0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mUOjF2U4gv true 0.09/0.30 % Computer : n027.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % WCLimit : 120 0.09/0.30 % DateTime : Tue Aug 9 05:17:36 EDT 2022 0.09/0.30 % CPUTime : 0.09/0.30 % Running portfolio for 960 s 0.09/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.30 % Number of cores: 8 0.09/0.30 % Python version: Python 3.6.8 0.09/0.30 % Running in HO mode 0.16/0.58 % Total configuration time : 828 0.16/0.58 % Estimated wc time : 1656 0.16/0.58 % Estimated cpu time (8 cpus) : 207.0 1.08/0.65 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.08/0.65 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.08/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.08/0.66 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.08/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.08/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.08/0.67 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.08/0.67 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 1.33/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 1.33/0.79 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 6.25/1.33 % Solved by lams/35_full_unif.sh. 6.25/1.33 % done 326 iterations in 0.496s 6.25/1.33 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 6.25/1.33 % SZS output start Refutation 6.25/1.33 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 6.25/1.33 thf('#sk6_type', type, '#sk6': $i > $i). 6.25/1.33 thf(p_type, type, p: $i > $o). 6.25/1.33 thf('#sk4_type', type, '#sk4': $i). 6.25/1.33 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 6.25/1.33 thf('#sk1_type', type, '#sk1': $i). 6.25/1.33 thf(mdia_s5_type, type, mdia_s5: ($i > $o) > $i > $o). 6.25/1.33 thf(msymmetric_type, type, msymmetric: ($i > $i > $o) > $o). 6.25/1.33 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 6.25/1.33 thf('#sk5_type', type, '#sk5': $i). 6.25/1.33 thf(rel_s5_type, type, rel_s5: $i > $i > $o). 6.25/1.33 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 6.25/1.33 thf(mequiv_type, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 6.25/1.33 thf(mbox_s5_type, type, mbox_s5: ($i > $o) > $i > $o). 6.25/1.33 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 6.25/1.33 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 6.25/1.33 thf(q_type, type, q: $i > $o). 6.25/1.33 thf('#form3_type', type, '#form3': $o). 6.25/1.33 thf('#sk2_type', type, '#sk2': $i). 6.25/1.33 thf(mdia_s5, axiom,(( mdia_s5 ) = 6.25/1.33 (^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) )))). 6.25/1.33 thf(mbox_s5, axiom,(( mbox_s5 ) = 6.25/1.33 (^[Phi:( $i > $o ),W:$i]: 6.25/1.33 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) )))). 6.25/1.33 thf('0', plain, 6.25/1.33 (( mbox_s5 ) = 6.25/1.33 ( ^[Phi:( $i > $o ),W:$i]: 6.25/1.33 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mbox_s5])). 6.25/1.33 thf('1', plain, 6.25/1.33 (( mbox_s5 ) = 6.25/1.33 ( ^[V_1:( $i > $o ),V_2:$i]: 6.25/1.33 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s5 @ V_2 @ X4 ) ) ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 6.25/1.33 thf('2', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mnot])). 6.25/1.33 thf('3', plain, 6.25/1.33 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf('4', plain, 6.25/1.33 (( mdia_s5 ) = 6.25/1.33 ( ^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mdia_s5, '1', '3'])). 6.25/1.33 thf('5', plain, 6.25/1.33 (( mdia_s5 ) = 6.25/1.33 ( ^[V_1:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(mvalid, axiom,(( mvalid ) = 6.25/1.33 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 6.25/1.33 thf('6', plain, 6.25/1.33 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mvalid])). 6.25/1.33 thf('7', plain, 6.25/1.33 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(mequiv, axiom,(( mequiv ) = 6.25/1.33 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 6.25/1.33 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) )))). 6.25/1.33 thf(mimplies, axiom,(( mimplies ) = 6.25/1.33 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 6.25/1.33 thf(mor, axiom,(( mor ) = 6.25/1.33 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 6.25/1.33 thf('8', plain, 6.25/1.33 (( mor ) = 6.25/1.33 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mor])). 6.25/1.33 thf('9', plain, 6.25/1.33 (( mor ) = 6.25/1.33 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 6.25/1.33 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf('10', plain, 6.25/1.33 (( mimplies ) = 6.25/1.33 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mimplies, '9', '3'])). 6.25/1.33 thf('11', plain, 6.25/1.33 (( mimplies ) = 6.25/1.33 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(mand, axiom,(( mand ) = 6.25/1.33 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 6.25/1.33 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 6.25/1.33 thf('12', plain, 6.25/1.33 (( mand ) = 6.25/1.33 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 6.25/1.33 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], [mand, '9', '3'])). 6.25/1.33 thf('13', plain, 6.25/1.33 (( mand ) = 6.25/1.33 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 6.25/1.33 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf('14', plain, 6.25/1.33 (( mequiv ) = 6.25/1.33 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 6.25/1.33 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) )), 6.25/1.33 inference('simplify_rw_rule', [status(thm)], 6.25/1.33 [mequiv, '11', '13', '9', '3'])). 6.25/1.33 thf('15', plain, 6.25/1.33 (( mequiv ) = 6.25/1.33 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 6.25/1.33 ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) )), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(prove, conjecture, 6.25/1.33 (mvalid @ 6.25/1.33 ( mequiv @ 6.25/1.33 ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ 6.25/1.33 ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ))). 6.25/1.33 thf(zf_stmt_0, conjecture, 6.25/1.33 (![X4:$i]: 6.25/1.33 ( ~( ( ~( ( ~( ( ~( ![X20:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X20 ) ) | ( q @ X20 ) ) ) ) | 6.25/1.33 ( ![X18:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X18 ) ) | ( ~( p @ X18 ) ) ) ) ) ) | 6.25/1.33 ( ![X14:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X14 ) ) | ( ~( p @ X14 ) ) | 6.25/1.33 ( ~( ![X16:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X14 @ X16 ) ) | ( q @ X16 ) ) ) ) ) ) ) ) | 6.25/1.33 ( ~( ( ~( ![X10:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X10 ) ) | ( ~( p @ X10 ) ) | 6.25/1.33 ( ~( ![X12:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X10 @ X12 ) ) | ( q @ X12 ) ) ) ) ) ) ) | 6.25/1.33 ( ![X6:$i]: ( ( ~( rel_s5 @ X4 @ X6 ) ) | ( ~( p @ X6 ) ) ) ) | 6.25/1.33 ( ~( ![X8:$i]: ( ( ~( rel_s5 @ X4 @ X8 ) ) | ( q @ X8 ) ) ) ) ) ) ) ))). 6.25/1.33 thf(zf_stmt_1, negated_conjecture, 6.25/1.33 (~( ![X4:$i]: 6.25/1.33 ( ~( ( ~( ( ~( ( ~( ![X20:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X20 ) ) | ( q @ X20 ) ) ) ) | 6.25/1.33 ( ![X18:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X18 ) ) | ( ~( p @ X18 ) ) ) ) ) ) | 6.25/1.33 ( ![X14:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X14 ) ) | ( ~( p @ X14 ) ) | 6.25/1.33 ( ~( ![X16:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X14 @ X16 ) ) | ( q @ X16 ) ) ) ) ) ) ) ) | 6.25/1.33 ( ~( ( ~( ![X10:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X4 @ X10 ) ) | ( ~( p @ X10 ) ) | 6.25/1.33 ( ~( ![X12:$i]: 6.25/1.33 ( ( ~( rel_s5 @ X10 @ X12 ) ) | ( q @ X12 ) ) ) ) ) ) ) | 6.25/1.33 ( ![X6:$i]: ( ( ~( rel_s5 @ X4 @ X6 ) ) | ( ~( p @ X6 ) ) ) ) | 6.25/1.33 ( ~( ![X8:$i]: ( ( ~( rel_s5 @ X4 @ X8 ) ) | ( q @ X8 ) ) ) ) ) ) ) ) )), 6.25/1.33 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 6.25/1.33 thf(zip_derived_cl3, plain, 6.25/1.33 (~ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((~) @ (((((~) @ (((((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (( 6.25/1.33 (( 6.25/1.33 (~) @ ( 6.25/1.33 rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1)))))))) | 6.25/1.33 (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ ( 6.25/1.33 rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (((~) @ ( 6.25/1.33 p @ Y1)))))))))))) | 6.25/1.33 (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ 6.25/1.33 Y1))) | 6.25/1.33 (((~) @ (p @ Y1))) | 6.25/1.33 (((~) @ (((!!) @ ( 6.25/1.33 ^[Y2 : $i]: 6.25/1.33 (((( 6.25/1.33 (~) @ ( 6.25/1.33 rel_s5 @ 6.25/1.33 Y1 @ Y2))) | 6.25/1.33 (q @ Y2))))))))))))))))) | 6.25/1.33 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ ( 6.25/1.33 rel_s5 @ Y0 @ 6.25/1.33 Y1))) | 6.25/1.33 (((~) @ (p @ Y1))) | 6.25/1.33 (((~) @ ( 6.25/1.33 ((!!) @ ( 6.25/1.33 ^[Y2 : $i]: 6.25/1.33 (((( 6.25/1.33 (~) @ ( 6.25/1.33 rel_s5 @ 6.25/1.33 Y1 @ Y2))) | 6.25/1.33 (q @ Y2))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ 6.25/1.33 Y1))) | 6.25/1.33 (((~) @ (p @ Y1)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ ( 6.25/1.33 rel_s5 @ Y0 @ 6.25/1.33 Y1))) | 6.25/1.33 (q @ Y1)))))))))))))))))))), 6.25/1.33 inference('cnf', [status(esa)], [zf_stmt_1])). 6.25/1.33 thf(zip_derived_cl4, plain, 6.25/1.33 ( (((((~) @ (((((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ 6.25/1.33 Y0))) | 6.25/1.33 (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ 6.25/1.33 Y1))) | 6.25/1.33 (q @ Y1))))))))))))))))) | 6.25/1.33 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ ( 6.25/1.33 rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (q @ Y0))))))))))))))), 6.25/1.33 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 6.25/1.33 thf(zip_derived_cl11, plain, 6.25/1.33 ((~ (((((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 6.25/1.33 thf(zip_derived_cl13, plain, 6.25/1.33 ((~ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 6.25/1.33 thf(zip_derived_cl14, plain, 6.25/1.33 ((~ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))) 6.25/1.33 | ~ (((((~) @ ($true))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('local_rewriting', [status(thm)], [zip_derived_cl13])). 6.25/1.33 thf(zip_derived_cl15, plain, 6.25/1.33 ((~ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))), 6.25/1.33 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl14])). 6.25/1.33 thf(zip_derived_cl16, plain, 6.25/1.33 ((~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))), 6.25/1.33 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 6.25/1.33 thf(zip_derived_cl17, plain, 6.25/1.33 (( ('#form3') 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(zip_derived_cl19, plain, 6.25/1.33 ((~ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))) 6.25/1.33 | ('#form3'))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 6.25/1.33 thf(zip_derived_cl58, plain, 6.25/1.33 ((~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk4'))) | (((~) @ (p @ '#sk4'))))) 6.25/1.33 | ('#form3'))), 6.25/1.33 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 6.25/1.33 thf(zip_derived_cl339, plain, (( (rel_s5 @ '#sk1' @ '#sk4') | ('#form3'))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 6.25/1.33 thf(zip_derived_cl12, plain, 6.25/1.33 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 6.25/1.33 thf(zip_derived_cl12, plain, 6.25/1.33 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))))) 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl11])). 6.25/1.33 thf(zip_derived_cl82, plain, 6.25/1.33 ((~ ('#form3') 6.25/1.33 | (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(zip_derived_cl17, plain, 6.25/1.33 (( ('#form3') 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))))))), 6.25/1.33 define([status(thm)])). 6.25/1.33 thf(zip_derived_cl84, plain, 6.25/1.33 (( ('#form3') 6.25/1.33 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ 6.25/1.33 Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))))) | 6.25/1.33 (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.33 (((~) @ (p @ Y0)))))))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.33 inference('renaming', [status(thm)], 6.25/1.33 [zip_derived_cl12, zip_derived_cl82, zip_derived_cl17])). 6.25/1.33 thf(zip_derived_cl210, plain, 6.25/1.33 (( (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y1 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 6.25/1.33 (q @ Y1))))))))))))) 6.25/1.33 | ('#form3'))), 6.25/1.33 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl84])). 6.25/1.33 thf(zip_derived_cl287, plain, 6.25/1.33 (![X2 : $i]: 6.25/1.33 ( (((((~) @ (rel_s5 @ '#sk1' @ X2))) | (((~) @ (p @ X2))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ X2 @ Y0))) | (q @ Y0)))))))))) 6.25/1.33 | ('#form3'))), 6.25/1.33 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl210])). 6.25/1.33 thf(zip_derived_cl444, plain, 6.25/1.33 (( (((((~) @ ($true))) | (((~) @ (p @ '#sk4'))) | 6.25/1.33 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.33 (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0)))))))))) 6.25/1.33 | ('#form3') 6.25/1.33 | ('#form3'))), 6.25/1.34 inference('sup+', [status(thm)], [zip_derived_cl339, zip_derived_cl287])). 6.25/1.34 thf(zip_derived_cl456, plain, 6.25/1.34 (( ('#form3') 6.25/1.34 | (((((~) @ ($true))) | (((~) @ (p @ '#sk4'))) | 6.25/1.34 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl444])). 6.25/1.34 thf(zip_derived_cl457, plain, 6.25/1.34 (( ('#form3') 6.25/1.34 | (((((~) @ (p @ '#sk4'))) | 6.25/1.34 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl456])). 6.25/1.34 thf(zip_derived_cl478, plain, 6.25/1.34 ((~ (p @ '#sk4') 6.25/1.34 | ~ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0)))))) 6.25/1.34 | ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl457])). 6.25/1.34 thf(zip_derived_cl340, plain, (( (p @ '#sk4') | ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 6.25/1.34 thf(zip_derived_cl486, plain, 6.25/1.34 (( ('#form3') 6.25/1.34 | ~ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0)))))))), 6.25/1.34 inference('clc', [status(thm)], [zip_derived_cl478, zip_derived_cl340])). 6.25/1.34 thf(zip_derived_cl16, plain, 6.25/1.34 ((~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.34 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))))))) 6.25/1.34 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.34 (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.34 (((~) @ (p @ Y0)))))))))))), 6.25/1.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 6.25/1.34 thf(zip_derived_cl17, plain, 6.25/1.34 (( ('#form3') 6.25/1.34 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.34 (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.34 (((~) @ (p @ Y0)))))))))))), 6.25/1.34 define([status(thm)])). 6.25/1.34 thf(zip_derived_cl20, plain, 6.25/1.34 ((~ ('#form3') 6.25/1.34 | ~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.34 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.34 inference('renaming', [status(thm)], [zip_derived_cl16, zip_derived_cl17])). 6.25/1.34 thf(zip_derived_cl59, plain, (( (rel_s5 @ '#sk1' @ '#sk2') | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 6.25/1.34 thf(zip_derived_cl82, plain, 6.25/1.34 ((~ ('#form3') 6.25/1.34 | (((((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))))) | 6.25/1.34 (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 6.25/1.34 (((~) @ (p @ Y0)))))))))))), 6.25/1.34 define([status(thm)])). 6.25/1.34 thf(zip_derived_cl83, plain, 6.25/1.34 ((~ (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))) 6.25/1.34 | (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl82])). 6.25/1.34 thf(zip_derived_cl85, plain, 6.25/1.34 ((~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk5'))) | (q @ '#sk5'))) 6.25/1.34 | ~ ('#form3') 6.25/1.34 | (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))))), 6.25/1.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 6.25/1.34 thf(zip_derived_cl166, plain, 6.25/1.34 (( (rel_s5 @ '#sk1' @ '#sk5') 6.25/1.34 | (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl85])). 6.25/1.34 thf(zip_derived_cl200, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 ( (((((~) @ (rel_s5 @ '#sk1' @ X2))) | (((~) @ (p @ X2))))) 6.25/1.34 | ~ ('#form3') 6.25/1.34 | (rel_s5 @ '#sk1' @ '#sk5'))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl166])). 6.25/1.34 thf(zip_derived_cl61, plain, 6.25/1.34 (( (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 6.25/1.34 thf(zip_derived_cl20, plain, 6.25/1.34 ((~ ('#form3') 6.25/1.34 | ~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.34 (((~) @ (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))))))))), 6.25/1.34 inference('renaming', [status(thm)], [zip_derived_cl16, zip_derived_cl17])). 6.25/1.34 thf(zip_derived_cl62, plain, 6.25/1.34 ((~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.34 (((~) @ ($true))))) 6.25/1.34 | ~ ('#form3') 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl61, zip_derived_cl20])). 6.25/1.34 thf(zip_derived_cl64, plain, 6.25/1.34 ((~ ('#form3') 6.25/1.34 | ~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))) | 6.25/1.34 (((~) @ ($true))))))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl62])). 6.25/1.34 thf(zip_derived_cl65, plain, 6.25/1.34 ((~ ('#form3') 6.25/1.34 | ~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | (((~) @ (p @ '#sk2'))))))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl64])). 6.25/1.34 thf(zip_derived_cl808, plain, 6.25/1.34 (( (rel_s5 @ '#sk1' @ '#sk5') | ~ ('#form3') | ~ ('#form3'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl200, zip_derived_cl65])). 6.25/1.34 thf(zip_derived_cl843, plain, ((~ ('#form3') | (rel_s5 @ '#sk1' @ '#sk5'))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl808])). 6.25/1.34 thf(zip_derived_cl59, plain, (( (rel_s5 @ '#sk1' @ '#sk2') | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 6.25/1.34 thf(msymmetric, axiom,(( msymmetric ) = 6.25/1.34 (^[R:( $i > $i > $o )]: 6.25/1.34 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) )))). 6.25/1.34 thf('16', plain, 6.25/1.34 (( msymmetric ) = 6.25/1.34 ( ^[R:( $i > $i > $o )]: 6.25/1.34 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) ) )), 6.25/1.34 inference('simplify_rw_rule', [status(thm)], [msymmetric])). 6.25/1.34 thf('17', plain, 6.25/1.34 (( msymmetric ) = 6.25/1.34 ( ^[V_1:( $i > $i > $o )]: 6.25/1.34 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_1 @ X6 @ X4 ) ) ) )), 6.25/1.34 define([status(thm)])).thf(a3, axiom, (msymmetric @ rel_s5)). 6.25/1.34 thf(zf_stmt_2, axiom, 6.25/1.34 (![X4:$i,X6:$i]: ( ( rel_s5 @ X4 @ X6 ) => ( rel_s5 @ X6 @ X4 ) ))). 6.25/1.34 thf(zip_derived_cl0, plain, 6.25/1.34 ( (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((!!) @ (^[Y1 : $i]: 6.25/1.34 (((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))))), 6.25/1.34 inference('cnf', [status(esa)], [zf_stmt_2])). 6.25/1.34 thf(zip_derived_cl6, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 (((!!) @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) => (rel_s5 @ Y0 @ X2))))))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 6.25/1.34 thf(zip_derived_cl8, plain, 6.25/1.34 (![X2 : $i, X4 : $i]: (((rel_s5 @ X2 @ X4) => (rel_s5 @ X4 @ X2)))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 6.25/1.34 thf(zip_derived_cl30, plain, 6.25/1.34 (![X2 : $i, X4 : $i]: (~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X4 @ X2))), 6.25/1.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 6.25/1.34 thf(zip_derived_cl94, plain, ((~ ('#form3') | (rel_s5 @ '#sk2' @ '#sk1'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl30])). 6.25/1.34 thf(mtransitive, axiom,(( mtransitive ) = 6.25/1.34 (^[R:( $i > $i > $o )]: 6.25/1.34 ( ![S:$i,T:$i,U:$i]: 6.25/1.34 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 6.25/1.34 thf('18', plain, 6.25/1.34 (( mtransitive ) = 6.25/1.34 ( ^[R:( $i > $i > $o )]: 6.25/1.34 ( ![S:$i,T:$i,U:$i]: 6.25/1.34 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 6.25/1.34 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 6.25/1.34 thf('19', plain, 6.25/1.34 (( mtransitive ) = 6.25/1.34 ( ^[V_1:( $i > $i > $o )]: 6.25/1.34 ( ![X4:$i,X6:$i,X8:$i]: 6.25/1.34 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 6.25/1.34 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s5)). 6.25/1.34 thf(zf_stmt_3, axiom, 6.25/1.34 (![X4:$i,X6:$i,X8:$i]: 6.25/1.34 ( ( ( rel_s5 @ X6 @ X8 ) & ( rel_s5 @ X4 @ X6 ) ) => ( rel_s5 @ X4 @ X8 ) ))). 6.25/1.34 thf(zip_derived_cl2, plain, 6.25/1.34 ( (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((!!) @ (^[Y1 : $i]: 6.25/1.34 (((!!) @ (^[Y2 : $i]: 6.25/1.34 (((((rel_s5 @ Y1 @ Y2) & (rel_s5 @ 6.25/1.34 Y0 @ Y1))) => 6.25/1.34 (rel_s5 @ Y0 @ Y2))))))))))))), 6.25/1.34 inference('cnf', [status(esa)], [zf_stmt_3])). 6.25/1.34 thf(zip_derived_cl7, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((!!) @ (^[Y1 : $i]: 6.25/1.34 (((((rel_s5 @ Y0 @ Y1) & (rel_s5 @ X2 @ Y0))) => 6.25/1.34 (rel_s5 @ X2 @ Y1)))))))))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 6.25/1.34 thf(zip_derived_cl9, plain, 6.25/1.34 (![X2 : $i, X4 : $i]: 6.25/1.34 (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((rel_s5 @ X4 @ Y0) & (rel_s5 @ X2 @ X4))) => 6.25/1.34 (rel_s5 @ X2 @ Y0))))))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 6.25/1.34 thf(zip_derived_cl10, plain, 6.25/1.34 (![X2 : $i, X4 : $i, X6 : $i]: 6.25/1.34 (((((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) => (rel_s5 @ X2 @ X6)))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 6.25/1.34 thf(zip_derived_cl172, plain, 6.25/1.34 (![X0 : $i]: 6.25/1.34 ( (((((rel_s5 @ '#sk1' @ X0) & ($true))) => (rel_s5 @ '#sk2' @ X0))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl10])). 6.25/1.34 thf(zip_derived_cl183, plain, 6.25/1.34 (![X0 : $i]: 6.25/1.34 ( (((rel_s5 @ '#sk1' @ X0) => (rel_s5 @ '#sk2' @ X0))) | ~ ('#form3'))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl172])). 6.25/1.34 thf(zip_derived_cl1033, plain, 6.25/1.34 (( ((($true) => (rel_s5 @ '#sk2' @ '#sk5'))) 6.25/1.34 | ~ ('#form3') 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('sup+', [status(thm)], [zip_derived_cl843, zip_derived_cl183])). 6.25/1.34 thf(zip_derived_cl1062, plain, 6.25/1.34 ((~ ('#form3') | ((($true) => (rel_s5 @ '#sk2' @ '#sk5'))))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl1033])). 6.25/1.34 thf(zip_derived_cl1063, plain, 6.25/1.34 ((~ ('#form3') | (rel_s5 @ '#sk2' @ '#sk5'))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], 6.25/1.34 [zip_derived_cl1062])). 6.25/1.34 thf(zip_derived_cl61, plain, 6.25/1.34 (( (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0)))))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 6.25/1.34 thf(zip_derived_cl63, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 ( (((((~) @ (rel_s5 @ '#sk2' @ X2))) | (q @ X2))) | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 6.25/1.34 thf(zip_derived_cl216, plain, 6.25/1.34 (![X2 : $i]: (~ (rel_s5 @ '#sk2' @ X2) | (q @ X2) | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])). 6.25/1.34 thf(zip_derived_cl1212, plain, 6.25/1.34 ((~ ('#form3') | ~ ('#form3') | (q @ '#sk5'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl1063, zip_derived_cl216])). 6.25/1.34 thf(zip_derived_cl1240, plain, (( (q @ '#sk5') | ~ ('#form3'))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl1212])). 6.25/1.34 thf(zip_derived_cl167, plain, 6.25/1.34 ((~ (q @ '#sk5') 6.25/1.34 | (((!!) @ (^[Y0 : $i]: 6.25/1.34 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (((~) @ (p @ Y0)))))))) 6.25/1.34 | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl85])). 6.25/1.34 thf(zip_derived_cl191, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 ( (((((~) @ (rel_s5 @ '#sk1' @ X2))) | (((~) @ (p @ X2))))) 6.25/1.34 | ~ ('#form3') 6.25/1.34 | ~ (q @ '#sk5'))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl167])). 6.25/1.34 thf(zip_derived_cl778, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 (~ (rel_s5 @ '#sk1' @ X2) | ~ (p @ X2) | ~ (q @ '#sk5') | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl191])). 6.25/1.34 thf(zip_derived_cl1270, plain, 6.25/1.34 (![X0 : $i]: 6.25/1.34 (~ ('#form3') | ~ ('#form3') | ~ (p @ X0) | ~ (rel_s5 @ '#sk1' @ X0))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl1240, zip_derived_cl778])). 6.25/1.34 thf(zip_derived_cl1286, plain, 6.25/1.34 (![X0 : $i]: (~ (rel_s5 @ '#sk1' @ X0) | ~ (p @ X0) | ~ ('#form3'))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl1270])). 6.25/1.34 thf(zip_derived_cl1308, plain, 6.25/1.34 ((~ ('#form3') | ~ ('#form3') | ~ (p @ '#sk2'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl1286])). 6.25/1.34 thf(zip_derived_cl1316, plain, ((~ (p @ '#sk2') | ~ ('#form3'))), 6.25/1.34 inference('simplify', [status(thm)], [zip_derived_cl1308])). 6.25/1.34 thf(zip_derived_cl60, plain, (( (p @ '#sk2') | ~ ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 6.25/1.34 thf(zip_derived_cl1326, plain, (~ ('#form3')), 6.25/1.34 inference('clc', [status(thm)], [zip_derived_cl1316, zip_derived_cl60])). 6.25/1.34 thf(zip_derived_cl1347, plain, 6.25/1.34 (~ (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk4' @ Y0))) | (q @ Y0))))))), 6.25/1.34 inference('demod', [status(thm)], [zip_derived_cl486, zip_derived_cl1326])). 6.25/1.34 thf(zip_derived_cl1352, plain, 6.25/1.34 (~ (((((~) @ (rel_s5 @ '#sk4' @ ('#sk6' @ '#sk4')))) | (q @ 6.25/1.34 ('#sk6' @ '#sk4'))))), 6.25/1.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1347])). 6.25/1.34 thf(zip_derived_cl1411, plain, (~ (q @ ('#sk6' @ '#sk4'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1352])). 6.25/1.34 thf(zip_derived_cl1352, plain, 6.25/1.34 (~ (((((~) @ (rel_s5 @ '#sk4' @ ('#sk6' @ '#sk4')))) | (q @ 6.25/1.34 ('#sk6' @ '#sk4'))))), 6.25/1.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1347])). 6.25/1.34 thf(zip_derived_cl1411, plain, (~ (q @ ('#sk6' @ '#sk4'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1352])). 6.25/1.34 thf(zip_derived_cl1412, plain, 6.25/1.34 (~ (((((~) @ (rel_s5 @ '#sk4' @ ('#sk6' @ '#sk4')))) | ($false)))), 6.25/1.34 inference('demod', [status(thm)], 6.25/1.34 [zip_derived_cl1352, zip_derived_cl1411])). 6.25/1.34 thf(zip_derived_cl1413, plain, 6.25/1.34 (~ (((~) @ (rel_s5 @ '#sk4' @ ('#sk6' @ '#sk4'))))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], 6.25/1.34 [zip_derived_cl1412])). 6.25/1.34 thf(zip_derived_cl1414, plain, ( (rel_s5 @ '#sk4' @ ('#sk6' @ '#sk4'))), 6.25/1.34 inference('simplify nested equalities', [status(thm)], 6.25/1.34 [zip_derived_cl1413])). 6.25/1.34 thf(zip_derived_cl339, plain, (( (rel_s5 @ '#sk1' @ '#sk4') | ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 6.25/1.34 thf(zip_derived_cl10, plain, 6.25/1.34 (![X2 : $i, X4 : $i, X6 : $i]: 6.25/1.34 (((((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) => (rel_s5 @ X2 @ X6)))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 6.25/1.34 thf(zip_derived_cl44, plain, 6.25/1.34 (![X2 : $i, X4 : $i, X6 : $i]: 6.25/1.34 (~ (((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) | (rel_s5 @ X2 @ X6))), 6.25/1.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 6.25/1.34 thf(zip_derived_cl361, plain, 6.25/1.34 (![X0 : $i]: 6.25/1.34 (~ (((rel_s5 @ '#sk4' @ X0) & ($true))) 6.25/1.34 | ('#form3') 6.25/1.34 | (rel_s5 @ '#sk1' @ X0))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl339, zip_derived_cl44])). 6.25/1.34 thf(zip_derived_cl386, plain, 6.25/1.34 (![X0 : $i]: 6.25/1.34 (~ (rel_s5 @ '#sk4' @ X0) | ('#form3') | (rel_s5 @ '#sk1' @ X0))), 6.25/1.34 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl361])). 6.25/1.34 thf(zip_derived_cl1326, plain, (~ ('#form3')), 6.25/1.34 inference('clc', [status(thm)], [zip_derived_cl1316, zip_derived_cl60])). 6.25/1.34 thf(zip_derived_cl1529, plain, 6.25/1.34 (![X0 : $i]: (~ (rel_s5 @ '#sk4' @ X0) | (rel_s5 @ '#sk1' @ X0))), 6.25/1.34 inference('demod', [status(thm)], [zip_derived_cl386, zip_derived_cl1326])). 6.25/1.34 thf(zip_derived_cl1575, plain, ( (rel_s5 @ '#sk1' @ ('#sk6' @ '#sk4'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl1414, zip_derived_cl1529])). 6.25/1.34 thf(zip_derived_cl18, plain, 6.25/1.34 (( (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | (q @ Y0)))))) 6.25/1.34 | ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl17])). 6.25/1.34 thf(zip_derived_cl24, plain, 6.25/1.34 (![X2 : $i]: 6.25/1.34 ( (((((~) @ (rel_s5 @ '#sk1' @ X2))) | (q @ X2))) | ('#form3'))), 6.25/1.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 6.25/1.34 thf(zip_derived_cl144, plain, 6.25/1.34 (![X2 : $i]: (~ (rel_s5 @ '#sk1' @ X2) | (q @ X2) | ('#form3'))), 6.25/1.34 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 6.25/1.34 thf(zip_derived_cl1326, plain, (~ ('#form3')), 6.25/1.34 inference('clc', [status(thm)], [zip_derived_cl1316, zip_derived_cl60])). 6.25/1.34 thf(zip_derived_cl1334, plain, 6.25/1.34 (![X2 : $i]: (~ (rel_s5 @ '#sk1' @ X2) | (q @ X2))), 6.25/1.34 inference('demod', [status(thm)], [zip_derived_cl144, zip_derived_cl1326])). 6.25/1.34 thf(zip_derived_cl1620, plain, ( (q @ ('#sk6' @ '#sk4'))), 6.25/1.34 inference('sup-', [status(thm)], [zip_derived_cl1575, zip_derived_cl1334])). 6.25/1.34 thf(zip_derived_cl1662, plain, ($false), 6.25/1.34 inference('demod', [status(thm)], 6.25/1.34 [zip_derived_cl1411, zip_derived_cl1620])). 6.25/1.34 6.25/1.34 % SZS output end Refutation 6.25/1.34 6.25/1.34 6.25/1.34 % Terminating... 6.25/1.40 % Runner terminated. 6.25/1.41 % Zipperpin 1.5 exiting 6.25/1.42 EOF