0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.eDTQAYN9iC true 0.15/0.35 % Computer : n013.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 06:18:47 EDT 2023 0.15/0.35 % CPUTime : 0.15/0.35 % Running portfolio for 1440 s 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.35 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.57/0.69 % Total configuration time : 828 0.57/0.69 % Estimated wc time : 1656 0.57/0.69 % Estimated cpu time (8 cpus) : 207.0 0.58/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.59/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 4.70/1.22 % Solved by lams/20_acsne_simpl.sh. 4.70/1.22 % done 27 iterations in 0.378s 4.70/1.22 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 4.70/1.22 % SZS output start Refutation 4.70/1.22 thf('#sk7_type', type, '#sk7': (($i > $o) > $o) > (($i > $o) > $o) > $o). 4.70/1.22 thf(c_less__eq__type, type, c_less__eq_: (($i > $o) > $o) > (($i > $o) > $o) > $o). 4.70/1.22 thf('#sk25_type', type, '#sk25': (($i > $o) > $o) > (($i > $o) > $o) > $o). 4.70/1.22 thf(cP_type, type, cP: (($i > $o) > $o) > $o). 4.70/1.22 thf(cSUCC_type, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o). 4.70/1.22 thf(cZERO_type, type, cZERO: ($i > $o) > $o). 4.70/1.22 thf(cONE_type, type, cONE: ($i > $o) > $o). 4.70/1.22 thf('#form24_type', type, '#form24': (($i > $o) > $o) > $o). 4.70/1.22 thf('#sk278_type', type, '#sk278': (($i > $o) > $o) > $o). 4.70/1.22 thf(c_less__eq__def, axiom,(( c_less__eq_ ) = 4.70/1.22 (^[Xx:( ( $i > $o ) > $o ),Xy:( ( $i > $o ) > $o )]: 4.70/1.22 ( ![Xp:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( Xp @ Xx ) & 4.70/1.22 ( ![Xz:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( Xp @ Xz ) => ( Xp @ ( cSUCC @ Xz ) ) ) ) ) => 4.70/1.22 ( Xp @ Xy ) ) )))). 4.70/1.22 thf(cSUCC_def, axiom,(( cSUCC ) = 4.70/1.22 (^[Xn:( ( $i > $o ) > $o ),Xp:( $i > $o )]: 4.70/1.22 ( ?[Xx:$i]: 4.70/1.22 ( ( Xn @ ( ^[Xt:$i]: ( ( ( Xt ) != ( Xx ) ) & ( Xp @ Xt ) ) ) ) & 4.70/1.22 ( Xp @ Xx ) ) )))). 4.70/1.22 thf('0', plain, 4.70/1.22 (( cSUCC ) = 4.70/1.22 ( ^[Xn:( ( $i > $o ) > $o ),Xp:( $i > $o )]: 4.70/1.22 ( ?[Xx:$i]: 4.70/1.22 ( ( Xn @ ( ^[Xt:$i]: ( ( ( Xt ) != ( Xx ) ) & ( Xp @ Xt ) ) ) ) & 4.70/1.22 ( Xp @ Xx ) ) ) )), 4.70/1.22 inference('simplify_rw_rule', [status(thm)], [cSUCC_def])). 4.70/1.22 thf('1', plain, 4.70/1.22 (( cSUCC ) = 4.70/1.22 ( ^[V_1:( ( $i > $o ) > $o ),V_2:( $i > $o )]: 4.70/1.22 ( ?[X4:$i]: 4.70/1.22 ( ( V_1 @ ( ^[V_3:$i]: ( ( ( V_3 ) != ( X4 ) ) & ( V_2 @ V_3 ) ) ) ) & 4.70/1.22 ( V_2 @ X4 ) ) ) )), 4.70/1.22 define([status(thm)])). 4.70/1.22 thf('2', plain, 4.70/1.22 (( c_less__eq_ ) = 4.70/1.22 ( ^[Xx:( ( $i > $o ) > $o ),Xy:( ( $i > $o ) > $o )]: 4.70/1.22 ( ![Xp:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( Xp @ Xx ) & 4.70/1.22 ( ![Xz:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( Xp @ Xz ) => ( Xp @ ( cSUCC @ Xz ) ) ) ) ) => 4.70/1.22 ( Xp @ Xy ) ) ) )), 4.70/1.22 inference('simplify_rw_rule', [status(thm)], [c_less__eq__def, '1'])). 4.70/1.22 thf('3', plain, 4.70/1.22 (( c_less__eq_ ) = 4.70/1.22 ( ^[V_1:( ( $i > $o ) > $o ),V_2:( ( $i > $o ) > $o )]: 4.70/1.22 ( ![X4:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( X4 @ V_1 ) & 4.70/1.22 ( ![X6:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( X4 @ X6 ) => ( X4 @ ( cSUCC @ X6 ) ) ) ) ) => 4.70/1.22 ( X4 @ V_2 ) ) ) )), 4.70/1.22 define([status(thm)])). 4.70/1.22 thf(cONE_def, axiom,(( cONE ) = (cSUCC @ cZERO))). 4.70/1.22 thf(cZERO_def, axiom,(( cZERO ) = 4.70/1.22 (^[Xp:( $i > $o )]: ( ~( ?[Xx:$i]: ( Xp @ Xx ) ) )))). 4.70/1.22 thf('4', plain, 4.70/1.22 (( cZERO ) = ( ^[Xp:( $i > $o )]: ( ~( ?[Xx:$i]: ( Xp @ Xx ) ) ) )), 4.70/1.22 inference('simplify_rw_rule', [status(thm)], [cZERO_def])). 4.70/1.22 thf('5', plain, 4.70/1.22 (( cZERO ) = ( ^[V_1:( $i > $o )]: ( ~( ?[X4:$i]: ( V_1 @ X4 ) ) ) )), 4.70/1.22 define([status(thm)])). 4.70/1.22 thf('6', plain, (( cONE ) = ( cSUCC @ cZERO )), 4.70/1.22 inference('simplify_rw_rule', [status(thm)], [cONE_def, '1', '5'])). 4.70/1.22 thf('7', plain, (( cONE ) = ( cSUCC @ cZERO )), define([status(thm)])). 4.70/1.22 thf(cBLEDSOE7A, conjecture, 4.70/1.22 (( cP @ cONE ) => 4.70/1.22 ( ?[Xx:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( c_less__eq_ @ Xx @ ( cSUCC @ cONE ) ) & ( cP @ Xx ) & 4.70/1.22 ( c_less__eq_ @ cZERO @ Xx ) ) ))). 4.70/1.22 thf(zf_stmt_0, conjecture, 4.70/1.22 (( cP @ 4.70/1.22 ( ^[V_1:( $i > $o )]: 4.70/1.22 ( ?[X4:$i]: 4.70/1.22 ( ( V_1 @ X4 ) & 4.70/1.22 ( ~( ?[X6:$i]: ( ( V_1 @ X6 ) & ( ( X6 ) != ( X4 ) ) ) ) ) ) ) ) ) => 4.70/1.22 ( ?[X8:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( ![X22:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( ![X26:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( X22 @ X26 ) => 4.70/1.22 ( X22 @ 4.70/1.22 ( ^[V_6:( $i > $o )]: 4.70/1.22 ( ?[X28:$i]: 4.70/1.22 ( ( V_6 @ X28 ) & 4.70/1.22 ( X26 @ 4.70/1.22 ( ^[V_7:$i]: 4.70/1.22 ( ( V_6 @ V_7 ) & ( ( V_7 ) != ( X28 ) ) ) ) ) ) ) ) ) ) ) & 4.70/1.22 ( X22 @ 4.70/1.22 ( ^[V_5:( $i > $o )]: ( ~( ?[X24:$i]: ( V_5 @ X24 ) ) ) ) ) ) => 4.70/1.22 ( X22 @ X8 ) ) ) & 4.70/1.22 ( cP @ X8 ) & 4.70/1.22 ( ![X10:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( ![X12:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( X10 @ X12 ) => 4.70/1.22 ( X10 @ 4.70/1.22 ( ^[V_2:( $i > $o )]: 4.70/1.22 ( ?[X14:$i]: 4.70/1.22 ( ( V_2 @ X14 ) & 4.70/1.22 ( X12 @ 4.70/1.22 ( ^[V_3:$i]: 4.70/1.22 ( ( V_2 @ V_3 ) & ( ( V_3 ) != ( X14 ) ) ) ) ) ) ) ) ) ) ) & 4.70/1.22 ( X10 @ X8 ) ) => 4.70/1.22 ( X10 @ 4.70/1.22 ( ^[V_4:( $i > $o )]: 4.70/1.22 ( ?[X16:$i]: 4.70/1.22 ( ( V_4 @ X16 ) & 4.70/1.22 ( ?[X18:$i]: 4.70/1.22 ( ( V_4 @ X18 ) & ( ( X18 ) != ( X16 ) ) & 4.70/1.22 ( ~( ?[X20:$i]: 4.70/1.22 ( ( V_4 @ X20 ) & ( ( X20 ) != ( X16 ) ) & 4.70/1.22 ( ( X20 ) != ( X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 4.70/1.22 thf(zf_stmt_1, negated_conjecture, 4.70/1.22 (~( ( cP @ 4.70/1.22 ( ^[V_1:( $i > $o )]: 4.70/1.22 ( ?[X4:$i]: 4.70/1.22 ( ( V_1 @ X4 ) & 4.70/1.22 ( ~( ?[X6:$i]: ( ( V_1 @ X6 ) & ( ( X6 ) != ( X4 ) ) ) ) ) ) ) ) ) => 4.70/1.22 ( ?[X8:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( ![X22:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( ![X26:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( X22 @ X26 ) => 4.70/1.22 ( X22 @ 4.70/1.22 ( ^[V_6:( $i > $o )]: 4.70/1.22 ( ?[X28:$i]: 4.70/1.22 ( ( V_6 @ X28 ) & 4.70/1.22 ( X26 @ 4.70/1.22 ( ^[V_7:$i]: 4.70/1.22 ( ( V_6 @ V_7 ) & ( ( V_7 ) != ( X28 ) ) ) ) ) ) ) ) ) ) ) & 4.70/1.22 ( X22 @ 4.70/1.22 ( ^[V_5:( $i > $o )]: ( ~( ?[X24:$i]: ( V_5 @ X24 ) ) ) ) ) ) => 4.70/1.22 ( X22 @ X8 ) ) ) & 4.70/1.22 ( cP @ X8 ) & 4.70/1.22 ( ![X10:( ( ( $i > $o ) > $o ) > $o )]: 4.70/1.22 ( ( ( ![X12:( ( $i > $o ) > $o )]: 4.70/1.22 ( ( X10 @ X12 ) => 4.70/1.22 ( X10 @ 4.70/1.22 ( ^[V_2:( $i > $o )]: 4.70/1.22 ( ?[X14:$i]: 4.70/1.22 ( ( V_2 @ X14 ) & 4.70/1.22 ( X12 @ 4.70/1.22 ( ^[V_3:$i]: 4.70/1.22 ( ( V_2 @ V_3 ) & ( ( V_3 ) != ( X14 ) ) ) ) ) ) ) ) ) ) ) & 4.70/1.22 ( X10 @ X8 ) ) => 4.70/1.22 ( X10 @ 4.70/1.22 ( ^[V_4:( $i > $o )]: 4.70/1.22 ( ?[X16:$i]: 4.70/1.22 ( ( V_4 @ X16 ) & 4.70/1.22 ( ?[X18:$i]: 4.70/1.22 ( ( V_4 @ X18 ) & ( ( X18 ) != ( X16 ) ) & 4.70/1.22 ( ~( ?[X20:$i]: 4.70/1.22 ( ( V_4 @ X20 ) & ( ( X20 ) != ( X16 ) ) & 4.70/1.22 ( ( X20 ) != ( X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 4.70/1.22 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 4.70/1.22 thf(zip_derived_cl0, plain, 4.70/1.22 (~ (((cP @ 4.70/1.22 (^[Y0 : $i > $o]: 4.70/1.22 (((??) @ (^[Y1 : $i]: 4.70/1.22 (((Y0 @ Y1) & 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) => 4.70/1.22 (((??) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.22 (((((!!) @ (^[Y1 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y2 : ($i > $o) > $o]: 4.70/1.22 (((Y1 @ Y2) => (Y1 @ 4.70/1.22 (^[Y3 : $i > $o]: 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y3 @ 4.70/1.22 Y4) & 4.70/1.22 (Y2 @ 4.70/1.22 ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 (Y3 @ 4.70/1.22 Y5) & 4.70/1.22 (( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))) & 4.70/1.22 (Y1 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (Y2 @ Y3)))))))))) => 4.70/1.22 (Y1 @ Y0)))))) & 4.70/1.22 (cP @ Y0) & 4.70/1.22 (((!!) @ (^[Y1 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y2 : ($i > $o) > $o]: 4.70/1.22 (((Y1 @ Y2) => (Y1 @ 4.70/1.22 (^[Y3 : $i > $o]: 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y3 @ 4.70/1.22 Y4) & 4.70/1.22 (Y2 @ 4.70/1.22 ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 (Y3 @ 4.70/1.22 Y5) & 4.70/1.22 (( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))) & 4.70/1.22 (Y1 @ Y0))) => 4.70/1.22 (Y1 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 ((( 4.70/1.22 Y2 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (~) @ ( 4.70/1.22 ( 4.70/1.22 (??) @ ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 ( 4.70/1.22 Y2 @ Y5) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y5) != 4.70/1.22 (Y3))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))))))))))))))))))), 4.70/1.22 inference('cnf', [status(esa)], [zf_stmt_1])). 4.70/1.22 thf(zip_derived_cl2, plain, 4.70/1.22 (~ (((??) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.22 (((((!!) @ (^[Y1 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y2 : ($i > $o) > $o]: 4.70/1.22 (((Y1 @ Y2) => (Y1 @ 4.70/1.22 (^[Y3 : $i > $o]: 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 (((Y3 @ 4.70/1.22 Y4) & 4.70/1.22 (Y2 @ 4.70/1.22 ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 (Y3 @ 4.70/1.22 Y5) & 4.70/1.22 (( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))) & 4.70/1.22 (Y1 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (Y2 @ Y3)))))))))) => 4.70/1.22 (Y1 @ Y0)))))) & 4.70/1.22 (cP @ Y0) & 4.70/1.22 (((!!) @ (^[Y1 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y2 : ($i > $o) > $o]: 4.70/1.22 (((Y1 @ Y2) => (Y1 @ 4.70/1.22 (^[Y3 : $i > $o]: 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 (((Y3 @ 4.70/1.22 Y4) & 4.70/1.22 (Y2 @ 4.70/1.22 ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 (Y3 @ 4.70/1.22 Y5) & 4.70/1.22 (( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))) & 4.70/1.22 (Y1 @ Y0))) => 4.70/1.22 (Y1 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & 4.70/1.22 (((??) @ (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != 4.70/1.22 (Y3))) & 4.70/1.22 (((~) @ ( 4.70/1.22 ( 4.70/1.22 (??) @ ( 4.70/1.22 ^[Y5 : $i]: 4.70/1.22 (( 4.70/1.22 ( 4.70/1.22 Y2 @ Y5) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y5) != 4.70/1.22 (Y3))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y5) != 4.70/1.22 (Y4))))))))))))))))))))))))))))))))), 4.70/1.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 4.70/1.22 thf(zip_derived_cl3, plain, 4.70/1.22 (![X2 : ($i > $o) > $o]: 4.70/1.22 ~ (((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ X2)))))) & 4.70/1.22 (cP @ X2) & 4.70/1.22 (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ X2))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3)))))))))))))))))))))))))))))), 4.70/1.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 4.70/1.22 thf(zip_derived_cl25, plain, 4.70/1.22 (~ (((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2)))))))))))))))))))))) & 4.70/1.22 (cP @ 4.70/1.22 (^[Y0 : $i > $o]: 4.70/1.22 (((??) @ (^[Y1 : $i]: 4.70/1.22 (((Y0 @ Y1) & 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) & 4.70/1.22 (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != 4.70/1.22 (Y2))))))))))))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 ((( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3)))))))))))))))))))))))))))))), 4.70/1.22 inference('triggered_bool_instantiation', [status(thm)], 4.70/1.22 [zip_derived_cl3])). 4.70/1.22 thf(zip_derived_cl1, plain, 4.70/1.22 ( (cP @ 4.70/1.22 (^[Y0 : $i > $o]: 4.70/1.22 (((??) @ (^[Y1 : $i]: 4.70/1.22 (((Y0 @ Y1) & 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))))), 4.70/1.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 4.70/1.22 thf(zip_derived_cl64, plain, 4.70/1.22 (~ (((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2)))))))))))))))))))))) & 4.70/1.22 ($true) & 4.70/1.22 (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != 4.70/1.22 (Y2))))))))))))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 ((( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3)))))))))))))))))))))))))))))), 4.70/1.22 inference('demod', [status(thm)], [zip_derived_cl25, zip_derived_cl1])). 4.70/1.22 thf(zip_derived_cl65, plain, 4.70/1.22 (~ (((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != 4.70/1.22 (Y2))))))))))))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 ((( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3))))))))))))))))))))))))))) & 4.70/1.22 (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))))))))))))))))))))))))), 4.70/1.22 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl64])). 4.70/1.22 thf(zip_derived_cl66, plain, 4.70/1.22 ((~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))))))))))))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 (((Y1 @ Y4) & 4.70/1.22 (( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 (( 4.70/1.22 (Y4) != 4.70/1.22 (Y3))))))))))))))))))))))))))) 4.70/1.22 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2)))))))))))))))))))))))), 4.70/1.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 4.70/1.22 thf(zip_derived_cl3, plain, 4.70/1.22 (![X2 : ($i > $o) > $o]: 4.70/1.22 ~ (((((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ X2)))))) & 4.70/1.22 (cP @ X2) & 4.70/1.22 (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ X2))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3)))))))))))))))))))))))))))))), 4.70/1.22 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 4.70/1.22 thf(zip_derived_cl4, plain, 4.70/1.22 (![X2 : ($i > $o) > $o]: 4.70/1.22 (~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.22 (Y0 @ X2)))))) 4.70/1.22 | ~ (cP @ X2) 4.70/1.22 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y2 @ Y3) & (Y1 @ 4.70/1.22 (^[Y4 : $i]: 4.70/1.22 (((Y2 @ Y4) & 4.70/1.22 (((Y4) != 4.70/1.22 (Y3))))))))))))))))))) & 4.70/1.22 (Y0 @ X2))) => 4.70/1.22 (Y0 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & 4.70/1.22 (((??) @ (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))) & 4.70/1.22 (((~) @ (((??) @ ( 4.70/1.22 ^[Y4 : $i]: 4.70/1.22 (( 4.70/1.22 ( 4.70/1.22 Y1 @ Y4) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y2))) & 4.70/1.22 ( 4.70/1.22 ( 4.70/1.22 (Y4) != 4.70/1.22 (Y3))))))))))))))))))))))))))))), 4.70/1.22 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3])). 4.70/1.22 thf(zip_derived_cl5, plain, 4.70/1.22 (![X2 : ($i > $o) > $o]: 4.70/1.22 (~ (((((((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.22 ((('#sk7' @ X2 @ Y0) => ('#sk7' @ X2 @ 4.70/1.22 (^[Y1 : $i > $o]: 4.70/1.22 (((??) @ (^[Y2 : $i]: 4.70/1.22 (((Y1 @ Y2) & (Y0 @ 4.70/1.22 (^[Y3 : $i]: 4.70/1.22 (((Y1 @ Y3) & 4.70/1.22 (((Y3) != (Y2))))))))))))))))))) & 4.70/1.22 ('#sk7' @ X2 @ 4.70/1.22 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))) => 4.70/1.22 ('#sk7' @ X2 @ X2))) 4.70/1.22 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.22 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.22 (((Y0 @ Y1) => (Y0 @ 4.70/1.22 (^[Y2 : $i > $o]: 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y2 @ Y3) & (Y1 @ 4.70/1.23 (^[Y4 : $i]: 4.70/1.23 (((Y2 @ Y4) & 4.70/1.23 (((Y4) != 4.70/1.23 (Y3))))))))))))))))))) & 4.70/1.23 (Y0 @ X2))) => 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2))) & 4.70/1.23 (((~) @ (((??) @ ( 4.70/1.23 ^[Y4 : $i]: 4.70/1.23 (( 4.70/1.23 ( 4.70/1.23 Y1 @ Y4) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y2))) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y3))))))))))))))))))))))))))) 4.70/1.23 | ~ (cP @ X2))), 4.70/1.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 4.70/1.23 thf(zip_derived_cl7, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 (~ ('#sk7' @ X2 @ X2) 4.70/1.23 | ~ (cP @ X2) 4.70/1.23 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.23 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.23 (((Y0 @ Y1) => (Y0 @ 4.70/1.23 (^[Y2 : $i > $o]: 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y2 @ Y3) & (Y1 @ 4.70/1.23 (^[Y4 : $i]: 4.70/1.23 (((Y2 @ Y4) & 4.70/1.23 (((Y4) != 4.70/1.23 (Y3))))))))))))))))))) & 4.70/1.23 (Y0 @ X2))) => 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2))) & 4.70/1.23 (((~) @ (((??) @ ( 4.70/1.23 ^[Y4 : $i]: 4.70/1.23 (( 4.70/1.23 ( 4.70/1.23 Y1 @ Y4) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y2))) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y3))))))))))))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 4.70/1.23 thf(zip_derived_cl10, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 ( ('#form24' @ X2) 4.70/1.23 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.23 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.23 (((Y0 @ Y1) => (Y0 @ 4.70/1.23 (^[Y2 : $i > $o]: 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y2 @ Y3) & (Y1 @ 4.70/1.23 (^[Y4 : $i]: 4.70/1.23 (((Y2 @ Y4) & 4.70/1.23 (((Y4) != 4.70/1.23 (Y3))))))))))))))))))) & 4.70/1.23 (Y0 @ X2))) => 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2))) & 4.70/1.23 (((~) @ (((??) @ ( 4.70/1.23 ^[Y4 : $i]: 4.70/1.23 (( 4.70/1.23 ( 4.70/1.23 Y1 @ Y4) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y2))) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y3))))))))))))))))))))))))))))), 4.70/1.23 define([status(thm)])). 4.70/1.23 thf(zip_derived_cl67, plain, 4.70/1.23 ((~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.23 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.23 (((Y0 @ Y1) => (Y0 @ 4.70/1.23 (^[Y2 : $i > $o]: 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y2 @ Y3) & (Y1 @ 4.70/1.23 (^[Y4 : $i]: 4.70/1.23 (((Y2 @ Y4) & 4.70/1.23 (((Y4) != (Y3))))))))))))))))))) & 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: (Y1 @ Y2)))))))))) => 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2)))))))))))))))))))))))), 4.70/1.23 inference('renaming', [status(thm)], [zip_derived_cl66, zip_derived_cl10])). 4.70/1.23 thf(zip_derived_cl68, plain, 4.70/1.23 ((~ (((((((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk278' @ Y0) => ('#sk278' @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & (((Y3) != (Y2))))))))))))))))))) & 4.70/1.23 ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))) => 4.70/1.23 ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 4.70/1.23 thf(zip_derived_cl69, plain, 4.70/1.23 (( (((((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk278' @ Y0) => ('#sk278' @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & (((Y3) != (Y2))))))))))))))))))) & 4.70/1.23 ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 4.70/1.23 thf(zip_derived_cl72, plain, 4.70/1.23 (( ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 4.70/1.23 thf(zip_derived_cl71, plain, 4.70/1.23 (( (((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk278' @ Y0) => ('#sk278' @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & (((Y3) != (Y2))))))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 4.70/1.23 thf(zip_derived_cl73, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 ( ((('#sk278' @ X2) => ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & (X2 @ 4.70/1.23 (^[Y2 : $i]: (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 4.70/1.23 thf(zip_derived_cl76, plain, 4.70/1.23 (( ((('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))) => 4.70/1.23 ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('triggered_bool_instantiation', [status(thm)], 4.70/1.23 [zip_derived_cl73])). 4.70/1.23 thf(zip_derived_cl79, plain, 4.70/1.23 ((~ ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))) 4.70/1.23 | ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 4.70/1.23 thf(zip_derived_cl70, plain, 4.70/1.23 ((~ ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 4.70/1.23 thf(zip_derived_cl80, plain, 4.70/1.23 ((~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ~ ('#sk278' @ 4.70/1.23 (^[Y0 : $i > $o]: (((~) @ (((??) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))), 4.70/1.23 inference('clc', [status(thm)], [zip_derived_cl79, zip_derived_cl70])). 4.70/1.23 thf(zip_derived_cl81, plain, 4.70/1.23 (~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))))), 4.70/1.23 inference('clc', [status(thm)], [zip_derived_cl72, zip_derived_cl80])). 4.70/1.23 thf(zip_derived_cl10, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 ( ('#form24' @ X2) 4.70/1.23 | ~ (((!!) @ (^[Y0 : (($i > $o) > $o) > $o]: 4.70/1.23 (((((((!!) @ (^[Y1 : ($i > $o) > $o]: 4.70/1.23 (((Y0 @ Y1) => (Y0 @ 4.70/1.23 (^[Y2 : $i > $o]: 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y2 @ Y3) & (Y1 @ 4.70/1.23 (^[Y4 : $i]: 4.70/1.23 (((Y2 @ Y4) & 4.70/1.23 (((Y4) != 4.70/1.23 (Y3))))))))))))))))))) & 4.70/1.23 (Y0 @ X2))) => 4.70/1.23 (Y0 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & 4.70/1.23 (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2))) & 4.70/1.23 (((~) @ (((??) @ ( 4.70/1.23 ^[Y4 : $i]: 4.70/1.23 (( 4.70/1.23 ( 4.70/1.23 Y1 @ Y4) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y2))) & 4.70/1.23 ( 4.70/1.23 ( 4.70/1.23 (Y4) != 4.70/1.23 (Y3))))))))))))))))))))))))))))), 4.70/1.23 define([status(thm)])). 4.70/1.23 thf(zip_derived_cl11, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 (~ (((((((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk25' @ X2 @ Y0) => ('#sk25' @ X2 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & 4.70/1.23 (((Y3) != (Y2))))))))))))))))))) & 4.70/1.23 ('#sk25' @ X2 @ X2))) => 4.70/1.23 ('#sk25' @ X2 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y1))) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y2)))))))))))))))))))))))) 4.70/1.23 | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 4.70/1.23 thf(zip_derived_cl15, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 ( (((((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk25' @ X2 @ Y0) => ('#sk25' @ X2 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & (((Y3) != (Y2))))))))))))))))))) & 4.70/1.23 ('#sk25' @ X2 @ X2))) 4.70/1.23 | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 4.70/1.23 thf(zip_derived_cl19, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: ( ('#sk25' @ X2 @ X2) | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 4.70/1.23 thf(zip_derived_cl18, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 ( (((!!) @ (^[Y0 : ($i > $o) > $o]: 4.70/1.23 ((('#sk25' @ X2 @ Y0) => ('#sk25' @ X2 @ 4.70/1.23 (^[Y1 : $i > $o]: 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y1 @ Y2) & (Y0 @ 4.70/1.23 (^[Y3 : $i]: 4.70/1.23 (((Y1 @ Y3) & (((Y3) != (Y2))))))))))))))))))) 4.70/1.23 | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 4.70/1.23 thf(zip_derived_cl21, plain, 4.70/1.23 (![X2 : ($i > $o) > $o, X4 : ($i > $o) > $o]: 4.70/1.23 ( ((('#sk25' @ X2 @ X4) => ('#sk25' @ X2 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & (X4 @ 4.70/1.23 (^[Y2 : $i]: (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))) 4.70/1.23 | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 4.70/1.23 thf(zip_derived_cl23, plain, 4.70/1.23 (![X0 : ($i > $o) > $o]: 4.70/1.23 ( ((('#sk25' @ X0 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))) => 4.70/1.23 ('#sk25' @ X0 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y1))) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y2)))))))))))))))))))))))) 4.70/1.23 | ('#form24' @ X0))), 4.70/1.23 inference('triggered_bool_instantiation', [status(thm)], 4.70/1.23 [zip_derived_cl21])). 4.70/1.23 thf(zip_derived_cl35, plain, 4.70/1.23 (![X0 : ($i > $o) > $o]: 4.70/1.23 (~ ('#sk25' @ X0 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & 4.70/1.23 (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ('#sk25' @ X0 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y1))) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y2)))))))))))))))))))))) 4.70/1.23 | ('#form24' @ X0))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 4.70/1.23 thf(zip_derived_cl110, plain, 4.70/1.23 (( ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))))))))))))))))) 4.70/1.23 | ('#sk25' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))) @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != (Y1))) & 4.70/1.23 (((Y3) != (Y2)))))))))))))))))))))))), 4.70/1.23 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl35])). 4.70/1.23 thf(zip_derived_cl81, plain, 4.70/1.23 (~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))))), 4.70/1.23 inference('clc', [status(thm)], [zip_derived_cl72, zip_derived_cl80])). 4.70/1.23 thf(zip_derived_cl81, plain, 4.70/1.23 (~ ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))))), 4.70/1.23 inference('clc', [status(thm)], [zip_derived_cl72, zip_derived_cl80])). 4.70/1.23 thf(zip_derived_cl111, plain, 4.70/1.23 ( ('#sk25' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))) @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != (Y1))) & 4.70/1.23 (((Y3) != (Y2))))))))))))))))))))))), 4.70/1.23 inference('demod', [status(thm)], 4.70/1.23 [zip_derived_cl110, zip_derived_cl81, zip_derived_cl81])). 4.70/1.23 thf(zip_derived_cl16, plain, 4.70/1.23 (![X2 : ($i > $o) > $o]: 4.70/1.23 (~ ('#sk25' @ X2 @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1))) & 4.70/1.23 (((~) @ (((??) @ (^[Y3 : $i]: 4.70/1.23 (((Y0 @ Y3) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y1))) & 4.70/1.23 (((Y3) != 4.70/1.23 (Y2)))))))))))))))))))))) 4.70/1.23 | ('#form24' @ X2))), 4.70/1.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 4.70/1.23 thf(zip_derived_cl122, plain, 4.70/1.23 ( ('#form24' @ 4.70/1.23 (^[Y0 : $i > $o]: 4.70/1.23 (((??) @ (^[Y1 : $i]: 4.70/1.23 (((Y0 @ Y1) & 4.70/1.23 (((~) @ (((??) @ (^[Y2 : $i]: 4.70/1.23 (((Y0 @ Y2) & (((Y2) != (Y1)))))))))))))))))), 4.70/1.23 inference('sup-', [status(thm)], [zip_derived_cl111, zip_derived_cl16])). 4.70/1.23 thf(zip_derived_cl127, plain, ($false), 4.70/1.23 inference('demod', [status(thm)], [zip_derived_cl81, zip_derived_cl122])). 4.70/1.23 4.70/1.23 % SZS output end Refutation 4.70/1.23 4.70/1.23 4.70/1.23 % Terminating... 5.06/1.29 % Runner terminated. 5.06/1.30 % Zipperpin 1.5 exiting 5.06/1.30 EOF