0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ZDdn8xKhZ4 true 0.10/0.31 % Computer : n027.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Tue Aug 9 06:31:06 EDT 2022 0.10/0.31 % CPUTime : 0.10/0.31 % Running portfolio for 960 s 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.10/0.31 % Number of cores: 8 0.16/0.31 % Python version: Python 3.6.8 0.16/0.31 % 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 0.99/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.99/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.99/0.68 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 1.37/0.74 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 1.41/0.89 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 1.62/1.07 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 88.12/11.66 % Solved by lams/15_e_short1.sh. 88.12/11.66 % running E: timeout 11 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.ZDdn8xKhZ4/e_inputd96699 --cpu-limit=9 --auto-schedule -s -p 88.12/11.66 % done 198 iterations in 10.918s 88.12/11.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 88.12/11.66 % SZS output start Refutation 88.12/11.66 thf(mu_type, type, mu: $tType). 88.12/11.66 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 88.12/11.66 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 88.12/11.66 thf(implies_type, type, implies: mu > mu > mu). 88.12/11.66 thf(and_type, type, and: mu > mu > mu). 88.12/11.66 thf(and_1_type, type, and_1: $i > $o). 88.12/11.66 thf(kn2_type, type, kn2: $i > $o). 88.12/11.66 thf(is_a_theorem_type, type, is_a_theorem: mu > $i > $o). 88.12/11.66 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 88.12/11.66 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 88.12/11.66 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 88.12/11.66 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 88.12/11.66 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 88.12/11.66 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 88.12/11.66 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 88.12/11.66 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 88.12/11.66 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 88.12/11.66 thf(cumulative_ax, axiom, 88.12/11.66 (![X:mu,V:$i,W:$i]: 88.12/11.66 ( ( ( exists_in_world @ X @ V ) & ( rel_s4 @ V @ W ) ) => 88.12/11.66 ( exists_in_world @ X @ W ) ))). 88.12/11.66 thf(zip_derived_cl3, plain, 88.12/11.66 ( (((!!) @ (^[Y0 : mu]: 88.12/11.66 (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((exists_in_world @ Y0 @ Y1) & 88.12/11.66 (rel_s4 @ Y1 @ Y2))) => 88.12/11.66 (exists_in_world @ Y0 @ Y2))))))))))))), 88.12/11.66 inference('cnf', [status(esa)], [cumulative_ax])). 88.12/11.66 thf(mtransitive, axiom,(( mtransitive ) = 88.12/11.66 (^[R:( $i > $i > $o )]: 88.12/11.66 ( ![S:$i,T:$i,U:$i]: 88.12/11.66 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 88.12/11.66 thf('0', plain, 88.12/11.66 (( mtransitive ) = 88.12/11.66 ( ^[R:( $i > $i > $o )]: 88.12/11.66 ( ![S:$i,T:$i,U:$i]: 88.12/11.66 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 88.12/11.66 thf('1', plain, 88.12/11.66 (( mtransitive ) = 88.12/11.66 ( ^[V_1:( $i > $i > $o )]: 88.12/11.66 ( ![X4:$i,X6:$i,X8:$i]: 88.12/11.66 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 88.12/11.66 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s4)). 88.12/11.66 thf(zf_stmt_0, axiom, 88.12/11.66 (![X4:$i,X6:$i,X8:$i]: 88.12/11.66 ( ( ( rel_s4 @ X6 @ X8 ) & ( rel_s4 @ X4 @ X6 ) ) => ( rel_s4 @ X4 @ X8 ) ))). 88.12/11.66 thf(zip_derived_cl1, plain, 88.12/11.66 ( (((!!) @ (^[Y0 : $i]: 88.12/11.66 (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 88.12/11.66 Y0 @ Y1))) => 88.12/11.66 (rel_s4 @ Y0 @ Y2))))))))))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_0])). 88.12/11.66 thf(mreflexive, axiom,(( mreflexive ) = 88.12/11.66 (^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) )))). 88.12/11.66 thf('2', plain, 88.12/11.66 (( mreflexive ) = ( ^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 88.12/11.66 thf('3', plain, 88.12/11.66 (( mreflexive ) = 88.12/11.66 ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 88.12/11.66 define([status(thm)])).thf(a1, axiom, (mreflexive @ rel_s4)). 88.12/11.66 thf(zf_stmt_1, axiom, (![X4:$i]: ( rel_s4 @ X4 @ X4 ))). 88.12/11.66 thf(zip_derived_cl2, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_1])). 88.12/11.66 thf(mbox_s4, axiom,(( mbox_s4 ) = 88.12/11.66 (^[Phi:( $i > $o ),W:$i]: 88.12/11.66 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) )))). 88.12/11.66 thf('4', plain, 88.12/11.66 (( mbox_s4 ) = 88.12/11.66 ( ^[Phi:( $i > $o ),W:$i]: 88.12/11.66 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 88.12/11.66 thf('5', plain, 88.12/11.66 (( mbox_s4 ) = 88.12/11.66 ( ^[V_1:( $i > $o ),V_2:$i]: 88.12/11.66 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s4 @ V_2 @ X4 ) ) ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(mvalid, axiom,(( mvalid ) = 88.12/11.66 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 88.12/11.66 thf('6', plain, 88.12/11.66 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mvalid])). 88.12/11.66 thf('7', plain, 88.12/11.66 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(hilbert_and_1, axiom, (mvalid @ ( mbox_s4 @ and_1 ))). 88.12/11.66 thf(zf_stmt_2, axiom, 88.12/11.66 (![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( and_1 @ X6 ) ))). 88.12/11.66 thf(zip_derived_cl41, plain, 88.12/11.66 ( (((!!) @ (^[Y0 : $i]: 88.12/11.66 (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (and_1 @ Y1)))))))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_2])). 88.12/11.66 thf(mforall_ind, axiom,(( mforall_ind ) = 88.12/11.66 (^[Phi:( mu > $i > $o ),W:$i]: 88.12/11.66 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 88.12/11.66 thf('8', plain, 88.12/11.66 (( mforall_ind ) = 88.12/11.66 ( ^[Phi:( mu > $i > $o ),W:$i]: 88.12/11.66 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 88.12/11.66 thf('9', plain, 88.12/11.66 (( mforall_ind ) = 88.12/11.66 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 88.12/11.66 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(mimplies, axiom,(( mimplies ) = 88.12/11.66 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 88.12/11.66 thf(mor, axiom,(( mor ) = 88.12/11.66 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 88.12/11.66 thf('10', plain, 88.12/11.66 (( mor ) = 88.12/11.66 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mor])). 88.12/11.66 thf('11', plain, 88.12/11.66 (( mor ) = 88.12/11.66 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 88.12/11.66 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 88.12/11.66 thf('12', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mnot])). 88.12/11.66 thf('13', plain, 88.12/11.66 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf('14', plain, 88.12/11.66 (( mimplies ) = 88.12/11.66 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mimplies, '11', '13'])). 88.12/11.66 thf('15', plain, 88.12/11.66 (( mimplies ) = 88.12/11.66 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(mand, axiom,(( mand ) = 88.12/11.66 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 88.12/11.66 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 88.12/11.66 thf('16', plain, 88.12/11.66 (( mand ) = 88.12/11.66 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 88.12/11.66 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 88.12/11.66 inference('simplify_rw_rule', [status(thm)], [mand, '11', '13'])). 88.12/11.66 thf('17', plain, 88.12/11.66 (( mand ) = 88.12/11.66 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 88.12/11.66 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 88.12/11.66 define([status(thm)])). 88.12/11.66 thf(and_1, axiom, 88.12/11.66 (mvalid @ 88.12/11.66 ( mand @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mimplies @ 88.12/11.66 ( mbox_s4 @ and_1 ) @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[X:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[Y:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) ) ) @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mimplies @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[X:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[Y:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) @ 88.12/11.66 ( mbox_s4 @ and_1 ) ) ) ))). 88.12/11.66 thf(zf_stmt_3, axiom, 88.12/11.66 (![X4:$i]: 88.12/11.66 ( ~( ( ~( ![X20:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X4 @ X20 ) ) | 88.12/11.66 ( ![X32:$i]: ( ( ~( rel_s4 @ X20 @ X32 ) ) | ( and_1 @ X32 ) ) ) | 88.12/11.66 ( ~( ![X22:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X20 @ X22 ) ) | 88.12/11.66 ( ![X24:mu]: 88.12/11.66 ( ( exists_in_world @ X24 @ X22 ) => 88.12/11.66 ( ![X26:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X22 @ X26 ) ) | 88.12/11.66 ( ![X28:mu]: 88.12/11.66 ( ( exists_in_world @ X28 @ X26 ) => 88.12/11.66 ( ![X30:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X26 @ X30 ) ) | 88.12/11.66 ( is_a_theorem @ 88.12/11.66 ( implies @ ( and @ X24 @ X28 ) @ X24 ) @ 88.12/11.66 X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 88.12/11.66 ( ~( ![X6:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 88.12/11.66 ( ![X10:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X6 @ X10 ) ) | 88.12/11.66 ( ![X12:mu]: 88.12/11.66 ( ( exists_in_world @ X12 @ X10 ) => 88.12/11.66 ( ![X14:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X10 @ X14 ) ) | 88.12/11.66 ( ![X16:mu]: 88.12/11.66 ( ( exists_in_world @ X16 @ X14 ) => 88.12/11.66 ( ![X18:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X14 @ X18 ) ) | 88.12/11.66 ( is_a_theorem @ 88.12/11.66 ( implies @ ( and @ X12 @ X16 ) @ X12 ) @ 88.12/11.66 X18 ) ) ) ) ) ) ) ) ) ) ) | 88.12/11.66 ( ~( ![X8:$i]: ( ( ~( rel_s4 @ X6 @ X8 ) ) | ( and_1 @ X8 ) ) ) ) ) ) ) ) ))). 88.12/11.66 thf(zip_derived_cl39, plain, 88.12/11.66 ( (((!!) @ (^[Y0 : $i]: 88.12/11.66 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (and_1 @ Y2)))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y2 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y3 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y3 @ 88.12/11.66 Y2) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y4 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y2 @ Y4))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y5 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y5 @ 88.12/11.66 Y4) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y6 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y4 @ Y6))) | 88.12/11.66 (is_a_theorem @ 88.12/11.66 ( 88.12/11.66 implies @ 88.12/11.66 ( 88.12/11.66 and @ 88.12/11.66 Y3 @ Y5) @ 88.12/11.66 Y3) @ Y6))))))))))))))))))))))))))))))))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (((!!) @ ( 88.12/11.66 ^[Y3 : mu]: 88.12/11.66 ( 88.12/11.66 ( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y3 @ 88.12/11.66 Y2) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y4 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y2 @ Y4))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y5 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y5 @ 88.12/11.66 Y4) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y6 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y4 @ Y6))) | 88.12/11.66 (is_a_theorem @ 88.12/11.66 ( 88.12/11.66 implies @ 88.12/11.66 ( 88.12/11.66 and @ 88.12/11.66 Y3 @ Y5) @ 88.12/11.66 Y3) @ Y6)))))))))))))))))))))))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y2 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (and_1 @ 88.12/11.66 Y2))))))))))))))))))))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_3])). 88.12/11.66 thf(kn2, axiom, 88.12/11.66 (mvalid @ 88.12/11.66 ( mand @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mimplies @ 88.12/11.66 ( mbox_s4 @ kn2 ) @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[P:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[Q:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) ) ) @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mimplies @ 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[P:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( mforall_ind @ 88.12/11.66 ( ^[Q:mu]: 88.12/11.66 ( mbox_s4 @ 88.12/11.66 ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) @ 88.12/11.66 ( mbox_s4 @ kn2 ) ) ) ))). 88.12/11.66 thf(zf_stmt_4, axiom, 88.12/11.66 (![X4:$i]: 88.12/11.66 ( ~( ( ~( ![X20:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X4 @ X20 ) ) | 88.12/11.66 ( ![X32:$i]: ( ( ~( rel_s4 @ X20 @ X32 ) ) | ( kn2 @ X32 ) ) ) | 88.12/11.66 ( ~( ![X22:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X20 @ X22 ) ) | 88.12/11.66 ( ![X24:mu]: 88.12/11.66 ( ( exists_in_world @ X24 @ X22 ) => 88.12/11.66 ( ![X26:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X22 @ X26 ) ) | 88.12/11.66 ( ![X28:mu]: 88.12/11.66 ( ( exists_in_world @ X28 @ X26 ) => 88.12/11.66 ( ![X30:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X26 @ X30 ) ) | 88.12/11.66 ( is_a_theorem @ 88.12/11.66 ( implies @ ( and @ X24 @ X28 ) @ X24 ) @ 88.12/11.66 X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 88.12/11.66 ( ~( ![X6:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 88.12/11.66 ( ![X10:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X6 @ X10 ) ) | 88.12/11.66 ( ![X12:mu]: 88.12/11.66 ( ( exists_in_world @ X12 @ X10 ) => 88.12/11.66 ( ![X14:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X10 @ X14 ) ) | 88.12/11.66 ( ![X16:mu]: 88.12/11.66 ( ( exists_in_world @ X16 @ X14 ) => 88.12/11.66 ( ![X18:$i]: 88.12/11.66 ( ( ~( rel_s4 @ X14 @ X18 ) ) | 88.12/11.66 ( is_a_theorem @ 88.12/11.66 ( implies @ ( and @ X12 @ X16 ) @ X12 ) @ 88.12/11.66 X18 ) ) ) ) ) ) ) ) ) ) ) | 88.12/11.66 ( ~( ![X8:$i]: ( ( ~( rel_s4 @ X6 @ X8 ) ) | ( kn2 @ X8 ) ) ) ) ) ) ) ) ))). 88.12/11.66 thf(zip_derived_cl6, plain, 88.12/11.66 ( (((!!) @ (^[Y0 : $i]: 88.12/11.66 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (kn2 @ Y2)))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y2 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y3 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y3 @ 88.12/11.66 Y2) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y4 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y2 @ Y4))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y5 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y5 @ 88.12/11.66 Y4) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y6 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y4 @ Y6))) | 88.12/11.66 (is_a_theorem @ 88.12/11.66 ( 88.12/11.66 implies @ 88.12/11.66 ( 88.12/11.66 and @ 88.12/11.66 Y3 @ Y5) @ 88.12/11.66 Y3) @ Y6))))))))))))))))))))))))))))))))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 88.12/11.66 (((!!) @ (^[Y2 : $i]: 88.12/11.66 (((((~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (((!!) @ ( 88.12/11.66 ^[Y3 : mu]: 88.12/11.66 ( 88.12/11.66 ( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y3 @ 88.12/11.66 Y2) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y4 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y2 @ Y4))) | 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y5 : mu]: 88.12/11.66 (( 88.12/11.66 (exists_in_world @ 88.12/11.66 Y5 @ 88.12/11.66 Y4) => 88.12/11.66 (( 88.12/11.66 (!!) @ ( 88.12/11.66 ^[Y6 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y4 @ Y6))) | 88.12/11.66 (is_a_theorem @ 88.12/11.66 ( 88.12/11.66 implies @ 88.12/11.66 ( 88.12/11.66 and @ 88.12/11.66 Y3 @ Y5) @ 88.12/11.66 Y3) @ Y6)))))))))))))))))))))))))) | 88.12/11.66 (((~) @ (((!!) @ (^[Y2 : $i]: 88.12/11.66 (( 88.12/11.66 (( 88.12/11.66 (~) @ ( 88.12/11.66 rel_s4 @ 88.12/11.66 Y1 @ Y2))) | 88.12/11.66 (kn2 @ 88.12/11.66 Y2))))))))))))))))))))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_4])). 88.12/11.66 thf(rosser_kn2, conjecture, (mvalid @ ( mbox_s4 @ kn2 ))). 88.12/11.66 thf(zf_stmt_5, conjecture, 88.12/11.66 (![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( kn2 @ X6 ) ))). 88.12/11.66 thf(zf_stmt_6, negated_conjecture, 88.12/11.66 (~( ![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( kn2 @ X6 ) ) )), 88.12/11.66 inference('cnf.neg', [status(esa)], [zf_stmt_5])). 88.12/11.66 thf(zip_derived_cl8, plain, 88.12/11.66 (~ (((!!) @ (^[Y0 : $i]: 88.12/11.66 (((!!) @ (^[Y1 : $i]: 88.12/11.66 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (kn2 @ Y1)))))))))), 88.12/11.66 inference('cnf', [status(esa)], [zf_stmt_6])). 88.12/11.66 thf(zip_derived_cl1652, plain, ($false), 88.12/11.66 inference('eprover', [status(thm)], 88.12/11.66 [zip_derived_cl3, zip_derived_cl1, zip_derived_cl2, 88.12/11.66 zip_derived_cl41, zip_derived_cl39, zip_derived_cl6, 88.12/11.66 zip_derived_cl8])). 88.12/11.66 88.12/11.66 % SZS output end Refutation 88.12/11.66 88.12/11.66 88.12/11.66 % Terminating... 88.12/11.73 % Runner terminated. 88.12/11.74 % Zipperpin 1.5 exiting 88.12/11.74 EOF