0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.uLCRPJhSPH true 0.11/0.32 % Computer : n019.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 04:53:06 EDT 2022 0.11/0.33 % CPUTime : 0.11/0.33 % Running portfolio for 960 s 0.11/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.11/0.33 % Number of cores: 8 0.11/0.33 % Python version: Python 3.6.8 0.11/0.33 % Running in HO mode 0.44/0.62 % Total configuration time : 828 0.44/0.62 % Estimated wc time : 1656 0.44/0.62 % Estimated cpu time (8 cpus) : 207.0 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.51/0.86 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 9.63/1.85 % Solved by lams/30_sp5.sh. 9.63/1.85 % done 929 iterations in 1.062s 9.63/1.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 9.63/1.85 % SZS output start Refutation 9.63/1.85 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf(p2_type, type, p2: $i > $o). 9.63/1.85 thf('#sk1_type', type, '#sk1': $i). 9.63/1.85 thf(p1_type, type, p1: $i > $o). 9.63/1.85 thf('#sk4_type', type, '#sk4': $i > $i). 9.63/1.85 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 9.63/1.85 thf(iimplies_type, type, iimplies: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 9.63/1.85 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf(ior_type, type, ior: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf('#sk3_type', type, '#sk3': $i > $i). 9.63/1.85 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf(ivalid_type, type, ivalid: ($i > $o) > $o). 9.63/1.85 thf(inot_type, type, inot: ($i > $o) > $i > $o). 9.63/1.85 thf(irel_type, type, irel: $i > $i > $o). 9.63/1.85 thf(iatom_type, type, iatom: ($i > $o) > $i > $o). 9.63/1.85 thf(iand_type, type, iand: ($i > $o) > ($i > $o) > $i > $o). 9.63/1.85 thf('#sk2_type', type, '#sk2': $i). 9.63/1.85 thf(refl_axiom, axiom, (![X:$i]: ( irel @ X @ X ))). 9.63/1.85 thf(zip_derived_cl1, plain, ( (((!!) @ (^[Y0 : $i]: (irel @ Y0 @ Y0))))), 9.63/1.85 inference('cnf', [status(esa)], [refl_axiom])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(ivalid, axiom,(( ivalid ) = 9.63/1.85 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 9.63/1.85 thf('0', plain, 9.63/1.85 (( ivalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [ivalid])). 9.63/1.85 thf('1', plain, 9.63/1.85 (( ivalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(iimplies, axiom,(( iimplies ) = 9.63/1.85 (^[P:( $i > $o ),Q:( $i > $o )]: 9.63/1.85 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) )))). 9.63/1.85 thf(mbox_s4, axiom,(( mbox_s4 ) = 9.63/1.85 (^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) )))). 9.63/1.85 thf('2', plain, 9.63/1.85 (( mbox_s4 ) = 9.63/1.85 ( ^[P:( $i > $o ),X:$i]: ( ![Y:$i]: ( ( irel @ X @ Y ) => ( P @ Y ) ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 9.63/1.85 thf('3', plain, 9.63/1.85 (( mbox_s4 ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:$i]: 9.63/1.85 ( ![X4:$i]: ( ( irel @ V_2 @ X4 ) => ( V_1 @ X4 ) ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(mimplies, axiom,(( mimplies ) = 9.63/1.85 (^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V )))). 9.63/1.85 thf(mor, axiom,(( mor ) = 9.63/1.85 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) )))). 9.63/1.85 thf('4', plain, 9.63/1.85 (( mor ) = 9.63/1.85 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) | ( Y @ U ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [mor])). 9.63/1.85 thf('5', plain, 9.63/1.85 (( mor ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 9.63/1.85 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(mnot, axiom,(( mnot ) = (^[X:( $i > $o ),U:$i]: ( ~( X @ U ) )))). 9.63/1.85 thf('6', plain, (( mnot ) = ( ^[X:( $i > $o ),U:$i]: ( ~( X @ U ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [mnot])). 9.63/1.85 thf('7', plain, 9.63/1.85 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf('8', plain, 9.63/1.85 (( mimplies ) = 9.63/1.85 ( ^[U:( $i > $o ),V:( $i > $o )]: ( mor @ ( mnot @ U ) @ V ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [mimplies, '5', '7'])). 9.63/1.85 thf('9', plain, 9.63/1.85 (( mimplies ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf('10', plain, 9.63/1.85 (( iimplies ) = 9.63/1.85 ( ^[P:( $i > $o ),Q:( $i > $o )]: 9.63/1.85 ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [iimplies, '3', '9'])). 9.63/1.85 thf('11', plain, 9.63/1.85 (( iimplies ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 9.63/1.85 ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(ior, axiom,(( ior ) = 9.63/1.85 (^[P:( $i > $o ),Q:( $i > $o )]: 9.63/1.85 ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) )))). 9.63/1.85 thf('12', plain, 9.63/1.85 (( ior ) = 9.63/1.85 ( ^[P:( $i > $o ),Q:( $i > $o )]: 9.63/1.85 ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [ior, '3', '5'])). 9.63/1.85 thf('13', plain, 9.63/1.85 (( ior ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 9.63/1.85 ( mor @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(iand, axiom,(( iand ) = 9.63/1.85 (^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q )))). 9.63/1.85 thf(mand, axiom,(( mand ) = 9.63/1.85 (^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) )))). 9.63/1.85 thf('14', plain, 9.63/1.85 (( mand ) = 9.63/1.85 ( ^[X:( $i > $o ),Y:( $i > $o ),U:$i]: ( ( X @ U ) & ( Y @ U ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [mand])). 9.63/1.85 thf('15', plain, 9.63/1.85 (( mand ) = 9.63/1.85 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 9.63/1.85 ( ( V_1 @ V_3 ) & ( V_2 @ V_3 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf('16', plain, 9.63/1.85 (( iand ) = ( ^[P:( $i > $o ),Q:( $i > $o )]: ( mand @ P @ Q ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [iand, '15'])). 9.63/1.85 thf('17', plain, 9.63/1.85 (( iand ) = ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mand @ V_1 @ V_2 ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(inot, axiom,(( inot ) = (^[P:( $i > $o )]: ( mnot @ ( mbox_s4 @ P ) )))). 9.63/1.85 thf('18', plain, 9.63/1.85 (( inot ) = ( ^[P:( $i > $o )]: ( mnot @ ( mbox_s4 @ P ) ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [inot, '3', '7'])). 9.63/1.85 thf('19', plain, 9.63/1.85 (( inot ) = ( ^[V_1:( $i > $o )]: ( mnot @ ( mbox_s4 @ V_1 ) ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(iatom, axiom,(( iatom ) = (^[P:( $i > $o )]: ( P )))). 9.63/1.85 thf('20', plain, (( iatom ) = ( ^[P:( $i > $o )]: ( P ) )), 9.63/1.85 inference('simplify_rw_rule', [status(thm)], [iatom])). 9.63/1.85 thf('21', plain, (( iatom ) = ( ^[V_1:( $i > $o )]: ( V_1 ) )), 9.63/1.85 define([status(thm)])). 9.63/1.85 thf(pel9, conjecture, 9.63/1.85 (ivalid @ 9.63/1.85 ( iimplies @ 9.63/1.85 ( iand @ 9.63/1.85 ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ 9.63/1.85 ( iand @ 9.63/1.85 ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ 9.63/1.85 ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ 9.63/1.85 ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ))). 9.63/1.85 thf(zf_stmt_0, conjecture, 9.63/1.85 (![X4:$i]: 9.63/1.85 ( ( ![X24:$i]: 9.63/1.85 ( ( irel @ X4 @ X24 ) => 9.63/1.85 ( ~( ![X26:$i]: 9.63/1.85 ( ( irel @ X24 @ X26 ) => 9.63/1.85 ( ( ![X32:$i]: 9.63/1.85 ( ( irel @ X26 @ X32 ) => 9.63/1.85 ( ~( ![X34:$i]: 9.63/1.85 ( ( irel @ X32 @ X34 ) => ( p2 @ X34 ) ) ) ) ) ) | 9.63/1.85 ( ![X28:$i]: 9.63/1.85 ( ( irel @ X26 @ X28 ) => 9.63/1.85 ( ~( ![X30:$i]: 9.63/1.85 ( ( irel @ X28 @ X30 ) => ( p1 @ X30 ) ) ) ) ) ) ) ) ) ) ) ) | 9.63/1.85 ( ~( ![X6:$i]: 9.63/1.85 ( ( irel @ X4 @ X6 ) => 9.63/1.85 ( ( ( ![X20:$i]: 9.63/1.85 ( ( irel @ X6 @ X20 ) => 9.63/1.85 ( ~( ![X22:$i]: ( ( irel @ X20 @ X22 ) => ( p2 @ X22 ) ) ) ) ) ) | 9.63/1.85 ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( p1 @ X18 ) ) ) ) & 9.63/1.85 ( ( ![X16:$i]: ( ( irel @ X6 @ X16 ) => ( p2 @ X16 ) ) ) | 9.63/1.85 ( ![X12:$i]: 9.63/1.85 ( ( irel @ X6 @ X12 ) => 9.63/1.85 ( ~( ![X14:$i]: ( ( irel @ X12 @ X14 ) => ( p1 @ X14 ) ) ) ) ) ) ) & 9.63/1.85 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( p2 @ X10 ) ) ) | 9.63/1.85 ( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( p1 @ X8 ) ) ) ) ) ) ) ) ))). 9.63/1.85 thf(zf_stmt_1, negated_conjecture, 9.63/1.85 (~( ![X4:$i]: 9.63/1.85 ( ( ![X24:$i]: 9.63/1.85 ( ( irel @ X4 @ X24 ) => 9.63/1.85 ( ~( ![X26:$i]: 9.63/1.85 ( ( irel @ X24 @ X26 ) => 9.63/1.85 ( ( ![X32:$i]: 9.63/1.85 ( ( irel @ X26 @ X32 ) => 9.63/1.85 ( ~( ![X34:$i]: 9.63/1.85 ( ( irel @ X32 @ X34 ) => ( p2 @ X34 ) ) ) ) ) ) | 9.63/1.85 ( ![X28:$i]: 9.63/1.85 ( ( irel @ X26 @ X28 ) => 9.63/1.85 ( ~( ![X30:$i]: 9.63/1.85 ( ( irel @ X28 @ X30 ) => ( p1 @ X30 ) ) ) ) ) ) ) ) ) ) ) ) | 9.63/1.85 ( ~( ![X6:$i]: 9.63/1.85 ( ( irel @ X4 @ X6 ) => 9.63/1.85 ( ( ( ![X20:$i]: 9.63/1.85 ( ( irel @ X6 @ X20 ) => 9.63/1.85 ( ~( ![X22:$i]: 9.63/1.85 ( ( irel @ X20 @ X22 ) => ( p2 @ X22 ) ) ) ) ) ) | 9.63/1.85 ( ![X18:$i]: ( ( irel @ X6 @ X18 ) => ( p1 @ X18 ) ) ) ) & 9.63/1.85 ( ( ![X16:$i]: ( ( irel @ X6 @ X16 ) => ( p2 @ X16 ) ) ) | 9.63/1.85 ( ![X12:$i]: 9.63/1.85 ( ( irel @ X6 @ X12 ) => 9.63/1.85 ( ~( ![X14:$i]: 9.63/1.85 ( ( irel @ X12 @ X14 ) => ( p1 @ X14 ) ) ) ) ) ) ) & 9.63/1.85 ( ( ![X10:$i]: ( ( irel @ X6 @ X10 ) => ( p2 @ X10 ) ) ) | 9.63/1.85 ( ![X8:$i]: ( ( irel @ X6 @ X8 ) => ( p1 @ X8 ) ) ) ) ) ) ) ) ) )), 9.63/1.85 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 9.63/1.85 thf(zip_derived_cl2, plain, 9.63/1.85 (~ (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ Y2) => 9.63/1.85 (((((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ Y3) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y4 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y3 @ 9.63/1.85 Y4) => 9.63/1.85 (p2 @ Y4))))))))))))) | 9.63/1.85 (((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ Y3) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y4 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y3 @ 9.63/1.85 Y4) => 9.63/1.85 (p1 @ Y4))))))))))))))))))))))))))) | 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((((((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p2 @ Y3))))))))))))) | 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p1 @ Y2)))))))) & 9.63/1.85 (((((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p2 @ Y2)))))) | 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p1 @ Y3))))))))))))))) & 9.63/1.85 (((((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p2 @ Y2)))))) | 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p1 @ Y2))))))))))))))))))))))), 9.63/1.85 inference('cnf', [status(esa)], [zf_stmt_1])). 9.63/1.85 thf(zip_derived_cl9, plain, 9.63/1.85 (~ (((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk1' @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p2 @ Y3))))))))))))) | 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ ( 9.63/1.85 ((!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (((irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p1 @ Y3))))))))))))))))))))))))))) | 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk1' @ Y0) => 9.63/1.85 (((((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (p2 @ Y2))))))))))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ 9.63/1.85 Y1)))))))) & 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ 9.63/1.85 Y1)))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (p1 @ Y2))))))))))))))) & 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ 9.63/1.85 Y1)))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ 9.63/1.85 Y1)))))))))))))))))))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 9.63/1.85 thf(zip_derived_cl11, plain, 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk1' @ Y0) => 9.63/1.85 (((((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p2 @ Y2))))))))))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) & 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1)))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => (p1 @ Y2))))))))))))))) & 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1)))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1)))))))))))))))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 9.63/1.85 thf(zip_derived_cl13, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 (((irel @ '#sk1' @ X2) => 9.63/1.85 (((((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ 9.63/1.85 Y1))))))))))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))) & 9.63/1.85 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ 9.63/1.85 Y1))))))))))))))) & 9.63/1.85 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0))))))))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 9.63/1.85 thf(zip_derived_cl16, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X2) 9.63/1.85 | (((((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ 9.63/1.85 Y1))))))))))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))) & 9.63/1.85 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ 9.63/1.85 Y1))))))))))))))) & 9.63/1.85 (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))))))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 9.63/1.85 thf(zip_derived_cl18, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1))))))))))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])). 9.63/1.85 thf(zip_derived_cl22, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1))))))))))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl18])). 9.63/1.85 thf(zip_derived_cl26, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (((irel @ X2 @ X4) => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X4 @ Y0) => (p2 @ Y0)))))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 9.63/1.85 thf(zip_derived_cl30, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (irel @ X2 @ X4) 9.63/1.85 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X4 @ Y0) => (p2 @ Y0)))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 9.63/1.85 thf(zip_derived_cl34, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (((irel @ X4 @ ('#sk3' @ X4)) => (p2 @ ('#sk3' @ X4)))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ X2 @ X4))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 9.63/1.85 thf(zip_derived_cl38, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 9.63/1.85 thf(zip_derived_cl44, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => (p1 @ X6))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 9.63/1.85 thf(zip_derived_cl49, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | (p1 @ X6) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 9.63/1.85 thf(zip_derived_cl95, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X1) 9.63/1.85 | ~ (irel @ X1 @ X0) 9.63/1.85 | (irel @ X0 @ ('#sk3' @ X0)) 9.63/1.85 | (p1 @ X0))), 9.63/1.85 inference('eq_fact', [status(thm)], [zip_derived_cl49])). 9.63/1.85 thf(zip_derived_cl375, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 ( (p1 @ X0) | (irel @ X0 @ ('#sk3' @ X0)) | ~ (irel @ '#sk1' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl95])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl10, plain, 9.63/1.85 (~ (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk1' @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ (( 9.63/1.85 (!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p2 @ Y3))))))))))))) | 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (((~) @ (( 9.63/1.85 (!!) @ ( 9.63/1.85 ^[Y3 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y2 @ 9.63/1.85 Y3) => 9.63/1.85 (p1 @ Y3)))))))))))))))))))))))))))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl9])). 9.63/1.85 thf(zip_derived_cl12, plain, 9.63/1.85 (~ (((irel @ '#sk1' @ '#sk2') => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk2' @ Y0) => 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (p2 @ Y2))))))))))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (( 9.63/1.85 (irel @ 9.63/1.85 Y1 @ 9.63/1.85 Y2) => 9.63/1.85 (p1 @ Y2))))))))))))))))))))))))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 9.63/1.85 thf(zip_derived_cl15, plain, 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ '#sk2' @ Y0) => 9.63/1.85 (((((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ Y2) => 9.63/1.85 (p2 @ Y2))))))))))))) | 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => 9.63/1.85 (((~) @ (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((irel @ Y1 @ Y2) => 9.63/1.85 (p1 @ Y2))))))))))))))))))))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(zip_derived_cl17, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 (((irel @ '#sk2' @ X2) => 9.63/1.85 (((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1))))))))))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1)))))))))))))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 9.63/1.85 thf(zip_derived_cl21, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ X2) 9.63/1.85 | (((((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ 9.63/1.85 Y1))))))))))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ 9.63/1.85 Y1))))))))))))))))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 9.63/1.85 thf(zip_derived_cl25, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p2 @ Y1))))))))))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 9.63/1.85 thf(zip_derived_cl29, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (((irel @ X2 @ X4) => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X4 @ Y0) => (p2 @ Y0)))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 9.63/1.85 thf(zip_derived_cl33, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (irel @ X2 @ X4) 9.63/1.85 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X4 @ Y0) => (p2 @ Y0)))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 9.63/1.85 thf(zip_derived_cl37, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (((irel @ X4 @ ('#sk3' @ X4)) => (p2 @ ('#sk3' @ X4)))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ X2 @ X4))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 9.63/1.85 thf(zip_derived_cl42, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 9.63/1.85 thf(zip_derived_cl47, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 9.63/1.85 thf(zip_derived_cl53, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 9.63/1.85 thf(zip_derived_cl55, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (((irel @ X6 @ ('#sk4' @ X6)) => (p1 @ ('#sk4' @ X6)))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X6))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 9.63/1.85 thf(zip_derived_cl57, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (irel @ X6 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 9.63/1.85 thf(zip_derived_cl177, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ X0) 9.63/1.85 | ~ (irel @ X0 @ X1) 9.63/1.85 | (irel @ X1 @ ('#sk3' @ X1)) 9.63/1.85 | (irel @ X0 @ ('#sk4' @ X0)))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl57])). 9.63/1.85 thf(zip_derived_cl860, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 ( (irel @ X0 @ ('#sk4' @ X0)) 9.63/1.85 | (irel @ X0 @ ('#sk3' @ X0)) 9.63/1.85 | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl177])). 9.63/1.85 thf(zip_derived_cl3633, plain, 9.63/1.85 (( (irel @ '#sk2' @ ('#sk3' @ '#sk2')) 9.63/1.85 | (irel @ '#sk2' @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl860])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl19, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])). 9.63/1.85 thf(zip_derived_cl23, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 9.63/1.85 thf(zip_derived_cl27, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (((irel @ X2 @ X4) => (p2 @ X4))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl23])). 9.63/1.85 thf(zip_derived_cl31, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 9.63/1.85 thf(zip_derived_cl35, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ X2 @ X4))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 9.63/1.85 thf(zip_derived_cl40, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 9.63/1.85 thf(zip_derived_cl46, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (((irel @ X6 @ ('#sk4' @ X6)) => (p1 @ ('#sk4' @ X6)))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ X2 @ X6))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 9.63/1.85 thf(zip_derived_cl51, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (irel @ X6 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 9.63/1.85 thf(zip_derived_cl133, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X0) 9.63/1.85 | (p2 @ X1) 9.63/1.85 | ~ (irel @ X0 @ X1) 9.63/1.85 | (irel @ X0 @ ('#sk4' @ X0)))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl51])). 9.63/1.85 thf(zip_derived_cl3692, plain, 9.63/1.85 (( (irel @ '#sk2' @ ('#sk4' @ '#sk2')) 9.63/1.85 | (irel @ '#sk2' @ ('#sk4' @ '#sk2')) 9.63/1.85 | (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | ~ (irel @ '#sk1' @ '#sk2'))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3633, zip_derived_cl133])). 9.63/1.85 thf(zip_derived_cl14, plain, ( (irel @ '#sk1' @ '#sk2')), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl43, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((irel @ X2 @ Y0) => 9.63/1.85 (((~) @ (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((irel @ Y0 @ Y1) => (p1 @ Y1))))))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 9.63/1.85 thf(zip_derived_cl48, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => 9.63/1.85 (((~) @ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))))))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 9.63/1.85 thf(zip_derived_cl54, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | ~ (((!!) @ (^[Y0 : $i]: (((irel @ X6 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 9.63/1.85 thf(zip_derived_cl56, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (((irel @ X6 @ ('#sk4' @ X6)) => (p1 @ ('#sk4' @ X6)))) 9.63/1.85 | ~ (irel @ '#sk2' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X6))), 9.63/1.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 9.63/1.85 thf(zip_derived_cl59, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (irel @ X6 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 9.63/1.85 thf(zip_derived_cl212, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ X0) 9.63/1.85 | ~ (irel @ X0 @ X1) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X1)) 9.63/1.85 | (irel @ X0 @ ('#sk4' @ X0)))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl59])). 9.63/1.85 thf(zip_derived_cl1402, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 ( (irel @ X0 @ ('#sk4' @ X0)) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)) 9.63/1.85 | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl212])). 9.63/1.85 thf(zip_derived_cl14, plain, ( (irel @ '#sk1' @ '#sk2')), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(trans_axiom, axiom, 9.63/1.85 (![X:$i,Y:$i,Z:$i]: 9.63/1.85 ( ( ( irel @ X @ Y ) & ( irel @ Y @ Z ) ) => ( irel @ X @ Z ) ))). 9.63/1.85 thf(zip_derived_cl0, plain, 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((!!) @ (^[Y2 : $i]: 9.63/1.85 (((((irel @ Y0 @ Y1) & (irel @ 9.63/1.85 Y1 @ Y2))) => 9.63/1.85 (irel @ Y0 @ Y2))))))))))))), 9.63/1.85 inference('cnf', [status(esa)], [trans_axiom])). 9.63/1.85 thf(zip_derived_cl4, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((!!) @ (^[Y1 : $i]: 9.63/1.85 (((((irel @ X2 @ Y0) & (irel @ Y0 @ Y1))) => 9.63/1.85 (irel @ X2 @ Y1)))))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 9.63/1.85 thf(zip_derived_cl5, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (((!!) @ (^[Y0 : $i]: 9.63/1.85 (((((irel @ X2 @ X4) & (irel @ X4 @ Y0))) => (irel @ 9.63/1.85 X2 @ Y0))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 9.63/1.85 thf(zip_derived_cl6, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (((((irel @ X2 @ X4) & (irel @ X4 @ X6))) => (irel @ X2 @ X6)))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 9.63/1.85 thf(zip_derived_cl7, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (((irel @ X2 @ X4) & (irel @ X4 @ X6))) | (irel @ X2 @ X6))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 9.63/1.85 thf(zip_derived_cl8, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X4) | ~ (irel @ X4 @ X6) | (irel @ X2 @ X6))), 9.63/1.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl7])). 9.63/1.85 thf(zip_derived_cl61, plain, 9.63/1.85 (![X0 : $i]: ( (irel @ '#sk1' @ X0) | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl8])). 9.63/1.85 thf(zip_derived_cl3214, plain, 9.63/1.85 ((~ (irel @ '#sk2' @ '#sk2') 9.63/1.85 | ~ (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | (irel @ '#sk1' @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl1402, zip_derived_cl61])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl3301, plain, 9.63/1.85 ((~ (p2 @ ('#sk3' @ '#sk2')) | (irel @ '#sk1' @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('demod', [status(thm)], [zip_derived_cl3214, zip_derived_cl3])). 9.63/1.85 thf(zip_derived_cl39, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 9.63/1.85 thf(zip_derived_cl45, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => (p1 @ X6))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl39])). 9.63/1.85 thf(zip_derived_cl50, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | (p1 @ X6) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 9.63/1.85 thf(zip_derived_cl3357, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | ~ (irel @ '#sk1' @ '#sk1') 9.63/1.85 | ~ (irel @ '#sk1' @ X0) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)) 9.63/1.85 | (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3301, zip_derived_cl50])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl14, plain, ( (irel @ '#sk1' @ '#sk2')), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl52, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (p1 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 9.63/1.85 thf(zip_derived_cl149, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X0) 9.63/1.85 | (p2 @ X1) 9.63/1.85 | ~ (irel @ X0 @ X1) 9.63/1.85 | ~ (p1 @ ('#sk4' @ X0)))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl52])). 9.63/1.85 thf(zip_derived_cl446, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (p1 @ ('#sk4' @ '#sk2')) | ~ (irel @ '#sk2' @ X0) | (p2 @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl149])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl58, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (p1 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | (irel @ X4 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 9.63/1.85 thf(zip_derived_cl191, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ X0) 9.63/1.85 | ~ (irel @ X0 @ X1) 9.63/1.85 | (irel @ X1 @ ('#sk3' @ X1)) 9.63/1.85 | ~ (p1 @ ('#sk4' @ X0)))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl58])). 9.63/1.85 thf(zip_derived_cl1126, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (p1 @ ('#sk4' @ '#sk2')) 9.63/1.85 | (irel @ X0 @ ('#sk3' @ X0)) 9.63/1.85 | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl191])). 9.63/1.85 thf(zip_derived_cl2731, plain, 9.63/1.85 (( (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')) 9.63/1.85 | ~ (irel @ '#sk2' @ '#sk2') 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('sup+', [status(thm)], [zip_derived_cl446, zip_derived_cl1126])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl2780, plain, 9.63/1.85 (( (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')) 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('demod', [status(thm)], [zip_derived_cl2731, zip_derived_cl3])). 9.63/1.85 thf(zip_derived_cl2781, plain, 9.63/1.85 ((~ (p1 @ ('#sk4' @ '#sk2')) | (p2 @ ('#sk3' @ '#sk2')))), 9.63/1.85 inference('simplify', [status(thm)], [zip_derived_cl2780])). 9.63/1.85 thf(zip_derived_cl60, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (p1 @ ('#sk4' @ X6)) 9.63/1.85 | ~ (irel @ X2 @ X6) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk2' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 9.63/1.85 thf(zip_derived_cl231, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ '#sk2') 9.63/1.85 | ~ (irel @ '#sk2' @ X0) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)) 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('eq_fact', [status(thm)], [zip_derived_cl60])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl237, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (irel @ '#sk2' @ X0) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)) 9.63/1.85 | ~ (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('demod', [status(thm)], [zip_derived_cl231, zip_derived_cl3])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl239, plain, 9.63/1.85 ((~ (p1 @ ('#sk4' @ '#sk2')) | ~ (p2 @ ('#sk3' @ '#sk2')))), 9.63/1.85 inference('sup+', [status(thm)], [zip_derived_cl237, zip_derived_cl3])). 9.63/1.85 thf(zip_derived_cl2837, plain, (~ (p1 @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('clc', [status(thm)], [zip_derived_cl2781, zip_derived_cl239])). 9.63/1.85 thf(zip_derived_cl3398, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 (~ (p2 @ ('#sk3' @ '#sk2')) 9.63/1.85 | ~ (irel @ '#sk1' @ X0) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)))), 9.63/1.85 inference('demod', [status(thm)], 9.63/1.85 [zip_derived_cl3357, zip_derived_cl3, zip_derived_cl2837])). 9.63/1.85 thf(zip_derived_cl3492, plain, 9.63/1.85 ((~ (p2 @ ('#sk3' @ '#sk2')) | ~ (p2 @ ('#sk3' @ '#sk2')))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl3398])). 9.63/1.85 thf(zip_derived_cl3522, plain, (~ (p2 @ ('#sk3' @ '#sk2'))), 9.63/1.85 inference('simplify', [status(thm)], [zip_derived_cl3492])). 9.63/1.85 thf(zip_derived_cl14, plain, ( (irel @ '#sk1' @ '#sk2')), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(zip_derived_cl3779, plain, 9.63/1.85 (( (irel @ '#sk2' @ ('#sk4' @ '#sk2')) 9.63/1.85 | (irel @ '#sk2' @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('demod', [status(thm)], 9.63/1.85 [zip_derived_cl3692, zip_derived_cl3522, zip_derived_cl14])). 9.63/1.85 thf(zip_derived_cl3780, plain, ( (irel @ '#sk2' @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('simplify', [status(thm)], [zip_derived_cl3779])). 9.63/1.85 thf(zip_derived_cl61, plain, 9.63/1.85 (![X0 : $i]: ( (irel @ '#sk1' @ X0) | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl8])). 9.63/1.85 thf(zip_derived_cl3826, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3780, zip_derived_cl61])). 9.63/1.85 thf(zip_derived_cl3, plain, (![X2 : $i]: (irel @ X2 @ X2)), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 9.63/1.85 thf(zip_derived_cl20, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) | 9.63/1.85 (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])). 9.63/1.85 thf(zip_derived_cl24, plain, 9.63/1.85 (![X2 : $i]: 9.63/1.85 ( (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p2 @ Y0)))))) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 9.63/1.85 thf(zip_derived_cl28, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 ( (((irel @ X2 @ X4) => (p2 @ X4))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 9.63/1.85 thf(zip_derived_cl32, plain, 9.63/1.85 (![X2 : $i, X4 : $i]: 9.63/1.85 (~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | (((!!) @ (^[Y0 : $i]: (((irel @ X2 @ Y0) => (p1 @ Y0)))))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 9.63/1.85 thf(zip_derived_cl36, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 ( (((irel @ X2 @ X6) => (p1 @ X6))) 9.63/1.85 | ~ (irel @ '#sk1' @ X2) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ X2 @ X4))), 9.63/1.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 9.63/1.85 thf(zip_derived_cl41, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | (p1 @ X6) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | (p2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 9.63/1.85 thf(zip_derived_cl74, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X0) | (p2 @ X1) | ~ (irel @ X0 @ X1) | (p1 @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3, zip_derived_cl41])). 9.63/1.85 thf(zip_derived_cl3998, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 ( (p1 @ ('#sk4' @ '#sk2')) 9.63/1.85 | ~ (irel @ ('#sk4' @ '#sk2') @ X0) 9.63/1.85 | (p2 @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3826, zip_derived_cl74])). 9.63/1.85 thf(zip_derived_cl2837, plain, (~ (p1 @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('clc', [status(thm)], [zip_derived_cl2781, zip_derived_cl239])). 9.63/1.85 thf(zip_derived_cl4052, plain, 9.63/1.85 (![X0 : $i]: (~ (irel @ ('#sk4' @ '#sk2') @ X0) | (p2 @ X0))), 9.63/1.85 inference('demod', [status(thm)], 9.63/1.85 [zip_derived_cl3998, zip_derived_cl2837])). 9.63/1.85 thf(zip_derived_cl4151, plain, 9.63/1.85 ((~ (irel @ '#sk1' @ ('#sk4' @ '#sk2')) 9.63/1.85 | (p1 @ ('#sk4' @ '#sk2')) 9.63/1.85 | (p2 @ ('#sk3' @ ('#sk4' @ '#sk2'))))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl375, zip_derived_cl4052])). 9.63/1.85 thf(zip_derived_cl3826, plain, ( (irel @ '#sk1' @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl3780, zip_derived_cl61])). 9.63/1.85 thf(zip_derived_cl2837, plain, (~ (p1 @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('clc', [status(thm)], [zip_derived_cl2781, zip_derived_cl239])). 9.63/1.85 thf(zip_derived_cl14, plain, ( (irel @ '#sk1' @ '#sk2')), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 9.63/1.85 thf(zip_derived_cl50, plain, 9.63/1.85 (![X2 : $i, X4 : $i, X6 : $i]: 9.63/1.85 (~ (irel @ X2 @ X6) 9.63/1.85 | (p1 @ X6) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X4)) 9.63/1.85 | ~ (irel @ X2 @ X4) 9.63/1.85 | ~ (irel @ '#sk1' @ X2))), 9.63/1.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 9.63/1.85 thf(zip_derived_cl115, plain, 9.63/1.85 (![X0 : $i, X1 : $i]: 9.63/1.85 (~ (irel @ '#sk1' @ X1) 9.63/1.85 | ~ (irel @ X1 @ X0) 9.63/1.85 | ~ (p2 @ ('#sk3' @ X0)) 9.63/1.85 | (p1 @ X0))), 9.63/1.85 inference('eq_fact', [status(thm)], [zip_derived_cl50])). 9.63/1.85 thf(zip_derived_cl411, plain, 9.63/1.85 (![X0 : $i]: 9.63/1.85 ( (p1 @ X0) | ~ (p2 @ ('#sk3' @ X0)) | ~ (irel @ '#sk2' @ X0))), 9.63/1.85 inference('sup-', [status(thm)], [zip_derived_cl14, zip_derived_cl115])). 9.63/1.85 thf(zip_derived_cl3780, plain, ( (irel @ '#sk2' @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('simplify', [status(thm)], [zip_derived_cl3779])). 9.63/1.85 thf(zip_derived_cl3842, plain, 9.63/1.85 ((~ (p2 @ ('#sk3' @ ('#sk4' @ '#sk2'))) | (p1 @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('sup+', [status(thm)], [zip_derived_cl411, zip_derived_cl3780])). 9.63/1.85 thf(zip_derived_cl2837, plain, (~ (p1 @ ('#sk4' @ '#sk2'))), 9.63/1.85 inference('clc', [status(thm)], [zip_derived_cl2781, zip_derived_cl239])). 9.63/1.85 thf(zip_derived_cl3866, plain, (~ (p2 @ ('#sk3' @ ('#sk4' @ '#sk2')))), 9.63/1.85 inference('demod', [status(thm)], 9.63/1.85 [zip_derived_cl3842, zip_derived_cl2837])). 9.63/1.85 thf(zip_derived_cl4163, plain, ($false), 9.63/1.85 inference('demod', [status(thm)], 9.63/1.85 [zip_derived_cl4151, zip_derived_cl3826, zip_derived_cl2837, 9.63/1.85 zip_derived_cl3866])). 9.63/1.85 9.63/1.85 % SZS output end Refutation 9.63/1.85 9.63/1.85 9.63/1.85 % Terminating... 10.67/1.96 % Runner terminated. 10.67/1.98 % Zipperpin 1.5 exiting 10.67/1.98 EOF