0.11/0.18 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.20 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.db2UNyorbQ true 0.19/0.41 % Computer : n006.cluster.edu 0.19/0.41 % Model : x86_64 x86_64 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.41 % Memory : 8042.1875MB 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64 0.19/0.41 % CPULimit : 1200 0.19/0.41 % WCLimit : 120 0.19/0.41 % DateTime : Tue Jul 13 14:26:56 EDT 2021 0.19/0.41 % CPUTime : 0.19/0.41 % Running portfolio for 120 s 0.19/0.41 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.41 % Number of cores: 8 0.19/0.41 % Python version: Python 3.6.8 0.19/0.41 % Running in HO mode 0.60/0.72 % Total configuration time : 828 0.60/0.72 % Estimated wc time : 983 0.60/0.72 % Estimated cpu time (8 cpus) : 122.875 0.62/0.82 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.62/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.62/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.62/0.82 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.62/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.62/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.62/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.62/0.85 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.65/0.89 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 0.65/1.02 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 33s 15.97/2.73 % Solved by lams/30_sp5.sh. 15.97/2.73 % done 313 iterations in 1.836s 15.97/2.73 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 15.97/2.73 % SZS output start Refutation 15.97/2.73 thf(reg_type, type, reg: $tType). 15.97/2.73 thf('#sk29_type', type, '#sk29': $i). 15.97/2.73 thf(paris_type, type, paris: reg). 15.97/2.73 thf(ec_type, type, ec: reg > reg > $o). 15.97/2.73 thf(a_type, type, a: $i > $i > $o). 15.97/2.73 thf(p_type, type, p: reg > reg > $o). 15.97/2.73 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 15.97/2.73 thf('#sk30_type', type, '#sk30': reg > reg > reg). 15.97/2.73 thf(o_type, type, o: reg > reg > $o). 15.97/2.73 thf(eq_type, type, eq: reg > reg > $o). 15.97/2.73 thf('#sk28_type', type, '#sk28': $i). 15.97/2.73 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 15.97/2.73 thf(c_type, type, c: reg > reg > $o). 15.97/2.73 thf('#form31_type', type, '#form31': reg > reg > $o). 15.97/2.73 thf(france_type, type, france: reg). 15.97/2.73 thf(pp_type, type, pp: reg > reg > $o). 15.97/2.73 thf(ntpp_type, type, ntpp: reg > reg > $o). 15.97/2.73 thf(o, axiom,(( o ) = 15.97/2.73 (^[X:reg,Y:reg]: ( ?[Z:reg]: ( ( p @ Z @ Y ) & ( p @ Z @ X ) ) )))). 15.97/2.73 thf(p, axiom,(( p ) = 15.97/2.73 (^[X:reg,Y:reg]: ( ![Z:reg]: ( ( c @ Z @ X ) => ( c @ Z @ Y ) ) )))). 15.97/2.73 thf('0', plain, 15.97/2.73 (( p ) = 15.97/2.73 ( ^[X:reg,Y:reg]: ( ![Z:reg]: ( ( c @ Z @ X ) => ( c @ Z @ Y ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [p])). 15.97/2.73 thf('1', plain, 15.97/2.73 (( p ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: 15.97/2.73 ( ![X4:reg]: ( ( c @ X4 @ V_1 ) => ( c @ X4 @ V_2 ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf('2', plain, 15.97/2.73 (( o ) = 15.97/2.73 ( ^[X:reg,Y:reg]: ( ?[Z:reg]: ( ( p @ Z @ Y ) & ( p @ Z @ X ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [o, '1'])). 15.97/2.73 thf('3', plain, 15.97/2.73 (( o ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: 15.97/2.73 ( ?[X4:reg]: ( ( p @ X4 @ V_2 ) & ( p @ X4 @ V_1 ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(eq, axiom,(( eq ) = 15.97/2.73 (^[X:reg,Y:reg]: ( ( p @ X @ Y ) & ( p @ Y @ X ) )))). 15.97/2.73 thf('4', plain, 15.97/2.73 (( eq ) = ( ^[X:reg,Y:reg]: ( ( p @ X @ Y ) & ( p @ Y @ X ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [eq, '1'])). 15.97/2.73 thf('5', plain, 15.97/2.73 (( eq ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: ( ( p @ V_1 @ V_2 ) & ( p @ V_2 @ V_1 ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(mvalid, axiom,(( mvalid ) = 15.97/2.73 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 15.97/2.73 thf('6', plain, 15.97/2.73 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [mvalid])). 15.97/2.73 thf('7', plain, 15.97/2.73 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(mbox, axiom,(( mbox ) = 15.97/2.73 (^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]: 15.97/2.73 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) )))). 15.97/2.73 thf('8', plain, 15.97/2.73 (( mbox ) = 15.97/2.73 ( ^[R:( $i > $i > $o ),Phi:( $i > $o ),W:$i]: 15.97/2.73 ( ![V:$i]: ( ( Phi @ V ) | ( ~( R @ W @ V ) ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [mbox])). 15.97/2.73 thf('9', plain, 15.97/2.73 (( mbox ) = 15.97/2.73 ( ^[V_1:( $i > $i > $o ),V_2:( $i > $o ),V_3:$i]: 15.97/2.73 ( ![X4:$i]: ( ( V_2 @ X4 ) | ( ~( V_1 @ V_3 @ X4 ) ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(con, conjecture, 15.97/2.73 (mvalid @ 15.97/2.73 ( mbox @ 15.97/2.73 a @ 15.97/2.73 ( ^[X:$i]: 15.97/2.73 ( ?[Z:reg,Y:reg]: 15.97/2.73 ( ( ~( eq @ Z @ Y ) ) & ( o @ Z @ france ) & ( o @ Z @ france ) ) ) ) ))). 15.97/2.73 thf(zf_stmt_0, conjecture, 15.97/2.73 (![X4:$i,X6:$i]: 15.97/2.73 ( ( ~( a @ X4 @ X6 ) ) | 15.97/2.73 ( ?[X8:reg,X10:reg]: 15.97/2.73 ( ( ?[X22:reg]: 15.97/2.73 ( ( ![X26:reg]: ( ( c @ X26 @ X22 ) => ( c @ X26 @ X8 ) ) ) & 15.97/2.73 ( ![X24:reg]: ( ( c @ X24 @ X22 ) => ( c @ X24 @ france ) ) ) ) ) & 15.97/2.73 ( ?[X16:reg]: 15.97/2.73 ( ( ![X20:reg]: ( ( c @ X20 @ X16 ) => ( c @ X20 @ X8 ) ) ) & 15.97/2.73 ( ![X18:reg]: ( ( c @ X18 @ X16 ) => ( c @ X18 @ france ) ) ) ) ) & 15.97/2.73 ( ~( ( ![X14:reg]: ( ( c @ X14 @ X10 ) => ( c @ X14 @ X8 ) ) ) & 15.97/2.73 ( ![X12:reg]: ( ( c @ X12 @ X8 ) => ( c @ X12 @ X10 ) ) ) ) ) ) ) ))). 15.97/2.73 thf(zf_stmt_1, negated_conjecture, 15.97/2.73 (~( ![X4:$i,X6:$i]: 15.97/2.73 ( ( ~( a @ X4 @ X6 ) ) | 15.97/2.73 ( ?[X8:reg,X10:reg]: 15.97/2.73 ( ( ?[X22:reg]: 15.97/2.73 ( ( ![X26:reg]: ( ( c @ X26 @ X22 ) => ( c @ X26 @ X8 ) ) ) & 15.97/2.73 ( ![X24:reg]: ( ( c @ X24 @ X22 ) => ( c @ X24 @ france ) ) ) ) ) & 15.97/2.73 ( ?[X16:reg]: 15.97/2.73 ( ( ![X20:reg]: ( ( c @ X20 @ X16 ) => ( c @ X20 @ X8 ) ) ) & 15.97/2.73 ( ![X18:reg]: ( ( c @ X18 @ X16 ) => ( c @ X18 @ france ) ) ) ) ) & 15.97/2.73 ( ~( ( ![X14:reg]: ( ( c @ X14 @ X10 ) => ( c @ X14 @ X8 ) ) ) & 15.97/2.73 ( ![X12:reg]: ( ( c @ X12 @ X8 ) => ( c @ X12 @ X10 ) ) ) ) ) ) ) ) )), 15.97/2.73 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 15.97/2.73 thf(zip_derived_cl2, plain, 15.97/2.73 (~ (((!!) @ (^[Y0 : $i]: 15.97/2.73 (((!!) @ (^[Y1 : $i]: 15.97/2.73 (((((~) @ (a @ Y0 @ Y1))) | 15.97/2.73 (((??) @ (^[Y2 : reg]: 15.97/2.73 (((??) @ (^[Y3 : reg]: 15.97/2.73 (((((??) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (((((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ Y2)))))) & 15.97/2.73 (((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 france))))))))))) & 15.97/2.73 (((??) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (((((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ Y2)))))) & 15.97/2.73 (((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 france))))))))))) & 15.97/2.73 (((~) @ (( 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y2)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y3))))))))))))))))))))))))))), 15.97/2.73 inference('cnf', [status(esa)], [zf_stmt_1])). 15.97/2.73 thf(zip_derived_cl41, plain, 15.97/2.73 (~ (((!!) @ (^[Y0 : $i]: 15.97/2.73 (((!!) @ (^[Y1 : $i]: 15.97/2.73 (((((~) @ (a @ Y0 @ Y1))) | 15.97/2.73 (((??) @ (^[Y2 : reg]: 15.97/2.73 (((??) @ (^[Y3 : reg]: 15.97/2.73 (((((??) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (((((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ Y2)))))) & 15.97/2.73 (((!!) @ ( 15.97/2.73 ^[Y5 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 Y4) => 15.97/2.73 (c @ 15.97/2.73 Y5 @ 15.97/2.73 france))))))))))) & 15.97/2.73 (((~) @ (( 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y2)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y3))))))))))))))))))))))))))), 15.97/2.73 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])). 15.97/2.73 thf(zip_derived_cl42, plain, 15.97/2.73 (~ (((!!) @ (^[Y0 : $i]: 15.97/2.73 (((((~) @ (a @ '#sk28' @ Y0))) | 15.97/2.73 (((??) @ (^[Y1 : reg]: 15.97/2.73 (((??) @ (^[Y2 : reg]: 15.97/2.73 (((((??) @ (^[Y3 : reg]: 15.97/2.73 (((((!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (((c @ Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ Y4 @ 15.97/2.73 Y1)))))) & 15.97/2.73 (((!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (((c @ Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ Y4 @ 15.97/2.73 france))))))))))) & 15.97/2.73 (((~) @ (((((!!) @ (^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ Y1)))))) & 15.97/2.73 (((!!) @ (^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ Y2)))))))))))))))))))))))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl41])). 15.97/2.73 thf(zip_derived_cl43, plain, 15.97/2.73 (~ (((((~) @ (a @ '#sk28' @ '#sk29'))) | 15.97/2.73 (((??) @ (^[Y0 : reg]: 15.97/2.73 (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((??) @ (^[Y2 : reg]: 15.97/2.73 (((((!!) @ (^[Y3 : reg]: 15.97/2.73 (((c @ Y3 @ 15.97/2.73 Y2) => (c @ 15.97/2.73 Y3 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y3 : reg]: 15.97/2.73 (((c @ Y3 @ 15.97/2.73 Y2) => (c @ 15.97/2.73 Y3 @ france))))))))))) & 15.97/2.73 (((~) @ (((((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y1) => 15.97/2.73 (c @ Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y0) => 15.97/2.73 (c @ Y2 @ Y1))))))))))))))))))))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl42])). 15.97/2.73 thf(zip_derived_cl44, plain, ( (a @ '#sk28' @ '#sk29')), 15.97/2.73 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 15.97/2.73 thf(c_reflexive, axiom, (![X:reg]: ( c @ X @ X ))). 15.97/2.73 thf(zip_derived_cl1, plain, ( (((!!) @ (^[Y0 : reg]: (c @ Y0 @ Y0))))), 15.97/2.73 inference('cnf', [status(esa)], [c_reflexive])). 15.97/2.73 thf(zip_derived_cl9, plain, (![X2 : reg]: (c @ X2 @ X2)), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 15.97/2.73 thf(zip_derived_cl44, plain, ( (a @ '#sk28' @ '#sk29')), 15.97/2.73 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 15.97/2.73 thf(ntpp, axiom,(( ntpp ) = 15.97/2.73 (^[X:reg,Y:reg]: 15.97/2.73 ( ( pp @ X @ Y ) & ( ~( ?[Z:reg]: ( ( ec @ Z @ Y ) & ( ec @ Z @ X ) ) ) ) )))). 15.97/2.73 thf(ec, axiom,(( ec ) = 15.97/2.73 (^[X:reg,Y:reg]: ( ( c @ X @ Y ) & ( ~( o @ X @ Y ) ) )))). 15.97/2.73 thf('10', plain, 15.97/2.73 (( ec ) = ( ^[X:reg,Y:reg]: ( ( c @ X @ Y ) & ( ~( o @ X @ Y ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [ec, '3', '1'])). 15.97/2.73 thf('11', plain, 15.97/2.73 (( ec ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: ( ( c @ V_1 @ V_2 ) & ( ~( o @ V_1 @ V_2 ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf('12', plain, 15.97/2.73 (( ntpp ) = 15.97/2.73 ( ^[X:reg,Y:reg]: 15.97/2.73 ( ( pp @ X @ Y ) & 15.97/2.73 ( ~( ?[Z:reg]: ( ( ec @ Z @ Y ) & ( ec @ Z @ X ) ) ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [ntpp, '11', '3', '1'])). 15.97/2.73 thf('13', plain, 15.97/2.73 (( ntpp ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: 15.97/2.73 ( ( pp @ V_1 @ V_2 ) & 15.97/2.73 ( ~( ?[X4:reg]: ( ( ec @ X4 @ V_2 ) & ( ec @ X4 @ V_1 ) ) ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(pp, axiom,(( pp ) = 15.97/2.73 (^[X:reg,Y:reg]: ( ( p @ X @ Y ) & ( ~( p @ Y @ X ) ) )))). 15.97/2.73 thf('14', plain, 15.97/2.73 (( pp ) = ( ^[X:reg,Y:reg]: ( ( p @ X @ Y ) & ( ~( p @ Y @ X ) ) ) )), 15.97/2.73 inference('simplify_rw_rule', [status(thm)], [pp, '1'])). 15.97/2.73 thf('15', plain, 15.97/2.73 (( pp ) = 15.97/2.73 ( ^[V_1:reg,V_2:reg]: ( ( p @ V_1 @ V_2 ) & ( ~( p @ V_2 @ V_1 ) ) ) )), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(ax3, axiom, 15.97/2.73 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))). 15.97/2.73 thf(zf_stmt_2, axiom, 15.97/2.73 (![X4:$i,X6:$i]: 15.97/2.73 ( ( ~( a @ X4 @ X6 ) ) | 15.97/2.73 ( ( ~( ?[X12:reg]: 15.97/2.73 ( ( ~( ?[X20:reg]: 15.97/2.73 ( ( ![X24:reg]: ( ( c @ X24 @ X20 ) => ( c @ X24 @ X12 ) ) ) & 15.97/2.73 ( ![X22:reg]: 15.97/2.73 ( ( c @ X22 @ X20 ) => ( c @ X22 @ paris ) ) ) ) ) ) & 15.97/2.73 ( c @ X12 @ paris ) & 15.97/2.73 ( ~( ?[X14:reg]: 15.97/2.73 ( ( ![X18:reg]: ( ( c @ X18 @ X14 ) => ( c @ X18 @ X12 ) ) ) & 15.97/2.73 ( ![X16:reg]: 15.97/2.73 ( ( c @ X16 @ X14 ) => ( c @ X16 @ france ) ) ) ) ) ) & 15.97/2.73 ( c @ X12 @ france ) ) ) ) & 15.97/2.73 ( ~( ![X10:reg]: ( ( c @ X10 @ france ) => ( c @ X10 @ paris ) ) ) ) & 15.97/2.73 ( ![X8:reg]: ( ( c @ X8 @ paris ) => ( c @ X8 @ france ) ) ) ) ))). 15.97/2.73 thf(zip_derived_cl6, plain, 15.97/2.73 ( (((!!) @ (^[Y0 : $i]: 15.97/2.73 (((!!) @ (^[Y1 : $i]: 15.97/2.73 (((((~) @ (a @ Y0 @ Y1))) | 15.97/2.73 (((((~) @ (((??) @ (^[Y2 : reg]: 15.97/2.73 (((((~) @ (((??) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y2)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 paris))))))))))))) & 15.97/2.73 (c @ Y2 @ paris) & 15.97/2.73 (((~) @ (((??) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ Y2)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y4 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 Y3) => 15.97/2.73 (c @ 15.97/2.73 Y4 @ 15.97/2.73 france))))))))))))) & 15.97/2.73 (c @ Y2 @ france)))))))) & 15.97/2.73 (((~) @ (((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ france) => 15.97/2.73 (c @ Y2 @ paris)))))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ paris) => (c @ 15.97/2.73 Y2 @ france))))))))))))))))), 15.97/2.73 inference('cnf', [status(esa)], [zf_stmt_2])). 15.97/2.73 thf(zip_derived_cl129, plain, 15.97/2.73 (![X2 : $i]: 15.97/2.73 (((!!) @ (^[Y0 : $i]: 15.97/2.73 (((((~) @ (a @ X2 @ Y0))) | 15.97/2.73 (((((~) @ (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((~) @ (((??) @ (^[Y2 : reg]: 15.97/2.73 (((( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ Y1)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 paris))))))))))))) & 15.97/2.73 (c @ Y1 @ paris) & 15.97/2.73 (((~) @ (((??) @ (^[Y2 : reg]: 15.97/2.73 (((( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ Y1)))))) & 15.97/2.73 (( 15.97/2.73 (!!) @ ( 15.97/2.73 ^[Y3 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 Y2) => 15.97/2.73 (c @ 15.97/2.73 Y3 @ 15.97/2.73 france))))))))))))) & 15.97/2.73 (c @ Y1 @ france)))))))) & 15.97/2.73 (((~) @ (((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ france) => (c @ Y1 @ 15.97/2.73 paris)))))))) & 15.97/2.73 (((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ paris) => (c @ Y1 @ france)))))))))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 15.97/2.73 thf(zip_derived_cl130, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 (((((~) @ (a @ X2 @ X4))) | 15.97/2.73 (((((~) @ (((??) @ (^[Y0 : reg]: 15.97/2.73 (((((~) @ (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((!!) @ (^[Y2 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 paris))))))))))))) & 15.97/2.73 (c @ Y0 @ paris) & 15.97/2.73 (((~) @ (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((!!) @ (^[Y2 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 ( 15.97/2.73 ( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 france))))))))))))) & 15.97/2.73 (c @ Y0 @ france)))))))) & 15.97/2.73 (((~) @ (((!!) @ (^[Y0 : reg]: 15.97/2.73 (((c @ Y0 @ france) => (c @ Y0 @ paris)))))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 15.97/2.73 thf(zip_derived_cl131, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 (~ (a @ X2 @ X4) 15.97/2.73 | (((((~) @ (((??) @ (^[Y0 : reg]: 15.97/2.73 (((((~) @ (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((!!) @ (^[Y2 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 paris))))))))))))) & 15.97/2.73 (c @ Y0 @ paris) & 15.97/2.73 (((~) @ (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((!!) @ (^[Y2 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (( 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 Y1) => 15.97/2.73 (c @ 15.97/2.73 Y2 @ 15.97/2.73 france))))))))))))) & 15.97/2.73 (c @ Y0 @ france)))))))) & 15.97/2.73 (((~) @ (((!!) @ (^[Y0 : reg]: 15.97/2.73 (((c @ Y0 @ france) => (c @ Y0 @ paris)))))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france)))))))))), 15.97/2.73 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 15.97/2.73 thf(zip_derived_cl134, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france)))))) 15.97/2.73 | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl131])). 15.97/2.73 thf(zip_derived_cl137, plain, 15.97/2.73 (![X2 : $i, X4 : $i, X6 : reg]: 15.97/2.73 ( (((c @ X6 @ paris) => (c @ X6 @ france))) | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 15.97/2.73 thf(zip_derived_cl141, plain, 15.97/2.73 (![X2 : $i, X4 : $i, X6 : reg]: 15.97/2.73 (~ (c @ X6 @ paris) | (c @ X6 @ france) | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 15.97/2.73 thf(zip_derived_cl835, plain, 15.97/2.73 (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ paris))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl141])). 15.97/2.73 thf(c_symmetric, axiom, (![X:reg,Y:reg]: ( ( c @ X @ Y ) => ( c @ Y @ X ) ))). 15.97/2.73 thf(zip_derived_cl0, plain, 15.97/2.73 ( (((!!) @ (^[Y0 : reg]: 15.97/2.73 (((!!) @ (^[Y1 : reg]: (((c @ Y0 @ Y1) => (c @ Y1 @ Y0)))))))))), 15.97/2.73 inference('cnf', [status(esa)], [c_symmetric])). 15.97/2.73 thf(zip_derived_cl10, plain, 15.97/2.73 (![X2 : reg]: 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ X2 @ Y0) => (c @ Y0 @ X2))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 15.97/2.73 thf(zip_derived_cl11, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: (((c @ X2 @ X4) => (c @ X4 @ X2)))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 15.97/2.73 thf(zip_derived_cl12, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 15.97/2.73 thf(zip_derived_cl852, plain, 15.97/2.73 (![X0 : reg]: (~ (c @ X0 @ paris) | (c @ france @ X0))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl835, zip_derived_cl12])). 15.97/2.73 thf(zip_derived_cl1004, plain, ( (c @ france @ paris)), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl852])). 15.97/2.73 thf(zip_derived_cl12, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 15.97/2.73 thf(zip_derived_cl1016, plain, ( (c @ paris @ france)), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl1004, zip_derived_cl12])). 15.97/2.73 thf(zip_derived_cl45, plain, 15.97/2.73 (~ (((??) @ (^[Y0 : reg]: 15.97/2.73 (((??) @ (^[Y1 : reg]: 15.97/2.73 (((((??) @ (^[Y2 : reg]: 15.97/2.73 (((((!!) @ (^[Y3 : reg]: 15.97/2.73 (((c @ Y3 @ Y2) => 15.97/2.73 (c @ Y3 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y3 : reg]: 15.97/2.73 (((c @ Y3 @ Y2) => 15.97/2.73 (c @ Y3 @ 15.97/2.73 france))))))))))) & 15.97/2.73 (((~) @ (((((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y1) => 15.97/2.73 (c @ Y2 @ Y0)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y0) => 15.97/2.73 (c @ Y2 @ Y1))))))))))))))))))), 15.97/2.73 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 15.97/2.73 thf(zip_derived_cl46, plain, 15.97/2.73 (![X2 : reg]: 15.97/2.73 ~ (((??) @ (^[Y0 : reg]: 15.97/2.73 (((((??) @ (^[Y1 : reg]: 15.97/2.73 (((((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y1) => (c @ 15.97/2.73 Y2 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y2 : reg]: 15.97/2.73 (((c @ Y2 @ Y1) => (c @ 15.97/2.73 Y2 @ france))))))))))) & 15.97/2.73 (((~) @ (((((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ Y0) => (c @ Y1 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ X2) => (c @ Y1 @ Y0)))))))))))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 15.97/2.73 thf(zip_derived_cl47, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 ~ (((((??) @ (^[Y0 : reg]: 15.97/2.73 (((((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ Y0) => (c @ Y1 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))) & 15.97/2.73 (((~) @ (((((!!) @ (^[Y0 : reg]: 15.97/2.73 (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: 15.97/2.73 (((c @ Y0 @ X2) => (c @ Y0 @ X4))))))))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl46])). 15.97/2.73 thf(zip_derived_cl48, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 (~ (((??) @ (^[Y0 : reg]: 15.97/2.73 (((((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ Y0) => (c @ Y1 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y1 : reg]: 15.97/2.73 (((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl47])). 15.97/2.73 thf(zip_derived_cl49, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ france)))))))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 15.97/2.73 thf(zip_derived_cl50, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ X2)))))) 15.97/2.73 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ france)))))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl49])). 15.97/2.73 thf(zip_derived_cl51, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (((c @ ('#sk30' @ X2 @ X6) @ X6) => (c @ ('#sk30' @ X2 @ X6) @ X2))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))) 15.97/2.73 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ france)))))))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 15.97/2.73 thf(zip_derived_cl52, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( (c @ ('#sk30' @ X2 @ X6) @ X6) 15.97/2.73 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ france)))))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 15.97/2.73 thf(zip_derived_cl54, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (((c @ ('#sk30' @ france @ X6) @ X6) => (c @ 15.97/2.73 ('#sk30' @ france @ X6) @ france))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))) 15.97/2.73 | (c @ ('#sk30' @ X2 @ X6) @ X6))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 15.97/2.73 thf(zip_derived_cl56, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( (c @ ('#sk30' @ france @ X6) @ X6) 15.97/2.73 | (c @ ('#sk30' @ X2 @ X6) @ X6) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 15.97/2.73 thf(zip_derived_cl60, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 (~ ('#form31' @ X2 @ X4) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(zip_derived_cl62, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))) 15.97/2.73 | ~ ('#form31' @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 15.97/2.73 thf(zip_derived_cl68, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( (((c @ X6 @ X2) => (c @ X6 @ X4))) | ~ ('#form31' @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 15.97/2.73 thf(zip_derived_cl70, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (c @ X6 @ X2) | (c @ X6 @ X4) | ~ ('#form31' @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 15.97/2.73 thf(zip_derived_cl1079, plain, 15.97/2.73 (![X0 : reg]: (~ ('#form31' @ france @ X0) | (c @ paris @ X0))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl1016, zip_derived_cl70])). 15.97/2.73 thf(zip_derived_cl12, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: (~ (c @ X2 @ X4) | (c @ X4 @ X2))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 15.97/2.73 thf(zip_derived_cl1965, plain, 15.97/2.73 (![X0 : reg]: (~ ('#form31' @ france @ X0) | (c @ X0 @ paris))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl1079, zip_derived_cl12])). 15.97/2.73 thf(zip_derived_cl133, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ france) => (c @ Y0 @ paris)))))) 15.97/2.73 | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl131])). 15.97/2.73 thf(zip_derived_cl136, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 (~ (((c @ ('#sk30' @ paris @ france) @ france) => (c @ 15.97/2.73 ('#sk30' @ paris @ france) @ paris))) 15.97/2.73 | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl133])). 15.97/2.73 thf(zip_derived_cl140, plain, 15.97/2.73 (![X2 : $i, X4 : $i]: 15.97/2.73 (~ (c @ ('#sk30' @ paris @ france) @ paris) | ~ (a @ X2 @ X4))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 15.97/2.73 thf(zip_derived_cl2236, plain, 15.97/2.73 (![X0 : $i, X1 : $i]: 15.97/2.73 (~ ('#form31' @ france @ ('#sk30' @ paris @ france)) | ~ (a @ X1 @ X0))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl1965, zip_derived_cl140])). 15.97/2.73 thf(zip_derived_cl2264, plain, 15.97/2.73 (~ ('#form31' @ france @ ('#sk30' @ paris @ france))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl2236])). 15.97/2.73 thf(zip_derived_cl56, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( (c @ ('#sk30' @ france @ X6) @ X6) 15.97/2.73 | (c @ ('#sk30' @ X2 @ X6) @ X6) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 15.97/2.73 thf(zip_derived_cl60, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 (~ ('#form31' @ X2 @ X4) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(zip_derived_cl63, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( ('#form31' @ X2 @ X4) 15.97/2.73 | (c @ ('#sk30' @ X2 @ X6) @ X6) 15.97/2.73 | (c @ ('#sk30' @ france @ X6) @ X6))), 15.97/2.73 inference('renaming', [status(thm)], [zip_derived_cl56, zip_derived_cl60])). 15.97/2.73 thf(zip_derived_cl2264, plain, 15.97/2.73 (~ ('#form31' @ france @ ('#sk30' @ paris @ france))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl2236])). 15.97/2.73 thf(zip_derived_cl2284, plain, 15.97/2.73 (![X0 : reg]: 15.97/2.73 ( (c @ ('#sk30' @ france @ X0) @ X0) 15.97/2.73 | (c @ ('#sk30' @ france @ X0) @ X0))), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl2264])). 15.97/2.73 thf(zip_derived_cl2289, plain, 15.97/2.73 (![X0 : reg]: (c @ ('#sk30' @ france @ X0) @ X0)), 15.97/2.73 inference('simplify', [status(thm)], [zip_derived_cl2284])). 15.97/2.73 thf(zip_derived_cl53, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (c @ ('#sk30' @ X2 @ X6) @ X2) 15.97/2.73 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X6) => (c @ Y0 @ france)))))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 15.97/2.73 thf(zip_derived_cl55, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (((c @ ('#sk30' @ france @ X6) @ X6) => (c @ 15.97/2.73 ('#sk30' @ france @ X6) @ france))) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))) 15.97/2.73 | ~ (c @ ('#sk30' @ X2 @ X6) @ X2))), 15.97/2.73 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 15.97/2.73 thf(zip_derived_cl59, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 (~ (c @ ('#sk30' @ france @ X6) @ france) 15.97/2.73 | ~ (c @ ('#sk30' @ X2 @ X6) @ X2) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 15.97/2.73 thf(zip_derived_cl60, plain, 15.97/2.73 (![X2 : reg, X4 : reg]: 15.97/2.73 (~ ('#form31' @ X2 @ X4) 15.97/2.73 | (((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X4) => (c @ Y0 @ X2)))))) & 15.97/2.73 (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ X4)))))))))), 15.97/2.73 define([status(thm)])). 15.97/2.73 thf(zip_derived_cl66, plain, 15.97/2.73 (![X2 : reg, X4 : reg, X6 : reg]: 15.97/2.73 ( ('#form31' @ X2 @ X4) 15.97/2.73 | ~ (c @ ('#sk30' @ X2 @ X6) @ X2) 15.97/2.73 | ~ (c @ ('#sk30' @ france @ X6) @ france))), 15.97/2.73 inference('renaming', [status(thm)], [zip_derived_cl59, zip_derived_cl60])). 15.97/2.73 thf(zip_derived_cl781, plain, 15.97/2.73 (![X0 : reg, X1 : reg]: 15.97/2.73 (~ (c @ ('#sk30' @ france @ X0) @ france) | ('#form31' @ france @ X1))), 15.97/2.73 inference('eq_fact', [status(thm)], [zip_derived_cl66])). 15.97/2.73 thf(zip_derived_cl2310, plain, (![X0 : reg]: ('#form31' @ france @ X0)), 15.97/2.73 inference('sup-', [status(thm)], [zip_derived_cl2289, zip_derived_cl781])). 15.97/2.73 thf(zip_derived_cl2341, plain, ($false), 15.97/2.73 inference('demod', [status(thm)], 15.97/2.73 [zip_derived_cl2264, zip_derived_cl2310])). 15.97/2.73 15.97/2.73 % SZS output end Refutation 15.97/2.73 15.97/2.73 15.97/2.73 % Terminating... 16.84/2.83 % Runner terminated. 16.84/2.85 % Zipperpin 1.5 exiting 16.84/2.85 EOF