0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mdOAr7G3KB true 0.13/0.35 % Computer : n006.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 04:50:14 EDT 2022 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 960 s 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.53/0.66 % Total configuration time : 828 0.53/0.66 % Estimated wc time : 1656 0.53/0.66 % Estimated cpu time (8 cpus) : 207.0 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.57/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.57/0.87 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 0.58/0.92 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 4.29/1.19 % Solved by lams/35_full_unif4.sh. 4.29/1.19 % done 546 iterations in 0.365s 4.29/1.19 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 4.29/1.19 % SZS output start Refutation 4.29/1.19 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 4.29/1.19 thf('#sk5_type', type, '#sk5': $i). 4.29/1.19 thf(p_type, type, p: $i > $o). 4.29/1.19 thf('#sk3_type', type, '#sk3': $i). 4.29/1.19 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 4.29/1.19 thf(mdia_s5_type, type, mdia_s5: ($i > $o) > $i > $o). 4.29/1.19 thf(msymmetric_type, type, msymmetric: ($i > $i > $o) > $o). 4.29/1.19 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 4.29/1.19 thf('#form4_type', type, '#form4': $o). 4.29/1.19 thf('#sk7_type', type, '#sk7': $i). 4.29/1.19 thf(rel_s5_type, type, rel_s5: $i > $i > $o). 4.29/1.19 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 4.29/1.19 thf(mequiv_type, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 4.29/1.19 thf(mbox_s5_type, type, mbox_s5: ($i > $o) > $i > $o). 4.29/1.19 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 4.29/1.19 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 4.29/1.19 thf(q_type, type, q: $i > $o). 4.29/1.19 thf('#sk2_type', type, '#sk2': $i). 4.29/1.19 thf('#sk1_type', type, '#sk1': $i). 4.29/1.19 thf('#sk6_type', type, '#sk6': $i). 4.29/1.19 thf(mdia_s5, axiom,(( mdia_s5 ) = 4.29/1.19 (^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) )))). 4.29/1.19 thf(mbox_s5, axiom,(( mbox_s5 ) = 4.29/1.19 (^[Phi:( $i > $o ),W:$i]: 4.29/1.19 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) )))). 4.29/1.19 thf('0', plain, 4.29/1.19 (( mbox_s5 ) = 4.29/1.19 ( ^[Phi:( $i > $o ),W:$i]: 4.29/1.19 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s5 @ W @ V ) ) ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mbox_s5])). 4.29/1.19 thf('1', plain, 4.29/1.19 (( mbox_s5 ) = 4.29/1.19 ( ^[V_1:( $i > $o ),V_2:$i]: 4.29/1.19 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s5 @ V_2 @ X4 ) ) ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 4.29/1.19 thf('2', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mnot])). 4.29/1.19 thf('3', plain, 4.29/1.19 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf('4', plain, 4.29/1.19 (( mdia_s5 ) = 4.29/1.19 ( ^[Phi:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mdia_s5, '1', '3'])). 4.29/1.19 thf('5', plain, 4.29/1.19 (( mdia_s5 ) = 4.29/1.19 ( ^[V_1:( $i > $o )]: ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(mvalid, axiom,(( mvalid ) = 4.29/1.19 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 4.29/1.19 thf('6', plain, 4.29/1.19 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mvalid])). 4.29/1.19 thf('7', plain, 4.29/1.19 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(mequiv, axiom,(( mequiv ) = 4.29/1.19 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 4.29/1.19 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) )))). 4.29/1.19 thf(mimplies, axiom,(( mimplies ) = 4.29/1.19 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 4.29/1.19 thf(mor, axiom,(( mor ) = 4.29/1.19 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 4.29/1.19 thf('8', plain, 4.29/1.19 (( mor ) = 4.29/1.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mor])). 4.29/1.19 thf('9', plain, 4.29/1.19 (( mor ) = 4.29/1.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 4.29/1.19 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf('10', plain, 4.29/1.19 (( mimplies ) = 4.29/1.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mimplies, '9', '3'])). 4.29/1.19 thf('11', plain, 4.29/1.19 (( mimplies ) = 4.29/1.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(mand, axiom,(( mand ) = 4.29/1.19 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 4.29/1.19 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 4.29/1.19 thf('12', plain, 4.29/1.19 (( mand ) = 4.29/1.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 4.29/1.19 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mand, '9', '3'])). 4.29/1.19 thf('13', plain, 4.29/1.19 (( mand ) = 4.29/1.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 4.29/1.19 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf('14', plain, 4.29/1.19 (( mequiv ) = 4.29/1.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 4.29/1.19 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], 4.29/1.19 [mequiv, '11', '13', '9', '3'])). 4.29/1.19 thf('15', plain, 4.29/1.19 (( mequiv ) = 4.29/1.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 4.29/1.19 ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) )), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(prove, conjecture, 4.29/1.19 (mvalid @ 4.29/1.19 ( mbox_s5 @ 4.29/1.19 ( mequiv @ 4.29/1.19 ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ 4.29/1.19 ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ))). 4.29/1.19 thf(zf_stmt_0, conjecture, 4.29/1.19 (![X4:$i,X6:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X4 @ X6 ) ) | 4.29/1.19 ( ~( ( ~( ( ![X20:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X20 ) ) | ( q @ X20 ) | 4.29/1.19 ( ![X22:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X20 @ X22 ) ) | ( ~( p @ X22 ) ) ) ) ) ) | 4.29/1.19 ( ~( ![X16:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X16 ) ) | 4.29/1.19 ( ![X18:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X16 @ X18 ) ) | ( q @ X18 ) ) ) | 4.29/1.19 ( ~( p @ X16 ) ) ) ) ) ) ) | 4.29/1.19 ( ~( ( ![X12:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X12 ) ) | 4.29/1.19 ( ![X14:$i]: ( ( ~( rel_s5 @ X12 @ X14 ) ) | ( q @ X14 ) ) ) | 4.29/1.19 ( ~( p @ X12 ) ) ) ) | 4.29/1.19 ( ~( ![X8:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X8 ) ) | ( q @ X8 ) | 4.29/1.19 ( ![X10:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X8 @ X10 ) ) | ( ~( p @ X10 ) ) ) ) ) ) ) ) ) ) ) ))). 4.29/1.19 thf(zf_stmt_1, negated_conjecture, 4.29/1.19 (~( ![X4:$i,X6:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X4 @ X6 ) ) | 4.29/1.19 ( ~( ( ~( ( ![X20:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X20 ) ) | ( q @ X20 ) | 4.29/1.19 ( ![X22:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X20 @ X22 ) ) | ( ~( p @ X22 ) ) ) ) ) ) | 4.29/1.19 ( ~( ![X16:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X16 ) ) | 4.29/1.19 ( ![X18:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X16 @ X18 ) ) | ( q @ X18 ) ) ) | 4.29/1.19 ( ~( p @ X16 ) ) ) ) ) ) ) | 4.29/1.19 ( ~( ( ![X12:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X12 ) ) | 4.29/1.19 ( ![X14:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X12 @ X14 ) ) | ( q @ X14 ) ) ) | 4.29/1.19 ( ~( p @ X12 ) ) ) ) | 4.29/1.19 ( ~( ![X8:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X6 @ X8 ) ) | ( q @ X8 ) | 4.29/1.19 ( ![X10:$i]: 4.29/1.19 ( ( ~( rel_s5 @ X8 @ X10 ) ) | ( ~( p @ X10 ) ) ) ) ) ) ) ) ) ) ) ) )), 4.29/1.19 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 4.29/1.19 thf(zip_derived_cl3, plain, 4.29/1.19 (~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (((((~) @ (((((!!) @ (^[Y2 : $i]: 4.29/1.19 (((( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (q @ Y2) | 4.29/1.19 (( 4.29/1.19 (!!) @ ( 4.29/1.19 ^[Y3 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y2 @ Y3))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y3))))))))))))) | 4.29/1.19 (((~) @ (((!!) @ ( 4.29/1.19 ^[Y2 : $i]: 4.29/1.19 (((( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (( 4.29/1.19 (!!) @ ( 4.29/1.19 ^[Y3 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y2 @ Y3))) | 4.29/1.19 (q @ Y3)))))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y2)))))))))))))) | 4.29/1.19 (((~) @ (((((!!) @ (^[Y2 : $i]: 4.29/1.19 (((( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (( 4.29/1.19 (!!) @ ( 4.29/1.19 ^[Y3 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y2 @ Y3))) | 4.29/1.19 (q @ Y3)))))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y2)))))))) | 4.29/1.19 (((~) @ (((!!) @ ( 4.29/1.19 ^[Y2 : $i]: 4.29/1.19 (((( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (q @ Y2) | 4.29/1.19 (( 4.29/1.19 (!!) @ ( 4.29/1.19 ^[Y3 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y2 @ Y3))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y3)))))))))))))))))))))))))))))))), 4.29/1.19 inference('cnf', [status(esa)], [zf_stmt_1])). 4.29/1.19 thf(zip_derived_cl25, plain, 4.29/1.19 (~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk1' @ Y0))) | 4.29/1.19 (((~) @ (((((~) @ (((((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (q @ Y1) | 4.29/1.19 (((!!) @ (^[Y2 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y2))))))))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (((!!) @ ( 4.29/1.19 ^[Y2 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (q @ Y2)))))) | 4.29/1.19 (((~) @ ( 4.29/1.19 p @ Y1)))))))))))))) | 4.29/1.19 (((~) @ (((((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (((!!) @ (^[Y2 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (q @ Y2)))))) | 4.29/1.19 (((~) @ (p @ Y1)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (q @ Y1) | 4.29/1.19 (((!!) @ ( 4.29/1.19 ^[Y2 : $i]: 4.29/1.19 (( 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y1 @ Y2))) | 4.29/1.19 (( 4.29/1.19 (~) @ ( 4.29/1.19 p @ Y2))))))))))))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 4.29/1.19 thf(zip_derived_cl26, plain, 4.29/1.19 (~ (((((~) @ (rel_s5 @ '#sk1' @ '#sk2'))) | 4.29/1.19 (((~) @ (((((~) @ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))))))) | 4.29/1.19 (((~) @ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ 4.29/1.19 '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ ( 4.29/1.19 rel_s5 @ 4.29/1.19 Y0 @ Y1))) | 4.29/1.19 (((~) @ ( 4.29/1.19 p @ Y1)))))))))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 4.29/1.19 thf(zip_derived_cl28, plain, 4.29/1.19 ( (((((~) @ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ 4.29/1.19 Y1))) | 4.29/1.19 (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))))))) | 4.29/1.19 (((~) @ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ 4.29/1.19 Y1))) | 4.29/1.19 (((~) @ (p @ Y1)))))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl26])). 4.29/1.19 thf(zip_derived_cl29, plain, 4.29/1.19 ((~ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))))) 4.29/1.19 | ~ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 4.29/1.19 Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl28])). 4.29/1.19 thf(zip_derived_cl30, plain, 4.29/1.19 ((~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) 4.29/1.19 | ~ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 4.29/1.19 Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 4.29/1.19 thf(zip_derived_cl32, plain, 4.29/1.19 ((~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) 4.29/1.19 | ~ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 4.29/1.19 Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ ($true))))))), 4.29/1.19 inference('local_rewriting', [status(thm)], [zip_derived_cl30])). 4.29/1.19 thf(zip_derived_cl33, plain, 4.29/1.19 ((~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl32])). 4.29/1.19 thf(zip_derived_cl34, plain, 4.29/1.19 ((~ (((((~) @ (rel_s5 @ '#sk2' @ '#sk3'))) | (q @ '#sk3') | 4.29/1.19 (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))))) 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 4.29/1.19 thf(zip_derived_cl39, plain, 4.29/1.19 (( (rel_s5 @ '#sk2' @ '#sk3') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 4.29/1.19 thf(zip_derived_cl43, plain, 4.29/1.19 (( ('#form4') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(zip_derived_cl44, plain, 4.29/1.19 ((~ (((((~) @ (rel_s5 @ '#sk2' @ '#sk5'))) | 4.29/1.19 (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk5' @ Y0))) | (q @ Y0)))))) | 4.29/1.19 (((~) @ (p @ '#sk5'))))) 4.29/1.19 | ('#form4'))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl50, plain, 4.29/1.19 ((~ (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ '#sk5' @ Y0))) | (q @ Y0)))))) 4.29/1.19 | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 4.29/1.19 thf(zip_derived_cl54, plain, 4.29/1.19 ((~ (((((~) @ (rel_s5 @ '#sk5' @ '#sk7'))) | (q @ '#sk7'))) | ('#form4'))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 4.29/1.19 thf(zip_derived_cl59, plain, ((~ (q @ '#sk7') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 4.29/1.19 thf(zip_derived_cl41, plain, 4.29/1.19 ((~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))) 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 4.29/1.19 thf(zip_derived_cl43, plain, 4.29/1.19 (( ('#form4') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(zip_derived_cl47, plain, 4.29/1.19 ((~ ('#form4') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk3' @ Y0))) | (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('renaming', [status(thm)], [zip_derived_cl41, zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl52, plain, 4.29/1.19 ((~ (((((~) @ (rel_s5 @ '#sk3' @ '#sk6'))) | (((~) @ (p @ '#sk6'))))) 4.29/1.19 | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 4.29/1.19 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 4.29/1.19 thf(msymmetric, axiom,(( msymmetric ) = 4.29/1.19 (^[R:( $i > $i > $o )]: 4.29/1.19 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) )))). 4.29/1.19 thf('16', plain, 4.29/1.19 (( msymmetric ) = 4.29/1.19 ( ^[R:( $i > $i > $o )]: 4.29/1.19 ( ![S:$i,T:$i]: ( ( R @ S @ T ) => ( R @ T @ S ) ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [msymmetric])). 4.29/1.19 thf('17', plain, 4.29/1.19 (( msymmetric ) = 4.29/1.19 ( ^[V_1:( $i > $i > $o )]: 4.29/1.19 ( ![X4:$i,X6:$i]: ( ( V_1 @ X4 @ X6 ) => ( V_1 @ X6 @ X4 ) ) ) )), 4.29/1.19 define([status(thm)])).thf(a3, axiom, (msymmetric @ rel_s5)). 4.29/1.19 thf(zf_stmt_2, axiom, 4.29/1.19 (![X4:$i,X6:$i]: ( ( rel_s5 @ X4 @ X6 ) => ( rel_s5 @ X6 @ X4 ) ))). 4.29/1.19 thf(zip_derived_cl0, plain, 4.29/1.19 ( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))))), 4.29/1.19 inference('cnf', [status(esa)], [zf_stmt_2])). 4.29/1.19 thf(zip_derived_cl5, plain, 4.29/1.19 (![X2 : $i]: 4.29/1.19 (((!!) @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) => (rel_s5 @ Y0 @ X2))))))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 4.29/1.19 thf(zip_derived_cl6, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: (((rel_s5 @ X2 @ X4) => (rel_s5 @ X4 @ X2)))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 4.29/1.19 thf(zip_derived_cl7, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: (~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X4 @ X2))), 4.29/1.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 4.29/1.19 thf(zip_derived_cl76, plain, ((~ ('#form4') | (rel_s5 @ '#sk6' @ '#sk3'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl7])). 4.29/1.19 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 4.29/1.19 thf(zip_derived_cl31, plain, 4.29/1.19 (( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) 4.29/1.19 | ~ (((((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ 4.29/1.19 Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 4.29/1.19 thf(zip_derived_cl35, plain, 4.29/1.19 (( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) 4.29/1.19 | ~ ((($false) | 4.29/1.19 (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))))))), 4.29/1.19 inference('local_rewriting', [status(thm)], [zip_derived_cl31])). 4.29/1.19 thf(zip_derived_cl36, plain, 4.29/1.19 (( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) 4.29/1.19 | ~ (((~) @ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))))), 4.29/1.19 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl35])). 4.29/1.19 thf(zip_derived_cl37, plain, 4.29/1.19 (( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))), 4.29/1.19 inference('simplify nested equalities', [status(thm)], [zip_derived_cl36])). 4.29/1.19 thf(zip_derived_cl38, plain, 4.29/1.19 (![X2 : $i]: 4.29/1.19 ( (((((~) @ (rel_s5 @ '#sk2' @ X2))) | 4.29/1.19 (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ X2 @ Y0))) | (q @ Y0)))))) | 4.29/1.19 (((~) @ (p @ X2))))) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl37])). 4.29/1.19 thf(zip_derived_cl42, plain, 4.29/1.19 (![X2 : $i]: 4.29/1.19 (~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s5 @ X2 @ Y0))) | (q @ Y0)))))) 4.29/1.19 | ~ (p @ X2) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 4.29/1.19 thf(zip_derived_cl48, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: 4.29/1.19 ( (((((~) @ (rel_s5 @ X2 @ X4))) | (q @ X4))) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))) 4.29/1.19 | ~ (p @ X2) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 4.29/1.19 thf(zip_derived_cl53, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: 4.29/1.19 (~ (rel_s5 @ X2 @ X4) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | ~ (p @ X2) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | (q @ Y0) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | 4.29/1.19 (((~) @ (p @ Y1))))))))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 4.29/1.19 thf(zip_derived_cl57, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 ( (((((~) @ (rel_s5 @ '#sk2' @ X6))) | (q @ X6) | 4.29/1.19 (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ X6 @ Y0))) | (((~) @ (p @ Y0)))))))))) 4.29/1.19 | ~ (p @ X2) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ X2 @ X4))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 4.29/1.19 thf(zip_derived_cl60, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 (~ (rel_s5 @ '#sk2' @ X6) 4.29/1.19 | (q @ X6) 4.29/1.19 | (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ X6 @ Y0))) | (((~) @ (p @ Y0)))))))) 4.29/1.19 | ~ (rel_s5 @ X2 @ X4) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | ~ (p @ X2))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])). 4.29/1.19 thf(zip_derived_cl61, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 4.29/1.19 ( (((((~) @ (rel_s5 @ X6 @ X8))) | (((~) @ (p @ X8))))) 4.29/1.19 | ~ (p @ X2) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ X2 @ X4) 4.29/1.19 | (q @ X6) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X6))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])). 4.29/1.19 thf(zip_derived_cl62, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 4.29/1.19 (~ (rel_s5 @ X6 @ X8) 4.29/1.19 | ~ (p @ X8) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X6) 4.29/1.19 | (q @ X6) 4.29/1.19 | ~ (rel_s5 @ X2 @ X4) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | ~ (p @ X2))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 4.29/1.19 thf(zip_derived_cl97, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ ('#form4') 4.29/1.19 | ~ (p @ X0) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ '#sk3') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk3') 4.29/1.19 | ~ (p @ '#sk6'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl62])). 4.29/1.19 thf(zip_derived_cl40, plain, 4.29/1.19 ((~ (q @ '#sk3') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 4.29/1.19 thf(zip_derived_cl43, plain, 4.29/1.19 (( ('#form4') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(zip_derived_cl46, plain, ((~ ('#form4') | ~ (q @ '#sk3'))), 4.29/1.19 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl565, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (p @ '#sk6') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk3') 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | ~ (p @ X0) 4.29/1.19 | ~ ('#form4'))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl97, zip_derived_cl46])). 4.29/1.19 thf(zip_derived_cl56, plain, (( (p @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 4.29/1.19 thf(zip_derived_cl566, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ ('#form4') 4.29/1.19 | ~ (p @ X0) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk3'))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl565, zip_derived_cl56])). 4.29/1.19 thf(zip_derived_cl39, plain, 4.29/1.19 (( (rel_s5 @ '#sk2' @ '#sk3') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 4.29/1.19 thf(zip_derived_cl43, plain, 4.29/1.19 (( ('#form4') 4.29/1.19 | ~ (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ '#sk2' @ Y0))) | 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((~) @ (rel_s5 @ Y0 @ Y1))) | (q @ Y1)))))) | 4.29/1.19 (((~) @ (p @ Y0)))))))))), 4.29/1.19 define([status(thm)])). 4.29/1.19 thf(zip_derived_cl45, plain, ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk3'))), 4.29/1.19 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl567, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | ~ (p @ X0) 4.29/1.19 | ~ ('#form4'))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl566, zip_derived_cl45])). 4.29/1.19 thf(zip_derived_cl571, plain, 4.29/1.19 ((~ ('#form4') 4.29/1.19 | ~ ('#form4') 4.29/1.19 | ~ (p @ '#sk6') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk6') 4.29/1.19 | (q @ '#sk3'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl567])). 4.29/1.19 thf(zip_derived_cl614, plain, 4.29/1.19 (( (q @ '#sk3') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk6') 4.29/1.19 | ~ (p @ '#sk6') 4.29/1.19 | ~ ('#form4'))), 4.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl571])). 4.29/1.19 thf(zip_derived_cl46, plain, ((~ ('#form4') | ~ (q @ '#sk3'))), 4.29/1.19 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl670, plain, 4.29/1.19 ((~ ('#form4') | ~ (p @ '#sk6') | ~ (rel_s5 @ '#sk2' @ '#sk6'))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl614, zip_derived_cl46])). 4.29/1.19 thf(zip_derived_cl56, plain, (( (p @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 4.29/1.19 thf(zip_derived_cl671, plain, 4.29/1.19 ((~ (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl670, zip_derived_cl56])). 4.29/1.19 thf(zip_derived_cl45, plain, ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk3'))), 4.29/1.19 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl43])). 4.29/1.19 thf(zip_derived_cl55, plain, (( (rel_s5 @ '#sk3' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 4.29/1.19 thf(mtransitive, axiom,(( mtransitive ) = 4.29/1.19 (^[R:( $i > $i > $o )]: 4.29/1.19 ( ![S:$i,T:$i,U:$i]: 4.29/1.19 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 4.29/1.19 thf('18', plain, 4.29/1.19 (( mtransitive ) = 4.29/1.19 ( ^[R:( $i > $i > $o )]: 4.29/1.19 ( ![S:$i,T:$i,U:$i]: 4.29/1.19 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 4.29/1.19 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 4.29/1.19 thf('19', plain, 4.29/1.19 (( mtransitive ) = 4.29/1.19 ( ^[V_1:( $i > $i > $o )]: 4.29/1.19 ( ![X4:$i,X6:$i,X8:$i]: 4.29/1.19 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 4.29/1.19 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s5)). 4.29/1.19 thf(zf_stmt_3, axiom, 4.29/1.19 (![X4:$i,X6:$i,X8:$i]: 4.29/1.19 ( ( ( rel_s5 @ X6 @ X8 ) & ( rel_s5 @ X4 @ X6 ) ) => ( rel_s5 @ X4 @ X8 ) ))). 4.29/1.19 thf(zip_derived_cl2, plain, 4.29/1.19 ( (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((!!) @ (^[Y2 : $i]: 4.29/1.19 (((((rel_s5 @ Y1 @ Y2) & (rel_s5 @ 4.29/1.19 Y0 @ Y1))) => 4.29/1.19 (rel_s5 @ Y0 @ Y2))))))))))))), 4.29/1.19 inference('cnf', [status(esa)], [zf_stmt_3])). 4.29/1.19 thf(zip_derived_cl12, plain, 4.29/1.19 (![X2 : $i]: 4.29/1.19 (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((!!) @ (^[Y1 : $i]: 4.29/1.19 (((((rel_s5 @ Y0 @ Y1) & (rel_s5 @ X2 @ Y0))) => 4.29/1.19 (rel_s5 @ X2 @ Y1)))))))))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 4.29/1.19 thf(zip_derived_cl13, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: 4.29/1.19 (((!!) @ (^[Y0 : $i]: 4.29/1.19 (((((rel_s5 @ X4 @ Y0) & (rel_s5 @ X2 @ X4))) => 4.29/1.19 (rel_s5 @ X2 @ Y0))))))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 4.29/1.19 thf(zip_derived_cl14, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 (((((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) => (rel_s5 @ X2 @ X6)))), 4.29/1.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 4.29/1.19 thf(zip_derived_cl15, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 (~ (((rel_s5 @ X4 @ X6) & (rel_s5 @ X2 @ X4))) | (rel_s5 @ X2 @ X6))), 4.29/1.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 4.29/1.19 thf(zip_derived_cl16, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 (~ (rel_s5 @ X4 @ X6) | ~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X2 @ X6))), 4.29/1.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 4.29/1.19 thf(zip_derived_cl75, plain, 4.29/1.19 (![X0 : $i]: 4.29/1.19 (~ ('#form4') | (rel_s5 @ X0 @ '#sk6') | ~ (rel_s5 @ X0 @ '#sk3'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl16])). 4.29/1.19 thf(zip_derived_cl194, plain, 4.29/1.19 ((~ ('#form4') | (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl45, zip_derived_cl75])). 4.29/1.19 thf(zip_derived_cl202, plain, (( (rel_s5 @ '#sk2' @ '#sk6') | ~ ('#form4'))), 4.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl194])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl676, plain, (~ (q @ '#sk7')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl675, plain, ( (rel_s5 @ '#sk5' @ '#sk7')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 4.29/1.19 thf(zip_derived_cl7, plain, 4.29/1.19 (![X2 : $i, X4 : $i]: (~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X4 @ X2))), 4.29/1.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 4.29/1.19 thf(zip_derived_cl84, plain, (( ('#form4') | (rel_s5 @ '#sk7' @ '#sk5'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl7])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl680, plain, ( (rel_s5 @ '#sk7' @ '#sk5')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl84, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl62, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 4.29/1.19 (~ (rel_s5 @ X6 @ X8) 4.29/1.19 | ~ (p @ X8) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X6) 4.29/1.19 | (q @ X6) 4.29/1.19 | ~ (rel_s5 @ X2 @ X4) 4.29/1.19 | (q @ X4) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X2) 4.29/1.19 | ~ (p @ X2))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 4.29/1.19 thf(zip_derived_cl715, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (p @ X0) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ '#sk7') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk7') 4.29/1.19 | ~ (p @ '#sk5'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl680, zip_derived_cl62])). 4.29/1.19 thf(zip_derived_cl51, plain, (( (p @ '#sk5') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl674, plain, ( (p @ '#sk5')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl721, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (p @ X0) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ '#sk7') 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ '#sk7'))), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl715, zip_derived_cl674])). 4.29/1.19 thf(zip_derived_cl49, plain, (( (rel_s5 @ '#sk2' @ '#sk5') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 4.29/1.19 thf(zip_derived_cl58, plain, (( (rel_s5 @ '#sk5' @ '#sk7') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 4.29/1.19 thf(zip_derived_cl16, plain, 4.29/1.19 (![X2 : $i, X4 : $i, X6 : $i]: 4.29/1.19 (~ (rel_s5 @ X4 @ X6) | ~ (rel_s5 @ X2 @ X4) | (rel_s5 @ X2 @ X6))), 4.29/1.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl15])). 4.29/1.19 thf(zip_derived_cl83, plain, 4.29/1.19 (![X0 : $i]: 4.29/1.19 ( ('#form4') | (rel_s5 @ X0 @ '#sk7') | ~ (rel_s5 @ X0 @ '#sk5'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl16])). 4.29/1.19 thf(zip_derived_cl292, plain, 4.29/1.19 (( ('#form4') | (rel_s5 @ '#sk2' @ '#sk7') | ('#form4'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl49, zip_derived_cl83])). 4.29/1.19 thf(zip_derived_cl300, plain, (( (rel_s5 @ '#sk2' @ '#sk7') | ('#form4'))), 4.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl292])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl684, plain, ( (rel_s5 @ '#sk2' @ '#sk7')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl300, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl1663, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (p @ X0) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ '#sk7'))), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl721, zip_derived_cl684])). 4.29/1.19 thf(zip_derived_cl676, plain, (~ (q @ '#sk7')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl59, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl1664, plain, 4.29/1.19 (![X0 : $i, X1 : $i]: 4.29/1.19 (~ (rel_s5 @ X0 @ X1) 4.29/1.19 | (q @ X1) 4.29/1.19 | ~ (rel_s5 @ '#sk2' @ X0) 4.29/1.19 | ~ (p @ X0))), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl1663, zip_derived_cl676])). 4.29/1.19 thf(zip_derived_cl1668, plain, 4.29/1.19 ((~ (p @ '#sk5') | ~ (rel_s5 @ '#sk2' @ '#sk5') | (q @ '#sk7'))), 4.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl675, zip_derived_cl1664])). 4.29/1.19 thf(zip_derived_cl674, plain, ( (p @ '#sk5')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl51, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl49, plain, (( (rel_s5 @ '#sk2' @ '#sk5') | ('#form4'))), 4.29/1.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 4.29/1.19 thf(zip_derived_cl672, plain, (~ ('#form4')), 4.29/1.19 inference('clc', [status(thm)], [zip_derived_cl671, zip_derived_cl202])). 4.29/1.19 thf(zip_derived_cl673, plain, ( (rel_s5 @ '#sk2' @ '#sk5')), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl672])). 4.29/1.19 thf(zip_derived_cl1694, plain, ( (q @ '#sk7')), 4.29/1.19 inference('demod', [status(thm)], 4.29/1.19 [zip_derived_cl1668, zip_derived_cl674, zip_derived_cl673])). 4.29/1.19 thf(zip_derived_cl1715, plain, ($false), 4.29/1.19 inference('demod', [status(thm)], [zip_derived_cl676, zip_derived_cl1694])). 4.29/1.19 4.29/1.19 % SZS output end Refutation 4.29/1.19 4.29/1.19 4.29/1.20 % Terminating... 4.60/1.36 % Runner terminated. 4.63/1.37 % Zipperpin 1.5 exiting 4.63/1.39 EOF