ Y1)))))) | 8.20/1.59 (((Y2) = (Y1))))) => 8.20/1.59 (((((!!) @ (^[Y3 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (Y0 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))))))))) & 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y3 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) & 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y6)))))))))))))) => 8.20/1.59 (Y3 @ Y1 @ Y2)))))) | 8.20/1.59 (((Y1) = (Y2))) | 8.20/1.59 (((!!) @ (^[Y3 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (Y0 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))))))))) & 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y6 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y3 @ 8.20/1.59 Y5 @ 8.20/1.59 Y6) & 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y5))) => 8.20/1.59 (Y3 @ 8.20/1.59 Y4 @ Y6)))))))))))))) => 8.20/1.59 (Y3 @ Y2 @ Y1)))))) | 8.20/1.59 (((Y2) = (Y1))))))))))))))))))), 8.20/1.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 8.20/1.59 thf(zip_derived_cl2, plain, 8.20/1.59 (~ (((((!!) @ (^[Y0 : $i]: 8.20/1.59 (((!!) @ (^[Y1 : $i]: 8.20/1.59 ((('#sk1' @ Y0 @ Y1) => ('#sk2' @ Y0 @ Y1))))))))) => 8.20/1.59 (((!!) @ (^[Y0 : $i]: 8.20/1.59 (((!!) @ (^[Y1 : $i]: 8.20/1.59 (((((((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y0 @ Y1)))))) | 8.20/1.59 (((Y0) = (Y1))) | 8.20/1.59 (((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y1 @ Y0)))))) | 8.20/1.59 (((Y1) = (Y0))))) => 8.20/1.59 (((((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk2' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y0 @ Y1)))))) | 8.20/1.59 (((Y0) = (Y1))) | 8.20/1.59 (((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk2' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y1 @ Y0)))))) | 8.20/1.59 (((Y1) = (Y0)))))))))))))))), 8.20/1.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 8.20/1.59 thf(zip_derived_cl4, plain, 8.20/1.59 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.59 (((!!) @ (^[Y1 : $i]: 8.20/1.59 (((((((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y0 @ Y1)))))) | 8.20/1.59 (((Y0) = (Y1))) | 8.20/1.59 (((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk1' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y1 @ Y0)))))) | 8.20/1.59 (((Y1) = (Y0))))) => 8.20/1.59 (((((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk2' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y0 @ Y1)))))) | 8.20/1.59 (((Y0) = (Y1))) | 8.20/1.59 (((!!) @ (^[Y2 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 ('#sk2' @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))))))))) & 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (!!) @ ( 8.20/1.59 ^[Y5 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y2 @ 8.20/1.59 Y4 @ 8.20/1.59 Y5) & 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y4))) => 8.20/1.59 (Y2 @ 8.20/1.59 Y3 @ Y5)))))))))))))) => 8.20/1.59 (Y2 @ Y1 @ Y0)))))) | 8.20/1.59 (((Y1) = (Y0)))))))))))))), 8.20/1.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 8.20/1.59 thf(zip_derived_cl6, plain, 8.20/1.59 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.59 (((((((!!) @ (^[Y1 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 ((('#sk1' @ 8.20/1.59 Y2 @ Y3) => 8.20/1.59 (Y1 @ Y2 @ 8.20/1.59 Y3))))))))) & 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y1 @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) & 8.20/1.59 (Y1 @ 8.20/1.59 Y2 @ Y3))) => 8.20/1.59 (Y1 @ 8.20/1.59 Y2 @ Y4)))))))))))))) => 8.20/1.59 (Y1 @ '#sk3' @ Y0)))))) | 8.20/1.59 ((('#sk3') = (Y0))) | 8.20/1.59 (((!!) @ (^[Y1 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 ((('#sk1' @ 8.20/1.59 Y2 @ Y3) => 8.20/1.59 (Y1 @ Y2 @ 8.20/1.59 Y3))))))))) & 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 (((!!) @ ( 8.20/1.59 ^[Y4 : $i]: 8.20/1.59 (( 8.20/1.59 (( 8.20/1.59 (Y1 @ 8.20/1.59 Y3 @ 8.20/1.59 Y4) & 8.20/1.59 (Y1 @ 8.20/1.59 Y2 @ Y3))) => 8.20/1.59 (Y1 @ 8.20/1.59 Y2 @ Y4)))))))))))))) => 8.20/1.59 (Y1 @ Y0 @ '#sk3')))))) | 8.20/1.59 (((Y0) = ('#sk3'))))) => 8.20/1.59 (((((!!) @ (^[Y1 : $i > $i > $o]: 8.20/1.59 (((((((!!) @ (^[Y2 : $i]: 8.20/1.59 (((!!) @ (^[Y3 : $i]: 8.20/1.59 ((('#sk2' @ 8.20/1.59 Y2 @ Y3) => 8.20/1.59 (Y1 @ Y2 @ 8.20/1.59 Y3))))))))) & 8.20/1.59 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((!!) @ ( 8.20/1.60 ^[Y4 : $i]: 8.20/1.60 (( 8.20/1.60 (( 8.20/1.60 (Y1 @ 8.20/1.60 Y3 @ 8.20/1.60 Y4) & 8.20/1.60 (Y1 @ 8.20/1.60 Y2 @ Y3))) => 8.20/1.60 (Y1 @ 8.20/1.60 Y2 @ Y4)))))))))))))) => 8.20/1.60 (Y1 @ '#sk3' @ Y0)))))) | 8.20/1.60 ((('#sk3') = (Y0))) | 8.20/1.60 (((!!) @ (^[Y1 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 ((('#sk2' @ 8.20/1.60 Y2 @ Y3) => 8.20/1.60 (Y1 @ Y2 @ 8.20/1.60 Y3))))))))) & 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((!!) @ ( 8.20/1.60 ^[Y4 : $i]: 8.20/1.60 (( 8.20/1.60 (( 8.20/1.60 (Y1 @ 8.20/1.60 Y3 @ 8.20/1.60 Y4) & 8.20/1.60 (Y1 @ 8.20/1.60 Y2 @ Y3))) => 8.20/1.60 (Y1 @ 8.20/1.60 Y2 @ Y4)))))))))))))) => 8.20/1.60 (Y1 @ Y0 @ '#sk3')))))) | 8.20/1.60 (((Y0) = ('#sk3'))))))))))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 8.20/1.60 thf(zip_derived_cl8, plain, 8.20/1.60 (~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) | 8.20/1.60 ((('#sk3') = ('#sk4'))) | 8.20/1.60 (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) | 8.20/1.60 ((('#sk4') = ('#sk3'))))) => 8.20/1.60 (((((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) | 8.20/1.60 ((('#sk3') = ('#sk4'))) | 8.20/1.60 (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) | 8.20/1.60 ((('#sk4') = ('#sk3')))))))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 8.20/1.60 thf(zip_derived_cl10, plain, 8.20/1.60 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) | 8.20/1.60 ((('#sk3') = ('#sk4'))) | 8.20/1.60 (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) | 8.20/1.60 ((('#sk4') = ('#sk3')))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 8.20/1.60 thf(zip_derived_cl12, plain, 8.20/1.60 (( (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 8.20/1.60 Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | ((('#sk3') = ('#sk4'))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) 8.20/1.60 | ((('#sk4') = ('#sk3'))))), 8.20/1.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])). 8.20/1.60 thf(zip_derived_cl17, plain, 8.20/1.60 (( (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 8.20/1.60 Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) 8.20/1.60 | (('#sk4') = ('#sk3')))), 8.20/1.60 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 8.20/1.60 thf(zip_derived_cl18, plain, 8.20/1.60 (( (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 8.20/1.60 Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 inference('simplify', [status(thm)], [zip_derived_cl17])). 8.20/1.60 thf(zip_derived_cl19, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) => 8.20/1.60 (X2 @ '#sk4' @ '#sk3'))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 8.20/1.60 thf(zip_derived_cl28, plain, 8.20/1.60 ((~ ('#form15') 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl29, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) => 8.20/1.60 (X2 @ '#sk3' @ '#sk4'))) 8.20/1.60 | ~ ('#form15'))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 8.20/1.60 thf(zip_derived_cl31, plain, 8.20/1.60 (( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ('#sk5' @ '#sk3' @ '#sk4'))) 8.20/1.60 | ~ ('#form15'))), 8.20/1.60 inference('triggered_bool_instantiation', [status(thm)], 8.20/1.60 [zip_derived_cl29])). 8.20/1.60 thf(zip_derived_cl11, plain, 8.20/1.60 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) | 8.20/1.60 ((('#sk3') = ('#sk4'))) | 8.20/1.60 (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3')))))) | 8.20/1.60 ((('#sk4') = ('#sk3')))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 8.20/1.60 thf(zip_derived_cl13, plain, 8.20/1.60 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 8.20/1.60 Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4'))))))), 8.20/1.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 8.20/1.60 thf(zip_derived_cl23, plain, 8.20/1.60 (~ (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ('#sk5' @ '#sk3' @ '#sk4')))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 8.20/1.60 thf(zip_derived_cl36, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 8.20/1.60 thf(zip_derived_cl19, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) => 8.20/1.60 (X2 @ '#sk4' @ '#sk3'))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 8.20/1.60 thf(zip_derived_cl25, plain, 8.20/1.60 (( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ('#sk6' @ '#sk4' @ '#sk3'))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')))), 8.20/1.60 inference('triggered_bool_instantiation', [status(thm)], 8.20/1.60 [zip_derived_cl19])). 8.20/1.60 thf(zip_derived_cl15, plain, 8.20/1.60 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 8.20/1.60 Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk4' @ '#sk3'))))))), 8.20/1.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 8.20/1.60 thf(zip_derived_cl26, plain, 8.20/1.60 (~ (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ('#sk6' @ '#sk4' @ '#sk3')))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 8.20/1.60 thf(zip_derived_cl38, plain, (~ ('#sk6' @ '#sk4' @ '#sk3')), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 8.20/1.60 thf(zip_derived_cl254, plain, 8.20/1.60 (( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ($false))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')))), 8.20/1.60 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl38])). 8.20/1.60 thf(zip_derived_cl14, plain, (~ ((('#sk3') = ('#sk4')))), 8.20/1.60 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 8.20/1.60 thf(zip_derived_cl24, plain, ((('#sk3') != ('#sk4'))), 8.20/1.60 inference('simplify nested equalities', [status(thm)], [zip_derived_cl14])). 8.20/1.60 thf(zip_derived_cl255, plain, 8.20/1.60 (( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ($false))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 inference('simplify_reflect-', [status(thm)], 8.20/1.60 [zip_derived_cl254, zip_derived_cl24])). 8.20/1.60 thf(zip_derived_cl256, plain, 8.20/1.60 (( (((~) @ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ 8.20/1.60 Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl255])). 8.20/1.60 thf(zip_derived_cl257, plain, 8.20/1.60 ((~ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 inference('simplify nested equalities', [status(thm)], 8.20/1.60 [zip_derived_cl256])). 8.20/1.60 thf(zip_derived_cl28, plain, 8.20/1.60 ((~ ('#form15') 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl258, plain, 8.20/1.60 (( ('#form15') 8.20/1.60 | ~ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ 8.20/1.60 Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))))))), 8.20/1.60 inference('renaming', [status(thm)], 8.20/1.60 [zip_derived_cl257, zip_derived_cl28])). 8.20/1.60 thf(zip_derived_cl259, plain, 8.20/1.60 ((~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2)))))))))))) 8.20/1.60 | ('#form15'))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl258])). 8.20/1.60 thf(zip_derived_cl19, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) => 8.20/1.60 (X2 @ '#sk4' @ '#sk3'))) 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ 8.20/1.60 Y2 @ Y3) & 8.20/1.60 (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ 8.20/1.60 Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))) 8.20/1.60 | (('#sk3') = ('#sk4')))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 8.20/1.60 thf(zip_derived_cl28, plain, 8.20/1.60 ((~ ('#form15') 8.20/1.60 | (((!!) @ (^[Y0 : $i > $i > $o]: 8.20/1.60 (((((((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((('#sk1' @ Y1 @ Y2) => 8.20/1.60 (Y0 @ Y1 @ Y2))))))))) & 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((!!) @ (^[Y3 : $i]: 8.20/1.60 (((((Y0 @ Y2 @ 8.20/1.60 Y3) & (Y0 @ 8.20/1.60 Y1 @ Y2))) => 8.20/1.60 (Y0 @ Y1 @ Y3)))))))))))))) => 8.20/1.60 (Y0 @ '#sk3' @ '#sk4')))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl34, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( ('#form15') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & 8.20/1.60 (X2 @ Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) => 8.20/1.60 (X2 @ '#sk4' @ '#sk3'))))), 8.20/1.60 inference('renaming', [status(thm)], [zip_derived_cl19, zip_derived_cl28])). 8.20/1.60 thf(zip_derived_cl39, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))) 8.20/1.60 | (X2 @ '#sk4' @ '#sk3') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | ('#form15'))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 8.20/1.60 thf(zip_derived_cl45, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))) 8.20/1.60 | ('#form15') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | (X2 @ '#sk4' @ '#sk3'))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl39])). 8.20/1.60 thf(zip_derived_cl51, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 ((('#sk1' @ ('#sk56' @ X2) @ Y0) => (X2 @ 8.20/1.60 ('#sk56' @ X2) @ Y0)))))) 8.20/1.60 | (X2 @ '#sk4' @ '#sk3') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | ('#form15') 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 8.20/1.60 thf(zip_derived_cl57, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk76' @ X2)) => (X2 @ 8.20/1.60 ('#sk56' @ X2) @ ('#sk76' @ X2)))) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))) 8.20/1.60 | ('#form15') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | (X2 @ '#sk4' @ '#sk3'))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl51])). 8.20/1.60 thf(zip_derived_cl63, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( ('#sk1' @ ('#sk56' @ X2) @ ('#sk76' @ X2)) 8.20/1.60 | (X2 @ '#sk4' @ '#sk3') 8.20/1.60 | (('#sk3') = ('#sk4')) 8.20/1.60 | ('#form15') 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 8.20/1.60 thf(zip_derived_cl69, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( ('#form126' @ X2) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl260, plain, 8.20/1.60 ((~ ('#form126' @ '#sk6') 8.20/1.60 | ('#form15') 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))))), 8.20/1.60 inference('renaming', [status(thm)], 8.20/1.60 [zip_derived_cl259, zip_derived_cl69])). 8.20/1.60 thf(zip_derived_cl69, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( ('#form126' @ X2) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl70, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((((X2 @ Y0 @ Y1) & (X2 @ 8.20/1.60 ('#sk127' @ X2) @ Y0))) => 8.20/1.60 (X2 @ ('#sk127' @ X2) @ Y1))))))))) 8.20/1.60 | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 8.20/1.60 thf(zip_derived_cl77, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((((X2 @ ('#sk174' @ X2) @ Y0) & (X2 @ 8.20/1.60 ('#sk127' @ X2) @ ('#sk174' @ X2)))) => 8.20/1.60 (X2 @ ('#sk127' @ X2) @ Y0)))))) 8.20/1.60 | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 8.20/1.60 thf(zip_derived_cl81, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (((((X2 @ ('#sk174' @ X2) @ ('#sk223' @ X2)) & (X2 @ 8.20/1.60 ('#sk127' @ X2) @ ('#sk174' @ X2)))) => 8.20/1.60 (X2 @ ('#sk127' @ X2) @ ('#sk223' @ X2)))) 8.20/1.60 | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 8.20/1.60 thf(zip_derived_cl82, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (((X2 @ ('#sk174' @ X2) @ ('#sk223' @ X2)) & (X2 @ 8.20/1.60 ('#sk127' @ X2) @ ('#sk174' @ X2)))) 8.20/1.60 | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 8.20/1.60 thf(zip_derived_cl85, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (X2 @ ('#sk127' @ X2) @ ('#sk174' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 8.20/1.60 thf(zip_derived_cl84, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (X2 @ ('#sk174' @ X2) @ ('#sk223' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 8.20/1.60 thf(zip_derived_cl37, plain, 8.20/1.60 ( (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & 8.20/1.60 ('#sk6' @ Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2))))))))))))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 8.20/1.60 thf(zip_derived_cl44, plain, 8.20/1.60 ( (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk6' @ Y1 @ Y2) & ('#sk6' @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 ('#sk6' @ Y0 @ Y2))))))))))))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 8.20/1.60 thf(zip_derived_cl50, plain, 8.20/1.60 (![X2 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((((('#sk6' @ Y0 @ Y1) & ('#sk6' @ X2 @ Y0))) => 8.20/1.60 ('#sk6' @ X2 @ Y1)))))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 8.20/1.60 thf(zip_derived_cl56, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 ((((('#sk6' @ X4 @ Y0) & ('#sk6' @ X2 @ X4))) => 8.20/1.60 ('#sk6' @ X2 @ Y0))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 8.20/1.60 thf(zip_derived_cl62, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 ((((('#sk6' @ X4 @ X6) & ('#sk6' @ X2 @ X4))) => ('#sk6' @ X2 @ X6)))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 8.20/1.60 thf(zip_derived_cl68, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 (~ ((('#sk6' @ X4 @ X6) & ('#sk6' @ X2 @ X4))) | ('#sk6' @ X2 @ X6))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 8.20/1.60 thf(zip_derived_cl76, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 (~ ('#sk6' @ X4 @ X6) | ~ ('#sk6' @ X2 @ X4) | ('#sk6' @ X2 @ X6))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 8.20/1.60 thf(zip_derived_cl138, plain, 8.20/1.60 (![X0 : $i]: 8.20/1.60 ( ('#form126' @ '#sk6') 8.20/1.60 | ('#sk6' @ X0 @ ('#sk223' @ '#sk6')) 8.20/1.60 | ~ ('#sk6' @ X0 @ ('#sk174' @ '#sk6')))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl76])). 8.20/1.60 thf(zip_derived_cl225, plain, 8.20/1.60 (( ('#form126' @ '#sk6') 8.20/1.60 | ('#sk6' @ ('#sk127' @ '#sk6') @ ('#sk223' @ '#sk6')) 8.20/1.60 | ('#form126' @ '#sk6'))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl138])). 8.20/1.60 thf(zip_derived_cl231, plain, 8.20/1.60 (( ('#sk6' @ ('#sk127' @ '#sk6') @ ('#sk223' @ '#sk6')) 8.20/1.60 | ('#form126' @ '#sk6'))), 8.20/1.60 inference('simplify', [status(thm)], [zip_derived_cl225])). 8.20/1.60 thf(zip_derived_cl83, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (X2 @ ('#sk127' @ X2) @ ('#sk223' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 8.20/1.60 thf(zip_derived_cl232, plain, ( ('#form126' @ '#sk6')), 8.20/1.60 inference('clc', [status(thm)], [zip_derived_cl231, zip_derived_cl83])). 8.20/1.60 thf(zip_derived_cl261, plain, 8.20/1.60 (( ('#form15') 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1))))))))))), 8.20/1.60 inference('demod', [status(thm)], [zip_derived_cl260, zip_derived_cl232])). 8.20/1.60 thf(zip_derived_cl262, plain, 8.20/1.60 ((~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 ((('#sk1' @ ('#sk56' @ '#sk6') @ Y0) => ('#sk6' @ 8.20/1.60 ('#sk56' @ '#sk6') @ Y0)))))) 8.20/1.60 | ('#form15'))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl261])). 8.20/1.60 thf(zip_derived_cl263, plain, 8.20/1.60 ((~ ((('#sk1' @ ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')) => ('#sk6' @ 8.20/1.60 ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')))) 8.20/1.60 | ('#form15'))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])). 8.20/1.60 thf(zip_derived_cl264, plain, 8.20/1.60 (( ('#sk1' @ ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')) | ('#form15'))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 8.20/1.60 thf(zip_derived_cl3, plain, 8.20/1.60 ( (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk2' @ Y0 @ Y1)))))))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 8.20/1.60 thf(zip_derived_cl5, plain, 8.20/1.60 (![X2 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: ((('#sk1' @ X2 @ Y0) => ('#sk2' @ X2 @ Y0))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 8.20/1.60 thf(zip_derived_cl7, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: ((('#sk1' @ X2 @ X4) => ('#sk2' @ X2 @ X4)))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 8.20/1.60 thf(zip_derived_cl9, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 8.20/1.60 thf(zip_derived_cl266, plain, 8.20/1.60 (( ('#form15') | ('#sk2' @ ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl264, zip_derived_cl9])). 8.20/1.60 thf(zip_derived_cl43, plain, 8.20/1.60 ( (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk6' @ Y0 @ Y1)))))))))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 8.20/1.60 thf(zip_derived_cl49, plain, 8.20/1.60 (![X2 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: ((('#sk2' @ X2 @ Y0) => ('#sk6' @ X2 @ Y0))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 8.20/1.60 thf(zip_derived_cl55, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: ((('#sk2' @ X2 @ X4) => ('#sk6' @ X2 @ X4)))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 8.20/1.60 thf(zip_derived_cl61, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: (~ ('#sk2' @ X2 @ X4) | ('#sk6' @ X2 @ X4))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 8.20/1.60 thf(zip_derived_cl272, plain, 8.20/1.60 (( ('#form15') | ('#sk6' @ ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl266, zip_derived_cl61])). 8.20/1.60 thf(zip_derived_cl265, plain, 8.20/1.60 ((~ ('#sk6' @ ('#sk56' @ '#sk6') @ ('#sk76' @ '#sk6')) | ('#form15'))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl263])). 8.20/1.60 thf(zip_derived_cl276, plain, ( ('#form15')), 8.20/1.60 inference('clc', [status(thm)], [zip_derived_cl272, zip_derived_cl265])). 8.20/1.60 thf(zip_derived_cl291, plain, 8.20/1.60 ( (((((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2)))))))))))))) => 8.20/1.60 ($false)))), 8.20/1.60 inference('demod', [status(thm)], 8.20/1.60 [zip_derived_cl31, zip_derived_cl36, zip_derived_cl276])). 8.20/1.60 thf(zip_derived_cl292, plain, 8.20/1.60 ( (((~) @ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ 8.20/1.60 Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2))))))))))))))))), 8.20/1.60 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl291])). 8.20/1.60 thf(zip_derived_cl293, plain, 8.20/1.60 (~ (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2))))))))))))))), 8.20/1.60 inference('simplify nested equalities', [status(thm)], 8.20/1.60 [zip_derived_cl292])). 8.20/1.60 thf(zip_derived_cl294, plain, 8.20/1.60 ((~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2)))))))))))))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl293])). 8.20/1.60 thf(zip_derived_cl69, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( ('#form126' @ X2) 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 (((((X2 @ Y1 @ Y2) & (X2 @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 (X2 @ Y0 @ Y2)))))))))))))), 8.20/1.60 define([status(thm)])). 8.20/1.60 thf(zip_derived_cl295, plain, 8.20/1.60 ((~ ('#form126' @ '#sk5') 8.20/1.60 | ~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))))), 8.20/1.60 inference('renaming', [status(thm)], 8.20/1.60 [zip_derived_cl294, zip_derived_cl69])). 8.20/1.60 thf(zip_derived_cl85, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (X2 @ ('#sk127' @ X2) @ ('#sk174' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 8.20/1.60 thf(zip_derived_cl84, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 ( (X2 @ ('#sk174' @ X2) @ ('#sk223' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 8.20/1.60 thf(zip_derived_cl35, plain, 8.20/1.60 ( (((((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & 8.20/1.60 ('#sk5' @ Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2))))))))))))))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 8.20/1.60 thf(zip_derived_cl42, plain, 8.20/1.60 ( (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 (((!!) @ (^[Y2 : $i]: 8.20/1.60 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 8.20/1.60 Y0 @ Y1))) => 8.20/1.60 ('#sk5' @ Y0 @ Y2))))))))))))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 8.20/1.60 thf(zip_derived_cl48, plain, 8.20/1.60 (![X2 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 8.20/1.60 ('#sk5' @ X2 @ Y1)))))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 8.20/1.60 thf(zip_derived_cl54, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: 8.20/1.60 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 8.20/1.60 ('#sk5' @ X2 @ Y0))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 8.20/1.60 thf(zip_derived_cl60, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 8.20/1.60 thf(zip_derived_cl67, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 8.20/1.60 thf(zip_derived_cl75, plain, 8.20/1.60 (![X2 : $i, X4 : $i, X6 : $i]: 8.20/1.60 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl67])). 8.20/1.60 thf(zip_derived_cl132, plain, 8.20/1.60 (![X0 : $i]: 8.20/1.60 ( ('#form126' @ '#sk5') 8.20/1.60 | ('#sk5' @ X0 @ ('#sk223' @ '#sk5')) 8.20/1.60 | ~ ('#sk5' @ X0 @ ('#sk174' @ '#sk5')))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl75])). 8.20/1.60 thf(zip_derived_cl221, plain, 8.20/1.60 (( ('#form126' @ '#sk5') 8.20/1.60 | ('#sk5' @ ('#sk127' @ '#sk5') @ ('#sk223' @ '#sk5')) 8.20/1.60 | ('#form126' @ '#sk5'))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl132])). 8.20/1.60 thf(zip_derived_cl222, plain, 8.20/1.60 (( ('#sk5' @ ('#sk127' @ '#sk5') @ ('#sk223' @ '#sk5')) 8.20/1.60 | ('#form126' @ '#sk5'))), 8.20/1.60 inference('simplify', [status(thm)], [zip_derived_cl221])). 8.20/1.60 thf(zip_derived_cl83, plain, 8.20/1.60 (![X2 : $i > $i > $o]: 8.20/1.60 (~ (X2 @ ('#sk127' @ X2) @ ('#sk223' @ X2)) | ('#form126' @ X2))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 8.20/1.60 thf(zip_derived_cl223, plain, ( ('#form126' @ '#sk5')), 8.20/1.60 inference('clc', [status(thm)], [zip_derived_cl222, zip_derived_cl83])). 8.20/1.60 thf(zip_derived_cl296, plain, 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1)))))))))), 8.20/1.60 inference('demod', [status(thm)], [zip_derived_cl295, zip_derived_cl223])). 8.20/1.60 thf(zip_derived_cl297, plain, 8.20/1.60 (~ (((!!) @ (^[Y0 : $i]: 8.20/1.60 ((('#sk1' @ ('#sk56' @ '#sk5') @ Y0) => ('#sk5' @ 8.20/1.60 ('#sk56' @ '#sk5') @ Y0))))))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl296])). 8.20/1.60 thf(zip_derived_cl298, plain, 8.20/1.60 (~ ((('#sk1' @ ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5')) => ('#sk5' @ 8.20/1.60 ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5'))))), 8.20/1.60 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl297])). 8.20/1.60 thf(zip_derived_cl300, plain, 8.20/1.60 (~ ('#sk5' @ ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5'))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 8.20/1.60 thf(zip_derived_cl299, plain, 8.20/1.60 ( ('#sk1' @ ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5'))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 8.20/1.60 thf(zip_derived_cl9, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 8.20/1.60 thf(zip_derived_cl301, plain, 8.20/1.60 ( ('#sk2' @ ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5'))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl9])). 8.20/1.60 thf(zip_derived_cl41, plain, 8.20/1.60 ( (((!!) @ (^[Y0 : $i]: 8.20/1.60 (((!!) @ (^[Y1 : $i]: 8.20/1.60 ((('#sk2' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1)))))))))), 8.20/1.60 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 8.20/1.60 thf(zip_derived_cl47, plain, 8.20/1.60 (![X2 : $i]: 8.20/1.60 (((!!) @ (^[Y0 : $i]: ((('#sk2' @ X2 @ Y0) => ('#sk5' @ X2 @ Y0))))))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 8.20/1.60 thf(zip_derived_cl53, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: ((('#sk2' @ X2 @ X4) => ('#sk5' @ X2 @ X4)))), 8.20/1.60 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 8.20/1.60 thf(zip_derived_cl59, plain, 8.20/1.60 (![X2 : $i, X4 : $i]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 8.20/1.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 8.20/1.60 thf(zip_derived_cl304, plain, 8.20/1.60 ( ('#sk5' @ ('#sk56' @ '#sk5') @ ('#sk76' @ '#sk5'))), 8.20/1.60 inference('sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl59])). 8.20/1.60 thf(zip_derived_cl309, plain, ($false), 8.20/1.60 inference('demod', [status(thm)], [zip_derived_cl300, zip_derived_cl304])). 8.20/1.60 8.20/1.60 % SZS output end Refutation 8.20/1.60 8.20/1.60 8.20/1.60 % Terminating... 9.16/1.72 % Runner terminated. 9.16/1.73 % Zipperpin 1.5 exiting 9.16/1.73 EOF