0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JZfGJZv30w true 0.20/0.47 % Computer : n006.cluster.edu 0.20/0.47 % Model : x86_64 x86_64 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.20/0.47 % Memory : 8046.5625MB 0.20/0.47 % OS : Linux 6.8.0-71-generic 0.20/0.47 % CPULimit : 1440 0.20/0.47 % WCLimit : 180 0.20/0.47 % DateTime : Mon Jul 27 13:15:19 UTC 2026 0.20/0.48 % CPUTime : 0.20/0.48 % Running portfolio for 1440 s 0.20/0.48 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.20/0.48 % Number of cores: 8 0.20/0.48 % Python version: Python 3.12.3 0.20/0.49 % Running in HO mode 0.44/0.82 % Total configuration time : 828 0.44/0.82 % Estimated wc time : 1656 0.44/0.82 % Estimated cpu time (8 cpus) : 207.0 0.46/0.92 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.46/1.02 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.46/1.03 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.46/1.03 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.46/1.03 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.46/1.04 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.46/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.46/1.04 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.33/1.09 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 49.01/7.83 % Solved by lams/20_acsne_simpl.sh. 49.01/7.83 % done 220 iterations in 6.495s 49.01/7.83 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 49.01/7.83 % SZS output start Refutation 49.01/7.83 thf('#form133_type', type, '#form133': ($i > $i > $o) > $o). 49.01/7.83 thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf('#sk1_type', type, '#sk1': $i > $i > $o). 49.01/7.83 thf('#sk278_type', type, '#sk278': ($i > $i > $o) > $i). 49.01/7.83 thf('#form307_type', type, '#form307': ($i > $i > $o) > $o). 49.01/7.83 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 49.01/7.83 thf(sc_type, type, sc: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf('#sk13_type', type, '#sk13': $i > $i > $i > $i > $o). 49.01/7.83 thf('#sk134_type', type, '#sk134': ($i > $i > $o) > $i). 49.01/7.83 thf(cr_type, type, cr: ($i > $i > $o) > $o). 49.01/7.83 thf(trsc_type, type, trsc: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf('#sk3_type', type, '#sk3': $i). 49.01/7.83 thf('#sk2_type', type, '#sk2': $i). 49.01/7.83 thf('#sk191_type', type, '#sk191': ($i > $i > $o) > $i). 49.01/7.83 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf(sconfl_type, type, sconfl: ($i > $i > $o) > $o). 49.01/7.83 thf('#sk14_type', type, '#sk14': $i > $i > $i). 49.01/7.83 thf('#sk77_type', type, '#sk77': ($i > $i > $o) > $i). 49.01/7.83 thf(join_type, type, join: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf(trans_type, type, trans: ($i > $i > $o) > $o). 49.01/7.83 thf('#form65_type', type, '#form65': $i > $o). 49.01/7.83 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 49.01/7.83 thf('#form12_type', type, '#form12': $o). 49.01/7.83 thf('#sk56_type', type, '#sk56': ($i > $i > $o) > $i). 49.01/7.83 thf(church_rosser, axiom,(( cr ) = 49.01/7.83 (^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i]: ( ( trsc @ R @ X @ Y ) => ( join @ R @ X @ Y ) ) )))). 49.01/7.83 thf(joinable, axiom,(( join ) = 49.01/7.83 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 49.01/7.83 ( ?[Z:$i]: ( ( trc @ R @ Y @ Z ) & ( trc @ R @ X @ Z ) ) )))). 49.01/7.83 thf(transitive_reflexive_closure, axiom,(( trc ) = 49.01/7.83 (^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) )))). 49.01/7.83 thf(transitive_closure, axiom,(( tc ) = 49.01/7.83 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 49.01/7.83 ( ![S:( $i > $i > $o )]: 49.01/7.83 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 49.01/7.83 thf(transitive, axiom,(( trans ) = 49.01/7.83 (^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i,Z:$i]: 49.01/7.83 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 49.01/7.83 thf('0', plain, 49.01/7.83 (( trans ) = 49.01/7.83 ( ^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i,Z:$i]: 49.01/7.83 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], [transitive])). 49.01/7.83 thf('1', plain, 49.01/7.83 (( trans ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o )]: 49.01/7.83 ( ![X4:$i,X6:$i,X8:$i]: 49.01/7.83 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf(subrel, axiom,(( subrel ) = 49.01/7.83 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 49.01/7.83 thf('2', plain, 49.01/7.83 (( subrel ) = 49.01/7.83 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], [subrel])). 49.01/7.83 thf('3', plain, 49.01/7.83 (( subrel ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 49.01/7.83 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf('4', plain, 49.01/7.83 (( tc ) = 49.01/7.83 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 49.01/7.83 ( ![S:( $i > $i > $o )]: 49.01/7.83 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [transitive_closure, '1', '3'])). 49.01/7.83 thf('5', plain, 49.01/7.83 (( tc ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 49.01/7.83 ( ![X4:( $i > $i > $o )]: 49.01/7.83 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf(reflexive_closure, axiom,(( rc ) = 49.01/7.83 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) )))). 49.01/7.83 thf('6', plain, 49.01/7.83 (( rc ) = 49.01/7.83 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], [reflexive_closure])). 49.01/7.83 thf('7', plain, 49.01/7.83 (( rc ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 49.01/7.83 ( ( ( V_2 ) = ( V_3 ) ) | ( V_1 @ V_2 @ V_3 ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf('8', plain, (( trc ) = ( ^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [transitive_reflexive_closure, '5', '1', '7', '3'])). 49.01/7.83 thf('9', plain, 49.01/7.83 (( trc ) = ( ^[V_1:( $i > $i > $o )]: ( rc @ ( tc @ V_1 ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf('10', plain, 49.01/7.83 (( join ) = 49.01/7.83 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 49.01/7.83 ( ?[Z:$i]: ( ( trc @ R @ Y @ Z ) & ( trc @ R @ X @ Z ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [joinable, '9', '5', '1', '7', '3'])). 49.01/7.83 thf('11', plain, 49.01/7.83 (( join ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 49.01/7.83 ( ?[X4:$i]: ( ( trc @ V_1 @ V_3 @ X4 ) & ( trc @ V_1 @ V_2 @ X4 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf(transitive_reflexive_symmetric_closure, axiom,(( trsc ) = 49.01/7.83 (^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) )))). 49.01/7.83 thf(symmetric_closure, axiom,(( sc ) = 49.01/7.83 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) )))). 49.01/7.83 thf('12', plain, 49.01/7.83 (( sc ) = 49.01/7.83 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( R @ Y @ X ) | ( R @ X @ Y ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], [symmetric_closure])). 49.01/7.83 thf('13', plain, 49.01/7.83 (( sc ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 49.01/7.83 ( ( V_1 @ V_3 @ V_2 ) | ( V_1 @ V_2 @ V_3 ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf('14', plain, 49.01/7.83 (( trsc ) = ( ^[R:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ R ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [transitive_reflexive_symmetric_closure, '5', '1', '13', '7', 49.01/7.83 '3'])). 49.01/7.83 thf('15', plain, 49.01/7.83 (( trsc ) = ( ^[V_1:( $i > $i > $o )]: ( sc @ ( rc @ ( tc @ V_1 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf('16', plain, 49.01/7.83 (( cr ) = 49.01/7.83 ( ^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i]: ( ( trsc @ R @ X @ Y ) => ( join @ R @ X @ Y ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [church_rosser, '11', '15', '9', '5', '1', '13', '7', '3'])). 49.01/7.83 thf('17', plain, 49.01/7.83 (( cr ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o )]: 49.01/7.83 ( ![X4:$i,X6:$i]: 49.01/7.83 ( ( trsc @ V_1 @ X4 @ X6 ) => ( join @ V_1 @ X4 @ X6 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf(semi_confluent, axiom,(( sconfl ) = 49.01/7.83 (^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i,Z:$i]: 49.01/7.83 ( ( ( R @ X @ Z ) & ( trc @ R @ X @ Y ) ) => ( join @ R @ Z @ Y ) ) )))). 49.01/7.83 thf('18', plain, 49.01/7.83 (( sconfl ) = 49.01/7.83 ( ^[R:( $i > $i > $o )]: 49.01/7.83 ( ![X:$i,Y:$i,Z:$i]: 49.01/7.83 ( ( ( R @ X @ Z ) & ( trc @ R @ X @ Y ) ) => ( join @ R @ Z @ Y ) ) ) )), 49.01/7.83 inference('simplify_rw_rule', [status(thm)], 49.01/7.83 [semi_confluent, '11', '9', '5', '1', '7', '3'])). 49.01/7.83 thf('19', plain, 49.01/7.83 (( sconfl ) = 49.01/7.83 ( ^[V_1:( $i > $i > $o )]: 49.01/7.83 ( ![X4:$i,X6:$i,X8:$i]: 49.01/7.83 ( ( ( V_1 @ X4 @ X8 ) & ( trc @ V_1 @ X4 @ X6 ) ) => 49.01/7.83 ( join @ V_1 @ X8 @ X6 ) ) ) )), 49.01/7.83 define([status(thm)])). 49.01/7.83 thf(semi_confluence_implies_church_rosser, conjecture, 49.01/7.83 (![R:( $i > $i > $o )]: ( ( sconfl @ R ) => ( cr @ R ) ))). 49.01/7.83 thf(zf_stmt_0, conjecture, 49.01/7.83 (![X4:( $i > $i > $o )]: 49.01/7.83 ( ( ![X6:$i,X8:$i,X10:$i]: 49.01/7.83 ( ( ( ( ![X12:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X20:$i,X22:$i]: 49.01/7.83 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 49.01/7.83 ( ![X14:$i,X16:$i,X18:$i]: 49.01/7.83 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 49.01/7.83 ( X12 @ X14 @ X18 ) ) ) ) => 49.01/7.83 ( X12 @ X6 @ X8 ) ) ) | 49.01/7.83 ( ( X6 ) = ( X8 ) ) ) & 49.01/7.83 ( X4 @ X6 @ X10 ) ) => 49.01/7.83 ( ?[X24:$i]: 49.01/7.83 ( ( ( ![X38:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X46:$i,X48:$i]: 49.01/7.83 ( ( X4 @ X46 @ X48 ) => ( X38 @ X46 @ X48 ) ) ) & 49.01/7.83 ( ![X40:$i,X42:$i,X44:$i]: 49.01/7.83 ( ( ( X38 @ X42 @ X44 ) & ( X38 @ X40 @ X42 ) ) => 49.01/7.83 ( X38 @ X40 @ X44 ) ) ) ) => 49.01/7.83 ( X38 @ X10 @ X24 ) ) ) | 49.01/7.83 ( ( X10 ) = ( X24 ) ) ) & 49.01/7.83 ( ( ![X26:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X34:$i,X36:$i]: 49.01/7.83 ( ( X4 @ X34 @ X36 ) => ( X26 @ X34 @ X36 ) ) ) & 49.01/7.83 ( ![X28:$i,X30:$i,X32:$i]: 49.01/7.83 ( ( ( X26 @ X30 @ X32 ) & ( X26 @ X28 @ X30 ) ) => 49.01/7.83 ( X26 @ X28 @ X32 ) ) ) ) => 49.01/7.83 ( X26 @ X8 @ X24 ) ) ) | 49.01/7.83 ( ( X8 ) = ( X24 ) ) ) ) ) ) ) => 49.01/7.83 ( ![X50:$i,X52:$i]: 49.01/7.83 ( ( ( ![X66:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X74:$i,X76:$i]: 49.01/7.83 ( ( X4 @ X74 @ X76 ) => ( X66 @ X74 @ X76 ) ) ) & 49.01/7.83 ( ![X68:$i,X70:$i,X72:$i]: 49.01/7.83 ( ( ( X66 @ X70 @ X72 ) & ( X66 @ X68 @ X70 ) ) => 49.01/7.83 ( X66 @ X68 @ X72 ) ) ) ) => 49.01/7.83 ( X66 @ X50 @ X52 ) ) ) | 49.01/7.83 ( ( X50 ) = ( X52 ) ) | 49.01/7.83 ( ![X54:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X62:$i,X64:$i]: 49.01/7.83 ( ( X4 @ X62 @ X64 ) => ( X54 @ X62 @ X64 ) ) ) & 49.01/7.83 ( ![X56:$i,X58:$i,X60:$i]: 49.01/7.83 ( ( ( X54 @ X58 @ X60 ) & ( X54 @ X56 @ X58 ) ) => 49.01/7.83 ( X54 @ X56 @ X60 ) ) ) ) => 49.01/7.83 ( X54 @ X52 @ X50 ) ) ) | 49.01/7.83 ( ( X52 ) = ( X50 ) ) ) => 49.01/7.83 ( ?[X78:$i]: 49.01/7.83 ( ( ( ![X92:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X100:$i,X102:$i]: 49.01/7.83 ( ( X4 @ X100 @ X102 ) => ( X92 @ X100 @ X102 ) ) ) & 49.01/7.83 ( ![X94:$i,X96:$i,X98:$i]: 49.01/7.83 ( ( ( X92 @ X96 @ X98 ) & ( X92 @ X94 @ X96 ) ) => 49.01/7.83 ( X92 @ X94 @ X98 ) ) ) ) => 49.01/7.83 ( X92 @ X50 @ X78 ) ) ) | 49.01/7.83 ( ( X50 ) = ( X78 ) ) ) & 49.01/7.83 ( ( ![X80:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X88:$i,X90:$i]: 49.01/7.83 ( ( X4 @ X88 @ X90 ) => ( X80 @ X88 @ X90 ) ) ) & 49.01/7.83 ( ![X82:$i,X84:$i,X86:$i]: 49.01/7.83 ( ( ( X80 @ X84 @ X86 ) & ( X80 @ X82 @ X84 ) ) => 49.01/7.83 ( X80 @ X82 @ X86 ) ) ) ) => 49.01/7.83 ( X80 @ X52 @ X78 ) ) ) | 49.01/7.83 ( ( X52 ) = ( X78 ) ) ) ) ) ) ) ))). 49.01/7.83 thf(zf_stmt_1, negated_conjecture, 49.01/7.83 (~( ![X4:( $i > $i > $o )]: 49.01/7.83 ( ( ![X6:$i,X8:$i,X10:$i]: 49.01/7.83 ( ( ( ( ![X12:( $i > $i > $o )]: 49.01/7.83 ( ( ( ![X20:$i,X22:$i]: 49.01/7.84 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 49.01/7.84 ( ![X14:$i,X16:$i,X18:$i]: 49.01/7.84 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 49.01/7.84 ( X12 @ X14 @ X18 ) ) ) ) => 49.01/7.84 ( X12 @ X6 @ X8 ) ) ) | 49.01/7.84 ( ( X6 ) = ( X8 ) ) ) & 49.01/7.84 ( X4 @ X6 @ X10 ) ) => 49.01/7.84 ( ?[X24:$i]: 49.01/7.84 ( ( ( ![X38:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X46:$i,X48:$i]: 49.01/7.84 ( ( X4 @ X46 @ X48 ) => ( X38 @ X46 @ X48 ) ) ) & 49.01/7.84 ( ![X40:$i,X42:$i,X44:$i]: 49.01/7.84 ( ( ( X38 @ X42 @ X44 ) & ( X38 @ X40 @ X42 ) ) => 49.01/7.84 ( X38 @ X40 @ X44 ) ) ) ) => 49.01/7.84 ( X38 @ X10 @ X24 ) ) ) | 49.01/7.84 ( ( X10 ) = ( X24 ) ) ) & 49.01/7.84 ( ( ![X26:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X34:$i,X36:$i]: 49.01/7.84 ( ( X4 @ X34 @ X36 ) => ( X26 @ X34 @ X36 ) ) ) & 49.01/7.84 ( ![X28:$i,X30:$i,X32:$i]: 49.01/7.84 ( ( ( X26 @ X30 @ X32 ) & ( X26 @ X28 @ X30 ) ) => 49.01/7.84 ( X26 @ X28 @ X32 ) ) ) ) => 49.01/7.84 ( X26 @ X8 @ X24 ) ) ) | 49.01/7.84 ( ( X8 ) = ( X24 ) ) ) ) ) ) ) => 49.01/7.84 ( ![X50:$i,X52:$i]: 49.01/7.84 ( ( ( ![X66:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X74:$i,X76:$i]: 49.01/7.84 ( ( X4 @ X74 @ X76 ) => ( X66 @ X74 @ X76 ) ) ) & 49.01/7.84 ( ![X68:$i,X70:$i,X72:$i]: 49.01/7.84 ( ( ( X66 @ X70 @ X72 ) & ( X66 @ X68 @ X70 ) ) => 49.01/7.84 ( X66 @ X68 @ X72 ) ) ) ) => 49.01/7.84 ( X66 @ X50 @ X52 ) ) ) | 49.01/7.84 ( ( X50 ) = ( X52 ) ) | 49.01/7.84 ( ![X54:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X62:$i,X64:$i]: 49.01/7.84 ( ( X4 @ X62 @ X64 ) => ( X54 @ X62 @ X64 ) ) ) & 49.01/7.84 ( ![X56:$i,X58:$i,X60:$i]: 49.01/7.84 ( ( ( X54 @ X58 @ X60 ) & ( X54 @ X56 @ X58 ) ) => 49.01/7.84 ( X54 @ X56 @ X60 ) ) ) ) => 49.01/7.84 ( X54 @ X52 @ X50 ) ) ) | 49.01/7.84 ( ( X52 ) = ( X50 ) ) ) => 49.01/7.84 ( ?[X78:$i]: 49.01/7.84 ( ( ( ![X92:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X100:$i,X102:$i]: 49.01/7.84 ( ( X4 @ X100 @ X102 ) => ( X92 @ X100 @ X102 ) ) ) & 49.01/7.84 ( ![X94:$i,X96:$i,X98:$i]: 49.01/7.84 ( ( ( X92 @ X96 @ X98 ) & ( X92 @ X94 @ X96 ) ) => 49.01/7.84 ( X92 @ X94 @ X98 ) ) ) ) => 49.01/7.84 ( X92 @ X50 @ X78 ) ) ) | 49.01/7.84 ( ( X50 ) = ( X78 ) ) ) & 49.01/7.84 ( ( ![X80:( $i > $i > $o )]: 49.01/7.84 ( ( ( ![X88:$i,X90:$i]: 49.01/7.84 ( ( X4 @ X88 @ X90 ) => ( X80 @ X88 @ X90 ) ) ) & 49.01/7.84 ( ![X82:$i,X84:$i,X86:$i]: 49.01/7.84 ( ( ( X80 @ X84 @ X86 ) & ( X80 @ X82 @ X84 ) ) => 49.01/7.84 ( X80 @ X82 @ X86 ) ) ) ) => 49.01/7.84 ( X80 @ X52 @ X78 ) ) ) | 49.01/7.84 ( ( X52 ) = ( X78 ) ) ) ) ) ) ) ) )), 49.01/7.84 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 49.01/7.84 thf(zip_derived_cl0, plain, 49.01/7.84 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((((((((!!) @ ( 49.01/7.84 ^[Y4 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y4 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) & 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y7)))))))))))))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y1 @ Y2)))))) | 49.01/7.84 (((Y1) = (Y2))))) & 49.01/7.84 (Y0 @ Y1 @ Y3))) => 49.01/7.84 (((??) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (((((( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) => 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y7))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y8 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y5 @ 49.01/7.84 Y7 @ 49.01/7.84 Y8) & 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y7))) => 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y8)))))))))))))) => 49.01/7.84 (Y5 @ 49.01/7.84 Y3 @ Y4)))))) | 49.01/7.84 (( 49.01/7.84 (Y3) = 49.01/7.84 (Y4))))) & 49.01/7.84 (((( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) => 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y7))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y8 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y5 @ 49.01/7.84 Y7 @ 49.01/7.84 Y8) & 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y7))) => 49.01/7.84 (Y5 @ 49.01/7.84 Y6 @ Y8)))))))))))))) => 49.01/7.84 (Y5 @ 49.01/7.84 Y2 @ Y4)))))) | 49.01/7.84 (( 49.01/7.84 (Y2) = 49.01/7.84 (Y4))))))))))))))))))))) => 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y1 @ Y2)))))) | 49.01/7.84 (((Y1) = (Y2))) | 49.01/7.84 (((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y2 @ Y1)))))) | 49.01/7.84 (((Y2) = (Y1))))) => 49.01/7.84 (((??) @ (^[Y3 : $i]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y4 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) & 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y7)))))))))))))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y1 @ Y3)))))) | 49.01/7.84 (((Y1) = (Y3))))) & 49.01/7.84 (((((!!) @ ( 49.01/7.84 ^[Y4 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (Y0 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y4 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) & 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y7)))))))))))))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y2 @ Y3)))))) | 49.01/7.84 (((Y2) = (Y3)))))))))))))))))))))))), 49.01/7.84 inference('cnf', [status(esa)], [zf_stmt_1])). 49.01/7.84 thf(zip_derived_cl1, plain, 49.01/7.84 (~ (((((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y0 @ 49.01/7.84 Y1)))))) | 49.01/7.84 (((Y0) = (Y1))))) & 49.01/7.84 ('#sk1' @ Y0 @ Y2))) => 49.01/7.84 (((??) @ (^[Y3 : $i]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y4 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) & 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y7)))))))))))))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y2 @ Y3)))))) | 49.01/7.84 (((Y2) = (Y3))))) & 49.01/7.84 (((((!!) @ ( 49.01/7.84 ^[Y4 : 49.01/7.84 $i > $i > $o]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y7 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y4 @ 49.01/7.84 Y6 @ 49.01/7.84 Y7) & 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y6))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y5 @ Y7)))))))))))))) => 49.01/7.84 (Y4 @ 49.01/7.84 Y1 @ Y3)))))) | 49.01/7.84 (((Y1) = (Y3))))))))))))))))))))) => 49.01/7.84 (((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ Y0 @ Y1)))))) | 49.01/7.84 (((Y0) = (Y1))) | 49.01/7.84 (((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ Y1 @ Y0)))))) | 49.01/7.84 (((Y1) = (Y0))))) => 49.01/7.84 (((??) @ (^[Y2 : $i]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y0 @ 49.01/7.84 Y2)))))) | 49.01/7.84 (((Y0) = (Y2))))) & 49.01/7.84 (((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y1 @ 49.01/7.84 Y2)))))) | 49.01/7.84 (((Y1) = (Y2))))))))))))))))))))), 49.01/7.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 49.01/7.84 thf(zip_derived_cl3, plain, 49.01/7.84 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ Y0 @ Y1)))))) | 49.01/7.84 (((Y0) = (Y1))) | 49.01/7.84 (((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ Y1 @ Y0)))))) | 49.01/7.84 (((Y1) = (Y0))))) => 49.01/7.84 (((??) @ (^[Y2 : $i]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y0 @ Y2)))))) | 49.01/7.84 (((Y0) = (Y2))))) & 49.01/7.84 (((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))))))))) & 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y6 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y3 @ 49.01/7.84 Y5 @ 49.01/7.84 Y6) & 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y5))) => 49.01/7.84 (Y3 @ 49.01/7.84 Y4 @ Y6)))))))))))))) => 49.01/7.84 (Y3 @ Y1 @ Y2)))))) | 49.01/7.84 (((Y1) = (Y2))))))))))))))))))), 49.01/7.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 49.01/7.84 thf(zip_derived_cl5, plain, 49.01/7.84 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ Y3) => 49.01/7.84 (Y1 @ Y2 @ 49.01/7.84 Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ '#sk2' @ Y0)))))) | 49.01/7.84 ((('#sk2') = (Y0))) | 49.01/7.84 (((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ Y3) => 49.01/7.84 (Y1 @ Y2 @ 49.01/7.84 Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ Y0 @ '#sk2')))))) | 49.01/7.84 (((Y0) = ('#sk2'))))) => 49.01/7.84 (((??) @ (^[Y1 : $i]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ '#sk2' @ Y1)))))) | 49.01/7.84 ((('#sk2') = (Y1))))) & 49.01/7.84 (((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 ('#sk1' @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))))))))) & 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (!!) @ ( 49.01/7.84 ^[Y5 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y2 @ 49.01/7.84 Y4 @ 49.01/7.84 Y5) & 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y4))) => 49.01/7.84 (Y2 @ 49.01/7.84 Y3 @ Y5)))))))))))))) => 49.01/7.84 (Y2 @ Y0 @ Y1)))))) | 49.01/7.84 (((Y0) = (Y1)))))))))))))))), 49.01/7.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 49.01/7.84 thf(zip_derived_cl7, plain, 49.01/7.84 (~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((((Y0 @ 49.01/7.84 Y2 @ Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ Y1 @ 49.01/7.84 Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk2' @ '#sk3')))))) | 49.01/7.84 ((('#sk2') = ('#sk3'))) | 49.01/7.84 (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((((Y0 @ 49.01/7.84 Y2 @ Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ Y1 @ 49.01/7.84 Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ '#sk2')))))) | 49.01/7.84 ((('#sk3') = ('#sk2'))))) => 49.01/7.84 (((??) @ (^[Y0 : $i]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ '#sk2' @ Y0)))))) | 49.01/7.84 ((('#sk2') = (Y0))))) & 49.01/7.84 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ '#sk3' @ Y0)))))) | 49.01/7.84 ((('#sk3') = (Y0))))))))))))), 49.01/7.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 49.01/7.84 thf(zip_derived_cl10, plain, 49.01/7.84 (~ (((??) @ (^[Y0 : $i]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ Y3) => 49.01/7.84 (Y1 @ Y2 @ 49.01/7.84 Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ '#sk2' @ Y0)))))) | 49.01/7.84 ((('#sk2') = (Y0))))) & 49.01/7.84 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 ((('#sk1' @ 49.01/7.84 Y2 @ Y3) => 49.01/7.84 (Y1 @ Y2 @ 49.01/7.84 Y3))))))))) & 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((!!) @ ( 49.01/7.84 ^[Y4 : $i]: 49.01/7.84 (( 49.01/7.84 (( 49.01/7.84 (Y1 @ 49.01/7.84 Y3 @ 49.01/7.84 Y4) & 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y3))) => 49.01/7.84 (Y1 @ 49.01/7.84 Y2 @ Y4)))))))))))))) => 49.01/7.84 (Y1 @ '#sk3' @ Y0)))))) | 49.01/7.84 ((('#sk3') = (Y0))))))))))), 49.01/7.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 49.01/7.84 thf(zip_derived_cl13, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 ~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk2' @ X2)))))) | 49.01/7.84 ((('#sk2') = (X2))))) & 49.01/7.84 (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2)))))))), 49.01/7.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 49.01/7.84 thf(zip_derived_cl19, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((((Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ Y1 @ 49.01/7.84 Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk2' @ X2)))))) | 49.01/7.84 ((('#sk2') = (X2))))) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])). 49.01/7.84 thf(zip_derived_cl26, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((((Y0 @ Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ Y1 @ 49.01/7.84 Y2))) => 49.01/7.84 (Y0 @ Y1 @ 49.01/7.84 Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk2' @ X2)))))) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 49.01/7.84 thf(zip_derived_cl36, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 (~ (((((((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.84 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 49.01/7.84 (((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((((('#sk13' @ '#sk2' @ 49.01/7.84 X2 @ Y1 @ Y2) & 49.01/7.84 ('#sk13' @ '#sk2' @ 49.01/7.84 X2 @ Y0 @ Y1))) => 49.01/7.84 ('#sk13' @ '#sk2' @ X2 @ 49.01/7.84 Y0 @ Y2)))))))))))))) => 49.01/7.84 ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2))) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 49.01/7.84 thf(zip_derived_cl47, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 ( (((((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.84 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 49.01/7.84 (((!!) @ (^[Y0 : $i]: 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((((('#sk13' @ '#sk2' @ X2 @ 49.01/7.84 Y1 @ Y2) & ('#sk13' @ 49.01/7.84 '#sk2' @ X2 @ Y0 @ Y1))) => 49.01/7.84 ('#sk13' @ '#sk2' @ X2 @ 49.01/7.84 Y0 @ Y2)))))))))))))) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 49.01/7.84 thf(zip_derived_cl59, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 ( ('#form65' @ X2) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 define([status(thm)])). 49.01/7.84 thf(zip_derived_cl61, plain, 49.01/7.84 (![X2 : $i]: (~ ((('#sk3') = (X2))) | ('#form65' @ X2))), 49.01/7.84 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 49.01/7.84 thf(zip_derived_cl83, plain, 49.01/7.84 (![X2 : $i]: ((('#sk3') != (X2)) | ('#form65' @ X2))), 49.01/7.84 inference('simplify nested equalities', [status(thm)], [zip_derived_cl61])). 49.01/7.84 thf(zip_derived_cl84, plain, ( ('#form65' @ '#sk3')), 49.01/7.84 inference('simplify', [status(thm)], [zip_derived_cl83])). 49.01/7.84 thf(zip_derived_cl48, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 (~ ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 ((('#sk1' @ Y1 @ Y2) => 49.01/7.84 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.84 (((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.84 (((!!) @ (^[Y3 : $i]: 49.01/7.84 (((( 49.01/7.84 (Y0 @ 49.01/7.84 Y2 @ 49.01/7.84 Y3) & 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y2))) => 49.01/7.84 (Y0 @ 49.01/7.84 Y1 @ Y3)))))))))))))) => 49.01/7.84 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.84 ((('#sk3') = (X2))))))), 49.01/7.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 49.01/7.84 thf(zip_derived_cl59, plain, 49.01/7.84 (![X2 : $i]: 49.01/7.84 ( ('#form65' @ X2) 49.01/7.84 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.84 (((((((!!) @ (^[Y1 : $i]: 49.01/7.84 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((( 49.01/7.85 (Y0 @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.85 ((('#sk3') = (X2))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl63, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 (~ ('#form65' @ X2) | ~ ('#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2))), 49.01/7.85 inference('renaming', [status(thm)], [zip_derived_cl48, zip_derived_cl59])). 49.01/7.85 thf(zip_derived_cl9, plain, 49.01/7.85 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) | 49.01/7.85 ((('#sk2') = ('#sk3'))) | 49.01/7.85 (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2')))))) | 49.01/7.85 ((('#sk3') = ('#sk2')))))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 49.01/7.85 thf(zip_derived_cl12, plain, 49.01/7.85 (( (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 49.01/7.85 Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | ((('#sk2') = ('#sk3'))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2')))))) 49.01/7.85 | ((('#sk3') = ('#sk2'))))), 49.01/7.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 49.01/7.85 thf(zip_derived_cl15, plain, 49.01/7.85 (( (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 49.01/7.85 Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | (('#sk2') = ('#sk3')) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2')))))) 49.01/7.85 | (('#sk3') = ('#sk2')))), 49.01/7.85 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 49.01/7.85 thf(zip_derived_cl16, plain, 49.01/7.85 (( (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 49.01/7.85 Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2')))))) 49.01/7.85 | (('#sk2') = ('#sk3')) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 inference('simplify', [status(thm)], [zip_derived_cl15])). 49.01/7.85 thf(zip_derived_cl17, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))) => 49.01/7.85 (X2 @ '#sk3' @ '#sk2'))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ 49.01/7.85 Y2 @ Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ 49.01/7.85 Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | (('#sk2') = ('#sk3')))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 49.01/7.85 thf(zip_derived_cl22, plain, 49.01/7.85 ((~ ('#form12') 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl23, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))) => 49.01/7.85 (X2 @ '#sk2' @ '#sk3'))) 49.01/7.85 | ~ ('#form12'))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 49.01/7.85 thf(zip_derived_cl35, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))) 49.01/7.85 | (X2 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form12'))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 49.01/7.85 thf(zip_derived_cl46, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))) 49.01/7.85 | ~ ('#form12') 49.01/7.85 | (X2 @ '#sk2' @ '#sk3'))), 49.01/7.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 49.01/7.85 thf(zip_derived_cl58, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 ((('#sk1' @ ('#sk56' @ X2) @ Y0) => (X2 @ 49.01/7.85 ('#sk56' @ X2) @ Y0)))))) 49.01/7.85 | (X2 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form12') 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])). 49.01/7.85 thf(zip_derived_cl79, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 49.01/7.85 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))) 49.01/7.85 | ~ ('#form12') 49.01/7.85 | (X2 @ '#sk2' @ '#sk3'))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 49.01/7.85 thf(zip_derived_cl95, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( ('#form133' @ X2) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl96, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((((X2 @ Y0 @ Y1) & (X2 @ 49.01/7.85 ('#sk134' @ X2) @ Y0))) => 49.01/7.85 (X2 @ ('#sk134' @ X2) @ Y1))))))))) 49.01/7.85 | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 49.01/7.85 thf(zip_derived_cl122, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((((X2 @ ('#sk191' @ X2) @ Y0) & (X2 @ 49.01/7.85 ('#sk134' @ X2) @ ('#sk191' @ X2)))) => 49.01/7.85 (X2 @ ('#sk134' @ X2) @ Y0)))))) 49.01/7.85 | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 49.01/7.85 thf(zip_derived_cl137, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (((((X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) & (X2 @ 49.01/7.85 ('#sk134' @ X2) @ ('#sk191' @ X2)))) => 49.01/7.85 (X2 @ ('#sk134' @ X2) @ ('#sk278' @ X2)))) 49.01/7.85 | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 49.01/7.85 thf(zip_derived_cl153, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (((X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) & (X2 @ 49.01/7.85 ('#sk134' @ X2) @ ('#sk191' @ X2)))) 49.01/7.85 | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 49.01/7.85 thf(zip_derived_cl164, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (X2 @ ('#sk191' @ X2) @ ('#sk278' @ X2)) | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 49.01/7.85 thf(zip_derived_cl165, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (X2 @ ('#sk134' @ X2) @ ('#sk191' @ X2)) | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl153])). 49.01/7.85 thf(zip_derived_cl154, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (X2 @ ('#sk134' @ X2) @ ('#sk278' @ X2)) | ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 49.01/7.85 thf(zip_derived_cl47, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 ( (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk2' @ X2 @ 49.01/7.85 Y1 @ Y2) & ('#sk13' @ 49.01/7.85 '#sk2' @ X2 @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk2' @ X2 @ 49.01/7.85 Y0 @ Y2)))))))))))))) 49.01/7.85 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((( 49.01/7.85 (Y0 @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.85 ((('#sk3') = (X2))))))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 49.01/7.85 thf(zip_derived_cl59, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 ( ('#form65' @ X2) 49.01/7.85 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((( 49.01/7.85 (Y0 @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.85 ((('#sk3') = (X2))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl62, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 (~ ('#form65' @ X2) 49.01/7.85 | (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk2' @ X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk2' @ 49.01/7.85 X2 @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk2' @ 49.01/7.85 X2 @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk2' @ X2 @ 49.01/7.85 Y0 @ Y2)))))))))))))))), 49.01/7.85 inference('renaming', [status(thm)], [zip_derived_cl47, zip_derived_cl59])). 49.01/7.85 thf(zip_derived_cl80, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 ( (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk2' @ 49.01/7.85 X2 @ Y0 @ Y1))))))))) 49.01/7.85 | ~ ('#form65' @ X2))), 49.01/7.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 49.01/7.85 thf(zip_derived_cl98, plain, 49.01/7.85 (![X2 : $i, X4 : $i]: 49.01/7.85 ( (((!!) @ (^[Y0 : $i]: 49.01/7.85 ((('#sk1' @ X4 @ Y0) => ('#sk13' @ '#sk2' @ X2 @ X4 @ 49.01/7.85 Y0)))))) 49.01/7.85 | ~ ('#form65' @ X2))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 49.01/7.85 thf(zip_derived_cl123, plain, 49.01/7.85 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.85 ( ((('#sk1' @ X4 @ X6) => ('#sk13' @ '#sk2' @ X2 @ X4 @ X6))) 49.01/7.85 | ~ ('#form65' @ X2))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 49.01/7.85 thf(zip_derived_cl138, plain, 49.01/7.85 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.85 (~ ('#sk1' @ X4 @ X6) 49.01/7.85 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X6) 49.01/7.85 | ~ ('#form65' @ X2))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 49.01/7.85 thf(zip_derived_cl79, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 49.01/7.85 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))) 49.01/7.85 | ~ ('#form12') 49.01/7.85 | (X2 @ '#sk2' @ '#sk3'))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 49.01/7.85 thf(zip_derived_cl95, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( ('#form133' @ X2) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl97, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ ('#form133' @ X2) 49.01/7.85 | (X2 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form12') 49.01/7.85 | ~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 49.01/7.85 ('#sk56' @ X2) @ ('#sk77' @ X2)))))), 49.01/7.85 inference('renaming', [status(thm)], [zip_derived_cl79, zip_derived_cl95])). 49.01/7.85 thf(zip_derived_cl121, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 (~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 49.01/7.85 | ~ ('#form12') 49.01/7.85 | (X2 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form133' @ X2))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 49.01/7.85 thf(zip_derived_cl727, plain, 49.01/7.85 (![X0 : $i > $i > $o]: 49.01/7.85 (((X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) != ('#form133' @ X0)) 49.01/7.85 | ~ ('#form133' @ X0) 49.01/7.85 | (X0 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form12'))), 49.01/7.85 inference('eq_fact', [status(thm)], [zip_derived_cl121])). 49.01/7.85 thf(zip_derived_cl735, plain, 49.01/7.85 (![X0 : $i > $i > $o]: 49.01/7.85 (~ (X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) 49.01/7.85 | ~ ('#form133' @ X0) 49.01/7.85 | (X0 @ '#sk2' @ '#sk3') 49.01/7.85 | ~ ('#form12'))), 49.01/7.85 inference('local_rewriting', [status(thm)], [zip_derived_cl727])). 49.01/7.85 thf(zip_derived_cl17, plain, 49.01/7.85 (![X2 : $i > $i > $o]: 49.01/7.85 ( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.85 Y0 @ Y1))) => 49.01/7.85 (X2 @ Y0 @ Y2)))))))))))))) => 49.01/7.85 (X2 @ '#sk3' @ '#sk2'))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ 49.01/7.85 Y2 @ Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ 49.01/7.85 Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | (('#sk2') = ('#sk3')))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 49.01/7.85 thf(zip_derived_cl185, plain, 49.01/7.85 (( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))) => 49.01/7.85 ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2'))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | (('#sk2') = ('#sk3')))), 49.01/7.85 inference('triggered_bool_instantiation', [status(thm)], 49.01/7.85 [zip_derived_cl17])). 49.01/7.85 thf(zip_derived_cl27, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 (~ ((('#sk2') = (X2))) 49.01/7.85 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((( 49.01/7.85 (Y0 @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.85 ((('#sk3') = (X2))))))), 49.01/7.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 49.01/7.85 thf(zip_derived_cl37, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 ((('#sk2') != (X2)) 49.01/7.85 | ~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((( 49.01/7.85 (Y0 @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) & 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ 49.01/7.85 Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ X2)))))) | 49.01/7.85 ((('#sk3') = (X2))))))), 49.01/7.85 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 49.01/7.85 thf(zip_derived_cl38, plain, 49.01/7.85 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2')))))) | 49.01/7.85 ((('#sk3') = ('#sk2')))))), 49.01/7.85 inference('simplify', [status(thm)], [zip_derived_cl37])). 49.01/7.85 thf(zip_derived_cl39, plain, 49.01/7.85 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 49.01/7.85 Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk3' @ '#sk2'))))))), 49.01/7.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 49.01/7.85 thf(zip_derived_cl49, plain, 49.01/7.85 (~ (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))) => 49.01/7.85 ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')))), 49.01/7.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl39])). 49.01/7.85 thf(zip_derived_cl65, plain, 49.01/7.85 (~ ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 49.01/7.85 thf(zip_derived_cl259, plain, 49.01/7.85 (( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))) => 49.01/7.85 ($false))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.85 | (('#sk2') = ('#sk3')))), 49.01/7.85 inference('demod', [status(thm)], [zip_derived_cl185, zip_derived_cl65])). 49.01/7.85 thf(zip_derived_cl40, plain, (~ ((('#sk3') = ('#sk2')))), 49.01/7.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 49.01/7.85 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 49.01/7.85 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 49.01/7.85 thf(zip_derived_cl260, plain, 49.01/7.85 (( (((((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))) => 49.01/7.85 ($false))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 inference('simplify_reflect-', [status(thm)], 49.01/7.85 [zip_derived_cl259, zip_derived_cl50])). 49.01/7.85 thf(zip_derived_cl261, plain, 49.01/7.85 (( (((~) @ (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl260])). 49.01/7.85 thf(zip_derived_cl262, plain, 49.01/7.85 ((~ (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.85 Y0 @ Y2)))))))))))))) 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 inference('simplify nested equalities', [status(thm)], 49.01/7.85 [zip_derived_cl261])). 49.01/7.85 thf(zip_derived_cl22, plain, 49.01/7.85 ((~ ('#form12') 49.01/7.85 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((('#sk1' @ Y1 @ Y2) => 49.01/7.85 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((((Y0 @ Y2 @ 49.01/7.85 Y3) & (Y0 @ 49.01/7.85 Y1 @ Y2))) => 49.01/7.85 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.85 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.85 define([status(thm)])). 49.01/7.85 thf(zip_derived_cl263, plain, 49.01/7.85 (( ('#form12') 49.01/7.85 | ~ (((((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ 49.01/7.85 '#sk3' @ '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y2)))))))))))))))), 49.01/7.85 inference('renaming', [status(thm)], 49.01/7.85 [zip_derived_cl262, zip_derived_cl22])). 49.01/7.85 thf(zip_derived_cl264, plain, 49.01/7.85 ((~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))))))))) 49.01/7.85 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 ((((('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y1 @ Y2) & 49.01/7.85 ('#sk13' @ '#sk3' @ 49.01/7.85 '#sk2' @ Y0 @ Y1))) => 49.01/7.85 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.85 Y0 @ Y2)))))))))))) 49.01/7.85 | ('#form12'))), 49.01/7.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl263])). 49.01/7.85 thf(zip_derived_cl2, plain, 49.01/7.85 ( (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 ( 49.01/7.85 ( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y4 @ 49.01/7.85 Y5) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))))))))) & 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 ( 49.01/7.85 ( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y3 @ 49.01/7.85 Y5 @ 49.01/7.85 Y6) & 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y6)))))))))))))) => 49.01/7.85 (Y3 @ Y0 @ Y1)))))) | 49.01/7.85 (((Y0) = (Y1))))) & 49.01/7.85 ('#sk1' @ Y0 @ Y2))) => 49.01/7.85 (((??) @ (^[Y3 : $i]: 49.01/7.85 (((((((!!) @ ( 49.01/7.85 ^[Y4 : 49.01/7.85 $i > $i > $o]: 49.01/7.85 (((((( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y5 @ 49.01/7.85 Y6) => 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y6))))))))) & 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y7 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y4 @ 49.01/7.85 Y6 @ 49.01/7.85 Y7) & 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y6))) => 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y7)))))))))))))) => 49.01/7.85 (Y4 @ Y2 @ 49.01/7.85 Y3)))))) | 49.01/7.85 (((Y2) = (Y3))))) & 49.01/7.85 (((((!!) @ ( 49.01/7.85 ^[Y4 : 49.01/7.85 $i > $i > $o]: 49.01/7.85 (((((( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y5 @ 49.01/7.85 Y6) => 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y6))))))))) & 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y7 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y4 @ 49.01/7.85 Y6 @ 49.01/7.85 Y7) & 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y6))) => 49.01/7.85 (Y4 @ 49.01/7.85 Y5 @ Y7)))))))))))))) => 49.01/7.85 (Y4 @ Y1 @ 49.01/7.85 Y3)))))) | 49.01/7.85 (((Y1) = (Y3)))))))))))))))))))))), 49.01/7.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 49.01/7.85 thf(zip_derived_cl4, plain, 49.01/7.85 (![X2 : $i]: 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((!!) @ (^[Y1 : $i]: 49.01/7.85 (((((((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y3 : $i]: 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y3 @ 49.01/7.85 Y4) => 49.01/7.85 (Y2 @ 49.01/7.85 Y3 @ Y4))))))))) & 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y2 @ 49.01/7.85 Y4 @ 49.01/7.85 Y5) & 49.01/7.85 (Y2 @ 49.01/7.85 Y3 @ Y4))) => 49.01/7.85 (Y2 @ 49.01/7.85 Y3 @ Y5)))))))))))))) => 49.01/7.85 (Y2 @ X2 @ Y0)))))) | 49.01/7.85 (((X2) = (Y0))))) & 49.01/7.85 ('#sk1' @ X2 @ Y1))) => 49.01/7.85 (((??) @ (^[Y2 : $i]: 49.01/7.85 (((((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y4 @ 49.01/7.85 Y5) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))))))))) & 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y3 @ 49.01/7.85 Y5 @ 49.01/7.85 Y6) & 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y6)))))))))))))) => 49.01/7.85 (Y3 @ Y1 @ 49.01/7.85 Y2)))))) | 49.01/7.85 (((Y1) = (Y2))))) & 49.01/7.85 (((((!!) @ (^[Y3 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 ('#sk1' @ 49.01/7.85 Y4 @ 49.01/7.85 Y5) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))))))))) & 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y5 : $i]: 49.01/7.85 (( 49.01/7.85 (!!) @ ( 49.01/7.85 ^[Y6 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y3 @ 49.01/7.85 Y5 @ 49.01/7.85 Y6) & 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y5))) => 49.01/7.85 (Y3 @ 49.01/7.85 Y4 @ Y6)))))))))))))) => 49.01/7.85 (Y3 @ Y0 @ 49.01/7.85 Y2)))))) | 49.01/7.85 (((Y0) = (Y2))))))))))))))))))), 49.01/7.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 49.01/7.85 thf(zip_derived_cl6, plain, 49.01/7.85 (![X2 : $i, X4 : $i]: 49.01/7.85 (((!!) @ (^[Y0 : $i]: 49.01/7.85 (((((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 ((('#sk1' @ 49.01/7.85 Y2 @ 49.01/7.85 Y3) => 49.01/7.85 (Y1 @ 49.01/7.85 Y2 @ Y3))))))))) & 49.01/7.85 (((!!) @ (^[Y2 : $i]: 49.01/7.85 (((!!) @ (^[Y3 : $i]: 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.85 (( 49.01/7.85 (( 49.01/7.85 (Y1 @ 49.01/7.85 Y3 @ 49.01/7.85 Y4) & 49.01/7.85 (Y1 @ 49.01/7.85 Y2 @ Y3))) => 49.01/7.85 (Y1 @ 49.01/7.85 Y2 @ Y4)))))))))))))) => 49.01/7.85 (Y1 @ X2 @ X4)))))) | 49.01/7.85 (((X2) = (X4))))) & 49.01/7.85 ('#sk1' @ X2 @ Y0))) => 49.01/7.85 (((??) @ (^[Y1 : $i]: 49.01/7.85 (((((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.85 (((((((!!) @ (^[Y3 : $i]: 49.01/7.85 (((!!) @ ( 49.01/7.85 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) => 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y4))))))))) & 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y5 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y2 @ 49.01/7.86 Y4 @ 49.01/7.86 Y5) & 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y4))) => 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y5)))))))))))))) => 49.01/7.86 (Y2 @ Y0 @ Y1)))))) | 49.01/7.86 (((Y0) = (Y1))))) & 49.01/7.86 (((((!!) @ (^[Y2 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y3 : $i]: 49.01/7.86 (((!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) => 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y4))))))))) & 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y5 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y2 @ 49.01/7.86 Y4 @ 49.01/7.86 Y5) & 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y4))) => 49.01/7.86 (Y2 @ 49.01/7.86 Y3 @ Y5)))))))))))))) => 49.01/7.86 (Y2 @ X4 @ Y1)))))) | 49.01/7.86 (((X4) = (Y1)))))))))))))))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 49.01/7.86 thf(zip_derived_cl8, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 (((((((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((( 49.01/7.86 (Y0 @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X2 @ X4)))))) | 49.01/7.86 (((X2) = (X4))))) & 49.01/7.86 ('#sk1' @ X2 @ X6))) => 49.01/7.86 (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 ((('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 ((('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0))))))))))))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 49.01/7.86 thf(zip_derived_cl11, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 (~ (((((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((( 49.01/7.86 (Y0 @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X2 @ X4)))))) | 49.01/7.86 (((X2) = (X4))))) & 49.01/7.86 ('#sk1' @ X2 @ X6))) 49.01/7.86 | (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0)))))))))))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 49.01/7.86 thf(zip_derived_cl14, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ 49.01/7.86 Y3)))))))))))))) => 49.01/7.86 (Y0 @ X2 @ X4)))))) | 49.01/7.86 (((X2) = (X4))))) 49.01/7.86 | ~ ('#sk1' @ X2 @ X6) 49.01/7.86 | (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0)))))))))))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 49.01/7.86 thf(zip_derived_cl21, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 (~ (((X2) = (X4))) 49.01/7.86 | (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0)))))))))) 49.01/7.86 | ~ ('#sk1' @ X2 @ X6))), 49.01/7.86 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])). 49.01/7.86 thf(zip_derived_cl31, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 (((X2) != (X4)) 49.01/7.86 | (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0)))))))))) 49.01/7.86 | ~ ('#sk1' @ X2 @ X6))), 49.01/7.86 inference('simplify nested equalities', [status(thm)], [zip_derived_cl21])). 49.01/7.86 thf(zip_derived_cl32, plain, 49.01/7.86 (![X4 : $i, X6 : $i]: 49.01/7.86 (~ ('#sk1' @ X4 @ X6) 49.01/7.86 | (((??) @ (^[Y0 : $i]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X6 @ Y0)))))) | 49.01/7.86 (((X6) = (Y0))))) & 49.01/7.86 (((((!!) @ (^[Y1 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 ('#sk1' @ 49.01/7.86 Y2 @ 49.01/7.86 Y3) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))))))))) & 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (( 49.01/7.86 (!!) @ ( 49.01/7.86 ^[Y4 : $i]: 49.01/7.86 (( 49.01/7.86 (( 49.01/7.86 (Y1 @ 49.01/7.86 Y3 @ 49.01/7.86 Y4) & 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y3))) => 49.01/7.86 (Y1 @ 49.01/7.86 Y2 @ Y4)))))))))))))) => 49.01/7.86 (Y1 @ X4 @ Y0)))))) | 49.01/7.86 (((X4) = (Y0)))))))))))), 49.01/7.86 inference('simplify', [status(thm)], [zip_derived_cl31])). 49.01/7.86 thf(zip_derived_cl33, plain, 49.01/7.86 (![X4 : $i, X6 : $i]: 49.01/7.86 ( (((((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((( 49.01/7.86 (Y0 @ 49.01/7.86 Y2 @ Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) | 49.01/7.86 (((X6) = ('#sk14' @ X4 @ X6))))) & 49.01/7.86 (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((( 49.01/7.86 (Y0 @ 49.01/7.86 Y2 @ Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X4 @ ('#sk14' @ X4 @ X6))))))) | 49.01/7.86 (((X4) = ('#sk14' @ X4 @ X6))))))) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6))), 49.01/7.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 49.01/7.86 thf(zip_derived_cl43, plain, 49.01/7.86 (![X4 : $i, X6 : $i]: 49.01/7.86 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ 49.01/7.86 Y2 @ Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ 49.01/7.86 Y3)))))))))))))) => 49.01/7.86 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) | 49.01/7.86 (((X6) = ('#sk14' @ X4 @ X6))))) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl33])). 49.01/7.86 thf(zip_derived_cl55, plain, 49.01/7.86 (![X4 : $i, X6 : $i]: 49.01/7.86 ( (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ Y2 @ 49.01/7.86 Y3) & (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) 49.01/7.86 | (((X6) = ('#sk14' @ X4 @ X6))) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6))), 49.01/7.86 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 49.01/7.86 thf(zip_derived_cl70, plain, 49.01/7.86 (![X4 : $i, X6 : $i]: 49.01/7.86 ( (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ Y2 @ 49.01/7.86 Y3) & (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ X6 @ ('#sk14' @ X4 @ X6))))))) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6))), 49.01/7.86 inference('simplify nested equalities', [status(thm)], [zip_derived_cl55])). 49.01/7.86 thf(zip_derived_cl71, plain, 49.01/7.86 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 49.01/7.86 ( (((((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X8 @ Y1 @ Y2) & (X8 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X8 @ Y0 @ Y2)))))))))))))) => 49.01/7.86 (X8 @ X6 @ ('#sk14' @ X4 @ X6)))) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 49.01/7.86 thf(zip_derived_cl91, plain, 49.01/7.86 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 49.01/7.86 (~ (((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X8 @ Y1 @ Y2) & (X8 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X8 @ Y0 @ Y2)))))))))))))) 49.01/7.86 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 49.01/7.86 thf(zip_derived_cl116, plain, 49.01/7.86 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 49.01/7.86 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X8 @ Y1 @ Y2) & (X8 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X8 @ Y0 @ Y2)))))))))))) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)) 49.01/7.86 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 49.01/7.86 thf(zip_derived_cl64, plain, 49.01/7.86 ( (((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y1 @ Y2) & ('#sk13' @ 49.01/7.86 '#sk3' @ '#sk2' @ Y0 @ Y1))) => 49.01/7.86 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y0 @ Y2))))))))))))))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 49.01/7.86 thf(zip_derived_cl86, plain, 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y1 @ Y2) & ('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y0 @ Y1))) => 49.01/7.86 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y0 @ Y2))))))))))))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 49.01/7.86 thf(zip_derived_cl103, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl95, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#form133' @ X2) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl133, plain, 49.01/7.86 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X8 @ Y0 @ Y1))) 49.01/7.86 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl116, zip_derived_cl103, zip_derived_cl95])). 49.01/7.86 thf(zip_derived_cl147, plain, 49.01/7.86 (![X4 : $i, X6 : $i, X8 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X8) 49.01/7.86 | (X8 @ X6 @ ('#sk14' @ X4 @ X6)) 49.01/7.86 | ((X6) = ('#sk14' @ X4 @ X6)) 49.01/7.86 | ~ ('#sk1' @ X4 @ X6) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 49.01/7.86 inference('ho_norm', [status(thm)], [zip_derived_cl133])). 49.01/7.86 thf(zip_derived_cl148, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 ( ('#form307' @ X8) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl265, plain, 49.01/7.86 ((~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')) 49.01/7.86 | ('#form12') 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y1 @ Y2) & 49.01/7.86 ('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y0 @ Y1))) => 49.01/7.86 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y0 @ Y2)))))))))))))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl264, zip_derived_cl148])). 49.01/7.86 thf(zip_derived_cl103, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl95, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#form133' @ X2) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl266, plain, 49.01/7.86 ((~ ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2')) 49.01/7.86 | ('#form12') 49.01/7.86 | ~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl265, zip_derived_cl103, zip_derived_cl95])). 49.01/7.86 thf(zip_derived_cl86, plain, 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y1 @ Y2) & ('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y0 @ Y1))) => 49.01/7.86 ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 Y0 @ Y2))))))))))))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 49.01/7.86 thf(zip_derived_cl103, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl95, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#form133' @ X2) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl105, plain, ( ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2'))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl86, zip_derived_cl103, zip_derived_cl95])). 49.01/7.86 thf(zip_derived_cl267, plain, 49.01/7.86 (( ('#form12') | ~ ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')))), 49.01/7.86 inference('demod', [status(thm)], [zip_derived_cl266, zip_derived_cl105])). 49.01/7.86 thf(zip_derived_cl148, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 ( ('#form307' @ X8) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X8 @ Y0 @ Y1))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl149, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 ((('#sk1' @ ('#sk56' @ X8) @ Y0) => (X8 @ 49.01/7.86 ('#sk56' @ X8) @ Y0)))))) 49.01/7.86 | ('#form307' @ X8))), 49.01/7.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl148])). 49.01/7.86 thf(zip_derived_cl162, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 (~ ((('#sk1' @ ('#sk56' @ X8) @ ('#sk77' @ X8)) => (X8 @ 49.01/7.86 ('#sk56' @ X8) @ ('#sk77' @ X8)))) 49.01/7.86 | ('#form307' @ X8))), 49.01/7.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 49.01/7.86 thf(zip_derived_cl175, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 (~ (X8 @ ('#sk56' @ X8) @ ('#sk77' @ X8)) | ('#form307' @ X8))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 49.01/7.86 thf(zip_derived_cl85, plain, 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => ('#sk13' @ '#sk3' @ 49.01/7.86 '#sk2' @ Y0 @ Y1)))))))))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl64])). 49.01/7.86 thf(zip_derived_cl102, plain, 49.01/7.86 (![X2 : $i]: 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 ((('#sk1' @ X2 @ Y0) => ('#sk13' @ '#sk3' @ '#sk2' @ 49.01/7.86 X2 @ Y0))))))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 49.01/7.86 thf(zip_derived_cl127, plain, 49.01/7.86 (![X2 : $i, X4 : $i]: 49.01/7.86 ((('#sk1' @ X2 @ X4) => ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4)))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 49.01/7.86 thf(zip_derived_cl142, plain, 49.01/7.86 (![X2 : $i, X4 : $i]: 49.01/7.86 (~ ('#sk1' @ X2 @ X4) | ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 49.01/7.86 thf(zip_derived_cl571, plain, 49.01/7.86 (( ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2')) 49.01/7.86 | ~ ('#sk1' @ ('#sk56' @ ('#sk13' @ '#sk3' @ '#sk2')) @ 49.01/7.86 ('#sk77' @ ('#sk13' @ '#sk3' @ '#sk2'))))), 49.01/7.86 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl142])). 49.01/7.86 thf(zip_derived_cl174, plain, 49.01/7.86 (![X8 : $i > $i > $o]: 49.01/7.86 ( ('#sk1' @ ('#sk56' @ X8) @ ('#sk77' @ X8)) | ('#form307' @ X8))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])). 49.01/7.86 thf(zip_derived_cl990, plain, ( ('#form307' @ ('#sk13' @ '#sk3' @ '#sk2'))), 49.01/7.86 inference('clc', [status(thm)], [zip_derived_cl571, zip_derived_cl174])). 49.01/7.86 thf(zip_derived_cl991, plain, ( ('#form12')), 49.01/7.86 inference('demod', [status(thm)], [zip_derived_cl267, zip_derived_cl990])). 49.01/7.86 thf(zip_derived_cl1075, plain, 49.01/7.86 (![X0 : $i > $i > $o]: 49.01/7.86 (~ (X0 @ ('#sk56' @ X0) @ ('#sk77' @ X0)) 49.01/7.86 | ~ ('#form133' @ X0) 49.01/7.86 | (X0 @ '#sk2' @ '#sk3'))), 49.01/7.86 inference('demod', [status(thm)], [zip_derived_cl735, zip_derived_cl991])). 49.01/7.86 thf(zip_derived_cl81, plain, 49.01/7.86 (![X2 : $i]: 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk2' @ X2 @ 49.01/7.86 Y1 @ Y2) & ('#sk13' @ 49.01/7.86 '#sk2' @ X2 @ Y0 @ Y1))) => 49.01/7.86 ('#sk13' @ '#sk2' @ X2 @ Y0 @ 49.01/7.86 Y2)))))))))))) 49.01/7.86 | ~ ('#form65' @ X2))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl62])). 49.01/7.86 thf(zip_derived_cl99, plain, 49.01/7.86 (![X2 : $i, X4 : $i]: 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk2' @ X2 @ Y0 @ Y1) & 49.01/7.86 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y0))) => 49.01/7.86 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y1))))))))) 49.01/7.86 | ~ ('#form65' @ X2))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 49.01/7.86 thf(zip_derived_cl124, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i]: 49.01/7.86 ( (((!!) @ (^[Y0 : $i]: 49.01/7.86 ((((('#sk13' @ '#sk2' @ X2 @ X6 @ Y0) & ('#sk13' @ 49.01/7.86 '#sk2' @ X2 @ X4 @ X6))) => 49.01/7.86 ('#sk13' @ '#sk2' @ X2 @ X4 @ Y0)))))) 49.01/7.86 | ~ ('#form65' @ X2))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 49.01/7.86 thf(zip_derived_cl139, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 49.01/7.86 ( ((((('#sk13' @ '#sk2' @ X2 @ X6 @ X8) & ('#sk13' @ '#sk2' @ X2 @ 49.01/7.86 X4 @ X6))) => 49.01/7.86 ('#sk13' @ '#sk2' @ X2 @ X4 @ X8))) 49.01/7.86 | ~ ('#form65' @ X2))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 49.01/7.86 thf(zip_derived_cl155, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 49.01/7.86 (~ ((('#sk13' @ '#sk2' @ X2 @ X6 @ X8) & ('#sk13' @ '#sk2' @ X2 @ 49.01/7.86 X4 @ X6))) 49.01/7.86 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X8) 49.01/7.86 | ~ ('#form65' @ X2))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 49.01/7.86 thf(zip_derived_cl166, plain, 49.01/7.86 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 49.01/7.86 (~ ('#sk13' @ '#sk2' @ X2 @ X6 @ X8) 49.01/7.86 | ~ ('#sk13' @ '#sk2' @ X2 @ X4 @ X6) 49.01/7.86 | ~ ('#form65' @ X2) 49.01/7.86 | ('#sk13' @ '#sk2' @ X2 @ X4 @ X8))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 49.01/7.86 thf(zip_derived_cl105, plain, ( ('#form133' @ ('#sk13' @ '#sk3' @ '#sk2'))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl86, zip_derived_cl103, zip_derived_cl95])). 49.01/7.86 thf(zip_derived_cl120, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 49.01/7.86 | ~ ('#form12') 49.01/7.86 | (X2 @ '#sk2' @ '#sk3') 49.01/7.86 | ~ ('#form133' @ X2))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 49.01/7.86 thf(zip_derived_cl17, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( (((((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))) => 49.01/7.86 (X2 @ '#sk3' @ '#sk2'))) 49.01/7.86 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ 49.01/7.86 Y2 @ Y3) & 49.01/7.86 (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ 49.01/7.86 Y3)))))))))))))) => 49.01/7.86 (Y0 @ '#sk2' @ '#sk3')))))) 49.01/7.86 | (('#sk2') = ('#sk3')))), 49.01/7.86 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 49.01/7.86 thf(zip_derived_cl22, plain, 49.01/7.86 ((~ ('#form12') 49.01/7.86 | (((!!) @ (^[Y0 : $i > $i > $o]: 49.01/7.86 (((((((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 ((('#sk1' @ Y1 @ Y2) => 49.01/7.86 (Y0 @ Y1 @ Y2))))))))) & 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((!!) @ (^[Y3 : $i]: 49.01/7.86 (((((Y0 @ Y2 @ 49.01/7.86 Y3) & (Y0 @ 49.01/7.86 Y1 @ Y2))) => 49.01/7.86 (Y0 @ Y1 @ Y3)))))))))))))) => 49.01/7.86 (Y0 @ '#sk2' @ '#sk3')))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl25, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#form12') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | (((((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & 49.01/7.86 (X2 @ Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))) => 49.01/7.86 (X2 @ '#sk3' @ '#sk2'))))), 49.01/7.86 inference('renaming', [status(thm)], [zip_derived_cl17, zip_derived_cl22])). 49.01/7.86 thf(zip_derived_cl34, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ (((((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 49.01/7.86 (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | ('#form12'))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 49.01/7.86 thf(zip_derived_cl45, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))) 49.01/7.86 | ('#form12') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2'))), 49.01/7.86 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 49.01/7.86 thf(zip_derived_cl57, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 ((('#sk1' @ ('#sk56' @ X2) @ Y0) => (X2 @ 49.01/7.86 ('#sk56' @ X2) @ Y0)))))) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | ('#form12') 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 49.01/7.86 thf(zip_derived_cl78, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ((('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) => (X2 @ 49.01/7.86 ('#sk56' @ X2) @ ('#sk77' @ X2)))) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))) 49.01/7.86 | ('#form12') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2'))), 49.01/7.86 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 49.01/7.86 thf(zip_derived_cl93, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | ('#form12') 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 49.01/7.86 thf(zip_derived_cl103, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl95, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 ( ('#form133' @ X2) 49.01/7.86 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.86 (((!!) @ (^[Y1 : $i]: 49.01/7.86 (((!!) @ (^[Y2 : $i]: 49.01/7.86 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.86 Y0 @ Y1))) => 49.01/7.86 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.86 define([status(thm)])). 49.01/7.86 thf(zip_derived_cl118, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X2 @ Y0 @ Y1))) 49.01/7.86 | ('#form12') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.86 inference('renaming', [status(thm)], 49.01/7.86 [zip_derived_cl93, zip_derived_cl103, zip_derived_cl95])). 49.01/7.86 thf(zip_derived_cl135, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | ('#form12') 49.01/7.86 | (('#sk2') = ('#sk3')) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.86 inference('ho_norm', [status(thm)], [zip_derived_cl118])). 49.01/7.86 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 49.01/7.86 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 49.01/7.86 thf(zip_derived_cl212, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ ('#form133' @ X2) 49.01/7.86 | ('#form12') 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.86 | ('#sk1' @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.86 inference('simplify_reflect-', [status(thm)], 49.01/7.86 [zip_derived_cl135, zip_derived_cl50])). 49.01/7.86 thf(zip_derived_cl65, plain, 49.01/7.86 (~ ('#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2')), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 49.01/7.86 thf(zip_derived_cl142, plain, 49.01/7.86 (![X2 : $i, X4 : $i]: 49.01/7.86 (~ ('#sk1' @ X2 @ X4) | ('#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4))), 49.01/7.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 49.01/7.86 thf(zip_derived_cl94, plain, 49.01/7.86 (![X2 : $i > $i > $o]: 49.01/7.86 (~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)) 49.01/7.86 | (X2 @ '#sk3' @ '#sk2') 49.01/7.87 | (('#sk2') = ('#sk3')) 49.01/7.87 | ('#form12') 49.01/7.87 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.87 (((!!) @ (^[Y1 : $i]: 49.01/7.87 (((!!) @ (^[Y2 : $i]: 49.01/7.87 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.87 Y0 @ Y1))) => 49.01/7.87 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 49.01/7.87 thf(zip_derived_cl103, plain, 49.01/7.87 (![X2 : $i > $i > $o]: 49.01/7.87 (~ ('#form133' @ X2) 49.01/7.87 | (((!!) @ (^[Y0 : $i]: 49.01/7.87 (((!!) @ (^[Y1 : $i]: 49.01/7.87 (((!!) @ (^[Y2 : $i]: 49.01/7.87 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.87 Y0 @ Y1))) => 49.01/7.87 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.87 define([status(thm)])). 49.01/7.87 thf(zip_derived_cl95, plain, 49.01/7.87 (![X2 : $i > $i > $o]: 49.01/7.87 ( ('#form133' @ X2) 49.01/7.87 | ~ (((!!) @ (^[Y0 : $i]: 49.01/7.87 (((!!) @ (^[Y1 : $i]: 49.01/7.87 (((!!) @ (^[Y2 : $i]: 49.01/7.87 (((((X2 @ Y1 @ Y2) & (X2 @ 49.01/7.87 Y0 @ Y1))) => 49.01/7.87 (X2 @ Y0 @ Y2)))))))))))))), 49.01/7.87 define([status(thm)])). 49.01/7.87 thf(zip_derived_cl119, plain, 49.01/7.87 (![X2 : $i > $i > $o]: 49.01/7.87 (~ ('#form133' @ (^[Y0 : $i,Y1 : $i]: (X2 @ Y0 @ Y1))) 49.01/7.87 | ('#form12') 49.01/7.87 | (('#sk2') = ('#sk3')) 49.01/7.87 | (X2 @ '#sk3' @ '#sk2') 49.01/7.87 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.87 inference('renaming', [status(thm)], 49.01/7.87 [zip_derived_cl94, zip_derived_cl103, zip_derived_cl95])). 49.01/7.87 thf(zip_derived_cl136, plain, 49.01/7.87 (![X2 : $i > $i > $o]: 49.01/7.87 (~ ('#form133' @ X2) 49.01/7.87 | ('#form12') 49.01/7.87 | (('#sk2') = ('#sk3')) 49.01/7.87 | (X2 @ '#sk3' @ '#sk2') 49.01/7.87 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.87 inference('ho_norm', [status(thm)], [zip_derived_cl119])). 49.01/7.87 thf(zip_derived_cl50, plain, ((('#sk3') != ('#sk2'))), 49.01/7.87 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 49.01/7.87 thf(zip_derived_cl228, plain, 49.01/7.87 (![X2 : $i > $i > $o]: 49.01/7.87 (~ ('#form133' @ X2) 49.01/7.87 | ('#form12') 49.01/7.87 | (X2 @ '#sk3' @ '#sk2') 49.01/7.87 | ~ (X2 @ ('#sk56' @ X2) @ ('#sk77' @ X2)))), 49.01/7.87 inference('simplify_reflect-', [status(thm)], 49.01/7.87 [zip_derived_cl136, zip_derived_cl50])). 49.01/7.87 thf(zip_derived_cl2580, plain, ($false), 49.01/7.87 inference('eprover', [status(thm)], 49.01/7.87 [zip_derived_cl84, zip_derived_cl63, zip_derived_cl164, 49.01/7.87 zip_derived_cl165, zip_derived_cl154, zip_derived_cl138, 49.01/7.87 zip_derived_cl1075, zip_derived_cl166, zip_derived_cl105, 49.01/7.87 zip_derived_cl120, zip_derived_cl212, zip_derived_cl65, 49.01/7.87 zip_derived_cl142, zip_derived_cl228])). 49.01/7.87 49.01/7.87 % SZS output end Refutation 49.01/7.87 49.01/7.87 49.01/7.87 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 49.01/7.87 % Terminating... 9.17/7.95 % Runner terminated. 9.23/8.02 % Zipperpin 1.5 exiting 9.23/8.05 EOF