0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bL5r5Uy1Fg true 0.13/0.34 % Computer : n003.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 05:32:21 EDT 2022 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 960 s 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.55/0.65 % Total configuration time : 828 0.55/0.65 % Estimated wc time : 1656 0.55/0.65 % Estimated cpu time (8 cpus) : 207.0 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 10.25/1.95 % Solved by lams/35_full_unif4.sh. 10.25/1.95 % done 68 iterations in 1.128s 10.25/1.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 10.25/1.95 % SZS output start Refutation 10.25/1.95 thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o). 10.25/1.95 thf('#sk164_type', type, '#sk164': ($i > $i > $o) > $i). 10.25/1.95 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 10.25/1.95 thf('#sk66_type', type, '#sk66': ($i > $i > $o) > $i). 10.25/1.95 thf('#sk5_type', type, '#sk5': $i > $i > $o). 10.25/1.95 thf(refl_type, type, refl: ($i > $i > $o) > $o). 10.25/1.95 thf('#sk117_type', type, '#sk117': ($i > $i > $o) > $i). 10.25/1.95 thf('#form116_type', type, '#form116': ($i > $i > $o) > $o). 10.25/1.95 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 10.25/1.95 thf(trans_type, type, trans: ($i > $i > $o) > $o). 10.25/1.95 thf('#sk213_type', type, '#sk213': ($i > $i > $o) > $i). 10.25/1.95 thf('#sk3_type', type, '#sk3': $i). 10.25/1.95 thf('#sk46_type', type, '#sk46': ($i > $i > $o) > $i). 10.25/1.95 thf('#sk2_type', type, '#sk2': $i). 10.25/1.95 thf('#sk4_type', type, '#sk4': $i). 10.25/1.95 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 10.25/1.95 thf('#sk1_type', type, '#sk1': $i > $i > $o). 10.25/1.95 thf(transitive_reflexive_closure, axiom,(( trc ) = 10.25/1.95 (^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) )))). 10.25/1.95 thf(transitive_closure, axiom,(( tc ) = 10.25/1.95 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 10.25/1.95 ( ![S:( $i > $i > $o )]: 10.25/1.95 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 10.25/1.95 thf(transitive, axiom,(( trans ) = 10.25/1.95 (^[R:( $i > $i > $o )]: 10.25/1.95 ( ![X:$i,Y:$i,Z:$i]: 10.25/1.95 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 10.25/1.95 thf('0', plain, 10.25/1.95 (( trans ) = 10.25/1.95 ( ^[R:( $i > $i > $o )]: 10.25/1.95 ( ![X:$i,Y:$i,Z:$i]: 10.25/1.95 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], [transitive])). 10.25/1.95 thf('1', plain, 10.25/1.95 (( trans ) = 10.25/1.95 ( ^[V_1:( $i > $i > $o )]: 10.25/1.95 ( ![X4:$i,X6:$i,X8:$i]: 10.25/1.95 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(subrel, axiom,(( subrel ) = 10.25/1.95 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 10.25/1.95 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 10.25/1.95 thf('2', plain, 10.25/1.95 (( subrel ) = 10.25/1.95 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 10.25/1.95 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], [subrel])). 10.25/1.95 thf('3', plain, 10.25/1.95 (( subrel ) = 10.25/1.95 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 10.25/1.95 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf('4', plain, 10.25/1.95 (( tc ) = 10.25/1.95 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 10.25/1.95 ( ![S:( $i > $i > $o )]: 10.25/1.95 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], 10.25/1.95 [transitive_closure, '1', '3'])). 10.25/1.95 thf('5', plain, 10.25/1.95 (( tc ) = 10.25/1.95 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 10.25/1.95 ( ![X4:( $i > $i > $o )]: 10.25/1.95 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(reflexive_closure, axiom,(( rc ) = 10.25/1.95 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) )))). 10.25/1.95 thf('6', plain, 10.25/1.95 (( rc ) = 10.25/1.95 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], [reflexive_closure])). 10.25/1.95 thf('7', plain, 10.25/1.95 (( rc ) = 10.25/1.95 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 10.25/1.95 ( ( ( V_2 ) = ( V_3 ) ) | ( V_1 @ V_2 @ V_3 ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf('8', plain, (( trc ) = ( ^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], 10.25/1.95 [transitive_reflexive_closure, '5', '1', '7', '3'])). 10.25/1.95 thf('9', plain, 10.25/1.95 (( trc ) = ( ^[V_1:( $i > $i > $o )]: ( rc @ ( tc @ V_1 ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(reflexive, axiom,(( refl ) = 10.25/1.95 (^[R:( $i > $i > $o )]: ( ![X:$i]: ( R @ X @ X ) )))). 10.25/1.95 thf('10', plain, 10.25/1.95 (( refl ) = ( ^[R:( $i > $i > $o )]: ( ![X:$i]: ( R @ X @ X ) ) )), 10.25/1.95 inference('simplify_rw_rule', [status(thm)], [reflexive])). 10.25/1.95 thf('11', plain, 10.25/1.95 (( refl ) = ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(transitive_reflexive_closure_is_transitive_reflexive, conjecture, 10.25/1.95 (![R:( $i > $i > $o )]: 10.25/1.95 ( ( trans @ ( trc @ R ) ) & ( refl @ ( trc @ R ) ) ))). 10.25/1.95 thf(zf_stmt_0, conjecture, 10.25/1.95 (![X4:( $i > $i > $o )]: 10.25/1.95 ( ( ![X48:$i]: 10.25/1.95 ( ( ![X50:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X58:$i,X60:$i]: 10.25/1.95 ( ( X4 @ X58 @ X60 ) => ( X50 @ X58 @ X60 ) ) ) & 10.25/1.95 ( ![X52:$i,X54:$i,X56:$i]: 10.25/1.95 ( ( ( X50 @ X54 @ X56 ) & ( X50 @ X52 @ X54 ) ) => 10.25/1.95 ( X50 @ X52 @ X56 ) ) ) ) => 10.25/1.95 ( X50 @ X48 @ X48 ) ) ) | 10.25/1.95 ( ( X48 ) = ( X48 ) ) ) ) & 10.25/1.95 ( ![X6:$i,X8:$i,X10:$i]: 10.25/1.95 ( ( ( ( ![X24:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X32:$i,X34:$i]: 10.25/1.95 ( ( X4 @ X32 @ X34 ) => ( X24 @ X32 @ X34 ) ) ) & 10.25/1.95 ( ![X26:$i,X28:$i,X30:$i]: 10.25/1.95 ( ( ( X24 @ X28 @ X30 ) & ( X24 @ X26 @ X28 ) ) => 10.25/1.95 ( X24 @ X26 @ X30 ) ) ) ) => 10.25/1.95 ( X24 @ X8 @ X10 ) ) ) | 10.25/1.95 ( ( X8 ) = ( X10 ) ) ) & 10.25/1.95 ( ( ![X12:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X20:$i,X22:$i]: 10.25/1.95 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 10.25/1.95 ( ![X14:$i,X16:$i,X18:$i]: 10.25/1.95 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 10.25/1.95 ( X12 @ X14 @ X18 ) ) ) ) => 10.25/1.95 ( X12 @ X6 @ X8 ) ) ) | 10.25/1.95 ( ( X6 ) = ( X8 ) ) ) ) => 10.25/1.95 ( ( ![X36:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X44:$i,X46:$i]: 10.25/1.95 ( ( X4 @ X44 @ X46 ) => ( X36 @ X44 @ X46 ) ) ) & 10.25/1.95 ( ![X38:$i,X40:$i,X42:$i]: 10.25/1.95 ( ( ( X36 @ X40 @ X42 ) & ( X36 @ X38 @ X40 ) ) => 10.25/1.95 ( X36 @ X38 @ X42 ) ) ) ) => 10.25/1.95 ( X36 @ X6 @ X10 ) ) ) | 10.25/1.95 ( ( X6 ) = ( X10 ) ) ) ) ) ))). 10.25/1.95 thf(zf_stmt_1, negated_conjecture, 10.25/1.95 (~( ![X4:( $i > $i > $o )]: 10.25/1.95 ( ( ![X48:$i]: 10.25/1.95 ( ( ![X50:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X58:$i,X60:$i]: 10.25/1.95 ( ( X4 @ X58 @ X60 ) => ( X50 @ X58 @ X60 ) ) ) & 10.25/1.95 ( ![X52:$i,X54:$i,X56:$i]: 10.25/1.95 ( ( ( X50 @ X54 @ X56 ) & ( X50 @ X52 @ X54 ) ) => 10.25/1.95 ( X50 @ X52 @ X56 ) ) ) ) => 10.25/1.95 ( X50 @ X48 @ X48 ) ) ) | 10.25/1.95 ( ( X48 ) = ( X48 ) ) ) ) & 10.25/1.95 ( ![X6:$i,X8:$i,X10:$i]: 10.25/1.95 ( ( ( ( ![X24:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X32:$i,X34:$i]: 10.25/1.95 ( ( X4 @ X32 @ X34 ) => ( X24 @ X32 @ X34 ) ) ) & 10.25/1.95 ( ![X26:$i,X28:$i,X30:$i]: 10.25/1.95 ( ( ( X24 @ X28 @ X30 ) & ( X24 @ X26 @ X28 ) ) => 10.25/1.95 ( X24 @ X26 @ X30 ) ) ) ) => 10.25/1.95 ( X24 @ X8 @ X10 ) ) ) | 10.25/1.95 ( ( X8 ) = ( X10 ) ) ) & 10.25/1.95 ( ( ![X12:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X20:$i,X22:$i]: 10.25/1.95 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 10.25/1.95 ( ![X14:$i,X16:$i,X18:$i]: 10.25/1.95 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 10.25/1.95 ( X12 @ X14 @ X18 ) ) ) ) => 10.25/1.95 ( X12 @ X6 @ X8 ) ) ) | 10.25/1.95 ( ( X6 ) = ( X8 ) ) ) ) => 10.25/1.95 ( ( ![X36:( $i > $i > $o )]: 10.25/1.95 ( ( ( ![X44:$i,X46:$i]: 10.25/1.95 ( ( X4 @ X44 @ X46 ) => ( X36 @ X44 @ X46 ) ) ) & 10.25/1.95 ( ![X38:$i,X40:$i,X42:$i]: 10.25/1.95 ( ( ( X36 @ X40 @ X42 ) & ( X36 @ X38 @ X40 ) ) => 10.25/1.95 ( X36 @ X38 @ X42 ) ) ) ) => 10.25/1.95 ( X36 @ X6 @ X10 ) ) ) | 10.25/1.95 ( ( X6 ) = ( X10 ) ) ) ) ) ) )), 10.25/1.95 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 10.25/1.95 thf(zip_derived_cl0, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((((!!) @ (^[Y2 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))))))))) & 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y2 @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) & 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y5)))))))))))))) => 10.25/1.95 (Y2 @ Y1 @ Y1)))))) | 10.25/1.95 (((Y1) = (Y1)))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((((((!!) @ ( 10.25/1.95 ^[Y4 : 10.25/1.95 $i > $i > $o]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y2 @ Y3)))))) | 10.25/1.95 (((Y2) = (Y3))))) & 10.25/1.95 (((((!!) @ ( 10.25/1.95 ^[Y4 : 10.25/1.95 $i > $i > $o]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y1 @ Y2)))))) | 10.25/1.95 (((Y1) = (Y2))))))) => 10.25/1.95 (((((!!) @ ( 10.25/1.95 ^[Y4 : 10.25/1.95 $i > $i > $o]: 10.25/1.95 (((( 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y1 @ Y3)))))) | 10.25/1.95 (((Y1) = (Y3)))))))))))))))))))))), 10.25/1.95 inference('cnf', [status(esa)], [zf_stmt_1])). 10.25/1.95 thf(zip_derived_cl1, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((((((!!) @ ( 10.25/1.95 ^[Y4 : 10.25/1.95 $i > $i > $o]: 10.25/1.95 (((( 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y2 @ Y3)))))) | 10.25/1.95 (((Y2) = (Y3))))) & 10.25/1.95 (((((!!) @ ( 10.25/1.95 ^[Y4 : 10.25/1.95 $i > $i > $o]: 10.25/1.95 (((( 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y1 @ Y2)))))) | 10.25/1.95 (((Y1) = (Y2))))))) => 10.25/1.95 (((((!!) @ ( 10.25/1.95 ^[Y4 : $i > $i > $o]: 10.25/1.95 (((((( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (Y0 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))))))))) & 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y7 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y4 @ 10.25/1.95 Y6 @ 10.25/1.95 Y7) & 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y6))) => 10.25/1.95 (Y4 @ 10.25/1.95 Y5 @ Y7)))))))))))))) => 10.25/1.95 (Y4 @ Y1 @ 10.25/1.95 Y3)))))) | 10.25/1.95 (((Y1) = (Y3)))))))))))))))))))), 10.25/1.95 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])). 10.25/1.95 thf(zip_derived_cl2, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))))))))) & 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y3 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) & 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y6)))))))))))))) => 10.25/1.95 (Y3 @ Y1 @ Y2)))))) | 10.25/1.95 (((Y1) = (Y2))))) & 10.25/1.95 (((((!!) @ (^[Y3 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))))))))) & 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y3 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) & 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y6)))))))))))))) => 10.25/1.95 (Y3 @ Y0 @ Y1)))))) | 10.25/1.95 (((Y0) = (Y1))))))) => 10.25/1.95 (((((!!) @ (^[Y3 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))))))))) & 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y6 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y3 @ 10.25/1.95 Y5 @ 10.25/1.95 Y6) & 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y5))) => 10.25/1.95 (Y3 @ 10.25/1.95 Y4 @ Y6)))))))))))))) => 10.25/1.95 (Y3 @ Y0 @ Y2)))))) | 10.25/1.95 (((Y0) = (Y2))))))))))))))))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 10.25/1.95 thf(zip_derived_cl3, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((((((((!!) @ (^[Y2 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))))))))) & 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y2 @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) & 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y5)))))))))))))) => 10.25/1.95 (Y2 @ Y0 @ Y1)))))) | 10.25/1.95 (((Y0) = (Y1))))) & 10.25/1.95 (((((!!) @ (^[Y2 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))))))))) & 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y2 @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) & 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y5)))))))))))))) => 10.25/1.95 (Y2 @ '#sk2' @ Y0)))))) | 10.25/1.95 ((('#sk2') = (Y0))))))) => 10.25/1.95 (((((!!) @ (^[Y2 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 ('#sk1' @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))))))))) & 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (!!) @ ( 10.25/1.95 ^[Y5 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y2 @ 10.25/1.95 Y4 @ 10.25/1.95 Y5) & 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y4))) => 10.25/1.95 (Y2 @ 10.25/1.95 Y3 @ Y5)))))))))))))) => 10.25/1.95 (Y2 @ '#sk2' @ Y1)))))) | 10.25/1.95 ((('#sk2') = (Y1)))))))))))))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 10.25/1.95 thf(zip_derived_cl4, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((((((((!!) @ (^[Y1 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 ((('#sk1' @ 10.25/1.95 Y2 @ 10.25/1.95 Y3) => 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y3))))))))) & 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y1 @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) & 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y3))) => 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y4)))))))))))))) => 10.25/1.95 (Y1 @ '#sk3' @ Y0)))))) | 10.25/1.95 ((('#sk3') = (Y0))))) & 10.25/1.95 (((((!!) @ (^[Y1 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 ((('#sk1' @ 10.25/1.95 Y2 @ 10.25/1.95 Y3) => 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y3))))))))) & 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y1 @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) & 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y3))) => 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y4)))))))))))))) => 10.25/1.95 (Y1 @ '#sk2' @ '#sk3')))))) | 10.25/1.95 ((('#sk2') = ('#sk3'))))))) => 10.25/1.95 (((((!!) @ (^[Y1 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 ((('#sk1' @ 10.25/1.95 Y2 @ Y3) => 10.25/1.95 (Y1 @ Y2 @ 10.25/1.95 Y3))))))))) & 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((!!) @ ( 10.25/1.95 ^[Y4 : $i]: 10.25/1.95 (( 10.25/1.95 (( 10.25/1.95 (Y1 @ 10.25/1.95 Y3 @ 10.25/1.95 Y4) & 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y3))) => 10.25/1.95 (Y1 @ 10.25/1.95 Y2 @ Y4)))))))))))))) => 10.25/1.95 (Y1 @ '#sk2' @ Y0)))))) | 10.25/1.95 ((('#sk2') = (Y0))))))))))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 10.25/1.95 thf(zip_derived_cl5, plain, 10.25/1.95 (~ (((((((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((( 10.25/1.95 (Y0 @ 10.25/1.95 Y2 @ Y3) & 10.25/1.95 (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ 10.25/1.95 Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk3' @ '#sk4')))))) | 10.25/1.95 ((('#sk3') = ('#sk4'))))) & 10.25/1.95 (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((( 10.25/1.95 (Y0 @ 10.25/1.95 Y2 @ Y3) & 10.25/1.95 (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ 10.25/1.95 Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk3')))))) | 10.25/1.95 ((('#sk2') = ('#sk3'))))))) => 10.25/1.95 (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ 10.25/1.95 Y2 @ Y3) & 10.25/1.95 (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ 10.25/1.95 Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk4')))))) | 10.25/1.95 ((('#sk2') = ('#sk4')))))))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 10.25/1.95 thf(zip_derived_cl6, plain, 10.25/1.95 ( (((((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & 10.25/1.95 (Y0 @ Y1 @ 10.25/1.95 Y2))) => 10.25/1.95 (Y0 @ Y1 @ 10.25/1.95 Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk3' @ '#sk4')))))) | 10.25/1.95 ((('#sk3') = ('#sk4'))))) & 10.25/1.95 (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & 10.25/1.95 (Y0 @ Y1 @ 10.25/1.95 Y2))) => 10.25/1.95 (Y0 @ Y1 @ 10.25/1.95 Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk3')))))) | 10.25/1.95 ((('#sk2') = ('#sk3')))))))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 10.25/1.95 thf(zip_derived_cl9, plain, 10.25/1.95 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk3')))))) | 10.25/1.95 ((('#sk2') = ('#sk3')))))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 10.25/1.95 thf(zip_derived_cl13, plain, 10.25/1.95 (( (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 10.25/1.95 Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk3')))))) 10.25/1.95 | ((('#sk2') = ('#sk3'))))), 10.25/1.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 10.25/1.95 thf(zip_derived_cl20, plain, 10.25/1.95 (( (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 10.25/1.95 Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk3')))))) 10.25/1.95 | (('#sk2') = ('#sk3')))), 10.25/1.95 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 10.25/1.95 thf(zip_derived_cl21, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))) => 10.25/1.95 (X2 @ '#sk2' @ '#sk3'))) 10.25/1.95 | (('#sk2') = ('#sk3')))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 10.25/1.95 thf(zip_derived_cl22, plain, 10.25/1.95 (( (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))))) => 10.25/1.95 ('#sk5' @ '#sk2' @ '#sk3'))) 10.25/1.95 | (('#sk2') = ('#sk3')))), 10.25/1.95 inference('triggered_bool_instantiation', [status(thm)], 10.25/1.95 [zip_derived_cl21])). 10.25/1.95 thf(zip_derived_cl163, plain, 10.25/1.95 ((~ (((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))))) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | (('#sk2') = ('#sk3')))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 10.25/1.95 thf(zip_derived_cl164, plain, 10.25/1.95 ((~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))) 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3'))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl163])). 10.25/1.95 thf(zip_derived_cl8, plain, 10.25/1.95 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk3' @ '#sk4')))))) | 10.25/1.95 ((('#sk3') = ('#sk4')))))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 10.25/1.95 thf(zip_derived_cl12, plain, 10.25/1.95 (( (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 10.25/1.95 Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk3' @ '#sk4')))))) 10.25/1.95 | ((('#sk3') = ('#sk4'))))), 10.25/1.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])). 10.25/1.95 thf(zip_derived_cl16, plain, 10.25/1.95 (( (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 10.25/1.95 Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk3' @ '#sk4')))))) 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 10.25/1.95 thf(zip_derived_cl17, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))) => 10.25/1.95 (X2 @ '#sk3' @ '#sk4'))) 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 10.25/1.95 thf(zip_derived_cl26, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))) 10.25/1.95 | (X2 @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 10.25/1.95 thf(zip_derived_cl30, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | (X2 @ '#sk3' @ '#sk4'))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 10.25/1.95 thf(zip_derived_cl34, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 ((('#sk1' @ ('#sk46' @ X2) @ Y0) => (X2 @ 10.25/1.95 ('#sk46' @ X2) @ Y0)))))) 10.25/1.95 | (X2 @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 10.25/1.95 thf(zip_derived_cl38, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ ((('#sk1' @ ('#sk46' @ X2) @ ('#sk66' @ X2)) => (X2 @ 10.25/1.95 ('#sk46' @ X2) @ ('#sk66' @ X2)))) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | (X2 @ '#sk3' @ '#sk4'))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 10.25/1.95 thf(zip_derived_cl42, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( ('#sk1' @ ('#sk46' @ X2) @ ('#sk66' @ X2)) 10.25/1.95 | (X2 @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 10.25/1.95 thf(zip_derived_cl47, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( ('#form116' @ X2) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(zip_derived_cl165, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))))), 10.25/1.95 inference('renaming', [status(thm)], 10.25/1.95 [zip_derived_cl164, zip_derived_cl47])). 10.25/1.95 thf(zip_derived_cl166, plain, 10.25/1.95 ((~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 ((('#sk1' @ ('#sk46' @ '#sk5') @ Y0) => ('#sk5' @ 10.25/1.95 ('#sk46' @ '#sk5') @ Y0)))))) 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl165])). 10.25/1.95 thf(zip_derived_cl167, plain, 10.25/1.95 ((~ ((('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) => ('#sk5' @ 10.25/1.95 ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))) 10.25/1.95 | ~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | (('#sk2') = ('#sk3')))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl166])). 10.25/1.95 thf(zip_derived_cl168, plain, 10.25/1.95 (( ('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 10.25/1.95 thf(zip_derived_cl7, plain, 10.25/1.95 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => 10.25/1.95 (Y0 @ Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk4')))))) | 10.25/1.95 ((('#sk2') = ('#sk4')))))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 10.25/1.95 thf(zip_derived_cl10, plain, 10.25/1.95 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 10.25/1.95 (((((((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 10.25/1.95 Y1 @ Y2))))))))) & 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((!!) @ (^[Y3 : $i]: 10.25/1.95 (((((Y0 @ Y2 @ 10.25/1.95 Y3) & (Y0 @ 10.25/1.95 Y1 @ Y2))) => 10.25/1.95 (Y0 @ Y1 @ Y3)))))))))))))) => 10.25/1.95 (Y0 @ '#sk2' @ '#sk4'))))))), 10.25/1.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 10.25/1.95 thf(zip_derived_cl14, plain, 10.25/1.95 (~ (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))))) => 10.25/1.95 ('#sk5' @ '#sk2' @ '#sk4')))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 10.25/1.95 thf(zip_derived_cl24, plain, 10.25/1.95 ( (((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2))))))))))))))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 10.25/1.95 thf(zip_derived_cl28, plain, 10.25/1.95 ( (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1)))))))))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl24])). 10.25/1.95 thf(zip_derived_cl32, plain, 10.25/1.95 (![X2 : $i]: 10.25/1.95 (((!!) @ (^[Y0 : $i]: ((('#sk1' @ X2 @ Y0) => ('#sk5' @ X2 @ Y0))))))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 10.25/1.95 thf(zip_derived_cl36, plain, 10.25/1.95 (![X2 : $i, X4 : $i]: ((('#sk1' @ X2 @ X4) => ('#sk5' @ X2 @ X4)))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 10.25/1.95 thf(zip_derived_cl40, plain, 10.25/1.95 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 10.25/1.95 thf(zip_derived_cl170, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl168, zip_derived_cl40])). 10.25/1.95 thf(zip_derived_cl169, plain, 10.25/1.95 ((~ ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 10.25/1.95 thf(zip_derived_cl196, plain, 10.25/1.95 (((('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl170, zip_derived_cl169])). 10.25/1.95 thf(zip_derived_cl17, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))) => 10.25/1.95 (X2 @ '#sk3' @ '#sk4'))) 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 10.25/1.95 thf(zip_derived_cl18, plain, 10.25/1.95 (( (((((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))))) => 10.25/1.95 ('#sk5' @ '#sk3' @ '#sk4'))) 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('triggered_bool_instantiation', [status(thm)], 10.25/1.95 [zip_derived_cl17])). 10.25/1.95 thf(zip_derived_cl92, plain, 10.25/1.95 ((~ (((((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))))) 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 10.25/1.95 thf(zip_derived_cl93, plain, 10.25/1.95 ((~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & 10.25/1.95 ('#sk5' @ Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2)))))))))))) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4'))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 10.25/1.95 thf(zip_derived_cl47, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( ('#form116' @ X2) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(zip_derived_cl94, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))))), 10.25/1.95 inference('renaming', [status(thm)], [zip_derived_cl93, zip_derived_cl47])). 10.25/1.95 thf(zip_derived_cl95, plain, 10.25/1.95 ((~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 ((('#sk1' @ ('#sk46' @ '#sk5') @ Y0) => ('#sk5' @ 10.25/1.95 ('#sk46' @ '#sk5') @ Y0)))))) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 10.25/1.95 thf(zip_derived_cl96, plain, 10.25/1.95 ((~ ((('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) => ('#sk5' @ 10.25/1.95 ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))) 10.25/1.95 | ~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 10.25/1.95 thf(zip_derived_cl98, plain, 10.25/1.95 ((~ ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 10.25/1.95 thf(zip_derived_cl97, plain, 10.25/1.95 (( ('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 10.25/1.95 thf(zip_derived_cl40, plain, 10.25/1.95 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 10.25/1.95 thf(zip_derived_cl99, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl40])). 10.25/1.95 thf(zip_derived_cl160, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl99])). 10.25/1.95 thf(zip_derived_cl29, plain, 10.25/1.95 ( (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 ('#sk5' @ Y0 @ Y2))))))))))))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl24])). 10.25/1.95 thf(zip_derived_cl33, plain, 10.25/1.95 (![X2 : $i]: 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 10.25/1.95 ('#sk5' @ X2 @ Y1)))))))))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 10.25/1.95 thf(zip_derived_cl37, plain, 10.25/1.95 (![X2 : $i, X4 : $i]: 10.25/1.95 (((!!) @ (^[Y0 : $i]: 10.25/1.95 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 10.25/1.95 ('#sk5' @ X2 @ Y0))))))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 10.25/1.95 thf(zip_derived_cl41, plain, 10.25/1.95 (![X2 : $i, X4 : $i, X6 : $i]: 10.25/1.95 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 10.25/1.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 10.25/1.95 thf(zip_derived_cl46, plain, 10.25/1.95 (![X2 : $i, X4 : $i, X6 : $i]: 10.25/1.95 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 10.25/1.95 thf(zip_derived_cl53, plain, 10.25/1.95 (![X2 : $i, X4 : $i, X6 : $i]: 10.25/1.95 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 10.25/1.95 thf(zip_derived_cl161, plain, 10.25/1.95 (![X0 : $i]: 10.25/1.95 ((('#sk3') = ('#sk4')) 10.25/1.95 | ~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ X0 @ '#sk4') 10.25/1.95 | ~ ('#sk5' @ X0 @ '#sk3'))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl160, zip_derived_cl53])). 10.25/1.95 thf(zip_derived_cl205, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk4') 10.25/1.95 | ~ ('#form116' @ '#sk5') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl161])). 10.25/1.95 thf(zip_derived_cl213, plain, 10.25/1.95 (((('#sk3') = ('#sk4')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk4') 10.25/1.95 | (('#sk2') = ('#sk3')) 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('simplify', [status(thm)], [zip_derived_cl205])). 10.25/1.95 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 10.25/1.95 thf(zip_derived_cl221, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') | (('#sk2') = ('#sk3')) | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl213, zip_derived_cl25])). 10.25/1.95 thf(zip_derived_cl47, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( ('#form116' @ X2) 10.25/1.95 | ~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((!!) @ (^[Y2 : $i]: 10.25/1.95 (((((X2 @ Y1 @ Y2) & (X2 @ 10.25/1.95 Y0 @ Y1))) => 10.25/1.95 (X2 @ Y0 @ Y2)))))))))))))), 10.25/1.95 define([status(thm)])). 10.25/1.95 thf(zip_derived_cl48, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((!!) @ (^[Y1 : $i]: 10.25/1.95 (((((X2 @ Y0 @ Y1) & (X2 @ 10.25/1.95 ('#sk117' @ X2) @ Y0))) => 10.25/1.95 (X2 @ ('#sk117' @ X2) @ Y1))))))))) 10.25/1.95 | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 10.25/1.95 thf(zip_derived_cl54, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((!!) @ (^[Y0 : $i]: 10.25/1.95 (((((X2 @ ('#sk164' @ X2) @ Y0) & (X2 @ 10.25/1.95 ('#sk117' @ X2) @ ('#sk164' @ X2)))) => 10.25/1.95 (X2 @ ('#sk117' @ X2) @ Y0)))))) 10.25/1.95 | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 10.25/1.95 thf(zip_derived_cl58, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (((((X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) & (X2 @ 10.25/1.95 ('#sk117' @ X2) @ ('#sk164' @ X2)))) => 10.25/1.95 (X2 @ ('#sk117' @ X2) @ ('#sk213' @ X2)))) 10.25/1.95 | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 10.25/1.95 thf(zip_derived_cl59, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (((X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) & (X2 @ 10.25/1.95 ('#sk117' @ X2) @ ('#sk164' @ X2)))) 10.25/1.95 | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 10.25/1.95 thf(zip_derived_cl62, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (X2 @ ('#sk117' @ X2) @ ('#sk164' @ X2)) | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 10.25/1.95 thf(zip_derived_cl61, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 ( (X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 10.25/1.95 thf(zip_derived_cl53, plain, 10.25/1.95 (![X2 : $i, X4 : $i, X6 : $i]: 10.25/1.95 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 10.25/1.95 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 10.25/1.95 thf(zip_derived_cl125, plain, 10.25/1.95 (![X0 : $i]: 10.25/1.95 ( ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ X0 @ ('#sk213' @ '#sk5')) 10.25/1.95 | ~ ('#sk5' @ X0 @ ('#sk164' @ '#sk5')))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl53])). 10.25/1.95 thf(zip_derived_cl317, plain, 10.25/1.95 (( ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ ('#sk117' @ '#sk5') @ ('#sk213' @ '#sk5')) 10.25/1.95 | ('#form116' @ '#sk5'))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl125])). 10.25/1.95 thf(zip_derived_cl321, plain, 10.25/1.95 (( ('#sk5' @ ('#sk117' @ '#sk5') @ ('#sk213' @ '#sk5')) 10.25/1.95 | ('#form116' @ '#sk5'))), 10.25/1.95 inference('simplify', [status(thm)], [zip_derived_cl317])). 10.25/1.95 thf(zip_derived_cl60, plain, 10.25/1.95 (![X2 : $i > $i > $o]: 10.25/1.95 (~ (X2 @ ('#sk117' @ X2) @ ('#sk213' @ X2)) | ('#form116' @ X2))), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 10.25/1.95 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 10.25/1.95 thf(zip_derived_cl326, plain, 10.25/1.95 (((('#sk2') = ('#sk3')) | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('demod', [status(thm)], [zip_derived_cl221, zip_derived_cl322])). 10.25/1.95 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 10.25/1.95 thf(zip_derived_cl339, plain, 10.25/1.95 ((~ ('#sk5' @ '#sk3' @ '#sk4') | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl326, zip_derived_cl25])). 10.25/1.95 thf(zip_derived_cl160, plain, 10.25/1.95 ((~ ('#form116' @ '#sk5') 10.25/1.95 | ('#sk5' @ '#sk3' @ '#sk4') 10.25/1.95 | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl99])). 10.25/1.95 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 10.25/1.95 thf(zip_derived_cl323, plain, 10.25/1.95 (( ('#sk5' @ '#sk3' @ '#sk4') | (('#sk3') = ('#sk4')))), 10.25/1.95 inference('demod', [status(thm)], [zip_derived_cl160, zip_derived_cl322])). 10.25/1.95 thf(zip_derived_cl414, plain, ((('#sk3') = ('#sk4'))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl323])). 10.25/1.95 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 10.25/1.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 10.25/1.95 thf(zip_derived_cl416, plain, (~ ('#sk5' @ '#sk2' @ '#sk3')), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl414, zip_derived_cl25])). 10.25/1.95 thf(zip_derived_cl196, plain, 10.25/1.95 (((('#sk2') = ('#sk3')) 10.25/1.95 | ('#sk5' @ '#sk2' @ '#sk3') 10.25/1.95 | ~ ('#form116' @ '#sk5'))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl170, zip_derived_cl169])). 10.25/1.95 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 10.25/1.95 thf(zip_derived_cl325, plain, 10.25/1.95 (((('#sk2') = ('#sk3')) | ('#sk5' @ '#sk2' @ '#sk3'))), 10.25/1.95 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl322])). 10.25/1.95 thf(zip_derived_cl414, plain, ((('#sk3') = ('#sk4'))), 10.25/1.95 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl323])). 10.25/1.95 thf(zip_derived_cl11, plain, (~ ((('#sk2') = ('#sk4')))), 10.25/1.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 10.25/1.95 thf(zip_derived_cl15, plain, ((('#sk2') != ('#sk4'))), 10.25/1.95 inference('simplify nested equalities', [status(thm)], [zip_derived_cl11])). 10.25/1.95 thf(zip_derived_cl417, plain, ((('#sk2') != ('#sk3'))), 10.25/1.95 inference('sup-', [status(thm)], [zip_derived_cl414, zip_derived_cl15])). 10.25/1.95 thf(zip_derived_cl487, plain, ( ('#sk5' @ '#sk2' @ '#sk3')), 10.25/1.95 inference('simplify_reflect-', [status(thm)], 10.25/1.95 [zip_derived_cl325, zip_derived_cl417])). 10.25/1.95 thf(zip_derived_cl488, plain, ($false), 10.25/1.95 inference('demod', [status(thm)], [zip_derived_cl416, zip_derived_cl487])). 10.25/1.95 10.25/1.95 % SZS output end Refutation 10.25/1.95 10.25/1.95 10.25/1.95 % Terminating... 10.61/2.11 % Runner terminated. 10.61/2.12 % Zipperpin 1.5 exiting 10.61/2.12 EOF