0.00/0.05 % 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.AP41QtmsRw true 0.19/0.44 % Computer : n018.cluster.edu 0.19/0.44 % Model : x86_64 x86_64 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.44 % Memory : 8046.5625MB 0.19/0.44 % OS : Linux 6.8.0-71-generic 0.19/0.44 % CPULimit : 1440 0.19/0.44 % WCLimit : 180 0.19/0.44 % DateTime : Mon Jul 27 13:57:08 UTC 2026 0.19/0.44 % CPUTime : 0.19/0.44 % Running portfolio for 1440 s 0.19/0.44 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.44 % Number of cores: 8 0.19/0.44 % Python version: Python 3.12.3 0.19/0.45 % Running in HO mode 0.40/0.83 % Total configuration time : 828 0.40/0.83 % Estimated wc time : 1656 0.40/0.83 % Estimated cpu time (8 cpus) : 207.0 0.41/0.95 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.41/1.02 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.41/1.03 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.41/1.04 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.41/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.41/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.41/1.05 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.41/1.06 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 2.56/1.20 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 2.91/1.60 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 121.16/17.35 % Solved by lams/30_sp5.sh. 121.16/17.35 % done 4724 iterations in 16.029s 121.16/17.35 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 121.16/17.35 % SZS output start Refutation 121.16/17.35 thf('#sk10_type', type, '#sk10': $i > $i). 121.16/17.35 thf(a2_type, type, a2: $i > $o). 121.16/17.35 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 121.16/17.35 thf('#sk11_type', type, '#sk11': $i > $i). 121.16/17.35 thf('#sk5_type', type, '#sk5': $i > $i). 121.16/17.35 thf(iimplies_type, type, iimplies: ($i > $o) > ($i > $o) > $i > $o). 121.16/17.35 thf(a1_type, type, a1: $i > $o). 121.16/17.35 thf('#sk6_type', type, '#sk6': $i > $i). 121.16/17.35 thf(irel_type, type, irel: $i > $i > $o). 121.16/17.35 thf('#sk9_type', type, '#sk9': $i > $i). 121.16/17.35 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 121.16/17.35 thf('#sk1_type', type, '#sk1': $i). 121.16/17.35 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 121.16/17.35 thf('#sk2_type', type, '#sk2': $i). 121.16/17.35 thf('#form3_type', type, '#form3': $o). 121.16/17.35 thf(iatom_type, type, iatom: ($i > $o) > $i > $o). 121.16/17.35 thf(b0_type, type, b0: $i > $o). 121.16/17.35 thf(a0_type, type, a0: $i > $o). 121.16/17.35 thf(b2_type, type, b2: $i > $o). 121.16/17.35 thf(f_type, type, f: $i > $o). 121.16/17.35 thf(b1_type, type, b1: $i > $o). 121.16/17.35 thf('#sk4_type', type, '#sk4': $i > $i). 121.16/17.35 thf(b3_type, type, b3: $i > $o). 121.16/17.35 thf('#sk7_type', type, '#sk7': $i > $i). 121.16/17.35 thf(iand_type, type, iand: ($i > $o) > ($i > $o) > $i > $o). 121.16/17.35 thf(a3_type, type, a3: $i > $o). 121.16/17.35 thf('#sk8_type', type, '#sk8': $i > $i). 121.16/17.35 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 121.16/17.35 thf(ivalid_type, type, ivalid: ($i > $o) > $o). 121.16/17.35 thf('#sk12_type', type, '#sk12': $i > $i). 121.16/17.35 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 121.16/17.35 thf(refl_axiom, axiom, (![X:$i]: ( irel @ X @ X ))). 121.16/17.35 thf(zip_derived_cl1, plain, ( (((!!) @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))), 121.16/17.35 inference('cnf', [status(esa)], [refl_axiom])). 121.16/17.35 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.35 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.35 thf(ivalid, axiom,(( ivalid ) = 121.16/17.35 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 121.16/17.35 thf('0', plain, 121.16/17.35 (( ivalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [ivalid])). 121.16/17.35 thf('1', plain, 121.16/17.35 (( ivalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(iimplies, axiom,(( iimplies ) = 121.16/17.35 (^[P:( $i > $o ),Q:( $i > $o )]: 121.16/17.35 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) )))). 121.16/17.35 thf(mbox_s4, axiom,(( mbox_s4 ) = 121.16/17.35 (^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) )))). 121.16/17.35 thf('2', plain, 121.16/17.35 (( mbox_s4 ) = 121.16/17.35 ( ^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 121.16/17.35 thf('3', plain, 121.16/17.35 (( mbox_s4 ) = 121.16/17.35 ( ^[V_1:( $i > $o ),V_2:$i]: 121.16/17.35 ( ![X4:$i]: ( ( irel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(mimplies, axiom,(( mimplies ) = 121.16/17.35 (^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V )))). 121.16/17.35 thf(mor, axiom,(( mor ) = 121.16/17.35 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))). 121.16/17.35 thf('4', plain, 121.16/17.35 (( mor ) = 121.16/17.35 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [mor])). 121.16/17.35 thf('5', plain, 121.16/17.35 (( mor ) = 121.16/17.35 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 121.16/17.35 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(mnot, axiom,(( mnot ) = (^[X:( $i > $o ),U:$i]: ( ~( X @ U ) )))). 121.16/17.35 thf('6', plain, (( mnot ) = ( ^[X:( $i > $o ),U:$i]: ( ~( X @ U ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [mnot])). 121.16/17.35 thf('7', plain, 121.16/17.35 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf('8', plain, 121.16/17.35 (( mimplies ) = 121.16/17.35 ( ^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [mimplies, '5', '7'])). 121.16/17.35 thf('9', plain, 121.16/17.35 (( mimplies ) = 121.16/17.35 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf('10', plain, 121.16/17.35 (( iimplies ) = 121.16/17.35 ( ^[P:( $i > $o ),Q:( $i > $o )]: 121.16/17.35 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [iimplies, '3', '9'])). 121.16/17.35 thf('11', plain, 121.16/17.35 (( iimplies ) = 121.16/17.35 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 121.16/17.35 ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(iand, axiom,(( iand ) = 121.16/17.35 (^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q )))). 121.16/17.35 thf(mand, axiom,(( mand ) = 121.16/17.35 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) )))). 121.16/17.35 thf('12', plain, 121.16/17.35 (( mand ) = 121.16/17.35 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [mand])). 121.16/17.35 thf('13', plain, 121.16/17.35 (( mand ) = 121.16/17.35 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 121.16/17.35 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf('14', plain, 121.16/17.35 (( iand ) = ( ^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [iand, '13'])). 121.16/17.35 thf('15', plain, 121.16/17.35 (( iand ) = ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mand @ V_1 @ V_2 ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(iatom, axiom,(( iatom ) = (^[P:( $i > $o )]: ( P )))). 121.16/17.35 thf('16', plain, (( iatom ) = ( ^[P:( $i > $o )]: ( P ) )), 121.16/17.35 inference('simplify_rw_rule', [status(thm)], [iatom])). 121.16/17.35 thf('17', plain, (( iatom ) = ( ^[V_1:( $i > $o )]: ( V_1 ) )), 121.16/17.35 define([status(thm)])). 121.16/17.35 thf(con, conjecture, 121.16/17.35 (ivalid @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b3 ) @ ( iatom @ b0 ) ) @ ( iatom @ a3 ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ 121.16/17.35 ( iatom @ a0 ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ 121.16/17.35 ( iatom @ a1 ) ) @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ 121.16/17.35 ( iatom @ a2 ) ) ) ) ) ) @ 121.16/17.35 ( iatom @ f ) ) @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ 121.16/17.35 ( iatom @ a0 ) ) @ 121.16/17.35 ( iand @ 121.16/17.35 ( iimplies @ 121.16/17.35 ( iimplies @ ( iatom @ b3 ) @ ( iatom @ b0 ) ) @ 121.16/17.35 ( iatom @ a3 ) ) @ 121.16/17.35 ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) @ 121.16/17.35 ( iatom @ f ) ) ))). 121.16/17.35 thf(zf_stmt_0, conjecture, 121.16/17.35 (![X4:$i]: 121.16/17.35 ( ( ( ![X84:$i]: ( ( irel @ X4 @ X84 ) => ( f @ X84 ) ) ) | 121.16/17.35 ( ~( ![X46:$i]: 121.16/17.35 ( ( irel @ X4 @ X46 ) => 121.16/17.35 ( ( ( ![X82:$i]: ( ( irel @ X46 @ X82 ) => ( f @ X82 ) ) ) | 121.16/17.35 ( ~( ![X80:$i]: ( ( irel @ X46 @ X80 ) => ( a0 @ X80 ) ) ) ) ) & 121.16/17.35 ( ( ![X78:$i]: ( ( irel @ X46 @ X78 ) => ( a3 @ X78 ) ) ) | 121.16/17.35 ( ~( ![X72:$i]: 121.16/17.35 ( ( irel @ X46 @ X72 ) => 121.16/17.36 ( ( ![X76:$i]: 121.16/17.36 ( ( irel @ X72 @ X76 ) => ( b0 @ X76 ) ) ) | 121.16/17.36 ( ~( ![X74:$i]: 121.16/17.36 ( ( irel @ X72 @ X74 ) => ( b3 @ X74 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X70:$i]: ( ( irel @ X46 @ X70 ) => ( a0 @ X70 ) ) ) | 121.16/17.36 ( ~( ![X64:$i]: 121.16/17.36 ( ( irel @ X46 @ X64 ) => 121.16/17.36 ( ( ![X68:$i]: 121.16/17.36 ( ( irel @ X64 @ X68 ) => ( a1 @ X68 ) ) ) | 121.16/17.36 ( ~( ![X66:$i]: 121.16/17.36 ( ( irel @ X64 @ X66 ) => ( b0 @ X66 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X62:$i]: ( ( irel @ X46 @ X62 ) => ( a1 @ X62 ) ) ) | 121.16/17.36 ( ~( ![X56:$i]: 121.16/17.36 ( ( irel @ X46 @ X56 ) => 121.16/17.36 ( ( ![X60:$i]: 121.16/17.36 ( ( irel @ X56 @ X60 ) => ( a2 @ X60 ) ) ) | 121.16/17.36 ( ~( ![X58:$i]: 121.16/17.36 ( ( irel @ X56 @ X58 ) => ( b1 @ X58 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X54:$i]: ( ( irel @ X46 @ X54 ) => ( a2 @ X54 ) ) ) | 121.16/17.36 ( ~( ![X48:$i]: 121.16/17.36 ( ( irel @ X46 @ X48 ) => 121.16/17.36 ( ( ![X52:$i]: 121.16/17.36 ( ( irel @ X48 @ X52 ) => ( a3 @ X52 ) ) ) | 121.16/17.36 ( ~( ![X50:$i]: 121.16/17.36 ( ( irel @ X48 @ X50 ) => ( b2 @ X50 ) ) ) ) ) ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X44:$i]: ( ( irel @ X4 @ X44 ) => ( f @ X44 ) ) ) | 121.16/17.36 ( ~( ![X6:$i]: 121.16/17.36 ( ( irel @ X4 @ X6 ) => 121.16/17.36 ( ( ( ![X42:$i]: ( ( irel @ X6 @ X42 ) => ( a2 @ X42 ) ) ) | 121.16/17.36 ( ~( ![X36:$i]: 121.16/17.36 ( ( irel @ X6 @ X36 ) => 121.16/17.36 ( ( ![X40:$i]: 121.16/17.36 ( ( irel @ X36 @ X40 ) => ( a3 @ X40 ) ) ) | 121.16/17.36 ( ~( ![X38:$i]: 121.16/17.36 ( ( irel @ X36 @ X38 ) => ( b2 @ X38 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X34:$i]: ( ( irel @ X6 @ X34 ) => ( a1 @ X34 ) ) ) | 121.16/17.36 ( ~( ![X28:$i]: 121.16/17.36 ( ( irel @ X6 @ X28 ) => 121.16/17.36 ( ( ![X32:$i]: 121.16/17.36 ( ( irel @ X28 @ X32 ) => ( a2 @ X32 ) ) ) | 121.16/17.36 ( ~( ![X30:$i]: 121.16/17.36 ( ( irel @ X28 @ X30 ) => ( b1 @ X30 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X26:$i]: ( ( irel @ X6 @ X26 ) => ( a0 @ X26 ) ) ) | 121.16/17.36 ( ~( ![X20:$i]: 121.16/17.36 ( ( irel @ X6 @ X20 ) => 121.16/17.36 ( ( ![X24:$i]: 121.16/17.36 ( ( irel @ X20 @ X24 ) => ( a1 @ X24 ) ) ) | 121.16/17.36 ( ~( ![X22:$i]: 121.16/17.36 ( ( irel @ X20 @ X22 ) => ( b0 @ X22 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( a3 @ X18 ) ) ) | 121.16/17.36 ( ~( ![X12:$i]: 121.16/17.36 ( ( irel @ X6 @ X12 ) => 121.16/17.36 ( ( ![X16:$i]: 121.16/17.36 ( ( irel @ X12 @ X16 ) => ( b0 @ X16 ) ) ) | 121.16/17.36 ( ~( ![X14:$i]: 121.16/17.36 ( ( irel @ X12 @ X14 ) => ( b3 @ X14 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( f @ X10 ) ) ) | 121.16/17.36 ( ~( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( a0 @ X8 ) ) ) ) ) ) ) ) ) ) ))). 121.16/17.36 thf(zf_stmt_1, negated_conjecture, 121.16/17.36 (~( ![X4:$i]: 121.16/17.36 ( ( ( ![X84:$i]: ( ( irel @ X4 @ X84 ) => ( f @ X84 ) ) ) | 121.16/17.36 ( ~( ![X46:$i]: 121.16/17.36 ( ( irel @ X4 @ X46 ) => 121.16/17.36 ( ( ( ![X82:$i]: ( ( irel @ X46 @ X82 ) => ( f @ X82 ) ) ) | 121.16/17.36 ( ~( ![X80:$i]: ( ( irel @ X46 @ X80 ) => ( a0 @ X80 ) ) ) ) ) & 121.16/17.36 ( ( ![X78:$i]: ( ( irel @ X46 @ X78 ) => ( a3 @ X78 ) ) ) | 121.16/17.36 ( ~( ![X72:$i]: 121.16/17.36 ( ( irel @ X46 @ X72 ) => 121.16/17.36 ( ( ![X76:$i]: 121.16/17.36 ( ( irel @ X72 @ X76 ) => ( b0 @ X76 ) ) ) | 121.16/17.36 ( ~( ![X74:$i]: 121.16/17.36 ( ( irel @ X72 @ X74 ) => ( b3 @ X74 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X70:$i]: ( ( irel @ X46 @ X70 ) => ( a0 @ X70 ) ) ) | 121.16/17.36 ( ~( ![X64:$i]: 121.16/17.36 ( ( irel @ X46 @ X64 ) => 121.16/17.36 ( ( ![X68:$i]: 121.16/17.36 ( ( irel @ X64 @ X68 ) => ( a1 @ X68 ) ) ) | 121.16/17.36 ( ~( ![X66:$i]: 121.16/17.36 ( ( irel @ X64 @ X66 ) => ( b0 @ X66 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X62:$i]: ( ( irel @ X46 @ X62 ) => ( a1 @ X62 ) ) ) | 121.16/17.36 ( ~( ![X56:$i]: 121.16/17.36 ( ( irel @ X46 @ X56 ) => 121.16/17.36 ( ( ![X60:$i]: 121.16/17.36 ( ( irel @ X56 @ X60 ) => ( a2 @ X60 ) ) ) | 121.16/17.36 ( ~( ![X58:$i]: 121.16/17.36 ( ( irel @ X56 @ X58 ) => ( b1 @ X58 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X54:$i]: ( ( irel @ X46 @ X54 ) => ( a2 @ X54 ) ) ) | 121.16/17.36 ( ~( ![X48:$i]: 121.16/17.36 ( ( irel @ X46 @ X48 ) => 121.16/17.36 ( ( ![X52:$i]: 121.16/17.36 ( ( irel @ X48 @ X52 ) => ( a3 @ X52 ) ) ) | 121.16/17.36 ( ~( ![X50:$i]: 121.16/17.36 ( ( irel @ X48 @ X50 ) => ( b2 @ X50 ) ) ) ) ) ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X44:$i]: ( ( irel @ X4 @ X44 ) => ( f @ X44 ) ) ) | 121.16/17.36 ( ~( ![X6:$i]: 121.16/17.36 ( ( irel @ X4 @ X6 ) => 121.16/17.36 ( ( ( ![X42:$i]: ( ( irel @ X6 @ X42 ) => ( a2 @ X42 ) ) ) | 121.16/17.36 ( ~( ![X36:$i]: 121.16/17.36 ( ( irel @ X6 @ X36 ) => 121.16/17.36 ( ( ![X40:$i]: 121.16/17.36 ( ( irel @ X36 @ X40 ) => ( a3 @ X40 ) ) ) | 121.16/17.36 ( ~( ![X38:$i]: 121.16/17.36 ( ( irel @ X36 @ X38 ) => ( b2 @ X38 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X34:$i]: ( ( irel @ X6 @ X34 ) => ( a1 @ X34 ) ) ) | 121.16/17.36 ( ~( ![X28:$i]: 121.16/17.36 ( ( irel @ X6 @ X28 ) => 121.16/17.36 ( ( ![X32:$i]: 121.16/17.36 ( ( irel @ X28 @ X32 ) => ( a2 @ X32 ) ) ) | 121.16/17.36 ( ~( ![X30:$i]: 121.16/17.36 ( ( irel @ X28 @ X30 ) => ( b1 @ X30 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X26:$i]: ( ( irel @ X6 @ X26 ) => ( a0 @ X26 ) ) ) | 121.16/17.36 ( ~( ![X20:$i]: 121.16/17.36 ( ( irel @ X6 @ X20 ) => 121.16/17.36 ( ( ![X24:$i]: 121.16/17.36 ( ( irel @ X20 @ X24 ) => ( a1 @ X24 ) ) ) | 121.16/17.36 ( ~( ![X22:$i]: 121.16/17.36 ( ( irel @ X20 @ X22 ) => ( b0 @ X22 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( a3 @ X18 ) ) ) | 121.16/17.36 ( ~( ![X12:$i]: 121.16/17.36 ( ( irel @ X6 @ X12 ) => 121.16/17.36 ( ( ![X16:$i]: 121.16/17.36 ( ( irel @ X12 @ X16 ) => ( b0 @ X16 ) ) ) | 121.16/17.36 ( ~( ![X14:$i]: 121.16/17.36 ( ( irel @ X12 @ X14 ) => ( b3 @ X14 ) ) ) ) ) ) ) ) ) & 121.16/17.36 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( f @ X10 ) ) ) | 121.16/17.36 ( ~( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( a0 @ X8 ) ) ) ) ) ) ) ) ) ) ) )), 121.16/17.36 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 121.16/17.36 thf(zip_derived_cl2, plain, 121.16/17.36 (~ (((!!) @ (^[Y0 : $i]: 121.16/17.36 (((((((!!) @ (^[Y1 : $i]: (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => 121.16/17.36 (((((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (f @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a0 @ Y2)))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a3 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b0 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b3 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a0 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a1 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b0 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a1 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a2 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b1 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a2 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a3 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b2 @ Y3)))))))))))))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => 121.16/17.36 (((((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a2 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a3 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b2 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a1 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a2 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b1 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a0 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (a1 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b0 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (a3 @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (( 121.16/17.36 (( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b0 @ Y3)))))) | 121.16/17.36 (( 121.16/17.36 (~) @ ( 121.16/17.36 ( 121.16/17.36 (!!) @ ( 121.16/17.36 ^[Y3 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y2 @ 121.16/17.36 Y3) => 121.16/17.36 (b3 @ Y3))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y2 : $i]: 121.16/17.36 (((irel @ Y1 @ 121.16/17.36 Y2) => (f @ 121.16/17.36 Y2)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.36 (( 121.16/17.36 (irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a0 @ Y2))))))))))))))))))))))))))), 121.16/17.36 inference('cnf', [status(esa)], [zf_stmt_1])). 121.16/17.36 thf(zip_derived_cl9, plain, 121.16/17.36 (~ (((((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.36 (((irel @ '#sk1' @ Y0) => 121.16/17.36 (((((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (f @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => (a0 @ Y1)))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a3 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => 121.16/17.36 (((((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b0 @ Y2)))))) | 121.16/17.36 (((~) @ ( 121.16/17.36 ((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b3 @ Y2))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a0 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => 121.16/17.36 (((((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a1 @ Y2)))))) | 121.16/17.36 (((~) @ ( 121.16/17.36 ((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b0 @ Y2))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => 121.16/17.36 (((((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a2 @ Y2)))))) | 121.16/17.36 (((~) @ ( 121.16/17.36 ((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b1 @ Y2))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => 121.16/17.36 (((((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a3 @ Y2)))))) | 121.16/17.36 (((~) @ ( 121.16/17.36 ((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b2 @ Y2)))))))))))))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.36 (((irel @ '#sk1' @ Y0) => 121.16/17.36 (((((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.36 Y1) => 121.16/17.36 (((((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (a3 @ Y2)))))) | 121.16/17.36 (((~) @ ( 121.16/17.36 ((!!) @ ( 121.16/17.36 ^[Y2 : $i]: 121.16/17.36 (((irel @ 121.16/17.36 Y1 @ 121.16/17.36 Y2) => 121.16/17.36 (b2 @ Y2))))))))))))))))))) & 121.16/17.36 (((((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.36 Y1)))))) | 121.16/17.36 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.36 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a3 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1)))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 121.16/17.37 thf(zip_derived_cl10, plain, 121.16/17.37 ((~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a3 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2)))))))))))))))))))))))))))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 121.16/17.37 thf(zip_derived_cl11, plain, 121.16/17.37 ((~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])). 121.16/17.37 thf(zip_derived_cl13, plain, 121.16/17.37 ((~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) 121.16/17.37 | ~ ((($true) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.37 inference('local_rewriting', [status(thm)], [zip_derived_cl11])). 121.16/17.37 thf(zip_derived_cl14, plain, 121.16/17.37 (~ (((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0))))))), 121.16/17.37 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl13])). 121.16/17.37 thf(zip_derived_cl15, plain, 121.16/17.37 (~ (((irel @ '#sk1' @ '#sk2') => (f @ '#sk2')))), 121.16/17.37 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 121.16/17.37 thf(zip_derived_cl17, plain, ( (irel @ '#sk1' @ '#sk2')), 121.16/17.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.37 thf(zip_derived_cl12, plain, 121.16/17.37 (( (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (b0 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a1 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a2 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a3 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2)))))))))))))))))))))))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])). 121.16/17.37 thf(zip_derived_cl16, plain, 121.16/17.37 (![X2 : $i]: 121.16/17.37 ( (((irel @ '#sk1' @ X2) => 121.16/17.37 (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (b0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b3 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b0 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b1 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b2 @ Y1))))))))))))))))))))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (f @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ 121.16/17.37 Y1))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 121.16/17.37 thf(zip_derived_cl19, plain, 121.16/17.37 (![X2 : $i]: 121.16/17.37 (~ (irel @ '#sk1' @ X2) 121.16/17.37 | (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (b0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b3 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b0 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b1 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b2 @ Y1))))))))))))))))))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (f @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ 121.16/17.37 Y1))))))))))))))))))))))), 121.16/17.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 121.16/17.37 thf(zip_derived_cl20, plain, 121.16/17.37 (![X2 : $i]: 121.16/17.37 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 ( 121.16/17.37 ( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (f @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ 121.16/17.37 Y1))))))))))))))))))))) 121.16/17.37 | ~ (irel @ '#sk1' @ X2))), 121.16/17.37 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.16/17.37 thf(zip_derived_cl25, plain, 121.16/17.37 (( ('#form3') 121.16/17.37 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a3 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a2 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (a1 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => 121.16/17.37 (((((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (((irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2)))))) | 121.16/17.37 (((~) @ ( 121.16/17.37 ((!!) @ ( 121.16/17.37 ^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ 121.16/17.37 Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.37 define([status(thm)])). 121.16/17.37 thf(zip_derived_cl27, plain, 121.16/17.37 (( (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ '#sk1' @ Y0) => 121.16/17.37 (((((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a3 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b2 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a2 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b1 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (a1 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b0 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (((((!!) @ (^[Y2 : $i]: 121.16/17.37 (((irel @ Y1 @ 121.16/17.37 Y2) => (b0 @ 121.16/17.37 Y2)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y2 : $i]: 121.16/17.37 (( 121.16/17.37 (irel @ 121.16/17.37 Y1 @ 121.16/17.37 Y2) => 121.16/17.37 (b3 @ Y2))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (f @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => (a0 @ Y1))))))))))))))))) 121.16/17.37 | ('#form3'))), 121.16/17.37 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 121.16/17.37 thf(zip_derived_cl35, plain, 121.16/17.37 (![X2 : $i]: 121.16/17.37 ( (((irel @ '#sk1' @ X2) => 121.16/17.37 (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a3 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b2 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a2 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b1 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (a1 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b0 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.37 (b0 @ Y1)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ 121.16/17.37 Y1) => (b3 @ Y1))))))))))))))))))) & 121.16/17.37 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))))) 121.16/17.37 | ('#form3'))), 121.16/17.37 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 121.16/17.37 thf(zip_derived_cl43, plain, 121.16/17.37 (![X2 : $i]: 121.16/17.37 (~ (irel @ '#sk1' @ X2) 121.16/17.37 | (((((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.37 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.37 (((irel @ X2 @ Y0) => 121.16/17.37 (((((!!) @ (^[Y1 : $i]: 121.16/17.37 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b2 @ Y1))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b1 @ Y1))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b0 @ Y1))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (b0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b3 @ Y1))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 121.16/17.38 thf(zip_derived_cl53, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 121.16/17.38 thf(zip_derived_cl63, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 121.16/17.38 thf(zip_derived_cl74, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (f @ X4))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 121.16/17.38 thf(zip_derived_cl87, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 121.16/17.38 thf(zip_derived_cl100, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk4' @ X2)) => (a0 @ ('#sk4' @ X2)))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl87])). 121.16/17.38 thf(zip_derived_cl118, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (a0 @ ('#sk4' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 121.16/17.38 thf(zip_derived_cl20, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))) 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (f @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ 121.16/17.38 Y1))))))))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.16/17.38 thf(zip_derived_cl25, plain, 121.16/17.38 (( ('#form3') 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (f @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.38 define([status(thm)])). 121.16/17.38 thf(zip_derived_cl28, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 (~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))))))), 121.16/17.38 inference('renaming', [status(thm)], [zip_derived_cl20, zip_derived_cl25])). 121.16/17.38 thf(zip_derived_cl33, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (f @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])). 121.16/17.38 thf(zip_derived_cl40, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (f @ X4))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 121.16/17.38 thf(zip_derived_cl48, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 121.16/17.38 thf(zip_derived_cl58, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk4' @ X2)) => (a0 @ ('#sk4' @ X2)))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 121.16/17.38 thf(zip_derived_cl69, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (a0 @ ('#sk4' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 121.16/17.38 thf(zip_derived_cl161, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ '#sk1' @ X2) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | ~ (a0 @ ('#sk4' @ X2)))), 121.16/17.38 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl69])). 121.16/17.38 thf(zip_derived_cl191, plain, 121.16/17.38 (![X0 : $i]: 121.16/17.38 (~ (a0 @ ('#sk4' @ '#sk2')) | ~ (irel @ '#sk2' @ X0) | (f @ X0))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl161])). 121.16/17.38 thf(zip_derived_cl200, plain, (( (f @ '#sk2') | ~ (a0 @ ('#sk4' @ '#sk2')))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl191])). 121.16/17.38 thf(zip_derived_cl18, plain, (~ (f @ '#sk2')), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.38 thf(zip_derived_cl203, plain, (~ (a0 @ ('#sk4' @ '#sk2'))), 121.16/17.38 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl18])). 121.16/17.38 thf(zip_derived_cl17, plain, ( (irel @ '#sk1' @ '#sk2')), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.38 thf(zip_derived_cl117, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ X2 @ ('#sk4' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 121.16/17.38 thf(zip_derived_cl68, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ X2 @ ('#sk4' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 121.16/17.38 thf(zip_derived_cl170, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ '#sk1' @ X2) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (irel @ X2 @ ('#sk4' @ X2)))), 121.16/17.38 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl68])). 121.16/17.38 thf(zip_derived_cl529, plain, 121.16/17.38 (( (irel @ '#sk1' @ ('#sk4' @ '#sk1')) 121.16/17.38 | (f @ '#sk2') 121.16/17.38 | ~ (irel @ '#sk1' @ '#sk1'))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl170])). 121.16/17.38 thf(zip_derived_cl18, plain, (~ (f @ '#sk2')), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.38 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.38 thf(zip_derived_cl543, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 121.16/17.38 inference('demod', [status(thm)], 121.16/17.38 [zip_derived_cl529, zip_derived_cl18, zip_derived_cl3])). 121.16/17.38 thf(zip_derived_cl51, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (b0 @ Y1))))))))))))))))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 121.16/17.38 thf(zip_derived_cl61, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])). 121.16/17.38 thf(zip_derived_cl72, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (a0 @ X4))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 121.16/17.38 thf(zip_derived_cl85, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 121.16/17.38 thf(zip_derived_cl98, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk6' @ X2)) => 121.16/17.38 (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl85])). 121.16/17.38 thf(zip_derived_cl114, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 121.16/17.38 thf(zip_derived_cl135, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl114])). 121.16/17.38 thf(zip_derived_cl143, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ ('#sk6' @ X2) @ ('#sk10' @ X2)) => (a1 @ ('#sk10' @ X2)))) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 121.16/17.38 thf(zip_derived_cl153, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ ('#sk6' @ X2) @ ('#sk10' @ X2)) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])). 121.16/17.38 thf(zip_derived_cl22, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (b0 @ Y1))))))))))))))))))) 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (f @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ 121.16/17.38 Y1))))))))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.16/17.38 thf(zip_derived_cl25, plain, 121.16/17.38 (( ('#form3') 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (f @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.38 define([status(thm)])). 121.16/17.38 thf(zip_derived_cl30, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 (~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b0 @ Y1))))))))))))))))))))), 121.16/17.38 inference('renaming', [status(thm)], [zip_derived_cl22, zip_derived_cl25])). 121.16/17.38 thf(zip_derived_cl37, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a0 @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 121.16/17.38 thf(zip_derived_cl45, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (a0 @ X4))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 121.16/17.38 thf(zip_derived_cl55, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b0 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 121.16/17.38 thf(zip_derived_cl65, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk6' @ X2)) => 121.16/17.38 (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 121.16/17.38 thf(zip_derived_cl78, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))))))) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 121.16/17.38 thf(zip_derived_cl90, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (a1 @ Y0)))))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl78])). 121.16/17.38 thf(zip_derived_cl103, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ ('#sk6' @ X2) @ ('#sk10' @ X2)) => (a1 @ ('#sk10' @ X2)))) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl90])). 121.16/17.38 thf(zip_derived_cl122, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ ('#sk6' @ X2) @ ('#sk10' @ X2)) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 121.16/17.38 thf(zip_derived_cl177, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (irel @ ('#sk6' @ X2) @ ('#sk10' @ X2)))), 121.16/17.38 inference('clc', [status(thm)], [zip_derived_cl153, zip_derived_cl122])). 121.16/17.38 thf(zip_derived_cl946, plain, 121.16/17.38 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk10' @ '#sk1')) 121.16/17.38 | ~ (irel @ '#sk1' @ '#sk1') 121.16/17.38 | (a0 @ ('#sk4' @ '#sk1')))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl543, zip_derived_cl177])). 121.16/17.38 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.38 thf(zip_derived_cl17, plain, ( (irel @ '#sk1' @ '#sk2')), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.38 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.38 thf(zip_derived_cl161, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ '#sk1' @ X2) 121.16/17.38 | (f @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | ~ (a0 @ ('#sk4' @ X2)))), 121.16/17.38 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl69])). 121.16/17.38 thf(zip_derived_cl192, plain, 121.16/17.38 (![X0 : $i]: 121.16/17.38 (~ (a0 @ ('#sk4' @ '#sk1')) | ~ (irel @ '#sk1' @ X0) | (f @ X0))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl161])). 121.16/17.38 thf(zip_derived_cl209, plain, (( (f @ '#sk2') | ~ (a0 @ ('#sk4' @ '#sk1')))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl192])). 121.16/17.38 thf(zip_derived_cl18, plain, (~ (f @ '#sk2')), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.16/17.38 thf(zip_derived_cl215, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 121.16/17.38 inference('demod', [status(thm)], [zip_derived_cl209, zip_derived_cl18])). 121.16/17.38 thf(zip_derived_cl968, plain, 121.16/17.38 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk10' @ '#sk1'))), 121.16/17.38 inference('demod', [status(thm)], 121.16/17.38 [zip_derived_cl946, zip_derived_cl3, zip_derived_cl215])). 121.16/17.38 thf(zip_derived_cl50, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (b1 @ Y1))))))))))))))))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 121.16/17.38 thf(zip_derived_cl60, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl50])). 121.16/17.38 thf(zip_derived_cl71, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (a1 @ X4))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 121.16/17.38 thf(zip_derived_cl84, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 121.16/17.38 thf(zip_derived_cl97, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk7' @ X2)) => 121.16/17.38 (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))))) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])). 121.16/17.38 thf(zip_derived_cl111, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ X2 @ ('#sk7' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 121.16/17.38 thf(zip_derived_cl23, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (b1 @ Y1))))))))))))))))))) 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 ( 121.16/17.38 ( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (f @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ 121.16/17.38 Y1))))))))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2))), 121.16/17.38 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.16/17.38 thf(zip_derived_cl25, plain, 121.16/17.38 (( ('#form3') 121.16/17.38 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ '#sk1' @ Y0) => 121.16/17.38 (((((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a3 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b2 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a1 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a2 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b1 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a0 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (a1 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => 121.16/17.38 (a3 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => 121.16/17.38 (((((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (((irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b0 @ Y2)))))) | 121.16/17.38 (((~) @ ( 121.16/17.38 ((!!) @ ( 121.16/17.38 ^[Y2 : $i]: 121.16/17.38 (( 121.16/17.38 (irel @ 121.16/17.38 Y1 @ 121.16/17.38 Y2) => 121.16/17.38 (b3 @ Y2))))))))))))))))))) & 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (f @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.16/17.38 define([status(thm)])). 121.16/17.38 thf(zip_derived_cl31, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 (~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ 121.16/17.38 Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ 121.16/17.38 Y1) => (b1 @ Y1))))))))))))))))))))), 121.16/17.38 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl25])). 121.16/17.38 thf(zip_derived_cl38, plain, 121.16/17.38 (![X2 : $i]: 121.16/17.38 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a1 @ Y0)))))) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 121.16/17.38 thf(zip_derived_cl46, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (((irel @ X2 @ X4) => (a1 @ X4))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))))), 121.16/17.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 121.16/17.38 thf(zip_derived_cl56, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ X2 @ Y0) => 121.16/17.38 (((((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (a2 @ Y1)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.38 (((irel @ Y0 @ Y1) => (b1 @ 121.16/17.38 Y1))))))))))))))) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 121.16/17.38 thf(zip_derived_cl66, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (((irel @ X2 @ ('#sk7' @ X2)) => 121.16/17.38 (((((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 121.16/17.38 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.38 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))))) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl56])). 121.16/17.38 thf(zip_derived_cl79, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 ( (irel @ X2 @ ('#sk7' @ X2)) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ ('#form3'))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 121.16/17.38 thf(zip_derived_cl167, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a1 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4) 121.16/17.38 | (irel @ X2 @ ('#sk7' @ X2)))), 121.16/17.38 inference('clc', [status(thm)], [zip_derived_cl111, zip_derived_cl79])). 121.16/17.38 thf(zip_derived_cl988, plain, 121.16/17.38 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk7' @ ('#sk6' @ '#sk1'))) 121.16/17.38 | (a1 @ ('#sk10' @ '#sk1')) 121.16/17.38 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')))), 121.16/17.38 inference('sup-', [status(thm)], [zip_derived_cl968, zip_derived_cl167])). 121.16/17.38 thf(zip_derived_cl543, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 121.16/17.38 inference('demod', [status(thm)], 121.16/17.38 [zip_derived_cl529, zip_derived_cl18, zip_derived_cl3])). 121.16/17.38 thf(zip_derived_cl154, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (a1 @ ('#sk10' @ X2)) 121.16/17.38 | ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])). 121.16/17.38 thf(zip_derived_cl123, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (a1 @ ('#sk10' @ X2)) 121.16/17.38 | ~ ('#form3') 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ X2 @ X4))), 121.16/17.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 121.16/17.38 thf(zip_derived_cl164, plain, 121.16/17.38 (![X2 : $i, X4 : $i]: 121.16/17.38 (~ (irel @ X2 @ X4) 121.16/17.38 | (a0 @ X4) 121.16/17.38 | ~ (irel @ '#sk1' @ X2) 121.16/17.38 | ~ (a1 @ ('#sk10' @ X2)))), 121.16/17.39 inference('clc', [status(thm)], [zip_derived_cl154, zip_derived_cl123])). 121.16/17.39 thf(zip_derived_cl560, plain, 121.16/17.39 ((~ (a1 @ ('#sk10' @ '#sk1')) 121.16/17.39 | ~ (irel @ '#sk1' @ '#sk1') 121.16/17.39 | (a0 @ ('#sk4' @ '#sk1')))), 121.16/17.39 inference('sup-', [status(thm)], [zip_derived_cl543, zip_derived_cl164])). 121.16/17.39 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.39 thf(zip_derived_cl215, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], [zip_derived_cl209, zip_derived_cl18])). 121.16/17.39 thf(zip_derived_cl590, plain, (~ (a1 @ ('#sk10' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl560, zip_derived_cl3, zip_derived_cl215])). 121.16/17.39 thf(zip_derived_cl543, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl529, zip_derived_cl18, zip_derived_cl3])). 121.16/17.39 thf(zip_derived_cl113, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (irel @ X2 @ ('#sk6' @ X2)) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a0 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 121.16/17.39 thf(zip_derived_cl77, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (irel @ X2 @ ('#sk6' @ X2)) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a0 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ~ ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 121.16/17.39 thf(zip_derived_cl168, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a0 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (irel @ X2 @ ('#sk6' @ X2)))), 121.16/17.39 inference('clc', [status(thm)], [zip_derived_cl113, zip_derived_cl77])). 121.16/17.39 thf(zip_derived_cl556, plain, 121.16/17.39 (( (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.16/17.39 | (a0 @ ('#sk4' @ '#sk1')) 121.16/17.39 | ~ (irel @ '#sk1' @ '#sk1'))), 121.16/17.39 inference('sup-', [status(thm)], [zip_derived_cl543, zip_derived_cl168])). 121.16/17.39 thf(zip_derived_cl215, plain, (~ (a0 @ ('#sk4' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], [zip_derived_cl209, zip_derived_cl18])). 121.16/17.39 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.16/17.39 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.16/17.39 thf(zip_derived_cl1011, plain, 121.16/17.39 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk7' @ ('#sk6' @ '#sk1')))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl988, zip_derived_cl590, zip_derived_cl586])). 121.16/17.39 thf(trans_axiom, axiom, 121.16/17.39 (![X:$i,Y:$i,Z:$i]: 121.16/17.39 ( ( ( irel @ X @ Y ) & ( irel @ Y @ Z ) ) => ( irel @ X @ Z ) ))). 121.16/17.39 thf(zip_derived_cl0, plain, 121.16/17.39 ( (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((!!) @ (^[Y2 : $i]: 121.16/17.39 (((((irel @ Y0 @ Y1) & (irel @ 121.16/17.39 Y1 @ Y2))) => 121.16/17.39 (irel @ Y0 @ Y2))))))))))))), 121.16/17.39 inference('cnf', [status(esa)], [trans_axiom])). 121.16/17.39 thf(zip_derived_cl4, plain, 121.16/17.39 (![X2 : $i]: 121.16/17.39 (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((((irel @ X2 @ Y0) & (irel @ Y0 @ Y1))) => 121.16/17.39 (irel @ X2 @ Y1)))))))))), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 121.16/17.39 thf(zip_derived_cl5, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((((irel @ X2 @ X4) & (irel @ X4 @ Y0))) => (irel @ 121.16/17.39 X2 @ Y0))))))), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 121.16/17.39 thf(zip_derived_cl6, plain, 121.16/17.39 (![X2 : $i, X4 : $i, X6 : $i]: 121.16/17.39 (((((irel @ X2 @ X4) & (irel @ X4 @ X6))) => (irel @ X2 @ X6)))), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 121.16/17.39 thf(zip_derived_cl7, plain, 121.16/17.39 (![X2 : $i, X4 : $i, X6 : $i]: 121.16/17.39 (~ (((irel @ X2 @ X4) & (irel @ X4 @ X6))) | (irel @ X2 @ X6))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 121.16/17.39 thf(zip_derived_cl8, plain, 121.16/17.39 (![X2 : $i, X4 : $i, X6 : $i]: 121.16/17.39 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 121.16/17.39 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 121.16/17.39 thf(zip_derived_cl1350, plain, 121.16/17.39 (![X0 : $i]: 121.16/17.39 ( (irel @ ('#sk6' @ '#sk1') @ X0) 121.16/17.39 | ~ (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ X0))), 121.16/17.39 inference('sup-', [status(thm)], [zip_derived_cl1011, zip_derived_cl8])). 121.16/17.39 thf(zip_derived_cl968, plain, 121.16/17.39 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk10' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl946, zip_derived_cl3, zip_derived_cl215])). 121.16/17.39 thf(zip_derived_cl112, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 121.16/17.39 thf(zip_derived_cl133, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) 121.16/17.39 | ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4))), 121.16/17.39 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl112])). 121.16/17.39 thf(zip_derived_cl141, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((irel @ ('#sk7' @ X2) @ ('#sk11' @ X2)) => (a2 @ ('#sk11' @ X2)))) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl133])). 121.16/17.39 thf(zip_derived_cl150, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (irel @ ('#sk7' @ X2) @ ('#sk11' @ X2)) 121.16/17.39 | ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl141])). 121.16/17.39 thf(zip_derived_cl80, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk7' @ X2) @ Y0) => (b1 @ Y0)))))))))) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ~ ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl66])). 121.16/17.39 thf(zip_derived_cl92, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk7' @ X2) @ Y0) => (a2 @ Y0)))))) 121.16/17.39 | ~ ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4))), 121.16/17.39 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 121.16/17.39 thf(zip_derived_cl105, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((irel @ ('#sk7' @ X2) @ ('#sk11' @ X2)) => (a2 @ ('#sk11' @ X2)))) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ~ ('#form3'))), 121.16/17.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl92])). 121.16/17.39 thf(zip_derived_cl125, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (irel @ ('#sk7' @ X2) @ ('#sk11' @ X2)) 121.16/17.39 | ~ ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 121.16/17.39 thf(zip_derived_cl176, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (irel @ X2 @ X4) 121.16/17.39 | (a1 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (irel @ ('#sk7' @ X2) @ ('#sk11' @ X2)))), 121.16/17.39 inference('clc', [status(thm)], [zip_derived_cl150, zip_derived_cl125])). 121.16/17.39 thf(zip_derived_cl983, plain, 121.16/17.39 (( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk11' @ ('#sk6' @ '#sk1'))) 121.16/17.39 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.16/17.39 | (a1 @ ('#sk10' @ '#sk1')))), 121.16/17.39 inference('sup-', [status(thm)], [zip_derived_cl968, zip_derived_cl176])). 121.16/17.39 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.16/17.39 thf(zip_derived_cl590, plain, (~ (a1 @ ('#sk10' @ '#sk1'))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl560, zip_derived_cl3, zip_derived_cl215])). 121.16/17.39 thf(zip_derived_cl1006, plain, 121.16/17.39 ( (irel @ ('#sk7' @ ('#sk6' @ '#sk1')) @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.16/17.39 inference('demod', [status(thm)], 121.16/17.39 [zip_derived_cl983, zip_derived_cl586, zip_derived_cl590])). 121.16/17.39 thf(zip_derived_cl13811, plain, 121.16/17.39 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.16/17.39 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl1006])). 121.16/17.39 thf(zip_derived_cl49, plain, 121.16/17.39 (![X2 : $i]: 121.16/17.39 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ X2 @ Y0) => 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (a3 @ 121.16/17.39 Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (b2 @ Y1))))))))))))))))))) 121.16/17.39 | ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2))), 121.16/17.39 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 121.16/17.39 thf(zip_derived_cl59, plain, 121.16/17.39 (![X2 : $i]: 121.16/17.39 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) 121.16/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ X2 @ Y0) => 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.16/17.39 Y1))))))))))))))) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl49])). 121.16/17.39 thf(zip_derived_cl70, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (((irel @ X2 @ X4) => (a2 @ X4))) 121.16/17.39 | ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ X2 @ Y0) => 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.16/17.39 Y1))))))))))))))))), 121.16/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl59])). 121.16/17.39 thf(zip_derived_cl83, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (irel @ X2 @ X4) 121.16/17.39 | (a2 @ X4) 121.16/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ X2 @ Y0) => 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.16/17.39 Y1))))))))))))))) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 121.16/17.39 thf(zip_derived_cl96, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 (~ (((irel @ X2 @ ('#sk8' @ X2)) => 121.16/17.39 (((((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ ('#sk8' @ X2) @ Y0) => (b2 @ Y0)))))))))))) 121.16/17.39 | ('#form3') 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | (a2 @ X4) 121.16/17.39 | ~ (irel @ X2 @ X4))), 121.16/17.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 121.16/17.39 thf(zip_derived_cl109, plain, 121.16/17.39 (![X2 : $i, X4 : $i]: 121.16/17.39 ( (irel @ X2 @ ('#sk8' @ X2)) 121.16/17.39 | ~ (irel @ X2 @ X4) 121.16/17.39 | (a2 @ X4) 121.16/17.39 | ~ (irel @ '#sk1' @ X2) 121.16/17.39 | ('#form3'))), 121.16/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 121.16/17.39 thf(zip_derived_cl24, plain, 121.16/17.39 (![X2 : $i]: 121.16/17.39 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ X2 @ Y0) => 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => (a3 @ 121.16/17.39 Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (b2 @ Y1))))))))))))))))))) 121.16/17.39 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ '#sk1' @ Y0) => 121.16/17.39 (((((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a2 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 ( 121.16/17.39 ( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (a3 @ Y2)))))) | 121.16/17.39 (((~) @ ( 121.16/17.39 ((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b2 @ Y2))))))))))))))))))) & 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a1 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 ( 121.16/17.39 ( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (a2 @ Y2)))))) | 121.16/17.39 (((~) @ ( 121.16/17.39 ((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b1 @ Y2))))))))))))))))))) & 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a0 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 ( 121.16/17.39 ( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (a1 @ Y2)))))) | 121.16/17.39 (((~) @ ( 121.16/17.39 ((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b0 @ Y2))))))))))))))))))) & 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a3 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 ( 121.16/17.39 ( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b0 @ Y2)))))) | 121.16/17.39 (((~) @ ( 121.16/17.39 ((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b3 @ Y2))))))))))))))))))) & 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (f @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => (a0 @ 121.16/17.39 Y1))))))))))))))))))))) 121.16/17.39 | ~ (irel @ '#sk1' @ X2))), 121.16/17.39 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.16/17.39 thf(zip_derived_cl25, plain, 121.16/17.39 (( ('#form3') 121.16/17.39 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.16/17.39 (((irel @ '#sk1' @ Y0) => 121.16/17.39 (((((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a2 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (((irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (a3 @ Y2)))))) | 121.16/17.39 (((~) @ ( 121.16/17.39 ((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.16/17.39 (( 121.16/17.39 (irel @ 121.16/17.39 Y1 @ 121.16/17.39 Y2) => 121.16/17.39 (b2 @ Y2))))))))))))))))))) & 121.16/17.39 (((((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ Y1) => 121.16/17.39 (a1 @ Y1)))))) | 121.16/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.16/17.39 (((irel @ Y0 @ 121.16/17.39 Y1) => 121.16/17.39 (((((!!) @ ( 121.16/17.39 ^[Y2 : $i]: 121.84/17.39 (((irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (a2 @ Y2)))))) | 121.84/17.39 (((~) @ ( 121.84/17.39 ((!!) @ ( 121.84/17.39 ^[Y2 : $i]: 121.84/17.39 (( 121.84/17.39 (irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (b1 @ Y2))))))))))))))))))) & 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => 121.84/17.39 (a0 @ Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ 121.84/17.39 Y1) => 121.84/17.39 (((((!!) @ ( 121.84/17.39 ^[Y2 : $i]: 121.84/17.39 (((irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (a1 @ Y2)))))) | 121.84/17.39 (((~) @ ( 121.84/17.39 ((!!) @ ( 121.84/17.39 ^[Y2 : $i]: 121.84/17.39 (( 121.84/17.39 (irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (b0 @ Y2))))))))))))))))))) & 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => 121.84/17.39 (a3 @ Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ 121.84/17.39 Y1) => 121.84/17.39 (((((!!) @ ( 121.84/17.39 ^[Y2 : $i]: 121.84/17.39 (((irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (b0 @ Y2)))))) | 121.84/17.39 (((~) @ ( 121.84/17.39 ((!!) @ ( 121.84/17.39 ^[Y2 : $i]: 121.84/17.39 (( 121.84/17.39 (irel @ 121.84/17.39 Y1 @ 121.84/17.39 Y2) => 121.84/17.39 (b3 @ Y2))))))))))))))))))) & 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (f @ 121.84/17.39 Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ 121.84/17.39 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.84/17.39 define([status(thm)])). 121.84/17.39 thf(zip_derived_cl32, plain, 121.84/17.39 (![X2 : $i]: 121.84/17.39 (~ ('#form3') 121.84/17.39 | ~ (irel @ '#sk1' @ X2) 121.84/17.39 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.39 (((irel @ X2 @ Y0) => 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (a3 @ 121.84/17.39 Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ 121.84/17.39 Y1) => (b2 @ Y1))))))))))))))))))))), 121.84/17.39 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl25])). 121.84/17.39 thf(zip_derived_cl39, plain, 121.84/17.39 (![X2 : $i]: 121.84/17.39 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a2 @ Y0)))))) 121.84/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.39 (((irel @ X2 @ Y0) => 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.84/17.39 Y1))))))))))))))) 121.84/17.39 | ~ (irel @ '#sk1' @ X2) 121.84/17.39 | ~ ('#form3'))), 121.84/17.39 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 121.84/17.39 thf(zip_derived_cl47, plain, 121.84/17.39 (![X2 : $i, X4 : $i]: 121.84/17.39 ( (((irel @ X2 @ X4) => (a2 @ X4))) 121.84/17.39 | ~ ('#form3') 121.84/17.39 | ~ (irel @ '#sk1' @ X2) 121.84/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.39 (((irel @ X2 @ Y0) => 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.84/17.39 Y1))))))))))))))))), 121.84/17.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 121.84/17.39 thf(zip_derived_cl57, plain, 121.84/17.39 (![X2 : $i, X4 : $i]: 121.84/17.39 (~ (irel @ X2 @ X4) 121.84/17.39 | (a2 @ X4) 121.84/17.39 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.39 (((irel @ X2 @ Y0) => 121.84/17.39 (((((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (a3 @ Y1)))))) | 121.84/17.39 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.39 (((irel @ Y0 @ Y1) => (b2 @ 121.84/17.39 Y1))))))))))))))) 121.84/17.39 | ~ (irel @ '#sk1' @ X2) 121.84/17.39 | ~ ('#form3'))), 121.84/17.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 121.84/17.39 thf(zip_derived_cl67, plain, 121.84/17.39 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ X2 @ ('#sk8' @ X2)) => 121.84/17.40 (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (b2 @ Y0)))))))))))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 121.84/17.40 thf(zip_derived_cl81, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ X2 @ ('#sk8' @ X2)) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 121.84/17.40 thf(zip_derived_cl166, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (irel @ X2 @ ('#sk8' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl109, zip_derived_cl81])). 121.84/17.40 thf(zip_derived_cl13961, plain, 121.84/17.40 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk8' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | (a2 @ ('#sk11' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl13811, zip_derived_cl166])). 121.84/17.40 thf(zip_derived_cl968, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk10' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl946, zip_derived_cl3, zip_derived_cl215])). 121.84/17.40 thf(zip_derived_cl151, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (a2 @ ('#sk11' @ X2)) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a1 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl141])). 121.84/17.40 thf(zip_derived_cl126, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (a2 @ ('#sk11' @ X2)) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a1 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 121.84/17.40 thf(zip_derived_cl163, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a1 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ (a2 @ ('#sk11' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl151, zip_derived_cl126])). 121.84/17.40 thf(zip_derived_cl992, plain, 121.84/17.40 ((~ (a2 @ ('#sk11' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.84/17.40 | (a1 @ ('#sk10' @ '#sk1')))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl968, zip_derived_cl163])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl590, plain, (~ (a1 @ ('#sk10' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl560, zip_derived_cl3, zip_derived_cl215])). 121.84/17.40 thf(zip_derived_cl1015, plain, (~ (a2 @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl992, zip_derived_cl586, zip_derived_cl590])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl13988, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk8' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl13961, zip_derived_cl1015, zip_derived_cl586])). 121.84/17.40 thf(zip_derived_cl8, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 121.84/17.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 121.84/17.40 thf(zip_derived_cl14331, plain, 121.84/17.40 (![X0 : $i]: 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ X0) 121.84/17.40 | ~ (irel @ ('#sk8' @ ('#sk6' @ '#sk1')) @ X0))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl13988, zip_derived_cl8])). 121.84/17.40 thf(zip_derived_cl13811, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl1006])). 121.84/17.40 thf(zip_derived_cl110, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (b2 @ Y0)))))))))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 121.84/17.40 thf(zip_derived_cl131, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl110])). 121.84/17.40 thf(zip_derived_cl139, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ ('#sk8' @ X2) @ ('#sk12' @ X2)) => (a3 @ ('#sk12' @ X2)))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 121.84/17.40 thf(zip_derived_cl147, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ ('#sk8' @ X2) @ ('#sk12' @ X2)) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 121.84/17.40 thf(zip_derived_cl82, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk8' @ X2) @ Y0) => (b2 @ Y0)))))))))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 121.84/17.40 thf(zip_derived_cl94, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk8' @ X2) @ Y0) => (a3 @ Y0)))))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl82])). 121.84/17.40 thf(zip_derived_cl107, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ ('#sk8' @ X2) @ ('#sk12' @ X2)) => (a3 @ ('#sk12' @ X2)))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl94])). 121.84/17.40 thf(zip_derived_cl128, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ ('#sk8' @ X2) @ ('#sk12' @ X2)) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 121.84/17.40 thf(zip_derived_cl175, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (irel @ ('#sk8' @ X2) @ ('#sk12' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl147, zip_derived_cl128])). 121.84/17.40 thf(zip_derived_cl13956, plain, 121.84/17.40 (( (irel @ ('#sk8' @ ('#sk6' @ '#sk1')) @ ('#sk12' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.84/17.40 | (a2 @ ('#sk11' @ ('#sk6' @ '#sk1'))))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl13811, zip_derived_cl175])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl1015, plain, (~ (a2 @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl992, zip_derived_cl586, zip_derived_cl590])). 121.84/17.40 thf(zip_derived_cl13983, plain, 121.84/17.40 ( (irel @ ('#sk8' @ ('#sk6' @ '#sk1')) @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl13956, zip_derived_cl586, zip_derived_cl1015])). 121.84/17.40 thf(zip_derived_cl29801, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup+', [status(thm)], 121.84/17.40 [zip_derived_cl14331, zip_derived_cl13983])). 121.84/17.40 thf(zip_derived_cl52, plain, 121.84/17.40 (![X2 : $i]: 121.84/17.40 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ 121.84/17.40 Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (b3 @ Y1))))))))))))))))))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2))), 121.84/17.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl43])). 121.84/17.40 thf(zip_derived_cl62, plain, 121.84/17.40 (![X2 : $i]: 121.84/17.40 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 121.84/17.40 thf(zip_derived_cl73, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (((irel @ X2 @ X4) => (a3 @ X4))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))))), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 121.84/17.40 thf(zip_derived_cl86, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 121.84/17.40 thf(zip_derived_cl99, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ X2 @ ('#sk5' @ X2)) => 121.84/17.40 (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b3 @ Y0)))))))))))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl86])). 121.84/17.40 thf(zip_derived_cl116, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b3 @ Y0)))))))))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 121.84/17.40 thf(zip_derived_cl137, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])). 121.84/17.40 thf(zip_derived_cl145, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ ('#sk5' @ X2) @ ('#sk9' @ X2)) => (b0 @ ('#sk9' @ X2)))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl137])). 121.84/17.40 thf(zip_derived_cl156, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ ('#sk5' @ X2) @ ('#sk9' @ X2)) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl145])). 121.84/17.40 thf(zip_derived_cl21, plain, 121.84/17.40 (![X2 : $i]: 121.84/17.40 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ 121.84/17.40 Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (b3 @ Y1))))))))))))))))))) 121.84/17.40 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ '#sk1' @ Y0) => 121.84/17.40 (((((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a2 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 ( 121.84/17.40 ( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a3 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b2 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a1 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 ( 121.84/17.40 ( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a2 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b1 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 ( 121.84/17.40 ( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a1 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b0 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a3 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 ( 121.84/17.40 ( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b0 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b3 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (f @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => (a0 @ 121.84/17.40 Y1))))))))))))))))))))) 121.84/17.40 | ~ (irel @ '#sk1' @ X2))), 121.84/17.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 121.84/17.40 thf(zip_derived_cl25, plain, 121.84/17.40 (( ('#form3') 121.84/17.40 | ~ (((((!!) @ (^[Y0 : $i]: (((irel @ '#sk1' @ Y0) => (f @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ '#sk1' @ Y0) => 121.84/17.40 (((((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a2 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (((irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a3 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b2 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a1 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (((irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a2 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b1 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (((irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (a1 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b0 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => 121.84/17.40 (a3 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => 121.84/17.40 (((((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (((irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b0 @ Y2)))))) | 121.84/17.40 (((~) @ ( 121.84/17.40 ((!!) @ ( 121.84/17.40 ^[Y2 : $i]: 121.84/17.40 (( 121.84/17.40 (irel @ 121.84/17.40 Y1 @ 121.84/17.40 Y2) => 121.84/17.40 (b3 @ Y2))))))))))))))))))) & 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (f @ 121.84/17.40 Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => (a0 @ Y1))))))))))))))))))))))), 121.84/17.40 define([status(thm)])). 121.84/17.40 thf(zip_derived_cl29, plain, 121.84/17.40 (![X2 : $i]: 121.84/17.40 (~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ 121.84/17.40 Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ 121.84/17.40 Y1) => (b3 @ Y1))))))))))))))))))))), 121.84/17.40 inference('renaming', [status(thm)], [zip_derived_cl21, zip_derived_cl25])). 121.84/17.40 thf(zip_derived_cl36, plain, 121.84/17.40 (![X2 : $i]: 121.84/17.40 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (a3 @ Y0)))))) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 121.84/17.40 thf(zip_derived_cl44, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (((irel @ X2 @ X4) => (a3 @ X4))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))))), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])). 121.84/17.40 thf(zip_derived_cl54, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ X2 @ Y0) => 121.84/17.40 (((((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b0 @ Y1)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y1 : $i]: 121.84/17.40 (((irel @ Y0 @ Y1) => (b3 @ 121.84/17.40 Y1))))))))))))))) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 121.84/17.40 thf(zip_derived_cl64, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ X2 @ ('#sk5' @ X2)) => 121.84/17.40 (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b3 @ Y0)))))))))))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 121.84/17.40 thf(zip_derived_cl76, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) | 121.84/17.40 (((~) @ (((!!) @ (^[Y0 : $i]: 121.84/17.40 (((irel @ ('#sk5' @ X2) @ Y0) => (b3 @ Y0)))))))))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 121.84/17.40 thf(zip_derived_cl88, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk5' @ X2) @ Y0) => (b0 @ Y0)))))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl76])). 121.84/17.40 thf(zip_derived_cl101, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (((irel @ ('#sk5' @ X2) @ ('#sk9' @ X2)) => (b0 @ ('#sk9' @ X2)))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl88])). 121.84/17.40 thf(zip_derived_cl119, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ ('#sk5' @ X2) @ ('#sk9' @ X2)) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 121.84/17.40 thf(zip_derived_cl178, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (irel @ ('#sk5' @ X2) @ ('#sk9' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl156, zip_derived_cl119])). 121.84/17.40 thf(zip_derived_cl37908, plain, 121.84/17.40 (( (irel @ ('#sk5' @ ('#sk6' @ '#sk1')) @ ('#sk9' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.84/17.40 | (a3 @ ('#sk12' @ ('#sk6' @ '#sk1'))))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl29801, zip_derived_cl178])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl13811, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup+', [status(thm)], [zip_derived_cl1350, zip_derived_cl1006])). 121.84/17.40 thf(zip_derived_cl148, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (a3 @ ('#sk12' @ X2)) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 121.84/17.40 thf(zip_derived_cl129, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (a3 @ ('#sk12' @ X2)) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 121.84/17.40 thf(zip_derived_cl162, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a2 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ (a3 @ ('#sk12' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl148, zip_derived_cl129])). 121.84/17.40 thf(zip_derived_cl13965, plain, 121.84/17.40 ((~ (a3 @ ('#sk12' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.84/17.40 | (a2 @ ('#sk11' @ ('#sk6' @ '#sk1'))))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl13811, zip_derived_cl162])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl1015, plain, (~ (a2 @ ('#sk11' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl992, zip_derived_cl586, zip_derived_cl590])). 121.84/17.40 thf(zip_derived_cl13992, plain, (~ (a3 @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl13965, zip_derived_cl586, zip_derived_cl1015])). 121.84/17.40 thf(zip_derived_cl37943, plain, 121.84/17.40 ( (irel @ ('#sk5' @ ('#sk6' @ '#sk1')) @ ('#sk9' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl37908, zip_derived_cl586, zip_derived_cl13992])). 121.84/17.40 thf(zip_derived_cl29801, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup+', [status(thm)], 121.84/17.40 [zip_derived_cl14331, zip_derived_cl13983])). 121.84/17.40 thf(zip_derived_cl115, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ X2 @ ('#sk5' @ X2)) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 121.84/17.40 thf(zip_derived_cl75, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (irel @ X2 @ ('#sk5' @ X2)) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 121.84/17.40 thf(zip_derived_cl169, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (irel @ X2 @ ('#sk5' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl115, zip_derived_cl75])). 121.84/17.40 thf(zip_derived_cl37913, plain, 121.84/17.40 (( (irel @ ('#sk6' @ '#sk1') @ ('#sk5' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | (a3 @ ('#sk12' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl29801, zip_derived_cl169])). 121.84/17.40 thf(zip_derived_cl13992, plain, (~ (a3 @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl13965, zip_derived_cl586, zip_derived_cl1015])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl37948, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk5' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl37913, zip_derived_cl13992, zip_derived_cl586])). 121.84/17.40 thf(zip_derived_cl8, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 121.84/17.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 121.84/17.40 thf(zip_derived_cl38269, plain, 121.84/17.40 (![X0 : $i]: 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ X0) 121.84/17.40 | ~ (irel @ ('#sk5' @ ('#sk6' @ '#sk1')) @ X0))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl37948, zip_derived_cl8])). 121.84/17.40 thf(zip_derived_cl45249, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk9' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup-', [status(thm)], 121.84/17.40 [zip_derived_cl37943, zip_derived_cl38269])). 121.84/17.40 thf(zip_derived_cl136, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl114])). 121.84/17.40 thf(zip_derived_cl144, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 ( (((irel @ ('#sk6' @ X2) @ X6) => (b0 @ X6))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ('#form3'))), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl136])). 121.84/17.40 thf(zip_derived_cl155, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ ('#sk6' @ X2) @ X6) 121.84/17.40 | (b0 @ X6) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 121.84/17.40 thf(zip_derived_cl91, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 ( (((!!) @ (^[Y0 : $i]: (((irel @ ('#sk6' @ X2) @ Y0) => (b0 @ Y0)))))) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl78])). 121.84/17.40 thf(zip_derived_cl104, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 ( (((irel @ ('#sk6' @ X2) @ X6) => (b0 @ X6))) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ ('#form3'))), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl91])). 121.84/17.40 thf(zip_derived_cl124, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ ('#sk6' @ X2) @ X6) 121.84/17.40 | (b0 @ X6) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 121.84/17.40 thf(zip_derived_cl173, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a0 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (b0 @ X6) 121.84/17.40 | ~ (irel @ ('#sk6' @ X2) @ X6))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl155, zip_derived_cl124])). 121.84/17.40 thf(zip_derived_cl45477, plain, 121.84/17.40 (![X0 : $i]: 121.84/17.40 ( (b0 @ ('#sk9' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ '#sk1') 121.84/17.40 | (a0 @ X0) 121.84/17.40 | ~ (irel @ '#sk1' @ X0))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl45249, zip_derived_cl173])). 121.84/17.40 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.84/17.40 thf(zip_derived_cl45512, plain, 121.84/17.40 (![X0 : $i]: 121.84/17.40 ( (b0 @ ('#sk9' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | (a0 @ X0) 121.84/17.40 | ~ (irel @ '#sk1' @ X0))), 121.84/17.40 inference('demod', [status(thm)], [zip_derived_cl45477, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl29801, plain, 121.84/17.40 ( (irel @ ('#sk6' @ '#sk1') @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('sup+', [status(thm)], 121.84/17.40 [zip_derived_cl14331, zip_derived_cl13983])). 121.84/17.40 thf(zip_derived_cl157, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (b0 @ ('#sk9' @ X2)) 121.84/17.40 | ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl145])). 121.84/17.40 thf(zip_derived_cl120, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (b0 @ ('#sk9' @ X2)) 121.84/17.40 | ~ ('#form3') 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4))), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 121.84/17.40 thf(zip_derived_cl165, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) 121.84/17.40 | (a3 @ X4) 121.84/17.40 | ~ (irel @ '#sk1' @ X2) 121.84/17.40 | ~ (b0 @ ('#sk9' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl157, zip_derived_cl120])). 121.84/17.40 thf(zip_derived_cl37917, plain, 121.84/17.40 ((~ (b0 @ ('#sk9' @ ('#sk6' @ '#sk1'))) 121.84/17.40 | ~ (irel @ '#sk1' @ ('#sk6' @ '#sk1')) 121.84/17.40 | (a3 @ ('#sk12' @ ('#sk6' @ '#sk1'))))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl29801, zip_derived_cl165])). 121.84/17.40 thf(zip_derived_cl586, plain, ( (irel @ '#sk1' @ ('#sk6' @ '#sk1'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl556, zip_derived_cl215, zip_derived_cl3])). 121.84/17.40 thf(zip_derived_cl13992, plain, (~ (a3 @ ('#sk12' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl13965, zip_derived_cl586, zip_derived_cl1015])). 121.84/17.40 thf(zip_derived_cl37952, plain, (~ (b0 @ ('#sk9' @ ('#sk6' @ '#sk1')))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl37917, zip_derived_cl586, zip_derived_cl13992])). 121.84/17.40 thf(zip_derived_cl45706, plain, 121.84/17.40 (![X0 : $i]: (~ (irel @ '#sk1' @ X0) | (a0 @ X0))), 121.84/17.40 inference('clc', [status(thm)], 121.84/17.40 [zip_derived_cl45512, zip_derived_cl37952])). 121.84/17.40 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 121.84/17.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 121.84/17.40 thf(zip_derived_cl170, plain, 121.84/17.40 (![X2 : $i, X4 : $i]: 121.84/17.40 (~ (irel @ '#sk1' @ X2) 121.84/17.40 | (f @ X4) 121.84/17.40 | ~ (irel @ X2 @ X4) 121.84/17.40 | (irel @ X2 @ ('#sk4' @ X2)))), 121.84/17.40 inference('clc', [status(thm)], [zip_derived_cl117, zip_derived_cl68])). 121.84/17.40 thf(zip_derived_cl530, plain, 121.84/17.40 (![X0 : $i]: 121.84/17.40 ( (irel @ X0 @ ('#sk4' @ X0)) | (f @ X0) | ~ (irel @ '#sk1' @ X0))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl170])). 121.84/17.40 thf(zip_derived_cl17, plain, ( (irel @ '#sk1' @ '#sk2')), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.84/17.40 thf(zip_derived_cl8, plain, 121.84/17.40 (![X2 : $i, X4 : $i, X6 : $i]: 121.84/17.40 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 121.84/17.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 121.84/17.40 thf(zip_derived_cl179, plain, 121.84/17.40 (![X0 : $i]: ( (irel @ '#sk1' @ X0) | ~ (irel @ '#sk2' @ X0))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl17, zip_derived_cl8])). 121.84/17.40 thf(zip_derived_cl4657, plain, 121.84/17.40 ((~ (irel @ '#sk1' @ '#sk2') 121.84/17.40 | (f @ '#sk2') 121.84/17.40 | (irel @ '#sk1' @ ('#sk4' @ '#sk2')))), 121.84/17.40 inference('sup-', [status(thm)], [zip_derived_cl530, zip_derived_cl179])). 121.84/17.40 thf(zip_derived_cl17, plain, ( (irel @ '#sk1' @ '#sk2')), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.84/17.40 thf(zip_derived_cl18, plain, (~ (f @ '#sk2')), 121.84/17.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 121.84/17.40 thf(zip_derived_cl4808, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk2'))), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl4657, zip_derived_cl17, zip_derived_cl18])). 121.84/17.40 thf(zip_derived_cl45797, plain, ( (a0 @ ('#sk4' @ '#sk2'))), 121.84/17.40 inference('sup+', [status(thm)], 121.84/17.40 [zip_derived_cl45706, zip_derived_cl4808])). 121.84/17.40 thf(zip_derived_cl46191, plain, ($false), 121.84/17.40 inference('demod', [status(thm)], 121.84/17.40 [zip_derived_cl203, zip_derived_cl45797])). 121.84/17.40 121.84/17.40 % SZS output end Refutation 121.84/17.40 121.84/17.40 121.84/17.40 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 121.84/17.40 % Terminating... 19.36/17.51 % Runner terminated. 19.36/17.56 % Zipperpin 1.5 exiting 19.36/17.58 EOF