%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:11:52 AM UTC 2026
% Result : Theorem 255.88s 33.00s
% Output : CNFRefutation 255.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 495 ( 23 equ; 0 cnn)
% Maximal formula atoms : 57 ( 6 avg)
% Number of connectives : 2343 ( 337 ~; 298 |; 16 &;1673 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 11 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 5 con; 0-5 aty)
% Number of variables : 257 ( 63 ^; 194 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
exists_in_world: mu > $i > $o ).
thf(decl_38,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_39,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_41,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_44,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
string: mu > $i > $o ).
thf(decl_59,type,
in: mu > mu > mu > $i > $o ).
thf(decl_60,type,
do: mu > mu > mu > $i > $o ).
thf(decl_61,type,
number: mu > mu > $i > $o ).
thf(decl_62,type,
entry_box: mu > $i > $o ).
thf(decl_63,type,
userid: mu > mu > $i > $o ).
thf(decl_64,type,
one: mu ).
thf(decl_65,type,
u: mu ).
thf(decl_67,type,
esk2_2: $i > $i > mu ).
thf(decl_68,type,
esk3_1: $i > mu ).
thf(decl_69,type,
esk4_5: $i > $i > mu > mu > mu > mu ).
thf(decl_70,type,
esk5_0: $i ).
thf(decl_71,type,
esk6_0: $i ).
thf(decl_72,type,
esk7_4: mu > mu > mu > mu > $i ).
thf(decl_73,type,
esk8_4: mu > mu > mu > mu > $i ).
thf(decl_74,type,
esk9_4: mu > mu > mu > mu > mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mimplies) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X13: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mexists_ind) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mbox_s4) ).
thf(con,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X20: mu] :
( mexists_ind
@ ^ [X21: mu] :
( mexists_ind
@ ^ [X23: mu] :
( mexists_ind
@ ^ [X25: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ X20 ) @ ( mand @ ( entry_box @ X21 ) @ ( number @ X21 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X24: mu] : ( mimplies @ ( do @ X25 @ X23 @ X24 ) @ ( in @ X20 @ X21 @ X24 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',con) ).
thf(ax3,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X22: mu] :
( mforall_ind
@ ^ [X20: mu] :
( mforall_ind
@ ^ [X21: mu] :
( mimplies @ ( mand @ ( string @ X20 ) @ ( entry_box @ X21 ) )
@ ( mexists_ind
@ ^ [X23: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X24: mu] : ( mimplies @ ( do @ X22 @ X23 @ X24 ) @ ( in @ X20 @ X21 @ X24 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',ax3) ).
thf(ax2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ X21 ) @ ( number @ X21 @ one ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',ax2) ).
thf(ax1,axiom,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X20: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ X20 ) @ ( string @ X20 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',ax1) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i,X17: $i,X18: $i] :
( ( ( X6 @ X16 @ X17 )
& ( X6 @ X17 @ X18 ) )
=> ( X6 @ X16 @ X18 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mtransitive) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',a2) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p',a1) ).
thf(c_0_16,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_17,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_18,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_19,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_20,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X34: mu] :
( ( exists_in_world @ X34 @ Z1 )
=> ~ ( Z0 @ X34 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_21,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_22,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_23,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_17]),c_0_18]) ).
thf(c_0_24,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X34: mu] :
( ( exists_in_world @ X34 @ Z1 )
=> ~ ( Z0 @ X34 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_17]),c_0_21]) ).
thf(c_0_25,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_26,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_27,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X20: mu] :
( mexists_ind
@ ^ [X21: mu] :
( mexists_ind
@ ^ [X23: mu] :
( mexists_ind
@ ^ [X25: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ X20 ) @ ( mand @ ( entry_box @ X21 ) @ ( number @ X21 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X24: mu] : ( mimplies @ ( do @ X25 @ X23 @ X24 ) @ ( in @ X20 @ X21 @ X24 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_28,plain,
! [X55: $i,X54: $i] :
( ~ ( rel_s4 @ X55 @ X54 )
| ! [X53: mu] :
( ( exists_in_world @ X53 @ X54 )
=> ! [X52: mu] :
( ( exists_in_world @ X52 @ X54 )
=> ! [X51: mu] :
( ( exists_in_world @ X51 @ X54 )
=> ( ~ ~ ( ~ ( string @ X52 @ X54 )
| ~ ( entry_box @ X51 @ X54 ) )
| ~ ! [X50: mu] :
( ( exists_in_world @ X50 @ X54 )
=> ~ ! [X49: $i] :
( ~ ( rel_s4 @ X54 @ X49 )
| ! [X48: mu] :
( ( exists_in_world @ X48 @ X49 )
=> ( ~ ( do @ X53 @ X50 @ X48 @ X49 )
| ( in @ X52 @ X51 @ X48 @ X49 ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax3]),c_0_22]),c_0_23]),c_0_21]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_29,negated_conjecture,
~ ! [X64: $i,X63: $i] :
( ~ ( rel_s4 @ X64 @ X63 )
| ~ ! [X62: mu] :
( ( exists_in_world @ X62 @ X63 )
=> ~ ~ ! [X61: mu] :
( ( exists_in_world @ X61 @ X63 )
=> ~ ~ ! [X60: mu] :
( ( exists_in_world @ X60 @ X63 )
=> ~ ~ ! [X59: mu] :
( ( exists_in_world @ X59 @ X63 )
=> ~ ~ ( ~ ! [X56: $i] :
( ~ ( rel_s4 @ X63 @ X56 )
| ~ ( ~ ( userid @ u @ X62 @ X56 )
| ~ ~ ( ~ ( entry_box @ X61 @ X56 )
| ~ ( number @ X61 @ one @ X56 ) ) ) )
| ~ ! [X58: $i] :
( ~ ( rel_s4 @ X63 @ X58 )
| ! [X57: mu] :
( ( exists_in_world @ X57 @ X58 )
=> ( ~ ( do @ X59 @ X60 @ X57 @ X58 )
| ( in @ X62 @ X61 @ X57 @ X58 ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_27]),c_0_22]),c_0_23]),c_0_21]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_30,plain,
! [X47: $i] :
~ ! [X46: mu] :
( ( exists_in_world @ X46 @ X47 )
=> ~ ! [X45: $i] :
( ~ ( rel_s4 @ X47 @ X45 )
| ~ ( ~ ( entry_box @ X46 @ X45 )
| ~ ( number @ X46 @ one @ X45 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax2]),c_0_22]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_31,plain,
! [X83: $i,X84: $i,X85: mu,X86: mu,X87: mu,X89: $i,X90: mu] :
( ( ( exists_in_world @ ( esk4_5 @ X83 @ X84 @ X85 @ X86 @ X87 ) @ X84 )
| ~ ( string @ X86 @ X84 )
| ~ ( entry_box @ X87 @ X84 )
| ~ ( exists_in_world @ X87 @ X84 )
| ~ ( exists_in_world @ X86 @ X84 )
| ~ ( exists_in_world @ X85 @ X84 )
| ~ ( rel_s4 @ X83 @ X84 ) )
& ( ~ ( rel_s4 @ X84 @ X89 )
| ~ ( exists_in_world @ X90 @ X89 )
| ~ ( do @ X85 @ ( esk4_5 @ X83 @ X84 @ X85 @ X86 @ X87 ) @ X90 @ X89 )
| ( in @ X86 @ X87 @ X90 @ X89 )
| ~ ( string @ X86 @ X84 )
| ~ ( entry_box @ X87 @ X84 )
| ~ ( exists_in_world @ X87 @ X84 )
| ~ ( exists_in_world @ X86 @ X84 )
| ~ ( exists_in_world @ X85 @ X84 )
| ~ ( rel_s4 @ X83 @ X84 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])])]) ).
thf(c_0_32,negated_conjecture,
! [X93: mu,X94: mu,X95: mu,X96: mu] :
( ( rel_s4 @ esk5_0 @ esk6_0 )
& ( ( rel_s4 @ esk6_0 @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ( exists_in_world @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ( do @ X96 @ X95 @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ~ ( in @ X93 @ X94 @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ( rel_s4 @ esk6_0 @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( userid @ u @ X93 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( entry_box @ X94 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( number @ X94 @ one @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ( exists_in_world @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( userid @ u @ X93 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( entry_box @ X94 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( number @ X94 @ one @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ( do @ X96 @ X95 @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( userid @ u @ X93 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( entry_box @ X94 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( number @ X94 @ one @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) )
& ( ~ ( in @ X93 @ X94 @ ( esk9_4 @ X93 @ X94 @ X95 @ X96 ) @ ( esk8_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( userid @ u @ X93 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( entry_box @ X94 @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( number @ X94 @ one @ ( esk7_4 @ X93 @ X94 @ X95 @ X96 ) )
| ~ ( exists_in_world @ X96 @ esk6_0 )
| ~ ( exists_in_world @ X95 @ esk6_0 )
| ~ ( exists_in_world @ X94 @ esk6_0 )
| ~ ( exists_in_world @ X93 @ esk6_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])])]) ).
thf(c_0_33,plain,
! [X80: $i,X82: $i] :
( ( exists_in_world @ ( esk3_1 @ X80 ) @ X80 )
& ( ( entry_box @ ( esk3_1 @ X80 ) @ X82 )
| ~ ( rel_s4 @ X80 @ X82 ) )
& ( ( number @ ( esk3_1 @ X80 ) @ one @ X82 )
| ~ ( rel_s4 @ X80 @ X82 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])])]) ).
thf(c_0_34,plain,
! [X44: $i,X43: $i] :
( ~ ( rel_s4 @ X44 @ X43 )
| ~ ! [X42: mu] :
( ( exists_in_world @ X42 @ X43 )
=> ~ ! [X41: $i] :
( ~ ( rel_s4 @ X43 @ X41 )
| ~ ( ~ ( userid @ u @ X42 @ X41 )
| ~ ( string @ X42 @ X41 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax1]),c_0_22]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_35,plain,
! [X7: $i,X12: mu,X14: mu,X19: mu,X16: $i,X10: mu,X3: $i] :
( ( in @ X14 @ X19 @ X10 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( do @ X12 @ ( esk4_5 @ X16 @ X3 @ X12 @ X14 @ X19 ) @ X10 @ X7 )
| ~ ( string @ X14 @ X3 )
| ~ ( entry_box @ X19 @ X3 )
| ~ ( exists_in_world @ X19 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( rel_s4 @ X16 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,negated_conjecture,
! [X10: mu,X12: mu,X19: mu,X14: mu] :
( ( do @ X10 @ X12 @ ( esk9_4 @ X14 @ X19 @ X12 @ X10 ) @ ( esk8_4 @ X14 @ X19 @ X12 @ X10 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X14 @ X19 @ X12 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ( exists_in_world @ ( esk9_4 @ X10 @ X12 @ X14 @ X19 ) @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_38,negated_conjecture,
! [X10: mu,X12: mu,X19: mu,X14: mu] :
( ( do @ X10 @ X12 @ ( esk9_4 @ X14 @ X19 @ X12 @ X10 ) @ ( esk8_4 @ X14 @ X19 @ X12 @ X10 ) )
| ~ ( userid @ u @ X14 @ ( esk7_4 @ X14 @ X19 @ X12 @ X10 ) )
| ~ ( entry_box @ X19 @ ( esk7_4 @ X14 @ X19 @ X12 @ X10 ) )
| ~ ( number @ X19 @ one @ ( esk7_4 @ X14 @ X19 @ X12 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ( exists_in_world @ ( esk9_4 @ X10 @ X12 @ X14 @ X19 ) @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( userid @ u @ X10 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( entry_box @ X12 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( number @ X12 @ one @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_40,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( userid @ u @ X10 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( entry_box @ X12 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( number @ X12 @ one @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,plain,
! [X3: $i,X7: $i] :
( ( number @ ( esk3_1 @ X3 ) @ one @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_42,plain,
! [X3: $i,X7: $i] :
( ( entry_box @ ( esk3_1 @ X3 ) @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_43,plain,
! [X76: $i,X77: $i,X79: $i] :
( ( ( exists_in_world @ ( esk2_2 @ X76 @ X77 ) @ X77 )
| ~ ( rel_s4 @ X76 @ X77 ) )
& ( ( userid @ u @ ( esk2_2 @ X76 @ X77 ) @ X79 )
| ~ ( rel_s4 @ X77 @ X79 )
| ~ ( rel_s4 @ X76 @ X77 ) )
& ( ( string @ ( esk2_2 @ X76 @ X77 ) @ X79 )
| ~ ( rel_s4 @ X77 @ X79 )
| ~ ( rel_s4 @ X76 @ X77 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])])]) ).
thf(c_0_44,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ( rel_s4 @ esk6_0 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( in @ X10 @ X12 @ ( esk9_4 @ X10 @ X12 @ X14 @ X19 ) @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_45,negated_conjecture,
! [X3: $i,X14: mu,X20: mu,X19: mu,X12: mu,X10: mu,X7: $i] :
( ( in @ X10 @ X12 @ ( esk9_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) @ ( esk8_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( rel_s4 @ X7 @ ( esk8_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ esk6_0 )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X20 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X12 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X20 @ X7 )
| ~ ( string @ X10 @ X7 )
| ~ ( entry_box @ X12 @ X7 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
thf(c_0_46,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ~ ( in @ X10 @ X12 @ ( esk9_4 @ X10 @ X12 @ X14 @ X19 ) @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( userid @ u @ X10 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( entry_box @ X12 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( number @ X12 @ one @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i,X14: mu,X20: mu,X19: mu,X12: mu,X10: mu,X7: $i] :
( ( in @ X10 @ X12 @ ( esk9_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) @ ( esk8_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( number @ X19 @ one @ ( esk7_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( userid @ u @ X14 @ ( esk7_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( rel_s4 @ X7 @ ( esk8_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( entry_box @ X19 @ ( esk7_4 @ X14 @ X19 @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ X20 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X3 @ X7 @ X20 @ X10 @ X12 ) @ esk6_0 )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X20 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X12 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X20 @ X7 )
| ~ ( string @ X10 @ X7 )
| ~ ( entry_box @ X12 @ X7 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_39]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i,X14: mu,X12: mu,X10: mu] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ X10 @ ( esk3_1 @ X3 ) @ X12 @ X14 ) )
| ~ ( userid @ u @ X10 @ ( esk7_4 @ X10 @ ( esk3_1 @ X3 ) @ X12 @ X14 ) )
| ~ ( rel_s4 @ X3 @ ( esk7_4 @ X10 @ ( esk3_1 @ X3 ) @ X12 @ X14 ) )
| ~ ( exists_in_world @ ( esk3_1 @ X3 ) @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
thf(c_0_49,plain,
! [X3: $i,X16: $i,X7: $i] :
( ( userid @ u @ ( esk2_2 @ X3 @ X7 ) @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
! [X3: $i,X14: mu,X12: mu,X10: mu,X7: $i] :
( ( rel_s4 @ esk6_0 @ ( esk7_4 @ X10 @ X12 @ ( esk4_5 @ X3 @ X7 @ X14 @ X10 @ X12 ) @ X14 ) )
| ~ ( rel_s4 @ X7 @ ( esk8_4 @ X10 @ X12 @ ( esk4_5 @ X3 @ X7 @ X14 @ X10 @ X12 ) @ X14 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X3 @ X7 @ X14 @ X10 @ X12 ) @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X12 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X14 @ X7 )
| ~ ( string @ X10 @ X7 )
| ~ ( entry_box @ X12 @ X7 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_51,negated_conjecture,
! [X19: mu,X14: mu,X12: mu,X10: mu] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ X10 @ X12 @ X14 @ X19 ) )
| ( rel_s4 @ esk6_0 @ ( esk7_4 @ X10 @ X12 @ X14 @ X19 ) )
| ~ ( exists_in_world @ X19 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_52,plain,
! [X3: $i,X14: mu,X12: mu,X10: mu,X7: $i] :
( ( exists_in_world @ ( esk4_5 @ X3 @ X7 @ X10 @ X12 @ X14 ) @ X7 )
| ~ ( string @ X12 @ X7 )
| ~ ( entry_box @ X14 @ X7 )
| ~ ( exists_in_world @ X14 @ X7 )
| ~ ( exists_in_world @ X12 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_53,plain,
( mtransitive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i,X17: $i,X18: $i] :
( ( ( Z0 @ X16 @ X17 )
& ( Z0 @ X17 @ X18 ) )
=> ( Z0 @ X16 @ X18 ) ) ) ),
inference(fof_simplification,[status(thm)],[mtransitive]) ).
thf(c_0_54,negated_conjecture,
! [X3: $i,X14: mu,X12: mu,X10: mu,X7: $i] :
( ~ ( number @ X10 @ one @ ( esk7_4 @ X12 @ X10 @ ( esk4_5 @ X3 @ X7 @ X14 @ X12 @ X10 ) @ X14 ) )
| ~ ( userid @ u @ X12 @ ( esk7_4 @ X12 @ X10 @ ( esk4_5 @ X3 @ X7 @ X14 @ X12 @ X10 ) @ X14 ) )
| ~ ( entry_box @ X10 @ ( esk7_4 @ X12 @ X10 @ ( esk4_5 @ X3 @ X7 @ X14 @ X12 @ X10 ) @ X14 ) )
| ~ ( rel_s4 @ X7 @ ( esk8_4 @ X12 @ X10 @ ( esk4_5 @ X3 @ X7 @ X14 @ X12 @ X10 ) @ X14 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X3 @ X7 @ X14 @ X12 @ X10 ) @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X12 @ X7 )
| ~ ( exists_in_world @ X14 @ X7 )
| ~ ( string @ X12 @ X7 )
| ~ ( entry_box @ X10 @ X7 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i,X16: $i,X12: mu,X10: mu,X7: $i] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ X16 ) @ X10 @ X12 ) )
| ~ ( rel_s4 @ X16 @ ( esk7_4 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ X16 ) @ X10 @ X12 ) )
| ~ ( rel_s4 @ X7 @ ( esk7_4 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ X16 ) @ X10 @ X12 ) )
| ~ ( exists_in_world @ ( esk2_2 @ X3 @ X7 ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk3_1 @ X16 ) @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i,X10: mu,X14: mu,X12: mu] :
( ( rel_s4 @ esk6_0 @ ( esk7_4 @ X10 @ X12 @ ( esk4_5 @ X3 @ esk6_0 @ X14 @ X10 @ X12 ) @ X14 ) )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 )
| ~ ( string @ X10 @ esk6_0 )
| ~ ( entry_box @ X12 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
thf(c_0_57,plain,
! [X3: $i] : ( exists_in_world @ ( esk3_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_58,plain,
! [X38: $i,X39: $i,X40: $i] :
( ( ( rel_s4 @ X38 @ X39 )
& ( rel_s4 @ X39 @ X40 ) )
=> ( rel_s4 @ X38 @ X40 ) ),
inference(apply_def,[status(thm)],[a2,c_0_53]) ).
thf(c_0_59,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X12: mu,X16: $i] :
( ~ ( userid @ u @ X10 @ ( esk7_4 @ X10 @ ( esk3_1 @ X3 ) @ ( esk4_5 @ X7 @ X16 @ X12 @ X10 @ ( esk3_1 @ X3 ) ) @ X12 ) )
| ~ ( rel_s4 @ X16 @ ( esk8_4 @ X10 @ ( esk3_1 @ X3 ) @ ( esk4_5 @ X7 @ X16 @ X12 @ X10 @ ( esk3_1 @ X3 ) ) @ X12 ) )
| ~ ( rel_s4 @ X3 @ ( esk7_4 @ X10 @ ( esk3_1 @ X3 ) @ ( esk4_5 @ X7 @ X16 @ X12 @ X10 @ ( esk3_1 @ X3 ) ) @ X12 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X7 @ X16 @ X12 @ X10 @ ( esk3_1 @ X3 ) ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk3_1 @ X3 ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk3_1 @ X3 ) @ X16 )
| ~ ( entry_box @ ( esk3_1 @ X3 ) @ X16 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( exists_in_world @ X10 @ X16 )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( string @ X10 @ X16 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_42]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i,X16: $i,X10: mu,X7: $i] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ esk6_0 ) @ ( esk4_5 @ X16 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ esk6_0 ) ) @ X10 ) )
| ~ ( rel_s4 @ X7 @ ( esk7_4 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ esk6_0 ) @ ( esk4_5 @ X16 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ esk6_0 ) ) @ X10 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X16 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ X7 ) @ ( esk3_1 @ esk6_0 ) ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk2_2 @ X3 @ X7 ) @ esk6_0 )
| ~ ( string @ ( esk2_2 @ X3 @ X7 ) @ esk6_0 )
| ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X16 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
thf(c_0_62,plain,
! [X3: $i,X7: $i] :
( ( exists_in_world @ ( esk2_2 @ X3 @ X7 ) @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_63,plain,
! [X68: $i,X69: $i,X70: $i] :
( ~ ( rel_s4 @ X68 @ X69 )
| ~ ( rel_s4 @ X69 @ X70 )
| ( rel_s4 @ X68 @ X70 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
thf(c_0_64,plain,
! [X37: $i] : ( rel_s4 @ X37 @ X37 ),
inference(apply_def,[status(thm)],[a1,c_0_59]) ).
thf(c_0_65,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X17: $i,X18: $i,X16: $i] :
( ~ ( rel_s4 @ X3 @ ( esk8_4 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) @ ( esk4_5 @ X18 @ X3 @ X10 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) ) @ X10 ) )
| ~ ( rel_s4 @ X17 @ ( esk7_4 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) @ ( esk4_5 @ X18 @ X3 @ X10 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) ) @ X10 ) )
| ~ ( rel_s4 @ X16 @ ( esk7_4 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) @ ( esk4_5 @ X18 @ X3 @ X10 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) ) @ X10 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X18 @ X3 @ X10 @ ( esk2_2 @ X7 @ X16 ) @ ( esk3_1 @ X17 ) ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk2_2 @ X7 @ X16 ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk3_1 @ X17 ) @ esk6_0 )
| ~ ( exists_in_world @ ( esk2_2 @ X7 @ X16 ) @ X3 )
| ~ ( string @ ( esk2_2 @ X7 @ X16 ) @ X3 )
| ~ ( exists_in_world @ ( esk3_1 @ X17 ) @ X3 )
| ~ ( entry_box @ ( esk3_1 @ X17 ) @ X3 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X18 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
thf(c_0_66,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( rel_s4 @ esk6_0 @ ( esk8_4 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) @ ( esk4_5 @ X7 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) ) @ X10 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X7 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) ) @ esk6_0 )
| ~ ( string @ ( esk2_2 @ X3 @ esk6_0 ) @ esk6_0 )
| ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X7 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_56]),c_0_57])]),c_0_62]) ).
thf(c_0_67,plain,
! [X3: $i,X7: $i,X16: $i] :
( ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_68,plain,
! [X67: $i] : ( rel_s4 @ X67 @ X67 ),
inference(variable_rename,[status(thm)],[c_0_64]) ).
thf(c_0_69,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ~ ( rel_s4 @ esk6_0 @ ( esk7_4 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) @ ( esk4_5 @ X7 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) ) @ X10 ) )
| ~ ( exists_in_world @ ( esk4_5 @ X7 @ esk6_0 @ X10 @ ( esk2_2 @ X3 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) ) @ esk6_0 )
| ~ ( string @ ( esk2_2 @ X3 @ esk6_0 ) @ esk6_0 )
| ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X7 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_57])]),c_0_62]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X14: mu,X12: mu] :
( ( rel_s4 @ X3 @ ( esk7_4 @ X10 @ X12 @ ( esk4_5 @ X7 @ esk6_0 @ X14 @ X10 @ X12 ) @ X14 ) )
| ~ ( rel_s4 @ X3 @ esk6_0 )
| ~ ( exists_in_world @ X14 @ esk6_0 )
| ~ ( exists_in_world @ X12 @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X7 @ esk6_0 )
| ~ ( string @ X10 @ esk6_0 )
| ~ ( entry_box @ X12 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
thf(c_0_71,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_72,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ~ ( exists_in_world @ ( esk4_5 @ X3 @ esk6_0 @ X10 @ ( esk2_2 @ X7 @ esk6_0 ) @ ( esk3_1 @ esk6_0 ) ) @ esk6_0 )
| ~ ( string @ ( esk2_2 @ X7 @ esk6_0 ) @ esk6_0 )
| ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( exists_in_world @ X10 @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 )
| ~ ( rel_s4 @ X7 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_57])]),c_0_62]) ).
thf(c_0_73,negated_conjecture,
! [X3: $i] :
( ~ ( string @ ( esk2_2 @ X3 @ esk6_0 ) @ esk6_0 )
| ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_52]),c_0_57])])]),c_0_62]) ).
thf(c_0_74,plain,
! [X3: $i,X16: $i,X7: $i] :
( ( string @ ( esk2_2 @ X3 @ X7 ) @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_75,negated_conjecture,
! [X3: $i] :
( ~ ( entry_box @ ( esk3_1 @ esk6_0 ) @ esk6_0 )
| ~ ( rel_s4 @ X3 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_71])]) ).
thf(c_0_76,negated_conjecture,
rel_s4 @ esk5_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_77,negated_conjecture,
! [X3: $i] :
~ ( rel_s4 @ X3 @ esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_42]),c_0_71])]) ).
thf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_76,c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n011.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 08:39:01 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.gG7SMAAGPT/E---3.1_4003701.p
% 255.88/33.00 % Version: 3.5.1-ho
% 255.88/33.00 % Preprocessing class: HSMSSMSSMLLNHSN.
% 255.88/33.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.88/33.00 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 255.88/33.00 % Starting post_as_ho3 with 300s (1) cores
% 255.88/33.00 % Starting new_ho_12 with 300s (1) cores
% 255.88/33.00 % Starting new_bool_2 with 300s (1) cores
% 255.88/33.00 % new_ho_10_cnf2 with pid 4003714 completed with status 0
% 255.88/33.00 % Result found by new_ho_10_cnf2
% 255.88/33.00 % Preprocessing class: HSMSSMSSMLLNHSN.
% 255.88/33.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.88/33.00 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 255.88/33.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 255.88/33.00 % No SInE strategy applied
% 255.88/33.00 % Search class: HGHNM-FFMF33-SHSSMFNN
% 255.88/33.00 % partial match(1): HGHNM-FFMF31-SHSSMFNN
% 255.88/33.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 255.88/33.00 % Starting SubtermCWHack with 136s (1) cores
% 255.88/33.00 % Starting new_ho_10_cnf2 with 151s (1) cores
% 255.88/33.00 % Starting full_lambda_10 with 136s (1) cores
% 255.88/33.00 % Starting full_lambda_9 with 136s (1) cores
% 255.88/33.00 % Starting new_ho_14 with 136s (1) cores
% 255.88/33.00 % new_ho_10_cnf2 with pid 4003720 completed with status 0
% 255.88/33.00 % Result found by new_ho_10_cnf2
% 255.88/33.00 % Preprocessing class: HSMSSMSSMLLNHSN.
% 255.88/33.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 255.88/33.00 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 255.88/33.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 255.88/33.00 % No SInE strategy applied
% 255.88/33.00 % Search class: HGHNM-FFMF33-SHSSMFNN
% 255.88/33.00 % partial match(1): HGHNM-FFMF31-SHSSMFNN
% 255.88/33.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 255.88/33.00 % Starting SubtermCWHack with 136s (1) cores
% 255.88/33.00 % Starting new_ho_10_cnf2 with 151s (1) cores
% 255.88/33.00 % Preprocessing time : 0.003 s
% 255.88/33.00 % Presaturation interreduction done
% 255.88/33.00
% 255.88/33.00 % Proof found!
% 255.88/33.00 % SZS status Theorem
% 255.88/33.00 % SZS output start CNFRefutation
% See solution above
% 255.88/33.00 % Parsed axioms : 86
% 255.88/33.00 % Removed by relevancy pruning/SinE : 0
% 255.88/33.00 % Initial clauses : 67
% 255.88/33.00 % Removed in clause preprocessing : 44
% 255.88/33.00 % Initial clauses in saturation : 23
% 255.88/33.00 % Processed clauses : 9239
% 255.88/33.00 % ...of these trivial : 0
% 255.88/33.00 % ...subsumed : 968
% 255.88/33.00 % ...remaining for further processing : 8271
% 255.88/33.00 % Other redundant clauses eliminated : 0
% 255.88/33.00 % Clauses deleted for lack of memory : 0
% 255.88/33.00 % Backward-subsumed : 5561
% 255.88/33.00 % Backward-rewritten : 0
% 255.88/33.00 % Generated clauses : 38139
% 255.88/33.00 % ...of the previous two non-redundant : 36856
% 255.88/33.00 % ...aggressively subsumed : 0
% 255.88/33.00 % Contextual simplify-reflections : 9
% 255.88/33.00 % Paramodulations : 38138
% 255.88/33.00 % Factorizations : 0
% 255.88/33.00 % NegExts : 0
% 255.88/33.00 % Equation resolutions : 0
% 255.88/33.00 % Disequality decompositions : 0
% 255.88/33.00 % Total rewrite steps : 1293
% 255.88/33.00 % ...of those cached : 647
% 255.88/33.00 % Propositional unsat checks : 0
% 255.88/33.00 % Propositional check models : 0
% 255.88/33.00 % Propositional check unsatisfiable : 0
% 255.88/33.00 % Propositional clauses : 0
% 255.88/33.00 % Propositional clauses after purity: 0
% 255.88/33.00 % Propositional unsat core size : 0
% 255.88/33.00 % Propositional preprocessing time : 0.000
% 255.88/33.00 % Propositional encoding time : 0.000
% 255.88/33.00 % Propositional solver time : 0.000
% 255.88/33.00 % Success case prop preproc time : 0.000
% 255.88/33.00 % Success case prop encoding time : 0.000
% 255.88/33.00 % Success case prop solver time : 0.000
% 255.88/33.00 % Current number of processed clauses : 2686
% 255.88/33.00 % Positive orientable unit clauses : 7
% 255.88/33.00 % Positive unorientable unit clauses: 0
% 255.88/33.00 % Negative unit clauses : 1
% 255.88/33.00 % Non-unit-clauses : 2678
% 255.88/33.00 % Current number of unprocessed clauses: 27663
% 255.88/33.00 % ...number of literals in the above : 221804
% 255.88/33.00 % Current number of archived formulas : 0
% 255.88/33.00 % Current number of archived clauses : 5585
% 255.88/33.00 % Clause-clause subsumption calls (NU) : 52543448
% 255.88/33.00 % Rec. Clause-clause subsumption calls : 6133482
% 255.88/33.00 % Non-unit clause-clause subsumptions : 985
% 255.88/33.00 % Unit Clause-clause subsumption calls : 5592
% 255.88/33.00 % Rewrite failures with RHS unbound : 0
% 255.88/33.00 % BW rewrite match attempts : 2
% 255.88/33.00 % BW rewrite match successes : 0
% 255.88/33.00 % Condensation attempts : 9239
% 255.88/33.00 % Condensation successes : 1
% 255.88/33.00 % Termbank termtop insertions : 2238780
% 255.88/33.00 % Search garbage collected termcells : 2508
% 255.88/33.00
% 255.88/33.00 % -------------------------------------------------
% 255.88/33.00 % User time : 32.393 s
% 255.88/33.00 % System time : 0.121 s
% 255.88/33.00 % Total time : 32.514 s
% 255.88/33.00 % Maximum resident set size: 3920 pages
% 255.88/33.00
% 255.88/33.00 % -------------------------------------------------
% 255.88/33.00 % User time : 160.250 s
% 255.88/33.00 % System time : 0.499 s
% 255.88/33.00 % Total time : 160.749 s
% 255.88/33.00 % Maximum resident set size: 4864 pages
% 255.88/33.00 % E exiting
%------------------------------------------------------------------------------