0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ohOMzLMcXg true 0.11/0.32 % Computer : n024.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 05:53:52 EDT 2022 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 960 s 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.47/0.60 % Total configuration time : 828 0.47/0.60 % Estimated wc time : 1656 0.47/0.60 % Estimated cpu time (8 cpus) : 207.0 0.49/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.68 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 50.66/7.00 % Solved by lams/20_acsne_simpl.sh. 50.66/7.00 % done 319 iterations in 6.131s 50.66/7.00 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 50.66/7.00 % SZS output start Refutation 50.66/7.00 thf('#form133_type', type, '#form133': ($i > $i > $o) > $o). 50.66/7.00 thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf('#sk1_type', type, '#sk1': $i > $i > $o). 50.66/7.00 thf('#sk278_type', type, '#sk278': ($i > $i > $o) > $i). 50.66/7.00 thf('#form307_type', type, '#form307': ($i > $i > $o) > $o). 50.66/7.00 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 50.66/7.00 thf(sc_type, type, sc: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf('#sk13_type', type, '#sk13': $i > $i > $i > $i > $o). 50.66/7.00 thf('#sk134_type', type, '#sk134': ($i > $i > $o) > $i). 50.66/7.00 thf(cr_type, type, cr: ($i > $i > $o) > $o). 50.66/7.00 thf(trsc_type, type, trsc: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf('#sk3_type', type, '#sk3': $i). 50.66/7.00 thf('#sk2_type', type, '#sk2': $i). 50.66/7.00 thf('#sk191_type', type, '#sk191': ($i > $i > $o) > $i). 50.66/7.00 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf(sconfl_type, type, sconfl: ($i > $i > $o) > $o). 50.66/7.00 thf('#sk14_type', type, '#sk14': $i > $i > $i). 50.66/7.00 thf('#sk77_type', type, '#sk77': ($i > $i > $o) > $i). 50.66/7.00 thf(join_type, type, join: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf(trans_type, type, trans: ($i > $i > $o) > $o). 50.66/7.00 thf('#form65_type', type, '#form65': $i > $o). 50.66/7.00 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 50.66/7.00 thf('#form12_type', type, '#form12': $o). 50.66/7.00 thf('#sk56_type', type, '#sk56': ($i > $i > $o) > $i). 50.66/7.00 thf(church_rosser, axiom,(( cr ) = 50.66/7.00 (^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i]: ( ( trsc @ R @ X @ Y ) => ( join @ R @ X @ Y ) ) )))). 50.66/7.00 thf(joinable, axiom,(( join ) = 50.66/7.00 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 50.66/7.00 ( ?[Z:$i]: ( ( trc @ R @ Y @ Z ) & ( trc @ R @ X @ Z ) ) )))). 50.66/7.00 thf(transitive_reflexive_closure, axiom,(( trc ) = 50.66/7.00 (^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) )))). 50.66/7.00 thf(transitive_closure, axiom,(( tc ) = 50.66/7.00 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 50.66/7.00 ( ![S:( $i > $i > $o )]: 50.66/7.00 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 50.66/7.00 thf(transitive, axiom,(( trans ) = 50.66/7.00 (^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i,Z:$i]: 50.66/7.00 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 50.66/7.00 thf('0', plain, 50.66/7.00 (( trans ) = 50.66/7.00 ( ^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i,Z:$i]: 50.66/7.00 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], [transitive])). 50.66/7.00 thf('1', plain, 50.66/7.00 (( trans ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o )]: 50.66/7.00 ( ![X4:$i,X6:$i,X8:$i]: 50.66/7.00 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(subrel, axiom,(( subrel ) = 50.66/7.00 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 50.66/7.00 thf('2', plain, 50.66/7.00 (( subrel ) = 50.66/7.00 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], [subrel])). 50.66/7.00 thf('3', plain, 50.66/7.00 (( subrel ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 50.66/7.00 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf('4', plain, 50.66/7.00 (( tc ) = 50.66/7.00 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 50.66/7.00 ( ![S:( $i > $i > $o )]: 50.66/7.00 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [transitive_closure, '1', '3'])). 50.66/7.00 thf('5', plain, 50.66/7.00 (( tc ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 50.66/7.00 ( ![X4:( $i > $i > $o )]: 50.66/7.00 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(reflexive_closure, axiom,(( rc ) = 50.66/7.00 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) )))). 50.66/7.00 thf('6', plain, 50.66/7.00 (( rc ) = 50.66/7.00 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], [reflexive_closure])). 50.66/7.00 thf('7', plain, 50.66/7.00 (( rc ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 50.66/7.00 ( ( ( V_2 ) = ( V_3 ) ) | ( V_1 @ V_2 @ V_3 ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf('8', plain, (( trc ) = ( ^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [transitive_reflexive_closure, '5', '1', '7', '3'])). 50.66/7.00 thf('9', plain, 50.66/7.00 (( trc ) = ( ^[V_1:( $i > $i > $o )]: ( rc @ ( tc @ V_1 ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf('10', plain, 50.66/7.00 (( join ) = 50.66/7.00 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 50.66/7.00 ( ?[Z:$i]: ( ( trc @ R @ Y @ Z ) & ( trc @ R @ X @ Z ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [joinable, '9', '5', '1', '7', '3'])). 50.66/7.00 thf('11', plain, 50.66/7.00 (( join ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 50.66/7.00 ( ?[X4:$i]: ( ( trc @ V_1 @ V_3 @ X4 ) & ( trc @ V_1 @ V_2 @ X4 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(transitive_reflexive_symmetric_closure, axiom,(( trsc ) = 50.66/7.00 (^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) )))). 50.66/7.00 thf(symmetric_closure, axiom,(( sc ) = 50.66/7.00 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) )))). 50.66/7.00 thf('12', plain, 50.66/7.00 (( sc ) = 50.66/7.00 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], [symmetric_closure])). 50.66/7.00 thf('13', plain, 50.66/7.00 (( sc ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 50.66/7.00 ( ( V_1 @ V_3 @ V_2 ) | ( V_1 @ V_2 @ V_3 ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf('14', plain, 50.66/7.00 (( trsc ) = ( ^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [transitive_reflexive_symmetric_closure, '5', '1', '13', '7', 50.66/7.00 '3'])). 50.66/7.00 thf('15', plain, 50.66/7.00 (( trsc ) = ( ^[V_1:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ V_1 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf('16', plain, 50.66/7.00 (( cr ) = 50.66/7.00 ( ^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i]: ( ( trsc @ R @ X @ Y ) => ( join @ R @ X @ Y ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [church_rosser, '11', '15', '9', '5', '1', '13', '7', '3'])). 50.66/7.00 thf('17', plain, 50.66/7.00 (( cr ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o )]: 50.66/7.00 ( ![X4:$i,X6:$i]: 50.66/7.00 ( ( trsc @ V_1 @ X4 @ X6 ) => ( join @ V_1 @ X4 @ X6 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(semi_confluent, axiom,(( sconfl ) = 50.66/7.00 (^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i,Z:$i]: 50.66/7.00 ( ( ( R @ X @ Z ) & ( trc @ R @ X @ Y ) ) => ( join @ R @ Z @ Y ) ) )))). 50.66/7.00 thf('18', plain, 50.66/7.00 (( sconfl ) = 50.66/7.00 ( ^[R:( $i > $i > $o )]: 50.66/7.00 ( ![X:$i,Y:$i,Z:$i]: 50.66/7.00 ( ( ( R @ X @ Z ) & ( trc @ R @ X @ Y ) ) => ( join @ R @ Z @ Y ) ) ) )), 50.66/7.00 inference('simplify_rw_rule', [status(thm)], 50.66/7.00 [semi_confluent, '11', '9', '5', '1', '7', '3'])). 50.66/7.00 thf('19', plain, 50.66/7.00 (( sconfl ) = 50.66/7.00 ( ^[V_1:( $i > $i > $o )]: 50.66/7.00 ( ![X4:$i,X6:$i,X8:$i]: 50.66/7.00 ( ( ( V_1 @ X4 @ X8 ) & ( trc @ V_1 @ X4 @ X6 ) ) => 50.66/7.00 ( join @ V_1 @ X8 @ X6 ) ) ) )), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(semi_confluence_implies_church_rosser, conjecture, 50.66/7.00 (![R:( $i > $i > $o )]: ( ( sconfl @ R ) => ( cr @ R ) ))). 50.66/7.00 thf(zf_stmt_0, conjecture, 50.66/7.00 (![X4:( $i > $i > $o )]: 50.66/7.00 ( ( ![X6:$i,X8:$i,X10:$i]: 50.66/7.00 ( ( ( ( ![X12:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X20:$i,X22:$i]: 50.66/7.00 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 50.66/7.00 ( ![X14:$i,X16:$i,X18:$i]: 50.66/7.00 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 50.66/7.00 ( X12 @ X14 @ X18 ) ) ) ) => 50.66/7.00 ( X12 @ X6 @ X8 ) ) ) | 50.66/7.00 ( ( X6 ) = ( X8 ) ) ) & 50.66/7.00 ( X4 @ X6 @ X10 ) ) => 50.66/7.00 ( ?[X24:$i]: 50.66/7.00 ( ( ( ![X38:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X46:$i,X48:$i]: 50.66/7.00 ( ( X4 @ X46 @ X48 ) => ( X38 @ X46 @ X48 ) ) ) & 50.66/7.00 ( ![X40:$i,X42:$i,X44:$i]: 50.66/7.00 ( ( ( X38 @ X42 @ X44 ) & ( X38 @ X40 @ X42 ) ) => 50.66/7.00 ( X38 @ X40 @ X44 ) ) ) ) => 50.66/7.00 ( X38 @ X10 @ X24 ) ) ) | 50.66/7.00 ( ( X10 ) = ( X24 ) ) ) & 50.66/7.00 ( ( ![X26:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X34:$i,X36:$i]: 50.66/7.00 ( ( X4 @ X34 @ X36 ) => ( X26 @ X34 @ X36 ) ) ) & 50.66/7.00 ( ![X28:$i,X30:$i,X32:$i]: 50.66/7.00 ( ( ( X26 @ X30 @ X32 ) & ( X26 @ X28 @ X30 ) ) => 50.66/7.00 ( X26 @ X28 @ X32 ) ) ) ) => 50.66/7.00 ( X26 @ X8 @ X24 ) ) ) | 50.66/7.00 ( ( X8 ) = ( X24 ) ) ) ) ) ) ) => 50.66/7.00 ( ![X50:$i,X52:$i]: 50.66/7.00 ( ( ( ![X66:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X74:$i,X76:$i]: 50.66/7.00 ( ( X4 @ X74 @ X76 ) => ( X66 @ X74 @ X76 ) ) ) & 50.66/7.00 ( ![X68:$i,X70:$i,X72:$i]: 50.66/7.00 ( ( ( X66 @ X70 @ X72 ) & ( X66 @ X68 @ X70 ) ) => 50.66/7.00 ( X66 @ X68 @ X72 ) ) ) ) => 50.66/7.00 ( X66 @ X50 @ X52 ) ) ) | 50.66/7.00 ( ( X50 ) = ( X52 ) ) | 50.66/7.00 ( ![X54:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X62:$i,X64:$i]: 50.66/7.00 ( ( X4 @ X62 @ X64 ) => ( X54 @ X62 @ X64 ) ) ) & 50.66/7.00 ( ![X56:$i,X58:$i,X60:$i]: 50.66/7.00 ( ( ( X54 @ X58 @ X60 ) & ( X54 @ X56 @ X58 ) ) => 50.66/7.00 ( X54 @ X56 @ X60 ) ) ) ) => 50.66/7.00 ( X54 @ X52 @ X50 ) ) ) | 50.66/7.00 ( ( X52 ) = ( X50 ) ) ) => 50.66/7.00 ( ?[X78:$i]: 50.66/7.00 ( ( ( ![X92:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X100:$i,X102:$i]: 50.66/7.00 ( ( X4 @ X100 @ X102 ) => ( X92 @ X100 @ X102 ) ) ) & 50.66/7.00 ( ![X94:$i,X96:$i,X98:$i]: 50.66/7.00 ( ( ( X92 @ X96 @ X98 ) & ( X92 @ X94 @ X96 ) ) => 50.66/7.00 ( X92 @ X94 @ X98 ) ) ) ) => 50.66/7.00 ( X92 @ X50 @ X78 ) ) ) | 50.66/7.00 ( ( X50 ) = ( X78 ) ) ) & 50.66/7.00 ( ( ![X80:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X88:$i,X90:$i]: 50.66/7.00 ( ( X4 @ X88 @ X90 ) => ( X80 @ X88 @ X90 ) ) ) & 50.66/7.00 ( ![X82:$i,X84:$i,X86:$i]: 50.66/7.00 ( ( ( X80 @ X84 @ X86 ) & ( X80 @ X82 @ X84 ) ) => 50.66/7.00 ( X80 @ X82 @ X86 ) ) ) ) => 50.66/7.00 ( X80 @ X52 @ X78 ) ) ) | 50.66/7.00 ( ( X52 ) = ( X78 ) ) ) ) ) ) ) ))). 50.66/7.00 thf(zf_stmt_1, negated_conjecture, 50.66/7.00 (~( ![X4:( $i > $i > $o )]: 50.66/7.00 ( ( ![X6:$i,X8:$i,X10:$i]: 50.66/7.00 ( ( ( ( ![X12:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X20:$i,X22:$i]: 50.66/7.00 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 50.66/7.00 ( ![X14:$i,X16:$i,X18:$i]: 50.66/7.00 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 50.66/7.00 ( X12 @ X14 @ X18 ) ) ) ) => 50.66/7.00 ( X12 @ X6 @ X8 ) ) ) | 50.66/7.00 ( ( X6 ) = ( X8 ) ) ) & 50.66/7.00 ( X4 @ X6 @ X10 ) ) => 50.66/7.00 ( ?[X24:$i]: 50.66/7.00 ( ( ( ![X38:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X46:$i,X48:$i]: 50.66/7.00 ( ( X4 @ X46 @ X48 ) => ( X38 @ X46 @ X48 ) ) ) & 50.66/7.00 ( ![X40:$i,X42:$i,X44:$i]: 50.66/7.00 ( ( ( X38 @ X42 @ X44 ) & ( X38 @ X40 @ X42 ) ) => 50.66/7.00 ( X38 @ X40 @ X44 ) ) ) ) => 50.66/7.00 ( X38 @ X10 @ X24 ) ) ) | 50.66/7.00 ( ( X10 ) = ( X24 ) ) ) & 50.66/7.00 ( ( ![X26:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X34:$i,X36:$i]: 50.66/7.00 ( ( X4 @ X34 @ X36 ) => ( X26 @ X34 @ X36 ) ) ) & 50.66/7.00 ( ![X28:$i,X30:$i,X32:$i]: 50.66/7.00 ( ( ( X26 @ X30 @ X32 ) & ( X26 @ X28 @ X30 ) ) => 50.66/7.00 ( X26 @ X28 @ X32 ) ) ) ) => 50.66/7.00 ( X26 @ X8 @ X24 ) ) ) | 50.66/7.00 ( ( X8 ) = ( X24 ) ) ) ) ) ) ) => 50.66/7.00 ( ![X50:$i,X52:$i]: 50.66/7.00 ( ( ( ![X66:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X74:$i,X76:$i]: 50.66/7.00 ( ( X4 @ X74 @ X76 ) => ( X66 @ X74 @ X76 ) ) ) & 50.66/7.00 ( ![X68:$i,X70:$i,X72:$i]: 50.66/7.00 ( ( ( X66 @ X70 @ X72 ) & ( X66 @ X68 @ X70 ) ) => 50.66/7.00 ( X66 @ X68 @ X72 ) ) ) ) => 50.66/7.00 ( X66 @ X50 @ X52 ) ) ) | 50.66/7.00 ( ( X50 ) = ( X52 ) ) | 50.66/7.00 ( ![X54:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X62:$i,X64:$i]: 50.66/7.00 ( ( X4 @ X62 @ X64 ) => ( X54 @ X62 @ X64 ) ) ) & 50.66/7.00 ( ![X56:$i,X58:$i,X60:$i]: 50.66/7.00 ( ( ( X54 @ X58 @ X60 ) & ( X54 @ X56 @ X58 ) ) => 50.66/7.00 ( X54 @ X56 @ X60 ) ) ) ) => 50.66/7.00 ( X54 @ X52 @ X50 ) ) ) | 50.66/7.00 ( ( X52 ) = ( X50 ) ) ) => 50.66/7.00 ( ?[X78:$i]: 50.66/7.00 ( ( ( ![X92:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X100:$i,X102:$i]: 50.66/7.00 ( ( X4 @ X100 @ X102 ) => ( X92 @ X100 @ X102 ) ) ) & 50.66/7.00 ( ![X94:$i,X96:$i,X98:$i]: 50.66/7.00 ( ( ( X92 @ X96 @ X98 ) & ( X92 @ X94 @ X96 ) ) => 50.66/7.00 ( X92 @ X94 @ X98 ) ) ) ) => 50.66/7.00 ( X92 @ X50 @ X78 ) ) ) | 50.66/7.00 ( ( X50 ) = ( X78 ) ) ) & 50.66/7.00 ( ( ![X80:( $i > $i > $o )]: 50.66/7.00 ( ( ( ![X88:$i,X90:$i]: 50.66/7.00 ( ( X4 @ X88 @ X90 ) => ( X80 @ X88 @ X90 ) ) ) & 50.66/7.00 ( ![X82:$i,X84:$i,X86:$i]: 50.66/7.00 ( ( ( X80 @ X84 @ X86 ) & ( X80 @ X82 @ X84 ) ) => 50.66/7.00 ( X80 @ X82 @ X86 ) ) ) ) => 50.66/7.00 ( X80 @ X52 @ X78 ) ) ) | 50.66/7.00 ( ( X52 ) = ( X78 ) ) ) ) ) ) ) ) )), 50.66/7.00 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 50.66/7.00 thf(zip_derived_cl0, plain, 50.66/7.00 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y1 @ Y2)))))) | 50.66/7.00 (((Y1) = (Y2))))) & 50.66/7.00 (Y0 @ Y1 @ Y3))) => 50.66/7.00 (((??) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) => 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y7))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y8 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y5 @ 50.66/7.00 Y7 @ 50.66/7.00 Y8) & 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y7))) => 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y8)))))))))))))) => 50.66/7.00 (Y5 @ 50.66/7.00 Y3 @ Y4)))))) | 50.66/7.00 (( 50.66/7.00 (Y3) = 50.66/7.00 (Y4))))) & 50.66/7.00 (((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) => 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y7))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y8 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y5 @ 50.66/7.00 Y7 @ 50.66/7.00 Y8) & 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y7))) => 50.66/7.00 (Y5 @ 50.66/7.00 Y6 @ Y8)))))))))))))) => 50.66/7.00 (Y5 @ 50.66/7.00 Y2 @ Y4)))))) | 50.66/7.00 (( 50.66/7.00 (Y2) = 50.66/7.00 (Y4))))))))))))))))))))) => 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y1 @ Y2)))))) | 50.66/7.00 (((Y1) = (Y2))) | 50.66/7.00 (((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y2 @ Y1)))))) | 50.66/7.00 (((Y2) = (Y1))))) => 50.66/7.00 (((??) @ (^[Y3 : $i]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y1 @ Y3)))))) | 50.66/7.00 (((Y1) = (Y3))))) & 50.66/7.00 (((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (Y0 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y2 @ Y3)))))) | 50.66/7.00 (((Y2) = (Y3)))))))))))))))))))))))), 50.66/7.00 inference('cnf', [status(esa)], [zf_stmt_1])). 50.66/7.00 thf(zip_derived_cl1, plain, 50.66/7.00 (~ (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y0 @ 50.66/7.00 Y1)))))) | 50.66/7.00 (((Y0) = (Y1))))) & 50.66/7.00 ('#sk1' @ Y0 @ Y2))) => 50.66/7.00 (((??) @ (^[Y3 : $i]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y2 @ Y3)))))) | 50.66/7.00 (((Y2) = (Y3))))) & 50.66/7.00 (((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y1 @ Y3)))))) | 50.66/7.00 (((Y1) = (Y3))))))))))))))))))))) => 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y0 @ Y1)))))) | 50.66/7.00 (((Y0) = (Y1))) | 50.66/7.00 (((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y1 @ Y0)))))) | 50.66/7.00 (((Y1) = (Y0))))) => 50.66/7.00 (((??) @ (^[Y2 : $i]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y0 @ 50.66/7.00 Y2)))))) | 50.66/7.00 (((Y0) = (Y2))))) & 50.66/7.00 (((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y1 @ 50.66/7.00 Y2)))))) | 50.66/7.00 (((Y1) = (Y2))))))))))))))))))))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 50.66/7.00 thf(zip_derived_cl3, plain, 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y0 @ Y1)))))) | 50.66/7.00 (((Y0) = (Y1))) | 50.66/7.00 (((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y1 @ Y0)))))) | 50.66/7.00 (((Y1) = (Y0))))) => 50.66/7.00 (((??) @ (^[Y2 : $i]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y0 @ Y2)))))) | 50.66/7.00 (((Y0) = (Y2))))) & 50.66/7.00 (((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y1 @ Y2)))))) | 50.66/7.00 (((Y1) = (Y2))))))))))))))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 50.66/7.00 thf(zip_derived_cl5, plain, 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ Y3) => 50.66/7.00 (Y1 @ Y2 @ 50.66/7.00 Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ '#sk2' @ Y0)))))) | 50.66/7.00 ((('#sk2') = (Y0))) | 50.66/7.00 (((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ Y3) => 50.66/7.00 (Y1 @ Y2 @ 50.66/7.00 Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ Y0 @ '#sk2')))))) | 50.66/7.00 (((Y0) = ('#sk2'))))) => 50.66/7.00 (((??) @ (^[Y1 : $i]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ '#sk2' @ Y1)))))) | 50.66/7.00 ((('#sk2') = (Y1))))) & 50.66/7.00 (((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y0 @ Y1)))))) | 50.66/7.00 (((Y0) = (Y1)))))))))))))))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 50.66/7.00 thf(zip_derived_cl7, plain, 50.66/7.00 (~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) | 50.66/7.00 ((('#sk2') = ('#sk3'))) | 50.66/7.00 (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) | 50.66/7.00 ((('#sk3') = ('#sk2'))))) => 50.66/7.00 (((??) @ (^[Y0 : $i]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ '#sk2' @ Y0)))))) | 50.66/7.00 ((('#sk2') = (Y0))))) & 50.66/7.00 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ '#sk3' @ Y0)))))) | 50.66/7.00 ((('#sk3') = (Y0))))))))))))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 50.66/7.00 thf(zip_derived_cl10, plain, 50.66/7.00 (~ (((??) @ (^[Y0 : $i]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ Y3) => 50.66/7.00 (Y1 @ Y2 @ 50.66/7.00 Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ '#sk2' @ Y0)))))) | 50.66/7.00 ((('#sk2') = (Y0))))) & 50.66/7.00 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ Y3) => 50.66/7.00 (Y1 @ Y2 @ 50.66/7.00 Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ '#sk3' @ Y0)))))) | 50.66/7.00 ((('#sk3') = (Y0))))))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 50.66/7.00 thf(zip_derived_cl13, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ X2)))))) | 50.66/7.00 ((('#sk2') = (X2))))) & 50.66/7.00 (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2)))))))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 50.66/7.00 thf(zip_derived_cl19, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ X2)))))) | 50.66/7.00 ((('#sk2') = (X2))))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 50.66/7.00 thf(zip_derived_cl26, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ X2)))))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 50.66/7.00 thf(zip_derived_cl36, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk2' @ 50.66/7.00 X2 @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk2' @ 50.66/7.00 X2 @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y0 @ Y2)))))))))))))) => 50.66/7.00 ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 50.66/7.00 thf(zip_derived_cl47, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y1 @ Y2) & ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y0 @ Y2)))))))))))))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 50.66/7.00 thf(zip_derived_cl59, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( ('#form65' @ X2) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl61, plain, 50.66/7.00 (![X2 : $i]: (~ ((('#sk3') = (X2))) | ('#form65' @ X2))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 50.66/7.00 thf(zip_derived_cl83, plain, 50.66/7.00 (![X2 : $i]: ((('#sk3') != (X2)) | ('#form65' @ X2))), 50.66/7.00 inference('simplify nested equalities', [status(thm)], [zip_derived_cl61])). 50.66/7.00 thf(zip_derived_cl84, plain, ( ('#form65' @ '#sk3')), 50.66/7.00 inference('simplify', [status(thm)], [zip_derived_cl83])). 50.66/7.00 thf(zip_derived_cl48, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 50.66/7.00 thf(zip_derived_cl59, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( ('#form65' @ X2) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl63, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ ('#form65' @ X2) | ~ ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2))), 50.66/7.00 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl59])). 50.66/7.00 thf(zip_derived_cl9, plain, 50.66/7.00 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) | 50.66/7.00 ((('#sk2') = ('#sk3'))) | 50.66/7.00 (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) | 50.66/7.00 ((('#sk3') = ('#sk2')))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 50.66/7.00 thf(zip_derived_cl12, plain, 50.66/7.00 (( (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.66/7.00 Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | ((('#sk2') = ('#sk3'))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) 50.66/7.00 | ((('#sk3') = ('#sk2'))))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 50.66/7.00 thf(zip_derived_cl15, plain, 50.66/7.00 (( (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.66/7.00 Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | (('#sk2') = ('#sk3')) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) 50.66/7.00 | (('#sk3') = ('#sk2')))), 50.66/7.00 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 50.66/7.00 thf(zip_derived_cl16, plain, 50.66/7.00 (( (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.66/7.00 Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) 50.66/7.00 | (('#sk2') = ('#sk3')) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 inference('simplify', [status(thm)], [zip_derived_cl15])). 50.66/7.00 thf(zip_derived_cl17, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))) => 50.66/7.00 (X2 @ '#sk3' @ '#sk2'))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | (('#sk2') = ('#sk3')))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.66/7.00 thf(zip_derived_cl22, plain, 50.66/7.00 ((~ ('#form12') 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl23, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))) => 50.66/7.00 (X2 @ '#sk2' @ '#sk3'))) 50.66/7.00 | ~ ('#form12'))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 50.66/7.00 thf(zip_derived_cl35, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))) 50.66/7.00 | (X2 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form12'))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 50.66/7.00 thf(zip_derived_cl46, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))) 50.66/7.00 | ~ ('#form12') 50.66/7.00 | (X2 @ '#sk2' @ '#sk3'))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 50.66/7.00 thf(zip_derived_cl58, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 ((('#sk1' @ ('#sk56' @ X2) @ Y0) => (X2 @ 50.66/7.00 ('#sk56' @ X2) @ Y0)))))) 50.66/7.00 | (X2 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form12') 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])). 50.66/7.00 thf(zip_derived_cl79, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 50.66/7.00 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))) 50.66/7.00 | ~ ('#form12') 50.66/7.00 | (X2 @ '#sk2' @ '#sk3'))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 50.66/7.00 thf(zip_derived_cl95, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( ('#form133' @ X2) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl96, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((((X2 @ Y0 @ Y1) & (X2 @ 50.66/7.00 ('#sk134' @ X2) @ Y0))) => 50.66/7.00 (X2 @ ('#sk134' @ X2) @ Y1))))))))) 50.66/7.00 | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 50.66/7.00 thf(zip_derived_cl122, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((((X2 @ ('#sk191' @ X2) @ Y0) & (X2 @ 50.66/7.00 ('#sk134' @ X2) @ ('#sk191' @ X2)))) => 50.66/7.00 (X2 @ ('#sk134' @ X2) @ Y0)))))) 50.66/7.00 | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 50.66/7.00 thf(zip_derived_cl137, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (((((X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) & (X2 @ 50.66/7.00 ('#sk134' @ X2) @ ('#sk191' @ X2)))) => 50.66/7.00 (X2 @ ('#sk134' @ X2) @ ('#sk278' @ X2)))) 50.66/7.00 | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 50.66/7.00 thf(zip_derived_cl153, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (((X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) & (X2 @ 50.66/7.00 ('#sk134' @ X2) @ ('#sk191' @ X2)))) 50.66/7.00 | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 50.66/7.00 thf(zip_derived_cl164, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 50.66/7.00 thf(zip_derived_cl165, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (X2 @ ('#sk134' @ X2) @ ('#sk191' @ X2)) | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 50.66/7.00 thf(zip_derived_cl154, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (X2 @ ('#sk134' @ X2) @ ('#sk278' @ X2)) | ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 50.66/7.00 thf(zip_derived_cl47, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y1 @ Y2) & ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y0 @ Y2)))))))))))))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 50.66/7.00 thf(zip_derived_cl59, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( ('#form65' @ X2) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl62, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ ('#form65' @ X2) 50.66/7.00 | (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk2' @ 50.66/7.00 X2 @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk2' @ 50.66/7.00 X2 @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk2' @ X2 @ 50.66/7.00 Y0 @ Y2)))))))))))))))), 50.66/7.00 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl59])). 50.66/7.00 thf(zip_derived_cl80, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ( (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk2' @ 50.66/7.00 X2 @ Y0 @ Y1))))))))) 50.66/7.00 | ~ ('#form65' @ X2))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 50.66/7.00 thf(zip_derived_cl98, plain, 50.66/7.00 (![X2 : $i, X4 : $i]: 50.66/7.00 ( (((!!) @ (^[Y0 : $i]: 50.66/7.00 ((('#sk1' @ X4 @ Y0) => ('#sk13' @ '#sk2' @ X2 @ X4 @ 50.66/7.00 Y0)))))) 50.66/7.00 | ~ ('#form65' @ X2))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 50.66/7.00 thf(zip_derived_cl123, plain, 50.66/7.00 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.00 ( ((('#sk1' @ X4 @ X6) => ('#sk13' @ '#sk2' @ X2 @ X4 @ X6))) 50.66/7.00 | ~ ('#form65' @ X2))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 50.66/7.00 thf(zip_derived_cl138, plain, 50.66/7.00 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.00 (~ ('#sk1' @ X4 @ X6) 50.66/7.00 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X6) 50.66/7.00 | ~ ('#form65' @ X2))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 50.66/7.00 thf(zip_derived_cl79, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 50.66/7.00 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))) 50.66/7.00 | ~ ('#form12') 50.66/7.00 | (X2 @ '#sk2' @ '#sk3'))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 50.66/7.00 thf(zip_derived_cl95, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( ('#form133' @ X2) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl97, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ ('#form133' @ X2) 50.66/7.00 | (X2 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form12') 50.66/7.00 | ~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 50.66/7.00 ('#sk56' @ X2) @ ('#sk77' @ X2)))))), 50.66/7.00 inference('renaming', [status(thm)], [zip_derived_cl79, zip_derived_cl95])). 50.66/7.00 thf(zip_derived_cl121, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 (~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 50.66/7.00 | ~ ('#form12') 50.66/7.00 | (X2 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form133' @ X2))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 50.66/7.00 thf(zip_derived_cl727, plain, 50.66/7.00 (![X0 : $i > $i > $o]: 50.66/7.00 (((X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) != ('#form133' @ X0)) 50.66/7.00 | ~ ('#form133' @ X0) 50.66/7.00 | (X0 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form12'))), 50.66/7.00 inference('eq_fact', [status(thm)], [zip_derived_cl121])). 50.66/7.00 thf(zip_derived_cl735, plain, 50.66/7.00 (![X0 : $i > $i > $o]: 50.66/7.00 (~ (X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) 50.66/7.00 | ~ ('#form133' @ X0) 50.66/7.00 | (X0 @ '#sk2' @ '#sk3') 50.66/7.00 | ~ ('#form12'))), 50.66/7.00 inference('local_rewriting', [status(thm)], [zip_derived_cl727])). 50.66/7.00 thf(zip_derived_cl17, plain, 50.66/7.00 (![X2 : $i > $i > $o]: 50.66/7.00 ( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.00 Y0 @ Y1))) => 50.66/7.00 (X2 @ Y0 @ Y2)))))))))))))) => 50.66/7.00 (X2 @ '#sk3' @ '#sk2'))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ 50.66/7.00 Y2 @ Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ 50.66/7.00 Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | (('#sk2') = ('#sk3')))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.66/7.00 thf(zip_derived_cl185, plain, 50.66/7.00 (( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))) => 50.66/7.00 ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2'))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | (('#sk2') = ('#sk3')))), 50.66/7.00 inference('triggered_bool_instantiation', [status(thm)], 50.66/7.00 [zip_derived_cl17])). 50.66/7.00 thf(zip_derived_cl27, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (~ ((('#sk2') = (X2))) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 50.66/7.00 thf(zip_derived_cl37, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 ((('#sk2') != (X2)) 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ X2)))))) | 50.66/7.00 ((('#sk3') = (X2))))))), 50.66/7.00 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 50.66/7.00 thf(zip_derived_cl38, plain, 50.66/7.00 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2')))))) | 50.66/7.00 ((('#sk3') = ('#sk2')))))), 50.66/7.00 inference('simplify', [status(thm)], [zip_derived_cl37])). 50.66/7.00 thf(zip_derived_cl39, plain, 50.66/7.00 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 50.66/7.00 Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk3' @ '#sk2'))))))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 50.66/7.00 thf(zip_derived_cl49, plain, 50.66/7.00 (~ (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))) => 50.66/7.00 ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')))), 50.66/7.00 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl39])). 50.66/7.00 thf(zip_derived_cl65, plain, 50.66/7.00 (~ ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 50.66/7.00 thf(zip_derived_cl259, plain, 50.66/7.00 (( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))) => 50.66/7.00 ($false))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.00 | (('#sk2') = ('#sk3')))), 50.66/7.00 inference('demod', [status(thm)], [zip_derived_cl185, zip_derived_cl65])). 50.66/7.00 thf(zip_derived_cl40, plain, (~ ((('#sk3') = ('#sk2')))), 50.66/7.00 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 50.66/7.00 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 50.66/7.00 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 50.66/7.00 thf(zip_derived_cl260, plain, 50.66/7.00 (( (((((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))) => 50.66/7.00 ($false))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 inference('simplify_reflect-', [status(thm)], 50.66/7.00 [zip_derived_cl259, zip_derived_cl50])). 50.66/7.00 thf(zip_derived_cl261, plain, 50.66/7.00 (( (((~) @ (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl260])). 50.66/7.00 thf(zip_derived_cl262, plain, 50.66/7.00 ((~ (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.00 Y0 @ Y2)))))))))))))) 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 inference('simplify nested equalities', [status(thm)], 50.66/7.00 [zip_derived_cl261])). 50.66/7.00 thf(zip_derived_cl22, plain, 50.66/7.00 ((~ ('#form12') 50.66/7.00 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((((Y0 @ Y2 @ 50.66/7.00 Y3) & (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.00 define([status(thm)])). 50.66/7.00 thf(zip_derived_cl263, plain, 50.66/7.00 (( ('#form12') 50.66/7.00 | ~ (((((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 50.66/7.00 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y2)))))))))))))))), 50.66/7.00 inference('renaming', [status(thm)], 50.66/7.00 [zip_derived_cl262, zip_derived_cl22])). 50.66/7.00 thf(zip_derived_cl264, plain, 50.66/7.00 ((~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))))))))) 50.66/7.00 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((((('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y1 @ Y2) & 50.66/7.00 ('#sk13' @ '#sk3' @ 50.66/7.00 '#sk2' @ Y0 @ Y1))) => 50.66/7.00 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.00 Y0 @ Y2)))))))))))) 50.66/7.00 | ('#form12'))), 50.66/7.00 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl263])). 50.66/7.00 thf(zip_derived_cl2, plain, 50.66/7.00 ( (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 ( 50.66/7.00 ( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 ( 50.66/7.00 ( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y0 @ Y1)))))) | 50.66/7.00 (((Y0) = (Y1))))) & 50.66/7.00 ('#sk1' @ Y0 @ Y2))) => 50.66/7.00 (((??) @ (^[Y3 : $i]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ Y2 @ 50.66/7.00 Y3)))))) | 50.66/7.00 (((Y2) = (Y3))))) & 50.66/7.00 (((((!!) @ ( 50.66/7.00 ^[Y4 : 50.66/7.00 $i > $i > $o]: 50.66/7.00 (((((( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))))))))) & 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y7 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y4 @ 50.66/7.00 Y6 @ 50.66/7.00 Y7) & 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y6))) => 50.66/7.00 (Y4 @ 50.66/7.00 Y5 @ Y7)))))))))))))) => 50.66/7.00 (Y4 @ Y1 @ 50.66/7.00 Y3)))))) | 50.66/7.00 (((Y1) = (Y3)))))))))))))))))))))), 50.66/7.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 50.66/7.00 thf(zip_derived_cl4, plain, 50.66/7.00 (![X2 : $i]: 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((((((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ X2 @ Y0)))))) | 50.66/7.00 (((X2) = (Y0))))) & 50.66/7.00 ('#sk1' @ X2 @ Y1))) => 50.66/7.00 (((??) @ (^[Y2 : $i]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y1 @ 50.66/7.00 Y2)))))) | 50.66/7.00 (((Y1) = (Y2))))) & 50.66/7.00 (((((!!) @ (^[Y3 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))))))))) & 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y6 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y3 @ 50.66/7.00 Y5 @ 50.66/7.00 Y6) & 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y5))) => 50.66/7.00 (Y3 @ 50.66/7.00 Y4 @ Y6)))))))))))))) => 50.66/7.00 (Y3 @ Y0 @ 50.66/7.00 Y2)))))) | 50.66/7.00 (((Y0) = (Y2))))))))))))))))))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 50.66/7.00 thf(zip_derived_cl6, plain, 50.66/7.00 (![X2 : $i, X4 : $i]: 50.66/7.00 (((!!) @ (^[Y0 : $i]: 50.66/7.00 (((((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y1 @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) & 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y4)))))))))))))) => 50.66/7.00 (Y1 @ X2 @ X4)))))) | 50.66/7.00 (((X2) = (X4))))) & 50.66/7.00 ('#sk1' @ X2 @ Y0))) => 50.66/7.00 (((??) @ (^[Y1 : $i]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ Y0 @ Y1)))))) | 50.66/7.00 (((Y0) = (Y1))))) & 50.66/7.00 (((((!!) @ (^[Y2 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 ('#sk1' @ 50.66/7.00 Y3 @ 50.66/7.00 Y4) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))))))))) & 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.00 (( 50.66/7.00 (!!) @ ( 50.66/7.00 ^[Y5 : $i]: 50.66/7.00 (( 50.66/7.00 (( 50.66/7.00 (Y2 @ 50.66/7.00 Y4 @ 50.66/7.00 Y5) & 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y4))) => 50.66/7.00 (Y2 @ 50.66/7.00 Y3 @ Y5)))))))))))))) => 50.66/7.00 (Y2 @ X4 @ Y1)))))) | 50.66/7.00 (((X4) = (Y1)))))))))))))))), 50.66/7.00 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 50.66/7.00 thf(zip_derived_cl8, plain, 50.66/7.00 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.00 (((((((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 ((('#sk1' @ Y1 @ Y2) => 50.66/7.00 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.00 (((!!) @ (^[Y1 : $i]: 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((( 50.66/7.00 (Y0 @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) & 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y2))) => 50.66/7.00 (Y0 @ 50.66/7.00 Y1 @ Y3)))))))))))))) => 50.66/7.00 (Y0 @ X2 @ X4)))))) | 50.66/7.00 (((X2) = (X4))))) & 50.66/7.00 ('#sk1' @ X2 @ X6))) => 50.66/7.00 (((??) @ (^[Y0 : $i]: 50.66/7.00 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.00 (((((((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 ((('#sk1' @ 50.66/7.00 Y2 @ 50.66/7.00 Y3) => 50.66/7.00 (Y1 @ 50.66/7.00 Y2 @ Y3))))))))) & 50.66/7.00 (((!!) @ (^[Y2 : $i]: 50.66/7.00 (((!!) @ (^[Y3 : $i]: 50.66/7.00 (((!!) @ ( 50.66/7.00 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 ((('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0))))))))))))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 50.66/7.01 thf(zip_derived_cl11, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.01 (~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((( 50.66/7.01 (Y0 @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ X2 @ X4)))))) | 50.66/7.01 (((X2) = (X4))))) & 50.66/7.01 ('#sk1' @ X2 @ X6))) 50.66/7.01 | (((??) @ (^[Y0 : $i]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0)))))))))))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 50.66/7.01 thf(zip_derived_cl14, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.01 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ 50.66/7.01 Y3)))))))))))))) => 50.66/7.01 (Y0 @ X2 @ X4)))))) | 50.66/7.01 (((X2) = (X4))))) 50.66/7.01 | ~ ('#sk1' @ X2 @ X6) 50.66/7.01 | (((??) @ (^[Y0 : $i]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0)))))))))))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 50.66/7.01 thf(zip_derived_cl21, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.01 (~ (((X2) = (X4))) 50.66/7.01 | (((??) @ (^[Y0 : $i]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0)))))))))) 50.66/7.01 | ~ ('#sk1' @ X2 @ X6))), 50.66/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])). 50.66/7.01 thf(zip_derived_cl31, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.01 (((X2) != (X4)) 50.66/7.01 | (((??) @ (^[Y0 : $i]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0)))))))))) 50.66/7.01 | ~ ('#sk1' @ X2 @ X6))), 50.66/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 50.66/7.01 thf(zip_derived_cl32, plain, 50.66/7.01 (![X4 : $i, X6 : $i]: 50.66/7.01 (~ ('#sk1' @ X4 @ X6) 50.66/7.01 | (((??) @ (^[Y0 : $i]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X6 @ Y0)))))) | 50.66/7.01 (((X6) = (Y0))))) & 50.66/7.01 (((((!!) @ (^[Y1 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 ('#sk1' @ 50.66/7.01 Y2 @ 50.66/7.01 Y3) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))))))))) & 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (( 50.66/7.01 (!!) @ ( 50.66/7.01 ^[Y4 : $i]: 50.66/7.01 (( 50.66/7.01 (( 50.66/7.01 (Y1 @ 50.66/7.01 Y3 @ 50.66/7.01 Y4) & 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y3))) => 50.66/7.01 (Y1 @ 50.66/7.01 Y2 @ Y4)))))))))))))) => 50.66/7.01 (Y1 @ X4 @ Y0)))))) | 50.66/7.01 (((X4) = (Y0)))))))))))), 50.66/7.01 inference('simplify', [status(thm)], [zip_derived_cl31])). 50.66/7.01 thf(zip_derived_cl33, plain, 50.66/7.01 (![X4 : $i, X6 : $i]: 50.66/7.01 ( (((((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((( 50.66/7.01 (Y0 @ 50.66/7.01 Y2 @ Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) | 50.66/7.01 (((X6) = ('#sk14' @ X4 @ X6))))) & 50.66/7.01 (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((( 50.66/7.01 (Y0 @ 50.66/7.01 Y2 @ Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ X4 @ ('#sk14' @ X4 @ X6))))))) | 50.66/7.01 (((X4) = ('#sk14' @ X4 @ X6))))))) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6))), 50.66/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 50.66/7.01 thf(zip_derived_cl43, plain, 50.66/7.01 (![X4 : $i, X6 : $i]: 50.66/7.01 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ 50.66/7.01 Y2 @ Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ 50.66/7.01 Y3)))))))))))))) => 50.66/7.01 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) | 50.66/7.01 (((X6) = ('#sk14' @ X4 @ X6))))) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl33])). 50.66/7.01 thf(zip_derived_cl55, plain, 50.66/7.01 (![X4 : $i, X6 : $i]: 50.66/7.01 ( (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ Y2 @ 50.66/7.01 Y3) & (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) 50.66/7.01 | (((X6) = ('#sk14' @ X4 @ X6))) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6))), 50.66/7.01 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 50.66/7.01 thf(zip_derived_cl70, plain, 50.66/7.01 (![X4 : $i, X6 : $i]: 50.66/7.01 ( (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ Y2 @ 50.66/7.01 Y3) & (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6))), 50.66/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl55])). 50.66/7.01 thf(zip_derived_cl71, plain, 50.66/7.01 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 50.66/7.01 ( (((((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X8 @ Y1 @ Y2) & (X8 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X8 @ Y0 @ Y2)))))))))))))) => 50.66/7.01 (X8 @ X6 @ ('#sk14' @ X4 @ X6)))) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 50.66/7.01 thf(zip_derived_cl91, plain, 50.66/7.01 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 50.66/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X8 @ Y1 @ Y2) & (X8 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X8 @ Y0 @ Y2)))))))))))))) 50.66/7.01 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 50.66/7.01 thf(zip_derived_cl116, plain, 50.66/7.01 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 50.66/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X8 @ Y1 @ Y2) & (X8 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X8 @ Y0 @ Y2)))))))))))) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)) 50.66/7.01 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 50.66/7.01 thf(zip_derived_cl64, plain, 50.66/7.01 ( (((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y1 @ Y2) & ('#sk13' @ 50.66/7.01 '#sk3' @ '#sk2' @ Y0 @ Y1))) => 50.66/7.01 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y0 @ Y2))))))))))))))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 50.66/7.01 thf(zip_derived_cl86, plain, 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y1 @ Y2) & ('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y0 @ Y1))) => 50.66/7.01 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y0 @ Y2))))))))))))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 50.66/7.01 thf(zip_derived_cl103, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl95, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form133' @ X2) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl133, plain, 50.66/7.01 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X8 @ Y0 @ Y1))) 50.66/7.01 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl116, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl147, plain, 50.66/7.01 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X8) 50.66/7.01 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 50.66/7.01 | ((X6) = ('#sk14' @ X4 @ X6)) 50.66/7.01 | ~ ('#sk1' @ X4 @ X6) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 50.66/7.01 inference('ho_norm', [status(thm)], [zip_derived_cl133])). 50.66/7.01 thf(zip_derived_cl148, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 ( ('#form307' @ X8) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl265, plain, 50.66/7.01 ((~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')) 50.66/7.01 | ('#form12') 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y1 @ Y2) & 50.66/7.01 ('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y0 @ Y1))) => 50.66/7.01 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y0 @ Y2)))))))))))))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl264, zip_derived_cl148])). 50.66/7.01 thf(zip_derived_cl103, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl95, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form133' @ X2) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl266, plain, 50.66/7.01 ((~ ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2')) 50.66/7.01 | ('#form12') 50.66/7.01 | ~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl265, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl86, plain, 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y1 @ Y2) & ('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y0 @ Y1))) => 50.66/7.01 ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 Y0 @ Y2))))))))))))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 50.66/7.01 thf(zip_derived_cl103, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl95, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form133' @ X2) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl105, plain, ( ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2'))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl86, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl267, plain, 50.66/7.01 (( ('#form12') | ~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')))), 50.66/7.01 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl105])). 50.66/7.01 thf(zip_derived_cl148, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 ( ('#form307' @ X8) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl149, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 ((('#sk1' @ ('#sk56' @ X8) @ Y0) => (X8 @ 50.66/7.01 ('#sk56' @ X8) @ Y0)))))) 50.66/7.01 | ('#form307' @ X8))), 50.66/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 50.66/7.01 thf(zip_derived_cl162, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 (~ ((('#sk1' @ ('#sk56' @ X8) @ ('#sk77' @ X8)) => (X8 @ 50.66/7.01 ('#sk56' @ X8) @ ('#sk77' @ X8)))) 50.66/7.01 | ('#form307' @ X8))), 50.66/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 50.66/7.01 thf(zip_derived_cl175, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 (~ (X8 @ ('#sk56' @ X8) @ ('#sk77' @ X8)) | ('#form307' @ X8))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 50.66/7.01 thf(zip_derived_cl85, plain, 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 50.66/7.01 '#sk2' @ Y0 @ Y1)))))))))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 50.66/7.01 thf(zip_derived_cl102, plain, 50.66/7.01 (![X2 : $i]: 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 ((('#sk1' @ X2 @ Y0) => ('#sk13' @ '#sk3' @ '#sk2' @ 50.66/7.01 X2 @ Y0))))))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 50.66/7.01 thf(zip_derived_cl127, plain, 50.66/7.01 (![X2 : $i, X4 : $i]: 50.66/7.01 ((('#sk1' @ X2 @ X4) => ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4)))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 50.66/7.01 thf(zip_derived_cl142, plain, 50.66/7.01 (![X2 : $i, X4 : $i]: 50.66/7.01 (~ ('#sk1' @ X2 @ X4) | ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 50.66/7.01 thf(zip_derived_cl571, plain, 50.66/7.01 (( ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')) 50.66/7.01 | ~ ('#sk1' @ ('#sk56' @ ('#sk13' @ '#sk3' @ '#sk2')) @ 50.66/7.01 ('#sk77' @ ('#sk13' @ '#sk3' @ '#sk2'))))), 50.66/7.01 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl142])). 50.66/7.01 thf(zip_derived_cl174, plain, 50.66/7.01 (![X8 : $i > $i > $o]: 50.66/7.01 ( ('#sk1' @ ('#sk56' @ X8) @ ('#sk77' @ X8)) | ('#form307' @ X8))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 50.66/7.01 thf(zip_derived_cl990, plain, ( ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2'))), 50.66/7.01 inference('clc', [status(thm)], [zip_derived_cl571, zip_derived_cl174])). 50.66/7.01 thf(zip_derived_cl991, plain, ( ('#form12')), 50.66/7.01 inference('demod', [status(thm)], [zip_derived_cl267, zip_derived_cl990])). 50.66/7.01 thf(zip_derived_cl1075, plain, 50.66/7.01 (![X0 : $i > $i > $o]: 50.66/7.01 (~ (X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) 50.66/7.01 | ~ ('#form133' @ X0) 50.66/7.01 | (X0 @ '#sk2' @ '#sk3'))), 50.66/7.01 inference('demod', [status(thm)], [zip_derived_cl735, zip_derived_cl991])). 50.66/7.01 thf(zip_derived_cl81, plain, 50.66/7.01 (![X2 : $i]: 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk2' @ X2 @ 50.66/7.01 Y1 @ Y2) & ('#sk13' @ 50.66/7.01 '#sk2' @ X2 @ Y0 @ Y1))) => 50.66/7.01 ('#sk13' @ '#sk2' @ X2 @ Y0 @ 50.66/7.01 Y2)))))))))))) 50.66/7.01 | ~ ('#form65' @ X2))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 50.66/7.01 thf(zip_derived_cl99, plain, 50.66/7.01 (![X2 : $i, X4 : $i]: 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk2' @ X2 @ Y0 @ Y1) & 50.66/7.01 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y0))) => 50.66/7.01 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y1))))))))) 50.66/7.01 | ~ ('#form65' @ X2))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 50.66/7.01 thf(zip_derived_cl124, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i]: 50.66/7.01 ( (((!!) @ (^[Y0 : $i]: 50.66/7.01 ((((('#sk13' @ '#sk2' @ X2 @ X6 @ Y0) & ('#sk13' @ 50.66/7.01 '#sk2' @ X2 @ X4 @ X6))) => 50.66/7.01 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y0)))))) 50.66/7.01 | ~ ('#form65' @ X2))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 50.66/7.01 thf(zip_derived_cl139, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.66/7.01 ( ((((('#sk13' @ '#sk2' @ X2 @ X6 @ X8) & ('#sk13' @ '#sk2' @ X2 @ 50.66/7.01 X4 @ X6))) => 50.66/7.01 ('#sk13' @ '#sk2' @ X2 @ X4 @ X8))) 50.66/7.01 | ~ ('#form65' @ X2))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 50.66/7.01 thf(zip_derived_cl155, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.66/7.01 (~ ((('#sk13' @ '#sk2' @ X2 @ X6 @ X8) & ('#sk13' @ '#sk2' @ X2 @ 50.66/7.01 X4 @ X6))) 50.66/7.01 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X8) 50.66/7.01 | ~ ('#form65' @ X2))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 50.66/7.01 thf(zip_derived_cl166, plain, 50.66/7.01 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 50.66/7.01 (~ ('#sk13' @ '#sk2' @ X2 @ X6 @ X8) 50.66/7.01 | ~ ('#sk13' @ '#sk2' @ X2 @ X4 @ X6) 50.66/7.01 | ~ ('#form65' @ X2) 50.66/7.01 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X8))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 50.66/7.01 thf(zip_derived_cl105, plain, ( ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2'))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl86, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl120, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 50.66/7.01 | ~ ('#form12') 50.66/7.01 | (X2 @ '#sk2' @ '#sk3') 50.66/7.01 | ~ ('#form133' @ X2))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 50.66/7.01 thf(zip_derived_cl17, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( (((((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))) => 50.66/7.01 (X2 @ '#sk3' @ '#sk2'))) 50.66/7.01 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ 50.66/7.01 Y2 @ Y3) & 50.66/7.01 (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ 50.66/7.01 Y3)))))))))))))) => 50.66/7.01 (Y0 @ '#sk2' @ '#sk3')))))) 50.66/7.01 | (('#sk2') = ('#sk3')))), 50.66/7.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 50.66/7.01 thf(zip_derived_cl22, plain, 50.66/7.01 ((~ ('#form12') 50.66/7.01 | (((!!) @ (^[Y0 : $i > $i > $o]: 50.66/7.01 (((((((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 ((('#sk1' @ Y1 @ Y2) => 50.66/7.01 (Y0 @ Y1 @ Y2))))))))) & 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((!!) @ (^[Y3 : $i]: 50.66/7.01 (((((Y0 @ Y2 @ 50.66/7.01 Y3) & (Y0 @ 50.66/7.01 Y1 @ Y2))) => 50.66/7.01 (Y0 @ Y1 @ Y3)))))))))))))) => 50.66/7.01 (Y0 @ '#sk2' @ '#sk3')))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl25, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (((((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & 50.66/7.01 (X2 @ Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))) => 50.66/7.01 (X2 @ '#sk3' @ '#sk2'))))), 50.66/7.01 inference('renaming', [status(thm)], [zip_derived_cl17, zip_derived_cl22])). 50.66/7.01 thf(zip_derived_cl34, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ (((((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 50.66/7.01 (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | ('#form12'))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 50.66/7.01 thf(zip_derived_cl45, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2'))), 50.66/7.01 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 50.66/7.01 thf(zip_derived_cl57, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 ((('#sk1' @ ('#sk56' @ X2) @ Y0) => (X2 @ 50.66/7.01 ('#sk56' @ X2) @ Y0)))))) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | ('#form12') 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 50.66/7.01 thf(zip_derived_cl78, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 50.66/7.01 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2'))), 50.66/7.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 50.66/7.01 thf(zip_derived_cl93, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | ('#form12') 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 50.66/7.01 thf(zip_derived_cl103, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl95, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form133' @ X2) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl118, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X2 @ Y0 @ Y1))) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl93, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl135, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('ho_norm', [status(thm)], [zip_derived_cl118])). 50.66/7.01 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 50.66/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 50.66/7.01 thf(zip_derived_cl212, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | ('#form12') 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('simplify_reflect-', [status(thm)], 50.66/7.01 [zip_derived_cl135, zip_derived_cl50])). 50.66/7.01 thf(zip_derived_cl65, plain, 50.66/7.01 (~ ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 50.66/7.01 thf(zip_derived_cl142, plain, 50.66/7.01 (![X2 : $i, X4 : $i]: 50.66/7.01 (~ ('#sk1' @ X2 @ X4) | ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 50.66/7.01 thf(zip_derived_cl94, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | ('#form12') 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 50.66/7.01 thf(zip_derived_cl103, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl95, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 ( ('#form133' @ X2) 50.66/7.01 | ~ (((!!) @ (^[Y0 : $i]: 50.66/7.01 (((!!) @ (^[Y1 : $i]: 50.66/7.01 (((!!) @ (^[Y2 : $i]: 50.66/7.01 (((((X2 @ Y1 @ Y2) & (X2 @ 50.66/7.01 Y0 @ Y1))) => 50.66/7.01 (X2 @ Y0 @ Y2)))))))))))))), 50.66/7.01 define([status(thm)])). 50.66/7.01 thf(zip_derived_cl119, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X2 @ Y0 @ Y1))) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('renaming', [status(thm)], 50.66/7.01 [zip_derived_cl94, zip_derived_cl103, zip_derived_cl95])). 50.66/7.01 thf(zip_derived_cl136, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | ('#form12') 50.66/7.01 | (('#sk2') = ('#sk3')) 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('ho_norm', [status(thm)], [zip_derived_cl119])). 50.66/7.01 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 50.66/7.01 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 50.66/7.01 thf(zip_derived_cl228, plain, 50.66/7.01 (![X2 : $i > $i > $o]: 50.66/7.01 (~ ('#form133' @ X2) 50.66/7.01 | ('#form12') 50.66/7.01 | (X2 @ '#sk3' @ '#sk2') 50.66/7.01 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 50.66/7.01 inference('simplify_reflect-', [status(thm)], 50.66/7.01 [zip_derived_cl136, zip_derived_cl50])). 50.66/7.01 thf(zip_derived_cl3677, plain, ($false), 50.66/7.01 inference('eprover', [status(thm)], 50.66/7.01 [zip_derived_cl84, zip_derived_cl63, zip_derived_cl164, 50.66/7.01 zip_derived_cl165, zip_derived_cl154, zip_derived_cl138, 50.66/7.01 zip_derived_cl1075, zip_derived_cl166, zip_derived_cl105, 50.66/7.01 zip_derived_cl120, zip_derived_cl212, zip_derived_cl65, 50.66/7.01 zip_derived_cl142, zip_derived_cl228])). 50.66/7.01 50.66/7.01 % SZS output end Refutation 50.66/7.01 50.66/7.01 50.66/7.01 % Terminating... 51.97/7.14 % Runner terminated. 51.97/7.15 % Zipperpin 1.5 exiting 51.97/7.15 EOF