0.00/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HWZaApoRY0 true 0.07/0.26 % Computer : n011.cluster.edu 0.07/0.26 % Model : x86_64 x86_64 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.07/0.26 % Memory : 8042.1875MB 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 0.07/0.26 % CPULimit : 1440 0.07/0.26 % WCLimit : 180 0.07/0.26 % DateTime : Mon Jul 3 10:28:09 EDT 2023 0.07/0.26 % CPUTime : 0.07/0.26 % Running portfolio for 1440 s 0.07/0.26 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.07/0.26 % Number of cores: 8 0.07/0.26 % Python version: Python 3.6.8 0.07/0.26 % Running in HO mode 0.57/0.55 % Total configuration time : 828 0.57/0.55 % Estimated wc time : 1656 0.57/0.55 % Estimated cpu time (8 cpus) : 207.0 0.57/0.58 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.57/0.60 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.57/0.61 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.17/0.63 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.17/0.63 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.17/0.63 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.17/0.63 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.17/0.63 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 238.21/30.69 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 314.84/40.45 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 472.99/60.68 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 549.60/70.48 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 627.76/80.54 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 628.30/80.65 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 628.30/80.65 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 706.40/90.67 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 706.40/90.68 % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s 752.02/96.53 % /export/starexec/sandbox2/solver/bin/lams/8_add_var_l_av.sh running for 16s 782.84/100.53 % /export/starexec/sandbox2/solver/bin/lams/8_new_sh_or.sh running for 16s 829.99/106.68 % /export/starexec/sandbox2/solver/bin/lams/30_old_zip1.sh running for 36s 859.85/110.50 % /export/starexec/sandbox2/solver/bin/lams/10_shallow_lift.sh running for 30s 859.85/110.51 % /export/starexec/sandbox2/solver/bin/lams/15_lcnf_noform.sh running for 30s 874.80/112.58 % /export/starexec/sandbox2/solver/bin/lams/8_sh.eqenc2.sh running for 10s 905.79/116.58 % /export/starexec/sandbox2/solver/bin/lams/8_cmb.lcnf4.sh running for 10s 936.57/120.53 % /export/starexec/sandbox2/solver/bin/lams/8_new_l_av.sh running for 24s 950.59/122.42 % /export/starexec/sandbox2/solver/bin/lams/10_forms1.sh running for 20s 968.94/124.76 % Solved by lams/10_forms1.sh. 968.94/124.76 % done 170 iterations in 2.261s 968.94/124.76 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 968.94/124.76 % SZS output start Refutation 968.94/124.76 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 968.94/124.76 thf('#sk3252_type', type, '#sk3252': $i). 968.94/124.76 thf('#sk142_type', type, '#sk142': $i > $i > $o). 968.94/124.76 thf(idem_type, type, idem: (($i > $i > $o) > $i > $i > $o) > $o). 968.94/124.76 thf('#sk1656_type', type, '#sk1656': ($i > $i > $o) > $i). 968.94/124.76 thf('#sk140_type', type, '#sk140': $i > $i > $o). 968.94/124.76 thf('#_fresh_sk2_type', type, '#_fresh_sk2': $i). 968.94/124.76 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 968.94/124.76 thf('#_fresh_sk3_type', type, '#_fresh_sk3': $i). 968.94/124.76 thf('#sk1_type', type, '#sk1': $i > $i > $o). 968.94/124.76 thf(trans_type, type, trans: ($i > $i > $o) > $o). 968.94/124.76 thf('#form141_type', type, '#form141': $o). 968.94/124.76 thf(transitive_closure, axiom,(( tc ) = 968.94/124.76 (^[R:( $i > $i > $o ),X:$i,Y:$i]: 968.94/124.76 ( ![S:( $i > $i > $o )]: 968.94/124.76 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) )))). 968.94/124.76 thf(transitive, axiom,(( trans ) = 968.94/124.76 (^[R:( $i > $i > $o )]: 968.94/124.76 ( ![X:$i,Y:$i,Z:$i]: 968.94/124.76 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) )))). 968.94/124.76 thf('0', plain, 968.94/124.76 (( trans ) = 968.94/124.76 ( ^[R:( $i > $i > $o )]: 968.94/124.76 ( ![X:$i,Y:$i,Z:$i]: 968.94/124.76 ( ( ( R @ X @ Y ) & ( R @ Y @ Z ) ) => ( R @ X @ Z ) ) ) )), 968.94/124.76 inference('simplify_rw_rule', [status(thm)], [transitive])). 968.94/124.76 thf('1', plain, 968.94/124.76 (( trans ) = 968.94/124.76 ( ^[V_1:( $i > $i > $o )]: 968.94/124.76 ( ![X4:$i,X6:$i,X8:$i]: 968.94/124.76 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(subrel, axiom,(( subrel ) = 968.94/124.76 (^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 968.94/124.76 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) )))). 968.94/124.76 thf('2', plain, 968.94/124.76 (( subrel ) = 968.94/124.76 ( ^[R:( $i > $i > $o ),S:( $i > $i > $o )]: 968.94/124.76 ( ![X:$i,Y:$i]: ( ( R @ X @ Y ) => ( S @ X @ Y ) ) ) )), 968.94/124.76 inference('simplify_rw_rule', [status(thm)], [subrel])). 968.94/124.76 thf('3', plain, 968.94/124.76 (( subrel ) = 968.94/124.76 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $i > $o )]: 968.94/124.76 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_2 @ X4 @ X6 ) ) ) )), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf('4', plain, 968.94/124.76 (( tc ) = 968.94/124.76 ( ^[R:( $i > $i > $o ),X:$i,Y:$i]: 968.94/124.76 ( ![S:( $i > $i > $o )]: 968.94/124.76 ( ( ( trans @ S ) & ( subrel @ R @ S ) ) => ( S @ X @ Y ) ) ) )), 968.94/124.76 inference('simplify_rw_rule', [status(thm)], 968.94/124.76 [transitive_closure, '1', '3'])). 968.94/124.76 thf('5', plain, 968.94/124.76 (( tc ) = 968.94/124.76 ( ^[V_1:( $i > $i > $o ),V_2:$i,V_3:$i]: 968.94/124.76 ( ![X4:( $i > $i > $o )]: 968.94/124.76 ( ( ( trans @ X4 ) & ( subrel @ V_1 @ X4 ) ) => ( X4 @ V_2 @ V_3 ) ) ) )), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(idempotent, axiom,(( idem ) = 968.94/124.76 (^[F:( ( $i > $i > $o ) > $i > $i > $o )]: 968.94/124.76 ( ![R:( $i > $i > $o )]: ( ( F @ ( F @ R ) ) = ( F @ R ) ) )))). 968.94/124.76 thf('6', plain, 968.94/124.76 (( idem ) = 968.94/124.76 ( ^[F:( ( $i > $i > $o ) > $i > $i > $o )]: 968.94/124.76 ( ![R:( $i > $i > $o )]: ( ( F @ ( F @ R ) ) = ( F @ R ) ) ) )), 968.94/124.76 inference('simplify_rw_rule', [status(thm)], [idempotent])). 968.94/124.76 thf('7', plain, 968.94/124.76 (( idem ) = 968.94/124.76 ( ^[V_1:( ( $i > $i > $o ) > $i > $i > $o )]: 968.94/124.76 ( ![X4:( $i > $i > $o )]: ( ( V_1 @ ( V_1 @ X4 ) ) = ( V_1 @ X4 ) ) ) )), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(transitive_closure_op_is_idempotent, conjecture, (idem @ tc)). 968.94/124.76 thf(zf_stmt_0, conjecture, 968.94/124.76 (![X4:( $i > $i > $o )]: 968.94/124.76 ( ( ^[V_1:$i,V_2:$i]: 968.94/124.76 ( ![X6:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X14:$i,X16:$i]: 968.94/124.76 ( ( ![X18:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X26:$i,X28:$i]: 968.94/124.76 ( ( X4 @ X26 @ X28 ) => ( X18 @ X26 @ X28 ) ) ) & 968.94/124.76 ( ![X20:$i,X22:$i,X24:$i]: 968.94/124.76 ( ( ( X18 @ X22 @ X24 ) & ( X18 @ X20 @ X22 ) ) => 968.94/124.76 ( X18 @ X20 @ X24 ) ) ) ) => 968.94/124.76 ( X18 @ X14 @ X16 ) ) ) => 968.94/124.76 ( X6 @ X14 @ X16 ) ) ) & 968.94/124.76 ( ![X8:$i,X10:$i,X12:$i]: 968.94/124.76 ( ( ( X6 @ X10 @ X12 ) & ( X6 @ X8 @ X10 ) ) => 968.94/124.76 ( X6 @ X8 @ X12 ) ) ) ) => 968.94/124.76 ( X6 @ V_1 @ V_2 ) ) ) ) = 968.94/124.76 ( ^[V_3:$i,V_4:$i]: 968.94/124.76 ( ![X30:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X38:$i,X40:$i]: 968.94/124.76 ( ( X4 @ X38 @ X40 ) => ( X30 @ X38 @ X40 ) ) ) & 968.94/124.76 ( ![X32:$i,X34:$i,X36:$i]: 968.94/124.76 ( ( ( X30 @ X34 @ X36 ) & ( X30 @ X32 @ X34 ) ) => 968.94/124.76 ( X30 @ X32 @ X36 ) ) ) ) => 968.94/124.76 ( X30 @ V_3 @ V_4 ) ) ) ) ))). 968.94/124.76 thf(zf_stmt_1, negated_conjecture, 968.94/124.76 (~( ![X4:( $i > $i > $o )]: 968.94/124.76 ( ( ^[V_1:$i,V_2:$i]: 968.94/124.76 ( ![X6:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X14:$i,X16:$i]: 968.94/124.76 ( ( ![X18:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X26:$i,X28:$i]: 968.94/124.76 ( ( X4 @ X26 @ X28 ) => ( X18 @ X26 @ X28 ) ) ) & 968.94/124.76 ( ![X20:$i,X22:$i,X24:$i]: 968.94/124.76 ( ( ( X18 @ X22 @ X24 ) & ( X18 @ X20 @ X22 ) ) => 968.94/124.76 ( X18 @ X20 @ X24 ) ) ) ) => 968.94/124.76 ( X18 @ X14 @ X16 ) ) ) => 968.94/124.76 ( X6 @ X14 @ X16 ) ) ) & 968.94/124.76 ( ![X8:$i,X10:$i,X12:$i]: 968.94/124.76 ( ( ( X6 @ X10 @ X12 ) & ( X6 @ X8 @ X10 ) ) => 968.94/124.76 ( X6 @ X8 @ X12 ) ) ) ) => 968.94/124.76 ( X6 @ V_1 @ V_2 ) ) ) ) = 968.94/124.76 ( ^[V_3:$i,V_4:$i]: 968.94/124.76 ( ![X30:( $i > $i > $o )]: 968.94/124.76 ( ( ( ![X38:$i,X40:$i]: 968.94/124.76 ( ( X4 @ X38 @ X40 ) => ( X30 @ X38 @ X40 ) ) ) & 968.94/124.76 ( ![X32:$i,X34:$i,X36:$i]: 968.94/124.76 ( ( ( X30 @ X34 @ X36 ) & ( X30 @ X32 @ X34 ) ) => 968.94/124.76 ( X30 @ X32 @ X36 ) ) ) ) => 968.94/124.76 ( X30 @ V_3 @ V_4 ) ) ) ) ) )), 968.94/124.76 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 968.94/124.76 thf(zip_derived_cl0, plain, 968.94/124.76 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 ((((^[Y1 : $i,Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : 968.94/124.76 $i > $i > $o]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y8 : $i]: 968.94/124.76 (( 968.94/124.76 (Y0 @ 968.94/124.76 Y7 @ 968.94/124.76 Y8) => 968.94/124.76 (Y6 @ 968.94/124.76 Y7 @ Y8))))))))) & 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y8 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y9 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y6 @ 968.94/124.76 Y8 @ 968.94/124.76 Y9) & 968.94/124.76 (Y6 @ 968.94/124.76 Y7 @ Y8))) => 968.94/124.76 (Y6 @ 968.94/124.76 Y7 @ Y9)))))))))))))) => 968.94/124.76 (Y6 @ 968.94/124.76 Y4 @ Y5)))))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ Y2)))))))) = 968.94/124.76 ((^[Y1 : $i,Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((Y0 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ Y2)))))))))))))), 968.94/124.76 inference('cnf', [status(esa)], [zf_stmt_1])). 968.94/124.76 thf(zip_derived_cl1, plain, 968.94/124.76 (~ ((((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((((!!) @ (^[Y5 : 968.94/124.76 $i > $i > $o]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y6 @ 968.94/124.76 Y7) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))))))))) & 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y8 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y5 @ 968.94/124.76 Y7 @ 968.94/124.76 Y8) & 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y8)))))))))))))) => 968.94/124.76 (Y5 @ 968.94/124.76 Y3 @ Y4)))))) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))))) = 968.94/124.76 ((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ Y3 @ Y4) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1))))))))))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 968.94/124.76 thf(zip_derived_cl2, plain, 968.94/124.76 ((((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((((!!) @ (^[Y5 : 968.94/124.76 $i > $i > $o]: 968.94/124.76 (((((( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y6 @ 968.94/124.76 Y7) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))))))))) & 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y8 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y5 @ 968.94/124.76 Y7 @ 968.94/124.76 Y8) & 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y8)))))))))))))) => 968.94/124.76 (Y5 @ Y3 @ 968.94/124.76 Y4)))))) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((((Y2 @ Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ Y3 @ 968.94/124.76 Y4))) => 968.94/124.76 (Y2 @ Y3 @ 968.94/124.76 Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))))) 968.94/124.76 != ((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ Y3 @ Y4) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))))))), 968.94/124.76 inference('simplify nested equalities', [status(thm)], [zip_derived_cl1])). 968.94/124.76 thf(zip_derived_cl3, plain, 968.94/124.76 ((((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((((!!) @ (^[Y5 : 968.94/124.76 $i > $i > $o]: 968.94/124.76 (((((( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y6 @ 968.94/124.76 Y7) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))))))))) & 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y7 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y8 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y5 @ 968.94/124.76 Y7 @ 968.94/124.76 Y8) & 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y7))) => 968.94/124.76 (Y5 @ 968.94/124.76 Y6 @ Y8)))))))))))))) => 968.94/124.76 (Y5 @ Y3 @ 968.94/124.76 Y4)))))) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((((Y2 @ Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ Y3 @ 968.94/124.76 Y4))) => 968.94/124.76 (Y2 @ Y3 @ 968.94/124.76 Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1))))))) @ 968.94/124.76 '#_fresh_sk2' @ '#_fresh_sk3') 968.94/124.76 != ((^[Y0 : $i,Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ Y3 @ Y4) => 968.94/124.76 (Y2 @ Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ (^[Y4 : $i]: 968.94/124.76 (((!!) @ (^[Y5 : $i]: 968.94/124.76 (((( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1))))))) @ 968.94/124.76 '#_fresh_sk2' @ '#_fresh_sk3'))), 968.94/124.76 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl2])). 968.94/124.76 thf(zip_derived_cl4, plain, 968.94/124.76 (((((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ Y2)))))) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))) 968.94/124.76 != (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('ho_norm', [status(thm)], [zip_derived_cl3])). 968.94/124.76 thf(zip_derived_cl5, plain, 968.94/124.76 (( (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ Y2)))))) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('eq_elim', [status(thm)], [zip_derived_cl4])). 968.94/124.76 thf(zip_derived_cl8, plain, 968.94/124.76 (![X2 : $i > $i > $o]: 968.94/124.76 ( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 (X2 @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((X2 @ Y1 @ Y2) & (X2 @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 (X2 @ Y0 @ Y2)))))))))))))) => 968.94/124.76 (X2 @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ 968.94/124.76 Y2 @ Y3) & 968.94/124.76 (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 968.94/124.76 thf(zip_derived_cl66, plain, 968.94/124.76 (( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk142' @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('triggered_bool_instantiation', [status(thm)], 968.94/124.76 [zip_derived_cl8])). 968.94/124.76 thf(zip_derived_cl4, plain, 968.94/124.76 (((((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ Y2)))))) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))) 968.94/124.76 != (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('ho_norm', [status(thm)], [zip_derived_cl3])). 968.94/124.76 thf(zip_derived_cl6, plain, 968.94/124.76 ((~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((!!) @ (^[Y3 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))))))))) & 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y6 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y3 @ 968.94/124.76 Y5 @ 968.94/124.76 Y6) & 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y5))) => 968.94/124.76 (Y3 @ 968.94/124.76 Y4 @ Y6)))))))))))))) => 968.94/124.76 (Y3 @ Y1 @ 968.94/124.76 Y2)))))) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))) 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('eq_elim', [status(thm)], [zip_derived_cl4])). 968.94/124.76 thf(zip_derived_cl42, plain, 968.94/124.76 ((~ (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk140' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk140' @ Y1 @ Y2) & 968.94/124.76 ('#sk140' @ Y0 @ Y1))) => 968.94/124.76 ('#sk140' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 968.94/124.76 thf(zip_derived_cl58, plain, 968.94/124.76 (( ('#form141') 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(zip_derived_cl67, plain, 968.94/124.76 ((~ (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ 968.94/124.76 Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk142' @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | ('#form141'))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 968.94/124.76 thf(zip_derived_cl84, plain, 968.94/124.76 ((~ ('#sk142' @ '#_fresh_sk2' @ '#_fresh_sk3') | ('#form141'))), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 968.94/124.76 thf(zip_derived_cl42, plain, 968.94/124.76 ((~ (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk140' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk140' @ Y1 @ Y2) & 968.94/124.76 ('#sk140' @ Y0 @ Y1))) => 968.94/124.76 ('#sk140' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 968.94/124.76 thf(zip_derived_cl58, plain, 968.94/124.76 (( ('#form141') 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(zip_derived_cl59, plain, 968.94/124.76 ((~ ('#form141') 968.94/124.76 | ~ (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk140' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk140' @ Y1 @ Y2) & 968.94/124.76 ('#sk140' @ Y0 @ Y1))) => 968.94/124.76 ('#sk140' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3'))))), 968.94/124.76 inference('renaming', [status(thm)], [zip_derived_cl42, zip_derived_cl58])). 968.94/124.76 thf(zip_derived_cl60, plain, 968.94/124.76 (( (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk140' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk140' @ Y1 @ Y2) & 968.94/124.76 ('#sk140' @ Y0 @ Y1))) => 968.94/124.76 ('#sk140' @ Y0 @ Y2)))))))))))))) 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 968.94/124.76 thf(zip_derived_cl62, plain, 968.94/124.76 (( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk140' @ Y0 @ Y1))))))))) 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 968.94/124.76 thf(zip_derived_cl127, plain, 968.94/124.76 (![X2 : $i]: 968.94/124.76 ( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((((!!) @ (^[Y1 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 ((('#sk1' @ 968.94/124.76 Y2 @ Y3) => 968.94/124.76 (Y1 @ Y2 @ 968.94/124.76 Y3))))))))) & 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y1 @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) & 968.94/124.76 (Y1 @ 968.94/124.76 Y2 @ Y3))) => 968.94/124.76 (Y1 @ 968.94/124.76 Y2 @ Y4)))))))))))))) => 968.94/124.76 (Y1 @ X2 @ Y0)))))) => 968.94/124.76 ('#sk140' @ X2 @ Y0)))))) 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 968.94/124.76 thf(zip_derived_cl130, plain, 968.94/124.76 (![X2 : $i, X4 : $i]: 968.94/124.76 ( (((((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ 968.94/124.76 Y2 @ Y3) & 968.94/124.76 (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ X2 @ X4)))))) => 968.94/124.76 ('#sk140' @ X2 @ X4))) 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl127])). 968.94/124.76 thf(zip_derived_cl131, plain, 968.94/124.76 (![X2 : $i, X4 : $i]: 968.94/124.76 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ X2 @ X4)))))) 968.94/124.76 | ('#sk140' @ X2 @ X4) 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('imp_elim', [status(thm)], [zip_derived_cl130])). 968.94/124.76 thf(zip_derived_cl8, plain, 968.94/124.76 (![X2 : $i > $i > $o]: 968.94/124.76 ( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 (X2 @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((X2 @ Y1 @ Y2) & (X2 @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 (X2 @ Y0 @ Y2)))))))))))))) => 968.94/124.76 (X2 @ '#_fresh_sk2' @ '#_fresh_sk3'))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ 968.94/124.76 Y2 @ Y3) & 968.94/124.76 (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 968.94/124.76 thf(zip_derived_cl14, plain, 968.94/124.76 (![X2 : $i > $i > $o]: 968.94/124.76 (~ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 (X2 @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((X2 @ Y1 @ Y2) & (X2 @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 (X2 @ Y0 @ Y2)))))))))))))) 968.94/124.76 | (X2 @ '#_fresh_sk2' @ '#_fresh_sk3') 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ 968.94/124.76 Y2 @ Y3) & 968.94/124.76 (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('imp_elim', [status(thm)], [zip_derived_cl8])). 968.94/124.76 thf(zip_derived_cl348, plain, 968.94/124.76 ((~ ('#form141') 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(zip_derived_cl355, plain, 968.94/124.76 ((~ ('#form141') 968.94/124.76 | ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3') 968.94/124.76 | ~ ('#form141'))), 968.94/124.76 inference('sup+', [status(thm)], [zip_derived_cl131, zip_derived_cl348])). 968.94/124.76 thf(zip_derived_cl368, plain, 968.94/124.76 (( ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3') | ~ ('#form141'))), 968.94/124.76 inference('simplify', [status(thm)], [zip_derived_cl355])). 968.94/124.76 thf(zip_derived_cl61, plain, 968.94/124.76 ((~ ('#sk140' @ '#_fresh_sk2' @ '#_fresh_sk3') | ~ ('#form141'))), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 968.94/124.76 thf(zip_derived_cl716, plain, (~ ('#form141')), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl368, zip_derived_cl61])). 968.94/124.76 thf(zip_derived_cl718, plain, (~ ('#sk142' @ '#_fresh_sk2' @ '#_fresh_sk3')), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl84, zip_derived_cl716])). 968.94/124.76 thf(zip_derived_cl1718, plain, 968.94/124.76 (( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ($false))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl66, zip_derived_cl718])). 968.94/124.76 thf(zip_derived_cl1719, plain, 968.94/124.76 (( (((~) @ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ ( 968.94/124.76 ^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ 968.94/124.76 Y2) & ('#sk142' @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('simplify boolean subterms', [status(thm)], 968.94/124.76 [zip_derived_cl1718])). 968.94/124.76 thf(zip_derived_cl1720, plain, 968.94/124.76 ((~ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ( 968.94/124.76 ( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 inference('simplify nested equalities', [status(thm)], 968.94/124.76 [zip_derived_cl1719])). 968.94/124.76 thf(zip_derived_cl348, plain, 968.94/124.76 ((~ ('#form141') 968.94/124.76 | (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(zip_derived_cl58, plain, 968.94/124.76 (( ('#form141') 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y2))) => 968.94/124.76 (Y0 @ Y1 @ 968.94/124.76 Y3)))))))))))))) => 968.94/124.76 (Y0 @ '#_fresh_sk2' @ '#_fresh_sk3')))))))), 968.94/124.76 define([status(thm)])). 968.94/124.76 thf(zip_derived_cl1721, plain, 968.94/124.76 (( ('#form141') 968.94/124.76 | ~ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))))), 968.94/124.76 inference('renaming', [status(thm)], 968.94/124.76 [zip_derived_cl1720, zip_derived_cl348, zip_derived_cl58])). 968.94/124.76 thf(zip_derived_cl716, plain, (~ ('#form141')), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl368, zip_derived_cl61])). 968.94/124.76 thf(zip_derived_cl1722, plain, 968.94/124.76 (~ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 ('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (( 968.94/124.76 (!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))))), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl1721, zip_derived_cl716])). 968.94/124.76 thf(zip_derived_cl1723, plain, 968.94/124.76 ((~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1))))))))) 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))), 968.94/124.76 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl1722])). 968.94/124.76 thf(zip_derived_cl83, plain, 968.94/124.76 (( (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) 968.94/124.76 | ('#form141'))), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 968.94/124.76 thf(zip_derived_cl86, plain, 968.94/124.76 (( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))) 968.94/124.76 | ('#form141'))), 968.94/124.76 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 968.94/124.76 thf(zip_derived_cl716, plain, (~ ('#form141')), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl368, zip_derived_cl61])). 968.94/124.76 thf(zip_derived_cl720, plain, 968.94/124.76 ( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl716])). 968.94/124.76 thf(zip_derived_cl1724, plain, 968.94/124.76 (~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((((!!) @ (^[Y2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 ((('#sk1' @ 968.94/124.76 Y3 @ 968.94/124.76 Y4) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))))))))) & 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y5 : $i]: 968.94/124.76 (( 968.94/124.76 (( 968.94/124.76 (Y2 @ 968.94/124.76 Y4 @ 968.94/124.76 Y5) & 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y4))) => 968.94/124.76 (Y2 @ 968.94/124.76 Y3 @ Y5)))))))))))))) => 968.94/124.76 (Y2 @ Y0 @ Y1)))))) => 968.94/124.76 ('#sk142' @ Y0 @ Y1)))))))))), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl1723, zip_derived_cl720])). 968.94/124.76 thf(zip_derived_cl1728, plain, 968.94/124.76 (~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((((!!) @ (^[Y1 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 ((('#sk1' @ 968.94/124.76 Y2 @ Y3) => 968.94/124.76 (Y1 @ Y2 @ Y3))))))))) & 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((!!) @ ( 968.94/124.76 ^[Y4 : $i]: 968.94/124.76 (((( 968.94/124.76 (Y1 @ 968.94/124.76 Y3 @ Y4) & 968.94/124.76 (Y1 @ 968.94/124.76 Y2 @ Y3))) => 968.94/124.76 (Y1 @ 968.94/124.76 Y2 @ Y4)))))))))))))) => 968.94/124.76 (Y1 @ ('#sk1656' @ '#sk142') @ Y0)))))) => 968.94/124.76 ('#sk142' @ ('#sk1656' @ '#sk142') @ Y0))))))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1724])). 968.94/124.76 thf(zip_derived_cl1867, plain, 968.94/124.76 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => 968.94/124.76 (Y0 @ Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ ('#sk1656' @ '#sk142') @ '#sk3252')))))) => 968.94/124.76 ('#sk142' @ ('#sk1656' @ '#sk142') @ '#sk3252')))), 968.94/124.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1728])). 968.94/124.76 thf(zip_derived_cl1877, plain, 968.94/124.76 ( (((!!) @ (^[Y0 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((('#sk1' @ Y1 @ Y2) => (Y0 @ 968.94/124.76 Y1 @ Y2))))))))) & 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((!!) @ (^[Y3 : $i]: 968.94/124.76 (((((Y0 @ Y2 @ 968.94/124.76 Y3) & (Y0 @ 968.94/124.76 Y1 @ Y2))) => 968.94/124.76 (Y0 @ Y1 @ Y3)))))))))))))) => 968.94/124.76 (Y0 @ ('#sk1656' @ '#sk142') @ '#sk3252'))))))), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1867])). 968.94/124.76 thf(zip_derived_cl1882, plain, 968.94/124.76 (![X2 : $i > $i > $o]: 968.94/124.76 (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 (((((X2 @ Y1 @ Y2) & (X2 @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 (X2 @ Y0 @ Y2)))))))))))))) => 968.94/124.76 (X2 @ ('#sk1656' @ '#sk142') @ '#sk3252')))), 968.94/124.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1877])). 968.94/124.76 thf(zip_derived_cl1884, plain, 968.94/124.76 ( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ 968.94/124.76 Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ('#sk142' @ ('#sk1656' @ '#sk142') @ '#sk3252')))), 968.94/124.76 inference('triggered_bool_instantiation', [status(thm)], 968.94/124.76 [zip_derived_cl1882])). 968.94/124.76 thf(zip_derived_cl1878, plain, 968.94/124.76 (~ ('#sk142' @ ('#sk1656' @ '#sk142') @ '#sk3252')), 968.94/124.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1867])). 968.94/124.76 thf(zip_derived_cl2280, plain, 968.94/124.76 ( (((((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ 968.94/124.76 Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))) => 968.94/124.76 ($false)))), 968.94/124.76 inference('demod', [status(thm)], 968.94/124.76 [zip_derived_cl1884, zip_derived_cl1878])). 968.94/124.76 thf(zip_derived_cl2281, plain, 968.94/124.76 ( (((~) @ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ 968.94/124.76 Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ 968.94/124.76 Y2) & ('#sk142' @ 968.94/124.76 Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))))))), 968.94/124.76 inference('simplify boolean subterms', [status(thm)], 968.94/124.76 [zip_derived_cl2280])). 968.94/124.76 thf(zip_derived_cl2282, plain, 968.94/124.76 (~ (((((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ Y1))))))))) & 968.94/124.76 (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))))), 968.94/124.76 inference('simplify nested equalities', [status(thm)], 968.94/124.76 [zip_derived_cl2281])). 968.94/124.76 thf(zip_derived_cl2283, plain, 968.94/124.76 ((~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ Y1))))))))) 968.94/124.76 | ~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2)))))))))))))), 968.94/124.76 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2282])). 968.94/124.76 thf(zip_derived_cl85, plain, 968.94/124.76 (( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ Y1))))))))) 968.94/124.76 | ('#form141'))), 968.94/124.76 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl83])). 968.94/124.76 thf(zip_derived_cl716, plain, (~ ('#form141')), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl368, zip_derived_cl61])). 968.94/124.76 thf(zip_derived_cl719, plain, 968.94/124.76 ( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 ((('#sk1' @ Y0 @ Y1) => ('#sk142' @ Y0 @ Y1)))))))))), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl716])). 968.94/124.76 thf(zip_derived_cl2284, plain, 968.94/124.76 (~ (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))), 968.94/124.76 inference('clc', [status(thm)], [zip_derived_cl2283, zip_derived_cl719])). 968.94/124.76 thf(zip_derived_cl720, plain, 968.94/124.76 ( (((!!) @ (^[Y0 : $i]: 968.94/124.76 (((!!) @ (^[Y1 : $i]: 968.94/124.76 (((!!) @ (^[Y2 : $i]: 968.94/124.76 ((((('#sk142' @ Y1 @ Y2) & 968.94/124.76 ('#sk142' @ Y0 @ Y1))) => 968.94/124.76 ('#sk142' @ Y0 @ Y2))))))))))))), 968.94/124.76 inference('demod', [status(thm)], [zip_derived_cl86, zip_derived_cl716])). 968.94/124.76 thf(zip_derived_cl2285, plain, ($false), 968.94/124.76 inference('sup+', [status(thm)], [zip_derived_cl2284, zip_derived_cl720])). 968.94/124.76 968.94/124.76 % SZS output end Refutation 968.94/124.76 968.94/124.76 968.94/124.76 % Terminating... 969.69/124.81 % Runner terminated. 969.69/124.82 % Zipperpin 1.5 exiting 969.69/124.82 EOF