TSTP Solution File: KRS272^7 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : KRS272^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:12:39 EDT 2024
% Result : Theorem 107.11s 14.00s
% Output : CNFRefutation 107.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 107 ( 30 unt; 29 typ; 0 def)
% Number of atoms : 477 ( 23 equ; 0 cnn)
% Maximal formula atoms : 57 ( 6 avg)
% Number of connectives : 2314 ( 336 ~; 298 |; 16 &;1645 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 5 con; 0-5 aty)
% Number of variables : 252 ( 58 ^ 194 !; 0 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_36,type,
exists_in_world: mu > $i > $o ).
thf(decl_37,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_38,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_43,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s4: $i > $i > $o ).
thf(decl_55,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
string: mu > $i > $o ).
thf(decl_58,type,
in: mu > mu > mu > $i > $o ).
thf(decl_59,type,
do: mu > mu > mu > $i > $o ).
thf(decl_60,type,
number: mu > mu > $i > $o ).
thf(decl_61,type,
entry_box: mu > $i > $o ).
thf(decl_62,type,
userid: mu > mu > $i > $o ).
thf(decl_63,type,
one: mu ).
thf(decl_64,type,
u: mu ).
thf(decl_66,type,
esk2_2: $i > $i > mu ).
thf(decl_67,type,
esk3_1: $i > mu ).
thf(decl_68,type,
esk4_5: $i > $i > mu > mu > mu > mu ).
thf(decl_69,type,
esk5_0: $i ).
thf(decl_70,type,
esk6_0: $i ).
thf(decl_71,type,
esk7_4: mu > mu > mu > mu > $i ).
thf(decl_72,type,
esk8_4: mu > mu > mu > mu > $i ).
thf(decl_73,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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mimplies) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X13: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mbox_s4) ).
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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',ax3) ).
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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',con) ).
thf(ax2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ X21 ) @ ( number @ X21 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',ax2) ).
thf(ax1,axiom,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X20: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ X20 ) @ ( string @ X20 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mtransitive) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',a2) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.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,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_28,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)],[inference(assume_negation,[status(cth)],[con])]),c_0_22]),c_0_23]),c_0_21]),c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_29,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_30,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_27])])])])])]) ).
thf(c_0_31,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_28])])])])])]) ).
thf(c_0_32,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_29])])])])])]) ).
thf(c_0_33,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_34,plain,
! [X16: $i,X7: $i,X19: mu,X14: mu,X12: mu,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_30]) ).
thf(c_0_35,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_31]) ).
thf(c_0_36,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_31]) ).
thf(c_0_37,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_31]) ).
thf(c_0_38,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_31]) ).
thf(c_0_39,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_31]) ).
thf(c_0_40,plain,
! [X3: $i,X7: $i] :
( ( number @ ( esk3_1 @ X3 ) @ one @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_41,plain,
! [X3: $i,X7: $i] :
( ( entry_box @ ( esk3_1 @ X3 ) @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,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_33])])])])])]) ).
thf(c_0_43,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_31]) ).
thf(c_0_44,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_34,c_0_35]),c_0_36]) ).
thf(c_0_45,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_31]) ).
thf(c_0_46,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_34,c_0_37]),c_0_38]) ).
thf(c_0_47,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_39,c_0_40]),c_0_41]) ).
thf(c_0_48,plain,
! [X16: $i,X3: $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_42]) ).
thf(c_0_49,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_43,c_0_44]) ).
thf(c_0_50,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_31]) ).
thf(c_0_51,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_30]) ).
thf(c_0_52,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_53,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_45,c_0_46]) ).
thf(c_0_54,negated_conjecture,
! [X16: $i,X3: $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_47,c_0_48]) ).
thf(c_0_55,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_49,c_0_50]),c_0_51]) ).
thf(c_0_56,plain,
! [X3: $i] : ( exists_in_world @ ( esk3_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_57,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_52]) ).
thf(c_0_58,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_59,negated_conjecture,
! [X7: $i,X12: mu,X10: mu,X3: $i,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_53,c_0_40]),c_0_41]) ).
thf(c_0_60,negated_conjecture,
! [X16: $i,X3: $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_54,c_0_55]),c_0_56])]) ).
thf(c_0_61,plain,
! [X3: $i,X7: $i] :
( ( exists_in_world @ ( esk2_2 @ X3 @ X7 ) @ X7 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_62,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_57])])]) ).
thf(c_0_63,plain,
! [X37: $i] : ( rel_s4 @ X37 @ X37 ),
inference(apply_def,[status(thm)],[a1,c_0_58]) ).
thf(c_0_64,negated_conjecture,
! [X18: $i,X17: $i,X10: mu,X7: $i,X3: $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_59,c_0_48]) ).
thf(c_0_65,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_60,c_0_55]),c_0_56])]),c_0_61]) ).
thf(c_0_66,plain,
! [X7: $i,X3: $i,X16: $i] :
( ( rel_s4 @ X3 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( rel_s4 @ X7 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_67,plain,
! [X67: $i] : ( rel_s4 @ X67 @ X67 ),
inference(variable_rename,[status(thm)],[c_0_63]) ).
thf(c_0_68,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_64,c_0_65]),c_0_56])]),c_0_61]) ).
thf(c_0_69,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_66,c_0_55]) ).
thf(c_0_70,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_71,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_68,c_0_69]),c_0_70]),c_0_56])]),c_0_61]) ).
thf(c_0_72,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_71,c_0_51]),c_0_56])])]),c_0_61]) ).
thf(c_0_73,plain,
! [X16: $i,X3: $i,X7: $i] :
( ( string @ ( esk2_2 @ X3 @ X7 ) @ X16 )
| ~ ( rel_s4 @ X7 @ X16 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_74,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_72,c_0_73]),c_0_70])]) ).
thf(c_0_75,negated_conjecture,
rel_s4 @ esk5_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_76,negated_conjecture,
! [X3: $i] :
~ ( rel_s4 @ X3 @ esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_41]),c_0_70])]) ).
thf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_75,c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KRS272^7 : TPTP v8.1.2. Released v5.5.0.
% 0.03/0.15 % Command : run_E %s %d THM
% 0.16/0.35 % Computer : n029.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 3 14:04:52 EDT 2024
% 0.16/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.xFdnLF7zQz/E---3.1_10802.p
% 107.11/14.00 # Version: 3.1.0-ho
% 107.11/14.00 # Preprocessing class: HSMSSMSSMLLNHSN.
% 107.11/14.00 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 107.11/14.00 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 107.11/14.00 # Starting post_as_ho3 with 300s (1) cores
% 107.11/14.00 # Starting new_ho_12 with 300s (1) cores
% 107.11/14.00 # Starting new_bool_2 with 300s (1) cores
% 107.11/14.00 # post_as_ho3 with pid 10881 completed with status 0
% 107.11/14.00 # Result found by post_as_ho3
% 107.11/14.00 # Preprocessing class: HSMSSMSSMLLNHSN.
% 107.11/14.00 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 107.11/14.00 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 107.11/14.00 # Starting post_as_ho3 with 300s (1) cores
% 107.11/14.00 # No SInE strategy applied
% 107.11/14.00 # Search class: HGHNM-FFMF33-SHSSMFNN
% 107.11/14.00 # partial match(1): HGHNM-FFMF31-SHSSMFNN
% 107.11/14.00 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 107.11/14.00 # Starting new_ho_10 with 163s (1) cores
% 107.11/14.00 # new_ho_10 with pid 10886 completed with status 0
% 107.11/14.00 # Result found by new_ho_10
% 107.11/14.00 # Preprocessing class: HSMSSMSSMLLNHSN.
% 107.11/14.00 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 107.11/14.00 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 107.11/14.00 # Starting post_as_ho3 with 300s (1) cores
% 107.11/14.00 # No SInE strategy applied
% 107.11/14.00 # Search class: HGHNM-FFMF33-SHSSMFNN
% 107.11/14.00 # partial match(1): HGHNM-FFMF31-SHSSMFNN
% 107.11/14.00 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 107.11/14.00 # Starting new_ho_10 with 163s (1) cores
% 107.11/14.00 # Preprocessing time : 0.003 s
% 107.11/14.00 # Presaturation interreduction done
% 107.11/14.00
% 107.11/14.00 # Proof found!
% 107.11/14.00 # SZS status Theorem
% 107.11/14.00 # SZS output start CNFRefutation
% See solution above
% 107.11/14.00 # Parsed axioms : 86
% 107.11/14.00 # Removed by relevancy pruning/SinE : 0
% 107.11/14.00 # Initial clauses : 67
% 107.11/14.00 # Removed in clause preprocessing : 44
% 107.11/14.00 # Initial clauses in saturation : 23
% 107.11/14.00 # Processed clauses : 9239
% 107.11/14.00 # ...of these trivial : 0
% 107.11/14.00 # ...subsumed : 968
% 107.11/14.00 # ...remaining for further processing : 8271
% 107.11/14.00 # Other redundant clauses eliminated : 0
% 107.11/14.00 # Clauses deleted for lack of memory : 0
% 107.11/14.00 # Backward-subsumed : 5561
% 107.11/14.00 # Backward-rewritten : 0
% 107.11/14.00 # Generated clauses : 38139
% 107.11/14.00 # ...of the previous two non-redundant : 36856
% 107.11/14.00 # ...aggressively subsumed : 0
% 107.11/14.00 # Contextual simplify-reflections : 9
% 107.11/14.00 # Paramodulations : 38138
% 107.11/14.00 # Factorizations : 0
% 107.11/14.00 # NegExts : 0
% 107.11/14.00 # Equation resolutions : 0
% 107.11/14.00 # Disequality decompositions : 0
% 107.11/14.00 # Total rewrite steps : 1293
% 107.11/14.00 # ...of those cached : 647
% 107.11/14.00 # Propositional unsat checks : 0
% 107.11/14.00 # Propositional check models : 0
% 107.11/14.00 # Propositional check unsatisfiable : 0
% 107.11/14.00 # Propositional clauses : 0
% 107.11/14.00 # Propositional clauses after purity: 0
% 107.11/14.00 # Propositional unsat core size : 0
% 107.11/14.00 # Propositional preprocessing time : 0.000
% 107.11/14.00 # Propositional encoding time : 0.000
% 107.11/14.00 # Propositional solver time : 0.000
% 107.11/14.00 # Success case prop preproc time : 0.000
% 107.11/14.00 # Success case prop encoding time : 0.000
% 107.11/14.00 # Success case prop solver time : 0.000
% 107.11/14.00 # Current number of processed clauses : 2686
% 107.11/14.00 # Positive orientable unit clauses : 7
% 107.11/14.00 # Positive unorientable unit clauses: 0
% 107.11/14.00 # Negative unit clauses : 1
% 107.11/14.00 # Non-unit-clauses : 2678
% 107.11/14.00 # Current number of unprocessed clauses: 27663
% 107.11/14.00 # ...number of literals in the above : 221804
% 107.11/14.00 # Current number of archived formulas : 0
% 107.11/14.00 # Current number of archived clauses : 5585
% 107.11/14.00 # Clause-clause subsumption calls (NU) : 38459249
% 107.11/14.00 # Rec. Clause-clause subsumption calls : 3356874
% 107.11/14.00 # Non-unit clause-clause subsumptions : 985
% 107.11/14.00 # Unit Clause-clause subsumption calls : 5591
% 107.11/14.00 # Rewrite failures with RHS unbound : 0
% 107.11/14.00 # BW rewrite match attempts : 2
% 107.11/14.00 # BW rewrite match successes : 0
% 107.11/14.00 # Condensation attempts : 9239
% 107.11/14.00 # Condensation successes : 1
% 107.11/14.00 # Termbank termtop insertions : 2238581
% 107.11/14.00 # Search garbage collected termcells : 2509
% 107.11/14.00
% 107.11/14.00 # -------------------------------------------------
% 107.11/14.00 # User time : 13.360 s
% 107.11/14.00 # System time : 0.075 s
% 107.11/14.00 # Total time : 13.435 s
% 107.11/14.00 # Maximum resident set size: 2328 pages
% 107.11/14.00
% 107.11/14.00 # -------------------------------------------------
% 107.11/14.00 # User time : 13.363 s
% 107.11/14.00 # System time : 0.077 s
% 107.11/14.00 # Total time : 13.440 s
% 107.11/14.00 # Maximum resident set size: 1800 pages
% 107.11/14.00 % E---3.1 exiting
% 107.11/14.00 % E exiting
%------------------------------------------------------------------------------