0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dznHtwKpBX true 0.14/0.34 % Computer : n029.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 05:00:54 EDT 2022 0.14/0.34 % CPUTime : 0.14/0.34 % Running portfolio for 960 s 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.34 % Number of cores: 8 0.14/0.34 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.52/0.63 % Total configuration time : 828 0.52/0.63 % Estimated wc time : 1656 0.52/0.63 % Estimated cpu time (8 cpus) : 207.0 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.87 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.88 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 0.55/0.90 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 3.64/1.23 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 3.66/1.29 % Solved by lams/35_full_unif4.sh. 3.66/1.29 % done 546 iterations in 0.442s 3.66/1.29 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 3.66/1.29 % SZS output start Refutation 3.66/1.29 thf('#sk6_type', type, '#sk6': $i). 3.66/1.29 thf(q_type, type, q: $i > $o). 3.66/1.29 thf(rel_s5_type, type, rel_s5: $i > $i > $o). 3.66/1.29 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 3.66/1.29 thf('#form4_type', type, '#form4': $o). 3.66/1.29 thf('#sk1_type', type, '#sk1': $i). 3.66/1.29 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 3.66/1.29 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 3.66/1.29 thf(p_type, type, p: $i > $o). 3.66/1.29 thf(mdia_s5_type, type, mdia_s5: ($i > $o) > $i > $o). 3.66/1.29 thf('#sk5_type', type, '#sk5': $i). 3.66/1.29 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 3.66/1.29 thf(mbox_s5_type, type, mbox_s5: ($i > $o) > $i > $o). 3.66/1.29 thf(msymmetric_type, type, msymmetric: ($i > $i > $o) > $o). 3.66/1.29 thf(mequiv_type, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 3.66/1.29 thf('#sk3_type', type, '#sk3': $i). 3.66/1.29 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 3.66/1.29 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 3.66/1.29 thf('#sk2_type', type, '#sk2': $i). 3.66/1.29 thf('#sk7_type', type, '#sk7': $i). 3.66/1.29 thf(mdia_s5, axiom,(( mdia_s5 ) = 3.66/1.29 (^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) )))). 3.66/1.29 thf(mbox_s5, axiom,(( mbox_s5 ) = 3.66/1.29 (^[Phi:( $i > $o ),W:$i]: 3.66/1.29 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) )))). 3.66/1.29 thf('0', plain, 3.66/1.29 (( mbox_s5 ) = 3.66/1.29 ( ^[Phi:( $i > $o ),W:$i]: 3.66/1.29 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mbox_s5])). 3.66/1.29 thf('1', plain, 3.66/1.29 (( mbox_s5 ) = 3.66/1.29 ( ^[V_1:( $i > $o ),V_2:$i]: 3.66/1.29 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s5 @ V_2 @ X4 ) ) ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 3.66/1.29 thf('2', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mnot])). 3.66/1.29 thf('3', plain, 3.66/1.29 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf('4', plain, 3.66/1.29 (( mdia_s5 ) = 3.66/1.29 ( ^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mdia_s5, '1', '3'])). 3.66/1.29 thf('5', plain, 3.66/1.29 (( mdia_s5 ) = 3.66/1.29 ( ^[V_1:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(mvalid, axiom,(( mvalid ) = 3.66/1.29 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 3.66/1.29 thf('6', plain, 3.66/1.29 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mvalid])). 3.66/1.29 thf('7', plain, 3.66/1.29 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(mequiv, axiom,(( mequiv ) = 3.66/1.29 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 3.66/1.29 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) )))). 3.66/1.29 thf(mimplies, axiom,(( mimplies ) = 3.66/1.29 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 3.66/1.29 thf(mor, axiom,(( mor ) = 3.66/1.29 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 3.66/1.29 thf('8', plain, 3.66/1.29 (( mor ) = 3.66/1.29 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mor])). 3.66/1.29 thf('9', plain, 3.66/1.29 (( mor ) = 3.66/1.29 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 3.66/1.29 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf('10', plain, 3.66/1.29 (( mimplies ) = 3.66/1.29 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mimplies, '9', '3'])). 3.66/1.29 thf('11', plain, 3.66/1.29 (( mimplies ) = 3.66/1.29 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(mand, axiom,(( mand ) = 3.66/1.29 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 3.66/1.29 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 3.66/1.29 thf('12', plain, 3.66/1.29 (( mand ) = 3.66/1.29 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 3.66/1.29 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mand, '9', '3'])). 3.66/1.29 thf('13', plain, 3.66/1.29 (( mand ) = 3.66/1.29 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 3.66/1.29 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf('14', plain, 3.66/1.29 (( mequiv ) = 3.66/1.29 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 3.66/1.29 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], 3.66/1.29 [mequiv, '11', '13', '9', '3'])). 3.66/1.29 thf('15', plain, 3.66/1.29 (( mequiv ) = 3.66/1.29 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 3.66/1.29 ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) )), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(prove, conjecture, 3.66/1.29 (mvalid @ 3.66/1.29 ( mbox_s5 @ 3.66/1.29 ( mequiv @ 3.66/1.29 ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ 3.66/1.29 ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ))). 3.66/1.29 thf(zf_stmt_0, conjecture, 3.66/1.29 (![X4:$i,X6:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X4 @ X6 ) ) | 3.66/1.29 ( ~( ( ~( ( ![X20:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X20 ) ) | ( q @ X20 ) | 3.66/1.29 ( ![X22:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X20 @ X22 ) ) | ( ~( p @ X22 ) ) ) ) ) ) | 3.66/1.29 ( ~( ![X16:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X16 ) ) | 3.66/1.29 ( ![X18:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X16 @ X18 ) ) | ( q @ X18 ) ) ) | 3.66/1.29 ( ~( p @ X16 ) ) ) ) ) ) ) | 3.66/1.29 ( ~( ( ![X12:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X12 ) ) | 3.66/1.29 ( ![X14:$i]: ( ( ~( rel_s5 @ X12 @ X14 ) ) | ( q @ X14 ) ) ) | 3.66/1.29 ( ~( p @ X12 ) ) ) ) | 3.66/1.29 ( ~( ![X8:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X8 ) ) | ( q @ X8 ) | 3.66/1.29 ( ![X10:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X8 @ X10 ) ) | ( ~( p @ X10 ) ) ) ) ) ) ) ) ) ) ) ))). 3.66/1.29 thf(zf_stmt_1, negated_conjecture, 3.66/1.29 (~( ![X4:$i,X6:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X4 @ X6 ) ) | 3.66/1.29 ( ~( ( ~( ( ![X20:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X20 ) ) | ( q @ X20 ) | 3.66/1.29 ( ![X22:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X20 @ X22 ) ) | ( ~( p @ X22 ) ) ) ) ) ) | 3.66/1.29 ( ~( ![X16:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X16 ) ) | 3.66/1.29 ( ![X18:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X16 @ X18 ) ) | ( q @ X18 ) ) ) | 3.66/1.29 ( ~( p @ X16 ) ) ) ) ) ) ) | 3.66/1.29 ( ~( ( ![X12:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X12 ) ) | 3.66/1.29 ( ![X14:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X12 @ X14 ) ) | ( q @ X14 ) ) ) | 3.66/1.29 ( ~( p @ X12 ) ) ) ) | 3.66/1.29 ( ~( ![X8:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X6 @ X8 ) ) | ( q @ X8 ) | 3.66/1.29 ( ![X10:$i]: 3.66/1.29 ( ( ~( rel_s5 @ X8 @ X10 ) ) | ( ~( p @ X10 ) ) ) ) ) ) ) ) ) ) ) ) )), 3.66/1.29 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 3.66/1.29 thf(zip_derived_cl3, plain, 3.66/1.29 (~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (((((~) @ (((((!!) @ (^[Y2 : $i]: 3.66/1.29 (((( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (q @ Y2) | 3.66/1.29 (( 3.66/1.29 (!!) @ ( 3.66/1.29 ^[Y3 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y2 @ Y3))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y3))))))))))))) | 3.66/1.29 (((~) @ (((!!) @ ( 3.66/1.29 ^[Y2 : $i]: 3.66/1.29 (((( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (( 3.66/1.29 (!!) @ ( 3.66/1.29 ^[Y3 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y2 @ Y3))) | 3.66/1.29 (q @ Y3)))))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y2)))))))))))))) | 3.66/1.29 (((~) @ (((((!!) @ (^[Y2 : $i]: 3.66/1.29 (((( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (( 3.66/1.29 (!!) @ ( 3.66/1.29 ^[Y3 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y2 @ Y3))) | 3.66/1.29 (q @ Y3)))))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y2)))))))) | 3.66/1.29 (((~) @ (((!!) @ ( 3.66/1.29 ^[Y2 : $i]: 3.66/1.29 (((( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (q @ Y2) | 3.66/1.29 (( 3.66/1.29 (!!) @ ( 3.66/1.29 ^[Y3 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y2 @ Y3))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y3)))))))))))))))))))))))))))))))), 3.66/1.29 inference('cnf', [status(esa)], [zf_stmt_1])). 3.66/1.29 thf(zip_derived_cl25, plain, 3.66/1.29 (~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 3.66/1.29 (((~) @ (((((~) @ (((((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (q @ Y1) | 3.66/1.29 (((!!) @ (^[Y2 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y2))))))))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (((!!) @ ( 3.66/1.29 ^[Y2 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (q @ Y2)))))) | 3.66/1.29 (((~) @ ( 3.66/1.29 p @ Y1)))))))))))))) | 3.66/1.29 (((~) @ (((((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (((!!) @ (^[Y2 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (q @ Y2)))))) | 3.66/1.29 (((~) @ (p @ Y1)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (q @ Y1) | 3.66/1.29 (((!!) @ ( 3.66/1.29 ^[Y2 : $i]: 3.66/1.29 (( 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y1 @ Y2))) | 3.66/1.29 (( 3.66/1.29 (~) @ ( 3.66/1.29 p @ Y2))))))))))))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 3.66/1.29 thf(zip_derived_cl26, plain, 3.66/1.29 (~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | 3.66/1.29 (((~) @ (((((~) @ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))))))) | 3.66/1.29 (((~) @ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ 3.66/1.29 '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ ( 3.66/1.29 rel_s5 @ 3.66/1.29 Y0 @ Y1))) | 3.66/1.29 (((~) @ ( 3.66/1.29 p @ Y1)))))))))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 3.66/1.29 thf(zip_derived_cl28, plain, 3.66/1.29 ( (((((~) @ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ 3.66/1.29 Y1))) | 3.66/1.29 (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))))))) | 3.66/1.29 (((~) @ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ 3.66/1.29 Y1))) | 3.66/1.29 (((~) @ (p @ Y1)))))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl26])). 3.66/1.29 thf(zip_derived_cl29, plain, 3.66/1.29 ((~ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))))) 3.66/1.29 | ~ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 3.66/1.29 Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])). 3.66/1.29 thf(zip_derived_cl30, plain, 3.66/1.29 ((~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) 3.66/1.29 | ~ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 3.66/1.29 Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 3.66/1.29 thf(zip_derived_cl32, plain, 3.66/1.29 ((~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) 3.66/1.29 | ~ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 3.66/1.29 Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ ($true))))))), 3.66/1.29 inference('local_rewriting', [status(thm)], [zip_derived_cl30])). 3.66/1.29 thf(zip_derived_cl33, plain, 3.66/1.29 ((~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl32])). 3.66/1.29 thf(zip_derived_cl34, plain, 3.66/1.29 ((~ (((((~) @ (rel_s5 @ '#sk2' @ '#sk3'))) | (q @ '#sk3') | 3.66/1.29 (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))))) 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 3.66/1.29 thf(zip_derived_cl39, plain, 3.66/1.29 (( (rel_s5 @ '#sk2' @ '#sk3') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 3.66/1.29 thf(zip_derived_cl43, plain, 3.66/1.29 (( ('#form4') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(zip_derived_cl44, plain, 3.66/1.29 ((~ (((((~) @ (rel_s5 @ '#sk2' @ '#sk5'))) | 3.66/1.29 (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk5' @ Y0))) | (q @ Y0)))))) | 3.66/1.29 (((~) @ (p @ '#sk5'))))) 3.66/1.29 | ('#form4'))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl50, plain, 3.66/1.29 ((~ (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk5' @ Y0))) | (q @ Y0)))))) 3.66/1.29 | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 3.66/1.29 thf(zip_derived_cl54, plain, 3.66/1.29 ((~ (((((~) @ (rel_s5 @ '#sk5' @ '#sk7'))) | (q @ '#sk7'))) | ('#form4'))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 3.66/1.29 thf(zip_derived_cl59, plain, ((~ (q @ '#sk7') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 3.66/1.29 thf(zip_derived_cl41, plain, 3.66/1.29 ((~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))) 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 3.66/1.29 thf(zip_derived_cl43, plain, 3.66/1.29 (( ('#form4') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(zip_derived_cl47, plain, 3.66/1.29 ((~ ('#form4') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('renaming', [status(thm)], [zip_derived_cl41, zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl52, plain, 3.66/1.29 ((~ (((((~) @ (rel_s5 @ '#sk3' @ '#sk6'))) | (((~) @ (p @ '#sk6'))))) 3.66/1.29 | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 3.66/1.29 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 3.66/1.29 thf(msymmetric, axiom,(( msymmetric ) = 3.66/1.29 (^[R:( $i > $i > $o )]: 3.66/1.29 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) )))). 3.66/1.29 thf('16', plain, 3.66/1.29 (( msymmetric ) = 3.66/1.29 ( ^[R:( $i > $i > $o )]: 3.66/1.29 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [msymmetric])). 3.66/1.29 thf('17', plain, 3.66/1.29 (( msymmetric ) = 3.66/1.29 ( ^[V_1:( $i > $i > $o )]: 3.66/1.29 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_1 @ X6 @ X4 ) ) ) )), 3.66/1.29 define([status(thm)])).thf(a3, axiom, (msymmetric @ rel_s5)). 3.66/1.29 thf(zf_stmt_2, axiom, 3.66/1.29 (![X4:$i,X6:$i]: ( ( rel_s5 @ X4 @ X6 ) => ( rel_s5 @ X6 @ X4 ) ))). 3.66/1.29 thf(zip_derived_cl0, plain, 3.66/1.29 ( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))))), 3.66/1.29 inference('cnf', [status(esa)], [zf_stmt_2])). 3.66/1.29 thf(zip_derived_cl5, plain, 3.66/1.29 (![X2 : $i]: 3.66/1.29 (((!!) @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) => (rel_s5 @ Y0 @ X2))))))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 3.66/1.29 thf(zip_derived_cl6, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: (((rel_s5 @ X2 @ X4) => (rel_s5 @ X4 @ X2)))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 3.66/1.29 thf(zip_derived_cl7, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: (~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X4 @ X2))), 3.66/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 3.66/1.29 thf(zip_derived_cl76, plain, ((~ ('#form4') | (rel_s5 @ '#sk6' @ '#sk3'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl7])). 3.66/1.29 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 3.66/1.29 thf(zip_derived_cl31, plain, 3.66/1.29 (( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) 3.66/1.29 | ~ (((((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 3.66/1.29 Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 3.66/1.29 thf(zip_derived_cl35, plain, 3.66/1.29 (( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) 3.66/1.29 | ~ ((($false) | 3.66/1.29 (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))))))), 3.66/1.29 inference('local_rewriting', [status(thm)], [zip_derived_cl31])). 3.66/1.29 thf(zip_derived_cl36, plain, 3.66/1.29 (( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) 3.66/1.29 | ~ (((~) @ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))))), 3.66/1.29 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl35])). 3.66/1.29 thf(zip_derived_cl37, plain, 3.66/1.29 (( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))), 3.66/1.29 inference('simplify nested equalities', [status(thm)], [zip_derived_cl36])). 3.66/1.29 thf(zip_derived_cl38, plain, 3.66/1.29 (![X2 : $i]: 3.66/1.29 ( (((((~) @ (rel_s5 @ '#sk2' @ X2))) | 3.66/1.29 (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ X2 @ Y0))) | (q @ Y0)))))) | 3.66/1.29 (((~) @ (p @ X2))))) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 3.66/1.29 thf(zip_derived_cl42, plain, 3.66/1.29 (![X2 : $i]: 3.66/1.29 (~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ X2 @ Y0))) | (q @ Y0)))))) 3.66/1.29 | ~ (p @ X2) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 3.66/1.29 thf(zip_derived_cl48, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: 3.66/1.29 ( (((((~) @ (rel_s5 @ X2 @ X4))) | (q @ X4))) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))) 3.66/1.29 | ~ (p @ X2) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 3.66/1.29 thf(zip_derived_cl53, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: 3.66/1.29 (~ (rel_s5 @ X2 @ X4) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | ~ (p @ X2) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 3.66/1.29 (((~) @ (p @ Y1))))))))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 3.66/1.29 thf(zip_derived_cl57, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 ( (((((~) @ (rel_s5 @ '#sk2' @ X6))) | (q @ X6) | 3.66/1.29 (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ X6 @ Y0))) | (((~) @ (p @ Y0)))))))))) 3.66/1.29 | ~ (p @ X2) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ X2 @ X4))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 3.66/1.29 thf(zip_derived_cl60, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 (~ (rel_s5 @ '#sk2' @ X6) 3.66/1.29 | (q @ X6) 3.66/1.29 | (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ X6 @ Y0))) | (((~) @ (p @ Y0)))))))) 3.66/1.29 | ~ (rel_s5 @ X2 @ X4) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | ~ (p @ X2))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])). 3.66/1.29 thf(zip_derived_cl61, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.66/1.29 ( (((((~) @ (rel_s5 @ X6 @ X8))) | (((~) @ (p @ X8))))) 3.66/1.29 | ~ (p @ X2) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ X2 @ X4) 3.66/1.29 | (q @ X6) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X6))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 3.66/1.29 thf(zip_derived_cl62, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.66/1.29 (~ (rel_s5 @ X6 @ X8) 3.66/1.29 | ~ (p @ X8) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X6) 3.66/1.29 | (q @ X6) 3.66/1.29 | ~ (rel_s5 @ X2 @ X4) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | ~ (p @ X2))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 3.66/1.29 thf(zip_derived_cl97, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ ('#form4') 3.66/1.29 | ~ (p @ X0) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ '#sk3') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk3') 3.66/1.29 | ~ (p @ '#sk6'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl62])). 3.66/1.29 thf(zip_derived_cl40, plain, 3.66/1.29 ((~ (q @ '#sk3') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 3.66/1.29 thf(zip_derived_cl43, plain, 3.66/1.29 (( ('#form4') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(zip_derived_cl46, plain, ((~ ('#form4') | ~ (q @ '#sk3'))), 3.66/1.29 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl565, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (p @ '#sk6') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk3') 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | ~ (p @ X0) 3.66/1.29 | ~ ('#form4'))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl97, zip_derived_cl46])). 3.66/1.29 thf(zip_derived_cl56, plain, (( (p @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 3.66/1.29 thf(zip_derived_cl566, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ ('#form4') 3.66/1.29 | ~ (p @ X0) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk3'))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl565, zip_derived_cl56])). 3.66/1.29 thf(zip_derived_cl39, plain, 3.66/1.29 (( (rel_s5 @ '#sk2' @ '#sk3') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 3.66/1.29 thf(zip_derived_cl43, plain, 3.66/1.29 (( ('#form4') 3.66/1.29 | ~ (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 3.66/1.29 (((~) @ (p @ Y0)))))))))), 3.66/1.29 define([status(thm)])). 3.66/1.29 thf(zip_derived_cl45, plain, ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk3'))), 3.66/1.29 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl567, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | ~ (p @ X0) 3.66/1.29 | ~ ('#form4'))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl566, zip_derived_cl45])). 3.66/1.29 thf(zip_derived_cl571, plain, 3.66/1.29 ((~ ('#form4') 3.66/1.29 | ~ ('#form4') 3.66/1.29 | ~ (p @ '#sk6') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk6') 3.66/1.29 | (q @ '#sk3'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl567])). 3.66/1.29 thf(zip_derived_cl614, plain, 3.66/1.29 (( (q @ '#sk3') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk6') 3.66/1.29 | ~ (p @ '#sk6') 3.66/1.29 | ~ ('#form4'))), 3.66/1.29 inference('simplify', [status(thm)], [zip_derived_cl571])). 3.66/1.29 thf(zip_derived_cl46, plain, ((~ ('#form4') | ~ (q @ '#sk3'))), 3.66/1.29 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl670, plain, 3.66/1.29 ((~ ('#form4') | ~ (p @ '#sk6') | ~ (rel_s5 @ '#sk2' @ '#sk6'))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl614, zip_derived_cl46])). 3.66/1.29 thf(zip_derived_cl56, plain, (( (p @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 3.66/1.29 thf(zip_derived_cl671, plain, 3.66/1.29 ((~ (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl670, zip_derived_cl56])). 3.66/1.29 thf(zip_derived_cl45, plain, ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk3'))), 3.66/1.29 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl43])). 3.66/1.29 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 3.66/1.29 thf(mtransitive, axiom,(( mtransitive ) = 3.66/1.29 (^[R:( $i > $i > $o )]: 3.66/1.29 ( ![S:$i,T:$i,U:$i]: 3.66/1.29 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 3.66/1.29 thf('18', plain, 3.66/1.29 (( mtransitive ) = 3.66/1.29 ( ^[R:( $i > $i > $o )]: 3.66/1.29 ( ![S:$i,T:$i,U:$i]: 3.66/1.29 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 3.66/1.29 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 3.66/1.29 thf('19', plain, 3.66/1.29 (( mtransitive ) = 3.66/1.29 ( ^[V_1:( $i > $i > $o )]: 3.66/1.29 ( ![X4:$i,X6:$i,X8:$i]: 3.66/1.29 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 3.66/1.29 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s5)). 3.66/1.29 thf(zf_stmt_3, axiom, 3.66/1.29 (![X4:$i,X6:$i,X8:$i]: 3.66/1.29 ( ( ( rel_s5 @ X6 @ X8 ) & ( rel_s5 @ X4 @ X6 ) ) => ( rel_s5 @ X4 @ X8 ) ))). 3.66/1.29 thf(zip_derived_cl2, plain, 3.66/1.29 ( (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((!!) @ (^[Y2 : $i]: 3.66/1.29 (((((rel_s5 @ Y1 @ Y2) & (rel_s5 @ 3.66/1.29 Y0 @ Y1))) => 3.66/1.29 (rel_s5 @ Y0 @ Y2))))))))))))), 3.66/1.29 inference('cnf', [status(esa)], [zf_stmt_3])). 3.66/1.29 thf(zip_derived_cl12, plain, 3.66/1.29 (![X2 : $i]: 3.66/1.29 (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((!!) @ (^[Y1 : $i]: 3.66/1.29 (((((rel_s5 @ Y0 @ Y1) & (rel_s5 @ X2 @ Y0))) => 3.66/1.29 (rel_s5 @ X2 @ Y1)))))))))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 3.66/1.29 thf(zip_derived_cl13, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: 3.66/1.29 (((!!) @ (^[Y0 : $i]: 3.66/1.29 (((((rel_s5 @ X4 @ Y0) & (rel_s5 @ X2 @ X4))) => 3.66/1.29 (rel_s5 @ X2 @ Y0))))))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 3.66/1.29 thf(zip_derived_cl14, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 (((((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) => (rel_s5 @ X2 @ X6)))), 3.66/1.29 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 3.66/1.29 thf(zip_derived_cl15, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 (~ (((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) | (rel_s5 @ X2 @ X6))), 3.66/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 3.66/1.29 thf(zip_derived_cl16, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 (~ (rel_s5 @ X4 @ X6) | ~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X2 @ X6))), 3.66/1.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 3.66/1.29 thf(zip_derived_cl75, plain, 3.66/1.29 (![X0 : $i]: 3.66/1.29 (~ ('#form4') | (rel_s5 @ X0 @ '#sk6') | ~ (rel_s5 @ X0 @ '#sk3'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl16])). 3.66/1.29 thf(zip_derived_cl194, plain, 3.66/1.29 ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl75])). 3.66/1.29 thf(zip_derived_cl202, plain, (( (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 3.66/1.29 inference('simplify', [status(thm)], [zip_derived_cl194])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl676, plain, (~ (q @ '#sk7')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl675, plain, ( (rel_s5 @ '#sk5' @ '#sk7')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 3.66/1.29 thf(zip_derived_cl7, plain, 3.66/1.29 (![X2 : $i, X4 : $i]: (~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X4 @ X2))), 3.66/1.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 3.66/1.29 thf(zip_derived_cl84, plain, (( ('#form4') | (rel_s5 @ '#sk7' @ '#sk5'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl7])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl680, plain, ( (rel_s5 @ '#sk7' @ '#sk5')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl84, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl62, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 3.66/1.29 (~ (rel_s5 @ X6 @ X8) 3.66/1.29 | ~ (p @ X8) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X6) 3.66/1.29 | (q @ X6) 3.66/1.29 | ~ (rel_s5 @ X2 @ X4) 3.66/1.29 | (q @ X4) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X2) 3.66/1.29 | ~ (p @ X2))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 3.66/1.29 thf(zip_derived_cl715, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (p @ X0) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ '#sk7') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk7') 3.66/1.29 | ~ (p @ '#sk5'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl680, zip_derived_cl62])). 3.66/1.29 thf(zip_derived_cl51, plain, (( (p @ '#sk5') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl674, plain, ( (p @ '#sk5')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl721, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (p @ X0) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ '#sk7') 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ '#sk7'))), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl715, zip_derived_cl674])). 3.66/1.29 thf(zip_derived_cl49, plain, (( (rel_s5 @ '#sk2' @ '#sk5') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 3.66/1.29 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 3.66/1.29 thf(zip_derived_cl16, plain, 3.66/1.29 (![X2 : $i, X4 : $i, X6 : $i]: 3.66/1.29 (~ (rel_s5 @ X4 @ X6) | ~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X2 @ X6))), 3.66/1.29 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 3.66/1.29 thf(zip_derived_cl83, plain, 3.66/1.29 (![X0 : $i]: 3.66/1.29 ( ('#form4') | (rel_s5 @ X0 @ '#sk7') | ~ (rel_s5 @ X0 @ '#sk5'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl16])). 3.66/1.29 thf(zip_derived_cl292, plain, 3.66/1.29 (( ('#form4') | (rel_s5 @ '#sk2' @ '#sk7') | ('#form4'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl83])). 3.66/1.29 thf(zip_derived_cl300, plain, (( (rel_s5 @ '#sk2' @ '#sk7') | ('#form4'))), 3.66/1.29 inference('simplify', [status(thm)], [zip_derived_cl292])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl684, plain, ( (rel_s5 @ '#sk2' @ '#sk7')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl300, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl1663, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (p @ X0) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ '#sk7'))), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl721, zip_derived_cl684])). 3.66/1.29 thf(zip_derived_cl676, plain, (~ (q @ '#sk7')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl1664, plain, 3.66/1.29 (![X0 : $i, X1 : $i]: 3.66/1.29 (~ (rel_s5 @ X0 @ X1) 3.66/1.29 | (q @ X1) 3.66/1.29 | ~ (rel_s5 @ '#sk2' @ X0) 3.66/1.29 | ~ (p @ X0))), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl1663, zip_derived_cl676])). 3.66/1.29 thf(zip_derived_cl1668, plain, 3.66/1.29 ((~ (p @ '#sk5') | ~ (rel_s5 @ '#sk2' @ '#sk5') | (q @ '#sk7'))), 3.66/1.29 inference('sup-', [status(thm)], [zip_derived_cl675, zip_derived_cl1664])). 3.66/1.29 thf(zip_derived_cl674, plain, ( (p @ '#sk5')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl49, plain, (( (rel_s5 @ '#sk2' @ '#sk5') | ('#form4'))), 3.66/1.29 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 3.66/1.29 thf(zip_derived_cl672, plain, (~ ('#form4')), 3.66/1.29 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 3.66/1.29 thf(zip_derived_cl673, plain, ( (rel_s5 @ '#sk2' @ '#sk5')), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl672])). 3.66/1.29 thf(zip_derived_cl1694, plain, ( (q @ '#sk7')), 3.66/1.29 inference('demod', [status(thm)], 3.66/1.29 [zip_derived_cl1668, zip_derived_cl674, zip_derived_cl673])). 3.66/1.29 thf(zip_derived_cl1715, plain, ($false), 3.66/1.29 inference('demod', [status(thm)], [zip_derived_cl676, zip_derived_cl1694])). 3.66/1.29 3.66/1.29 % SZS output end Refutation 3.66/1.29 3.66/1.29 3.66/1.29 % Terminating... 4.35/1.49 % Runner terminated. 4.35/1.52 % Zipperpin 1.5 exiting 4.35/1.53 EOF