0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.05qFJyLL3n true 0.14/0.35 % Computer : n003.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Aug 9 05:32:21 EDT 2022 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 960 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.52/0.64 % Total configuration time : 828 0.52/0.64 % Estimated wc time : 1656 0.52/0.64 % Estimated cpu time (8 cpus) : 207.0 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 9.41/1.82 % Solved by lams/35_full_unif4.sh. 9.41/1.82 % done 68 iterations in 0.981s 9.41/1.82 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 9.41/1.82 % SZS output start Refutation 9.41/1.82 thf('#sk213_type', type, '#sk213': ($i > $i > $o) > $i). 9.41/1.82 thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o). 9.41/1.82 thf(trans_type, type, trans: ($i > $i > $o) > $o). 9.41/1.82 thf('#sk164_type', type, '#sk164': ($i > $i > $o) > $i). 9.41/1.82 thf('#sk66_type', type, '#sk66': ($i > $i > $o) > $i). 9.41/1.82 thf('#sk4_type', type, '#sk4': $i). 9.41/1.82 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 9.41/1.82 thf('#form116_type', type, '#form116': ($i > $i > $o) > $o). 9.41/1.82 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 9.41/1.82 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 9.41/1.82 thf('#sk2_type', type, '#sk2': $i). 9.41/1.82 thf('#sk46_type', type, '#sk46': ($i > $i > $o) > $i). 9.41/1.82 thf(refl_type, type, refl: ($i > $i > $o) > $o). 9.41/1.82 thf('#sk1_type', type, '#sk1': $i > $i > $o). 9.41/1.82 thf('#sk3_type', type, '#sk3': $i). 9.41/1.82 thf('#sk117_type', type, '#sk117': ($i > $i > $o) > $i). 9.41/1.82 thf('#sk5_type', type, '#sk5': $i > $i > $o). 9.41/1.82 thf(transitive_reflexive_closure, axiom,(( trc ) = 9.41/1.82 (^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) )))). 9.41/1.82 thf(transitive_closure, axiom,(( tc ) = 9.41/1.82 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 9.41/1.82 ( ![S:( $i > $i > $o )]: 9.41/1.82 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 9.41/1.82 thf(transitive, axiom,(( trans ) = 9.41/1.82 (^[R:( $i > $i > $o )]: 9.41/1.82 ( ![X:$i,Y:$i,Z:$i]: 9.41/1.82 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 9.41/1.82 thf('0', plain, 9.41/1.82 (( trans ) = 9.41/1.82 ( ^[R:( $i > $i > $o )]: 9.41/1.82 ( ![X:$i,Y:$i,Z:$i]: 9.41/1.82 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], [transitive])). 9.41/1.82 thf('1', plain, 9.41/1.82 (( trans ) = 9.41/1.82 ( ^[V_1:( $i > $i > $o )]: 9.41/1.82 ( ![X4:$i,X6:$i,X8:$i]: 9.41/1.82 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(subrel, axiom,(( subrel ) = 9.41/1.82 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 9.41/1.82 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 9.41/1.82 thf('2', plain, 9.41/1.82 (( subrel ) = 9.41/1.82 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 9.41/1.82 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], [subrel])). 9.41/1.82 thf('3', plain, 9.41/1.82 (( subrel ) = 9.41/1.82 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 9.41/1.82 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf('4', plain, 9.41/1.82 (( tc ) = 9.41/1.82 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 9.41/1.82 ( ![S:( $i > $i > $o )]: 9.41/1.82 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], 9.41/1.82 [transitive_closure, '1', '3'])). 9.41/1.82 thf('5', plain, 9.41/1.82 (( tc ) = 9.41/1.82 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 9.41/1.82 ( ![X4:( $i > $i > $o )]: 9.41/1.82 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(reflexive_closure, axiom,(( rc ) = 9.41/1.82 (^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) )))). 9.41/1.82 thf('6', plain, 9.41/1.82 (( rc ) = 9.41/1.82 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: ( ( ( X ) = ( Y ) ) | ( R @ X @ Y ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], [reflexive_closure])). 9.41/1.82 thf('7', plain, 9.41/1.82 (( rc ) = 9.41/1.82 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 9.41/1.82 ( ( ( V_2 ) = ( V_3 ) ) | ( V_1 @ V_2 @ V_3 ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf('8', plain, (( trc ) = ( ^[R:( $i > $i > $o )]: ( rc @ ( tc @ R ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], 9.41/1.82 [transitive_reflexive_closure, '5', '1', '7', '3'])). 9.41/1.82 thf('9', plain, 9.41/1.82 (( trc ) = ( ^[V_1:( $i > $i > $o )]: ( rc @ ( tc @ V_1 ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(reflexive, axiom,(( refl ) = 9.41/1.82 (^[R:( $i > $i > $o )]: ( ![X:$i]: ( R @ X @ X ) )))). 9.41/1.82 thf('10', plain, 9.41/1.82 (( refl ) = ( ^[R:( $i > $i > $o )]: ( ![X:$i]: ( R @ X @ X ) ) )), 9.41/1.82 inference('simplify_rw_rule', [status(thm)], [reflexive])). 9.41/1.82 thf('11', plain, 9.41/1.82 (( refl ) = ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(transitive_reflexive_closure_is_transitive_reflexive, conjecture, 9.41/1.82 (![R:( $i > $i > $o )]: 9.41/1.82 ( ( trans @ ( trc @ R ) ) & ( refl @ ( trc @ R ) ) ))). 9.41/1.82 thf(zf_stmt_0, conjecture, 9.41/1.82 (![X4:( $i > $i > $o )]: 9.41/1.82 ( ( ![X48:$i]: 9.41/1.82 ( ( ![X50:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X58:$i,X60:$i]: 9.41/1.82 ( ( X4 @ X58 @ X60 ) => ( X50 @ X58 @ X60 ) ) ) & 9.41/1.82 ( ![X52:$i,X54:$i,X56:$i]: 9.41/1.82 ( ( ( X50 @ X54 @ X56 ) & ( X50 @ X52 @ X54 ) ) => 9.41/1.82 ( X50 @ X52 @ X56 ) ) ) ) => 9.41/1.82 ( X50 @ X48 @ X48 ) ) ) | 9.41/1.82 ( ( X48 ) = ( X48 ) ) ) ) & 9.41/1.82 ( ![X6:$i,X8:$i,X10:$i]: 9.41/1.82 ( ( ( ( ![X24:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X32:$i,X34:$i]: 9.41/1.82 ( ( X4 @ X32 @ X34 ) => ( X24 @ X32 @ X34 ) ) ) & 9.41/1.82 ( ![X26:$i,X28:$i,X30:$i]: 9.41/1.82 ( ( ( X24 @ X28 @ X30 ) & ( X24 @ X26 @ X28 ) ) => 9.41/1.82 ( X24 @ X26 @ X30 ) ) ) ) => 9.41/1.82 ( X24 @ X8 @ X10 ) ) ) | 9.41/1.82 ( ( X8 ) = ( X10 ) ) ) & 9.41/1.82 ( ( ![X12:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X20:$i,X22:$i]: 9.41/1.82 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 9.41/1.82 ( ![X14:$i,X16:$i,X18:$i]: 9.41/1.82 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 9.41/1.82 ( X12 @ X14 @ X18 ) ) ) ) => 9.41/1.82 ( X12 @ X6 @ X8 ) ) ) | 9.41/1.82 ( ( X6 ) = ( X8 ) ) ) ) => 9.41/1.82 ( ( ![X36:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X44:$i,X46:$i]: 9.41/1.82 ( ( X4 @ X44 @ X46 ) => ( X36 @ X44 @ X46 ) ) ) & 9.41/1.82 ( ![X38:$i,X40:$i,X42:$i]: 9.41/1.82 ( ( ( X36 @ X40 @ X42 ) & ( X36 @ X38 @ X40 ) ) => 9.41/1.82 ( X36 @ X38 @ X42 ) ) ) ) => 9.41/1.82 ( X36 @ X6 @ X10 ) ) ) | 9.41/1.82 ( ( X6 ) = ( X10 ) ) ) ) ) ))). 9.41/1.82 thf(zf_stmt_1, negated_conjecture, 9.41/1.82 (~( ![X4:( $i > $i > $o )]: 9.41/1.82 ( ( ![X48:$i]: 9.41/1.82 ( ( ![X50:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X58:$i,X60:$i]: 9.41/1.82 ( ( X4 @ X58 @ X60 ) => ( X50 @ X58 @ X60 ) ) ) & 9.41/1.82 ( ![X52:$i,X54:$i,X56:$i]: 9.41/1.82 ( ( ( X50 @ X54 @ X56 ) & ( X50 @ X52 @ X54 ) ) => 9.41/1.82 ( X50 @ X52 @ X56 ) ) ) ) => 9.41/1.82 ( X50 @ X48 @ X48 ) ) ) | 9.41/1.82 ( ( X48 ) = ( X48 ) ) ) ) & 9.41/1.82 ( ![X6:$i,X8:$i,X10:$i]: 9.41/1.82 ( ( ( ( ![X24:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X32:$i,X34:$i]: 9.41/1.82 ( ( X4 @ X32 @ X34 ) => ( X24 @ X32 @ X34 ) ) ) & 9.41/1.82 ( ![X26:$i,X28:$i,X30:$i]: 9.41/1.82 ( ( ( X24 @ X28 @ X30 ) & ( X24 @ X26 @ X28 ) ) => 9.41/1.82 ( X24 @ X26 @ X30 ) ) ) ) => 9.41/1.82 ( X24 @ X8 @ X10 ) ) ) | 9.41/1.82 ( ( X8 ) = ( X10 ) ) ) & 9.41/1.82 ( ( ![X12:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X20:$i,X22:$i]: 9.41/1.82 ( ( X4 @ X20 @ X22 ) => ( X12 @ X20 @ X22 ) ) ) & 9.41/1.82 ( ![X14:$i,X16:$i,X18:$i]: 9.41/1.82 ( ( ( X12 @ X16 @ X18 ) & ( X12 @ X14 @ X16 ) ) => 9.41/1.82 ( X12 @ X14 @ X18 ) ) ) ) => 9.41/1.82 ( X12 @ X6 @ X8 ) ) ) | 9.41/1.82 ( ( X6 ) = ( X8 ) ) ) ) => 9.41/1.82 ( ( ![X36:( $i > $i > $o )]: 9.41/1.82 ( ( ( ![X44:$i,X46:$i]: 9.41/1.82 ( ( X4 @ X44 @ X46 ) => ( X36 @ X44 @ X46 ) ) ) & 9.41/1.82 ( ![X38:$i,X40:$i,X42:$i]: 9.41/1.82 ( ( ( X36 @ X40 @ X42 ) & ( X36 @ X38 @ X40 ) ) => 9.41/1.82 ( X36 @ X38 @ X42 ) ) ) ) => 9.41/1.82 ( X36 @ X6 @ X10 ) ) ) | 9.41/1.82 ( ( X6 ) = ( X10 ) ) ) ) ) ) )), 9.41/1.82 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 9.41/1.82 thf(zip_derived_cl0, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((((!!) @ (^[Y2 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))))))))) & 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y2 @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) & 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y5)))))))))))))) => 9.41/1.82 (Y2 @ Y1 @ Y1)))))) | 9.41/1.82 (((Y1) = (Y1)))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((((((!!) @ ( 9.41/1.82 ^[Y4 : 9.41/1.82 $i > $i > $o]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y2 @ Y3)))))) | 9.41/1.82 (((Y2) = (Y3))))) & 9.41/1.82 (((((!!) @ ( 9.41/1.82 ^[Y4 : 9.41/1.82 $i > $i > $o]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y1 @ Y2)))))) | 9.41/1.82 (((Y1) = (Y2))))))) => 9.41/1.82 (((((!!) @ ( 9.41/1.82 ^[Y4 : 9.41/1.82 $i > $i > $o]: 9.41/1.82 (((( 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y1 @ Y3)))))) | 9.41/1.82 (((Y1) = (Y3)))))))))))))))))))))), 9.41/1.82 inference('cnf', [status(esa)], [zf_stmt_1])). 9.41/1.82 thf(zip_derived_cl1, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((((((!!) @ ( 9.41/1.82 ^[Y4 : 9.41/1.82 $i > $i > $o]: 9.41/1.82 (((( 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y2 @ Y3)))))) | 9.41/1.82 (((Y2) = (Y3))))) & 9.41/1.82 (((((!!) @ ( 9.41/1.82 ^[Y4 : 9.41/1.82 $i > $i > $o]: 9.41/1.82 (((( 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y1 @ Y2)))))) | 9.41/1.82 (((Y1) = (Y2))))))) => 9.41/1.82 (((((!!) @ ( 9.41/1.82 ^[Y4 : $i > $i > $o]: 9.41/1.82 (((((( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (Y0 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))))))))) & 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y7 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y4 @ 9.41/1.82 Y6 @ 9.41/1.82 Y7) & 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y6))) => 9.41/1.82 (Y4 @ 9.41/1.82 Y5 @ Y7)))))))))))))) => 9.41/1.82 (Y4 @ Y1 @ 9.41/1.82 Y3)))))) | 9.41/1.82 (((Y1) = (Y3)))))))))))))))))))), 9.41/1.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])). 9.41/1.82 thf(zip_derived_cl2, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((((((!!) @ (^[Y3 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))))))))) & 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y3 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) & 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y6)))))))))))))) => 9.41/1.82 (Y3 @ Y1 @ Y2)))))) | 9.41/1.82 (((Y1) = (Y2))))) & 9.41/1.82 (((((!!) @ (^[Y3 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))))))))) & 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y3 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) & 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y6)))))))))))))) => 9.41/1.82 (Y3 @ Y0 @ Y1)))))) | 9.41/1.82 (((Y0) = (Y1))))))) => 9.41/1.82 (((((!!) @ (^[Y3 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))))))))) & 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y6 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y3 @ 9.41/1.82 Y5 @ 9.41/1.82 Y6) & 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y5))) => 9.41/1.82 (Y3 @ 9.41/1.82 Y4 @ Y6)))))))))))))) => 9.41/1.82 (Y3 @ Y0 @ Y2)))))) | 9.41/1.82 (((Y0) = (Y2))))))))))))))))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 9.41/1.82 thf(zip_derived_cl3, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((((((((!!) @ (^[Y2 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))))))))) & 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y2 @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) & 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y5)))))))))))))) => 9.41/1.82 (Y2 @ Y0 @ Y1)))))) | 9.41/1.82 (((Y0) = (Y1))))) & 9.41/1.82 (((((!!) @ (^[Y2 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))))))))) & 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y2 @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) & 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y5)))))))))))))) => 9.41/1.82 (Y2 @ '#sk2' @ Y0)))))) | 9.41/1.82 ((('#sk2') = (Y0))))))) => 9.41/1.82 (((((!!) @ (^[Y2 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 ('#sk1' @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))))))))) & 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (!!) @ ( 9.41/1.82 ^[Y5 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y2 @ 9.41/1.82 Y4 @ 9.41/1.82 Y5) & 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y4))) => 9.41/1.82 (Y2 @ 9.41/1.82 Y3 @ Y5)))))))))))))) => 9.41/1.82 (Y2 @ '#sk2' @ Y1)))))) | 9.41/1.82 ((('#sk2') = (Y1)))))))))))))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 9.41/1.82 thf(zip_derived_cl4, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((((((((!!) @ (^[Y1 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 ((('#sk1' @ 9.41/1.82 Y2 @ 9.41/1.82 Y3) => 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y3))))))))) & 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y1 @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) & 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y3))) => 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y4)))))))))))))) => 9.41/1.82 (Y1 @ '#sk3' @ Y0)))))) | 9.41/1.82 ((('#sk3') = (Y0))))) & 9.41/1.82 (((((!!) @ (^[Y1 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 ((('#sk1' @ 9.41/1.82 Y2 @ 9.41/1.82 Y3) => 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y3))))))))) & 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y1 @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) & 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y3))) => 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y4)))))))))))))) => 9.41/1.82 (Y1 @ '#sk2' @ '#sk3')))))) | 9.41/1.82 ((('#sk2') = ('#sk3'))))))) => 9.41/1.82 (((((!!) @ (^[Y1 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 ((('#sk1' @ 9.41/1.82 Y2 @ Y3) => 9.41/1.82 (Y1 @ Y2 @ 9.41/1.82 Y3))))))))) & 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((!!) @ ( 9.41/1.82 ^[Y4 : $i]: 9.41/1.82 (( 9.41/1.82 (( 9.41/1.82 (Y1 @ 9.41/1.82 Y3 @ 9.41/1.82 Y4) & 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y3))) => 9.41/1.82 (Y1 @ 9.41/1.82 Y2 @ Y4)))))))))))))) => 9.41/1.82 (Y1 @ '#sk2' @ Y0)))))) | 9.41/1.82 ((('#sk2') = (Y0))))))))))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 9.41/1.82 thf(zip_derived_cl5, plain, 9.41/1.82 (~ (((((((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((( 9.41/1.82 (Y0 @ 9.41/1.82 Y2 @ Y3) & 9.41/1.82 (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ 9.41/1.82 Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk3' @ '#sk4')))))) | 9.41/1.82 ((('#sk3') = ('#sk4'))))) & 9.41/1.82 (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((( 9.41/1.82 (Y0 @ 9.41/1.82 Y2 @ Y3) & 9.41/1.82 (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ 9.41/1.82 Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk3')))))) | 9.41/1.82 ((('#sk2') = ('#sk3'))))))) => 9.41/1.82 (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ 9.41/1.82 Y2 @ Y3) & 9.41/1.82 (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ 9.41/1.82 Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk4')))))) | 9.41/1.82 ((('#sk2') = ('#sk4')))))))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 9.41/1.82 thf(zip_derived_cl6, plain, 9.41/1.82 ( (((((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & 9.41/1.82 (Y0 @ Y1 @ 9.41/1.82 Y2))) => 9.41/1.82 (Y0 @ Y1 @ 9.41/1.82 Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk3' @ '#sk4')))))) | 9.41/1.82 ((('#sk3') = ('#sk4'))))) & 9.41/1.82 (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & 9.41/1.82 (Y0 @ Y1 @ 9.41/1.82 Y2))) => 9.41/1.82 (Y0 @ Y1 @ 9.41/1.82 Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk3')))))) | 9.41/1.82 ((('#sk2') = ('#sk3')))))))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 9.41/1.82 thf(zip_derived_cl9, plain, 9.41/1.82 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk3')))))) | 9.41/1.82 ((('#sk2') = ('#sk3')))))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 9.41/1.82 thf(zip_derived_cl13, plain, 9.41/1.82 (( (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 9.41/1.82 Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk3')))))) 9.41/1.82 | ((('#sk2') = ('#sk3'))))), 9.41/1.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 9.41/1.82 thf(zip_derived_cl20, plain, 9.41/1.82 (( (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 9.41/1.82 Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk3')))))) 9.41/1.82 | (('#sk2') = ('#sk3')))), 9.41/1.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 9.41/1.82 thf(zip_derived_cl21, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))) => 9.41/1.82 (X2 @ '#sk2' @ '#sk3'))) 9.41/1.82 | (('#sk2') = ('#sk3')))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 9.41/1.82 thf(zip_derived_cl22, plain, 9.41/1.82 (( (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))))) => 9.41/1.82 ('#sk5' @ '#sk2' @ '#sk3'))) 9.41/1.82 | (('#sk2') = ('#sk3')))), 9.41/1.82 inference('triggered_bool_instantiation', [status(thm)], 9.41/1.82 [zip_derived_cl21])). 9.41/1.82 thf(zip_derived_cl163, plain, 9.41/1.82 ((~ (((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))))) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | (('#sk2') = ('#sk3')))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 9.41/1.82 thf(zip_derived_cl164, plain, 9.41/1.82 ((~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))) 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3'))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl163])). 9.41/1.82 thf(zip_derived_cl8, plain, 9.41/1.82 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk3' @ '#sk4')))))) | 9.41/1.82 ((('#sk3') = ('#sk4')))))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl6])). 9.41/1.82 thf(zip_derived_cl12, plain, 9.41/1.82 (( (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 9.41/1.82 Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk3' @ '#sk4')))))) 9.41/1.82 | ((('#sk3') = ('#sk4'))))), 9.41/1.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl8])). 9.41/1.82 thf(zip_derived_cl16, plain, 9.41/1.82 (( (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 9.41/1.82 Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk3' @ '#sk4')))))) 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 9.41/1.82 thf(zip_derived_cl17, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))) => 9.41/1.82 (X2 @ '#sk3' @ '#sk4'))) 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 9.41/1.82 thf(zip_derived_cl26, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))) 9.41/1.82 | (X2 @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 9.41/1.82 thf(zip_derived_cl30, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | (X2 @ '#sk3' @ '#sk4'))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl26])). 9.41/1.82 thf(zip_derived_cl34, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 ((('#sk1' @ ('#sk46' @ X2) @ Y0) => (X2 @ 9.41/1.82 ('#sk46' @ X2) @ Y0)))))) 9.41/1.82 | (X2 @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 9.41/1.82 thf(zip_derived_cl38, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ ((('#sk1' @ ('#sk46' @ X2) @ ('#sk66' @ X2)) => (X2 @ 9.41/1.82 ('#sk46' @ X2) @ ('#sk66' @ X2)))) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | (X2 @ '#sk3' @ '#sk4'))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 9.41/1.82 thf(zip_derived_cl42, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( ('#sk1' @ ('#sk46' @ X2) @ ('#sk66' @ X2)) 9.41/1.82 | (X2 @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 9.41/1.82 thf(zip_derived_cl47, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( ('#form116' @ X2) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(zip_derived_cl165, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))))), 9.41/1.82 inference('renaming', [status(thm)], 9.41/1.82 [zip_derived_cl164, zip_derived_cl47])). 9.41/1.82 thf(zip_derived_cl166, plain, 9.41/1.82 ((~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 ((('#sk1' @ ('#sk46' @ '#sk5') @ Y0) => ('#sk5' @ 9.41/1.82 ('#sk46' @ '#sk5') @ Y0)))))) 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl165])). 9.41/1.82 thf(zip_derived_cl167, plain, 9.41/1.82 ((~ ((('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) => ('#sk5' @ 9.41/1.82 ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))) 9.41/1.82 | ~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | (('#sk2') = ('#sk3')))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl166])). 9.41/1.82 thf(zip_derived_cl168, plain, 9.41/1.82 (( ('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 9.41/1.82 thf(zip_derived_cl7, plain, 9.41/1.82 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => 9.41/1.82 (Y0 @ Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk4')))))) | 9.41/1.82 ((('#sk2') = ('#sk4')))))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 9.41/1.82 thf(zip_derived_cl10, plain, 9.41/1.82 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 9.41/1.82 (((((((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 9.41/1.82 Y1 @ Y2))))))))) & 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((!!) @ (^[Y3 : $i]: 9.41/1.82 (((((Y0 @ Y2 @ 9.41/1.82 Y3) & (Y0 @ 9.41/1.82 Y1 @ Y2))) => 9.41/1.82 (Y0 @ Y1 @ Y3)))))))))))))) => 9.41/1.82 (Y0 @ '#sk2' @ '#sk4'))))))), 9.41/1.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 9.41/1.82 thf(zip_derived_cl14, plain, 9.41/1.82 (~ (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))))) => 9.41/1.82 ('#sk5' @ '#sk2' @ '#sk4')))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 9.41/1.82 thf(zip_derived_cl24, plain, 9.41/1.82 ( (((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2))))))))))))))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 9.41/1.82 thf(zip_derived_cl28, plain, 9.41/1.82 ( (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1)))))))))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl24])). 9.41/1.82 thf(zip_derived_cl32, plain, 9.41/1.82 (![X2 : $i]: 9.41/1.82 (((!!) @ (^[Y0 : $i]: ((('#sk1' @ X2 @ Y0) => ('#sk5' @ X2 @ Y0))))))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 9.41/1.82 thf(zip_derived_cl36, plain, 9.41/1.82 (![X2 : $i, X4 : $i]: ((('#sk1' @ X2 @ X4) => ('#sk5' @ X2 @ X4)))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 9.41/1.82 thf(zip_derived_cl40, plain, 9.41/1.82 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 9.41/1.82 thf(zip_derived_cl170, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl168, zip_derived_cl40])). 9.41/1.82 thf(zip_derived_cl169, plain, 9.41/1.82 ((~ ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 9.41/1.82 thf(zip_derived_cl196, plain, 9.41/1.82 (((('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl170, zip_derived_cl169])). 9.41/1.82 thf(zip_derived_cl17, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))) => 9.41/1.82 (X2 @ '#sk3' @ '#sk4'))) 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 9.41/1.82 thf(zip_derived_cl18, plain, 9.41/1.82 (( (((((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))))) => 9.41/1.82 ('#sk5' @ '#sk3' @ '#sk4'))) 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('triggered_bool_instantiation', [status(thm)], 9.41/1.82 [zip_derived_cl17])). 9.41/1.82 thf(zip_derived_cl92, plain, 9.41/1.82 ((~ (((((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) & 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))))) 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 9.41/1.82 thf(zip_derived_cl93, plain, 9.41/1.82 ((~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & 9.41/1.82 ('#sk5' @ Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2)))))))))))) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4'))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 9.41/1.82 thf(zip_derived_cl47, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( ('#form116' @ X2) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(zip_derived_cl94, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((('#sk1' @ Y0 @ Y1) => ('#sk5' @ Y0 @ Y1))))))))))), 9.41/1.82 inference('renaming', [status(thm)], [zip_derived_cl93, zip_derived_cl47])). 9.41/1.82 thf(zip_derived_cl95, plain, 9.41/1.82 ((~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 ((('#sk1' @ ('#sk46' @ '#sk5') @ Y0) => ('#sk5' @ 9.41/1.82 ('#sk46' @ '#sk5') @ Y0)))))) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 9.41/1.82 thf(zip_derived_cl96, plain, 9.41/1.82 ((~ ((('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) => ('#sk5' @ 9.41/1.82 ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))) 9.41/1.82 | ~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl95])). 9.41/1.82 thf(zip_derived_cl98, plain, 9.41/1.82 ((~ ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 9.41/1.82 thf(zip_derived_cl97, plain, 9.41/1.82 (( ('#sk1' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')) 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 9.41/1.82 thf(zip_derived_cl40, plain, 9.41/1.82 (![X2 : $i, X4 : $i]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 9.41/1.82 thf(zip_derived_cl99, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ ('#sk46' @ '#sk5') @ ('#sk66' @ '#sk5')))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl97, zip_derived_cl40])). 9.41/1.82 thf(zip_derived_cl160, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl99])). 9.41/1.82 thf(zip_derived_cl29, plain, 9.41/1.82 ( (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 ((((('#sk5' @ Y1 @ Y2) & ('#sk5' @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 ('#sk5' @ Y0 @ Y2))))))))))))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl24])). 9.41/1.82 thf(zip_derived_cl33, plain, 9.41/1.82 (![X2 : $i]: 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ X2 @ Y0))) => 9.41/1.82 ('#sk5' @ X2 @ Y1)))))))))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])). 9.41/1.82 thf(zip_derived_cl37, plain, 9.41/1.82 (![X2 : $i, X4 : $i]: 9.41/1.82 (((!!) @ (^[Y0 : $i]: 9.41/1.82 ((((('#sk5' @ X4 @ Y0) & ('#sk5' @ X2 @ X4))) => 9.41/1.82 ('#sk5' @ X2 @ Y0))))))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 9.41/1.82 thf(zip_derived_cl41, plain, 9.41/1.82 (![X2 : $i, X4 : $i, X6 : $i]: 9.41/1.82 ((((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) => ('#sk5' @ X2 @ X6)))), 9.41/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 9.41/1.82 thf(zip_derived_cl46, plain, 9.41/1.82 (![X2 : $i, X4 : $i, X6 : $i]: 9.41/1.82 (~ ((('#sk5' @ X4 @ X6) & ('#sk5' @ X2 @ X4))) | ('#sk5' @ X2 @ X6))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 9.41/1.82 thf(zip_derived_cl53, plain, 9.41/1.82 (![X2 : $i, X4 : $i, X6 : $i]: 9.41/1.82 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 9.41/1.82 thf(zip_derived_cl161, plain, 9.41/1.82 (![X0 : $i]: 9.41/1.82 ((('#sk3') = ('#sk4')) 9.41/1.82 | ~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ X0 @ '#sk4') 9.41/1.82 | ~ ('#sk5' @ X0 @ '#sk3'))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl160, zip_derived_cl53])). 9.41/1.82 thf(zip_derived_cl205, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk4') 9.41/1.82 | ~ ('#form116' @ '#sk5') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl196, zip_derived_cl161])). 9.41/1.82 thf(zip_derived_cl213, plain, 9.41/1.82 (((('#sk3') = ('#sk4')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk4') 9.41/1.82 | (('#sk2') = ('#sk3')) 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('simplify', [status(thm)], [zip_derived_cl205])). 9.41/1.82 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 9.41/1.82 thf(zip_derived_cl221, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') | (('#sk2') = ('#sk3')) | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl213, zip_derived_cl25])). 9.41/1.82 thf(zip_derived_cl47, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( ('#form116' @ X2) 9.41/1.82 | ~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((!!) @ (^[Y2 : $i]: 9.41/1.82 (((((X2 @ Y1 @ Y2) & (X2 @ 9.41/1.82 Y0 @ Y1))) => 9.41/1.82 (X2 @ Y0 @ Y2)))))))))))))), 9.41/1.82 define([status(thm)])). 9.41/1.82 thf(zip_derived_cl48, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((!!) @ (^[Y1 : $i]: 9.41/1.82 (((((X2 @ Y0 @ Y1) & (X2 @ 9.41/1.82 ('#sk117' @ X2) @ Y0))) => 9.41/1.82 (X2 @ ('#sk117' @ X2) @ Y1))))))))) 9.41/1.82 | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 9.41/1.82 thf(zip_derived_cl54, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((!!) @ (^[Y0 : $i]: 9.41/1.82 (((((X2 @ ('#sk164' @ X2) @ Y0) & (X2 @ 9.41/1.82 ('#sk117' @ X2) @ ('#sk164' @ X2)))) => 9.41/1.82 (X2 @ ('#sk117' @ X2) @ Y0)))))) 9.41/1.82 | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 9.41/1.82 thf(zip_derived_cl58, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (((((X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) & (X2 @ 9.41/1.82 ('#sk117' @ X2) @ ('#sk164' @ X2)))) => 9.41/1.82 (X2 @ ('#sk117' @ X2) @ ('#sk213' @ X2)))) 9.41/1.82 | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 9.41/1.82 thf(zip_derived_cl59, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (((X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) & (X2 @ 9.41/1.82 ('#sk117' @ X2) @ ('#sk164' @ X2)))) 9.41/1.82 | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 9.41/1.82 thf(zip_derived_cl62, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (X2 @ ('#sk117' @ X2) @ ('#sk164' @ X2)) | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 9.41/1.82 thf(zip_derived_cl61, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 ( (X2 @ ('#sk164' @ X2) @ ('#sk213' @ X2)) | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl59])). 9.41/1.82 thf(zip_derived_cl53, plain, 9.41/1.82 (![X2 : $i, X4 : $i, X6 : $i]: 9.41/1.82 (~ ('#sk5' @ X4 @ X6) | ~ ('#sk5' @ X2 @ X4) | ('#sk5' @ X2 @ X6))), 9.41/1.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 9.41/1.82 thf(zip_derived_cl125, plain, 9.41/1.82 (![X0 : $i]: 9.41/1.82 ( ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ X0 @ ('#sk213' @ '#sk5')) 9.41/1.82 | ~ ('#sk5' @ X0 @ ('#sk164' @ '#sk5')))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl53])). 9.41/1.82 thf(zip_derived_cl317, plain, 9.41/1.82 (( ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ ('#sk117' @ '#sk5') @ ('#sk213' @ '#sk5')) 9.41/1.82 | ('#form116' @ '#sk5'))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl125])). 9.41/1.82 thf(zip_derived_cl321, plain, 9.41/1.82 (( ('#sk5' @ ('#sk117' @ '#sk5') @ ('#sk213' @ '#sk5')) 9.41/1.82 | ('#form116' @ '#sk5'))), 9.41/1.82 inference('simplify', [status(thm)], [zip_derived_cl317])). 9.41/1.82 thf(zip_derived_cl60, plain, 9.41/1.82 (![X2 : $i > $i > $o]: 9.41/1.82 (~ (X2 @ ('#sk117' @ X2) @ ('#sk213' @ X2)) | ('#form116' @ X2))), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 9.41/1.82 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 9.41/1.82 thf(zip_derived_cl326, plain, 9.41/1.82 (((('#sk2') = ('#sk3')) | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('demod', [status(thm)], [zip_derived_cl221, zip_derived_cl322])). 9.41/1.82 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 9.41/1.82 thf(zip_derived_cl339, plain, 9.41/1.82 ((~ ('#sk5' @ '#sk3' @ '#sk4') | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl326, zip_derived_cl25])). 9.41/1.82 thf(zip_derived_cl160, plain, 9.41/1.82 ((~ ('#form116' @ '#sk5') 9.41/1.82 | ('#sk5' @ '#sk3' @ '#sk4') 9.41/1.82 | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl98, zip_derived_cl99])). 9.41/1.82 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 9.41/1.82 thf(zip_derived_cl323, plain, 9.41/1.82 (( ('#sk5' @ '#sk3' @ '#sk4') | (('#sk3') = ('#sk4')))), 9.41/1.82 inference('demod', [status(thm)], [zip_derived_cl160, zip_derived_cl322])). 9.41/1.82 thf(zip_derived_cl414, plain, ((('#sk3') = ('#sk4'))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl323])). 9.41/1.82 thf(zip_derived_cl25, plain, (~ ('#sk5' @ '#sk2' @ '#sk4')), 9.41/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 9.41/1.82 thf(zip_derived_cl416, plain, (~ ('#sk5' @ '#sk2' @ '#sk3')), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl414, zip_derived_cl25])). 9.41/1.82 thf(zip_derived_cl196, plain, 9.41/1.82 (((('#sk2') = ('#sk3')) 9.41/1.82 | ('#sk5' @ '#sk2' @ '#sk3') 9.41/1.82 | ~ ('#form116' @ '#sk5'))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl170, zip_derived_cl169])). 9.41/1.82 thf(zip_derived_cl322, plain, ( ('#form116' @ '#sk5')), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl321, zip_derived_cl60])). 9.41/1.82 thf(zip_derived_cl325, plain, 9.41/1.82 (((('#sk2') = ('#sk3')) | ('#sk5' @ '#sk2' @ '#sk3'))), 9.41/1.82 inference('demod', [status(thm)], [zip_derived_cl196, zip_derived_cl322])). 9.41/1.82 thf(zip_derived_cl414, plain, ((('#sk3') = ('#sk4'))), 9.41/1.82 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl323])). 9.41/1.82 thf(zip_derived_cl11, plain, (~ ((('#sk2') = ('#sk4')))), 9.41/1.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 9.41/1.82 thf(zip_derived_cl15, plain, ((('#sk2') != ('#sk4'))), 9.41/1.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl11])). 9.41/1.82 thf(zip_derived_cl417, plain, ((('#sk2') != ('#sk3'))), 9.41/1.82 inference('sup-', [status(thm)], [zip_derived_cl414, zip_derived_cl15])). 9.41/1.82 thf(zip_derived_cl487, plain, ( ('#sk5' @ '#sk2' @ '#sk3')), 9.41/1.82 inference('simplify_reflect-', [status(thm)], 9.41/1.82 [zip_derived_cl325, zip_derived_cl417])). 9.41/1.82 thf(zip_derived_cl488, plain, ($false), 9.41/1.82 inference('demod', [status(thm)], [zip_derived_cl416, zip_derived_cl487])). 9.41/1.82 9.41/1.82 % SZS output end Refutation 9.41/1.82 9.41/1.82 9.41/1.82 % Terminating... 9.41/1.82 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 9.72/1.90 % Runner terminated. 9.72/1.92 % Zipperpin 1.5 exiting 9.72/1.93 EOF