%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN397^7 : 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 : n020.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 08:41:04 AM UTC 2026
% Result : Theorem 3.76s 0.82s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 15
% Syntax : Number of formulae : 157 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 689 ( 23 equ; 0 cnn)
% Maximal formula atoms : 163 ( 4 avg)
% Number of connectives : 2440 ( 302 ~; 397 |; 45 &;1684 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 259 ( 54 ^; 204 !; 1 ?; 259 :)
% 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,
f: mu > $i > $o ).
thf(decl_59,type,
esk1_1: $i > mu ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: $i ).
thf(decl_62,type,
esk4_2: $i > mu > $i ).
thf(decl_63,type,
esk5_0: $i ).
thf(decl_64,type,
esk6_0: mu ).
thf(decl_65,type,
esk7_0: $i ).
thf(decl_66,type,
esk8_0: $i ).
thf(decl_67,type,
esk9_3: $i > mu > $i > $i ).
thf(decl_68,type,
esk10_0: $i ).
thf(decl_69,type,
esk11_0: mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.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.fJlLEjAUJw/E---3.1_1240290.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.fJlLEjAUJw/E---3.1_1240290.p',mforall_ind) ).
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.fJlLEjAUJw/E---3.1_1240290.p',mtransitive) ).
thf(kalish204,conjecture,
( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X20: mu] : ( mbox_s4 @ ( f @ X20 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X21 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X22: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X22 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X23: mu] : ( mbox_s4 @ ( f @ X23 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',kalish204) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.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.fJlLEjAUJw/E---3.1_1240290.p',mbox_s4) ).
thf(a2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',a2) ).
thf(cumulative_ax,axiom,
! [X19: mu,X7: $i,X3: $i] :
( ( ( exists_in_world @ X19 @ X7 )
& ( rel_s4 @ X7 @ X3 ) )
=> ( exists_in_world @ X19 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',cumulative_ax) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',a1) ).
thf(nonempty_ax,axiom,
! [X7: $i] :
? [X10: mu] : ( exists_in_world @ X10 @ X7 ),
file('/export/starexec/sandbox/tmp/tmp.fJlLEjAUJw/E---3.1_1240290.p',nonempty_ax) ).
thf(c_0_15,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_19,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X30: mu] :
( ( exists_in_world @ X30 @ Z1 )
=> ~ ( Z0 @ X30 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_20,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_21,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_22,negated_conjecture,
~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X20: mu] : ( mbox_s4 @ ( f @ X20 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X21 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X22: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X22 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X23: mu] : ( mbox_s4 @ ( f @ X23 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kalish204]) ).
thf(c_0_23,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_15,c_0_16]),c_0_17]) ).
thf(c_0_24,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_18,c_0_16]),c_0_17]) ).
thf(c_0_25,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X30: mu] :
( ( exists_in_world @ X30 @ Z1 )
=> ~ ( Z0 @ X30 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_16]),c_0_20]) ).
thf(c_0_26,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_27,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_28,plain,
! [X34: $i,X35: $i,X36: $i] :
( ( ( rel_s4 @ X34 @ X35 )
& ( rel_s4 @ X35 @ X36 ) )
=> ( rel_s4 @ X34 @ X36 ) ),
inference(apply_def,[status(thm)],[a2,c_0_21]) ).
thf(c_0_29,negated_conjecture,
~ ! [X53: $i] :
~ ( ~ ! [X44: $i] :
( ~ ( rel_s4 @ X53 @ X44 )
| ~ ! [X39: $i] :
( ~ ( rel_s4 @ X44 @ X39 )
| ~ ~ ! [X38: mu] :
( ( exists_in_world @ X38 @ X39 )
=> ~ ! [X37: $i] :
( ~ ( rel_s4 @ X39 @ X37 )
| ( f @ X38 @ X37 ) ) ) )
| ! [X43: $i] :
( ~ ( rel_s4 @ X44 @ X43 )
| ! [X42: mu] :
( ( exists_in_world @ X42 @ X43 )
=> ! [X41: $i] :
( ~ ( rel_s4 @ X43 @ X41 )
| ~ ! [X40: $i] :
( ~ ( rel_s4 @ X41 @ X40 )
| ( f @ X42 @ X40 ) ) ) ) ) )
| ~ ! [X52: $i] :
( ~ ( rel_s4 @ X53 @ X52 )
| ~ ! [X48: $i] :
( ~ ( rel_s4 @ X52 @ X48 )
| ! [X47: mu] :
( ( exists_in_world @ X47 @ X48 )
=> ! [X46: $i] :
( ~ ( rel_s4 @ X48 @ X46 )
| ~ ! [X45: $i] :
( ~ ( rel_s4 @ X46 @ X45 )
| ( f @ X47 @ X45 ) ) ) ) )
| ! [X51: $i] :
( ~ ( rel_s4 @ X52 @ X51 )
| ~ ~ ! [X50: mu] :
( ( exists_in_world @ X50 @ X51 )
=> ~ ! [X49: $i] :
( ~ ( rel_s4 @ X51 @ X49 )
| ( f @ X50 @ 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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_22]),c_0_16]),c_0_23]),c_0_24]),c_0_20]),c_0_25]),c_0_26]),c_0_27])]) ).
thf(c_0_30,plain,
! [X57: $i,X58: $i,X59: $i] :
( ~ ( rel_s4 @ X57 @ X58 )
| ~ ( rel_s4 @ X58 @ X59 )
| ( rel_s4 @ X57 @ X59 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
thf(c_0_31,negated_conjecture,
! [X65: $i,X66: mu,X71: $i,X73: $i,X74: mu,X75: $i,X79: $i] :
( ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ X65 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ~ ( f @ X66 @ ( esk4_2 @ X65 @ X66 ) )
| ~ ( exists_in_world @ X66 @ X65 )
| ~ ( rel_s4 @ esk3_0 @ X65 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk8_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( rel_s4 @ X75 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ~ ( f @ X74 @ ( esk9_3 @ X73 @ X74 @ X75 ) )
| ~ ( rel_s4 @ X73 @ X75 )
| ~ ( exists_in_world @ X74 @ X73 )
| ~ ( rel_s4 @ esk8_0 @ X73 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) )
& ( ~ ( rel_s4 @ esk10_0 @ X79 )
| ( f @ esk11_0 @ X79 )
| ~ ( rel_s4 @ esk7_0 @ X71 )
| ( f @ esk6_0 @ X71 ) ) ),
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_32,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_30]) ).
thf(c_0_33,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,plain,
! [X60: mu,X61: $i,X62: $i] :
( ~ ( exists_in_world @ X60 @ X61 )
| ~ ( rel_s4 @ X61 @ X62 )
| ( exists_in_world @ X60 @ X62 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).
thf(c_0_35,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_36,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
! [X3: $i,X10: mu,X7: $i] :
( ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_39,negated_conjecture,
( ( rel_s4 @ esk3_0 @ esk7_0 )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
thf(c_0_41,negated_conjecture,
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_43,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk7_0 )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_45,negated_conjecture,
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_46,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_47,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ esk8_0 @ esk10_0 )
| ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_48,negated_conjecture,
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ esk8_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_49,plain,
! [X33: $i] : ( rel_s4 @ X33 @ X33 ),
inference(apply_def,[status(thm)],[a1,c_0_46]) ).
thf(c_0_50,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_51,negated_conjecture,
rel_s4 @ esk8_0 @ esk10_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43]),c_0_39]) ).
thf(c_0_52,plain,
! [X56: $i] : ( rel_s4 @ X56 @ X56 ),
inference(variable_rename,[status(thm)],[c_0_49]) ).
thf(c_0_53,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_54,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_55,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_56,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_58,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_59,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_60,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( rel_s4 @ esk3_0 @ esk5_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_61,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
thf(c_0_63,negated_conjecture,
rel_s4 @ esk3_0 @ esk5_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_51]),c_0_54])]),c_0_56]) ).
thf(c_0_64,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_65,negated_conjecture,
! [X10: mu,X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_66,negated_conjecture,
( ( rel_s4 @ esk3_0 @ esk7_0 )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_67,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_59]) ).
thf(c_0_68,negated_conjecture,
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk10_0 )
| ~ ( rel_s4 @ X3 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_51]) ).
thf(c_0_71,plain,
! [X54: $i] : ( exists_in_world @ ( esk1_1 @ X54 ) @ X54 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[nonempty_ax])]) ).
thf(c_0_72,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_73,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk7_0 )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_74,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_54])]) ).
thf(c_0_75,plain,
! [X3: $i] : ( exists_in_world @ ( esk1_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_76,negated_conjecture,
! [X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_77,negated_conjecture,
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_78,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
thf(c_0_79,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
thf(c_0_80,negated_conjecture,
! [X10: mu,X3: $i] :
( ( exists_in_world @ esk11_0 @ esk10_0 )
| ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_81,negated_conjecture,
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( exists_in_world @ esk11_0 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_82,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ X10 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_83,negated_conjecture,
exists_in_world @ esk11_0 @ esk10_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_73]),c_0_66]) ).
thf(c_0_84,negated_conjecture,
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_84]) ).
thf(c_0_86,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_87,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_79]) ).
thf(c_0_88,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_89,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
thf(c_0_90,negated_conjecture,
rel_s4 @ esk5_0 @ esk7_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_51]),c_0_83])]),c_0_79]) ).
thf(c_0_91,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X12: mu,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( rel_s4 @ X16 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_90]) ).
thf(c_0_93,negated_conjecture,
! [X3: $i,X10: mu,X12: mu,X7: $i] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X12 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( exists_in_world @ X10 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X12 @ X7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_63])]) ).
thf(c_0_94,negated_conjecture,
! [X3: $i,X12: mu,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X12 ) )
| ~ ( exists_in_world @ X12 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_70]),c_0_54])]) ).
thf(c_0_95,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_90]) ).
thf(c_0_96,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_97,negated_conjecture,
! [X3: $i,X12: mu,X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X12 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X12 @ esk10_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
thf(c_0_98,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_51]) ).
thf(c_0_99,negated_conjecture,
! [X10: mu,X12: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X12 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 )
| ~ ( exists_in_world @ X12 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_97,c_0_54]) ).
thf(c_0_100,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_98,c_0_54]) ).
thf(c_0_101,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_99,c_0_83]) ).
thf(c_0_102,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_100,c_0_83]) ).
thf(c_0_103,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ( f @ esk6_0 @ X16 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ esk7_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_104,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
thf(c_0_105,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 ) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
thf(c_0_106,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_54]) ).
thf(c_0_107,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_70]),c_0_54])]) ).
thf(c_0_108,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk5_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_106,c_0_83]) ).
thf(c_0_109,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ X10 @ X3 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_54]) ).
thf(c_0_110,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_54]) ).
thf(c_0_111,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ X10 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_108]) ).
thf(c_0_112,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_108]) ).
thf(c_0_113,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ X10 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_70]),c_0_54])]) ).
thf(c_0_114,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X12: mu,X16: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( f @ X12 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_115,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_110,c_0_83]) ).
thf(c_0_116,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_111,c_0_102]) ).
thf(c_0_117,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk3_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_112,c_0_63]) ).
thf(c_0_118,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_113,c_0_75]) ).
thf(c_0_119,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ X7 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk8_0 @ X7 )
| ~ ( rel_s4 @ X7 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_117]) ).
thf(c_0_120,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ X10 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_98,c_0_118]) ).
thf(c_0_121,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ X10 @ X3 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_70]),c_0_54])]) ).
thf(c_0_122,negated_conjecture,
( ( rel_s4 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_120,c_0_83]) ).
thf(c_0_123,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ( rel_s4 @ X7 @ ( esk4_2 @ X7 @ X10 ) )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk3_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_124,negated_conjecture,
! [X10: mu] :
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ X10 @ esk10_0 ) )
| ~ ( exists_in_world @ X10 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_121,c_0_54]) ).
thf(c_0_125,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ X3 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_122]) ).
thf(c_0_126,negated_conjecture,
! [X3: $i,X10: mu] :
( ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_92]),c_0_63])]) ).
thf(c_0_127,negated_conjecture,
rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ),
inference(spm,[status(thm)],[c_0_124,c_0_83]) ).
thf(c_0_128,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ X3 )
| ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_129,negated_conjecture,
( ( rel_s4 @ esk10_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_125,c_0_118]) ).
thf(c_0_130,negated_conjecture,
! [X10: mu] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
thf(c_0_131,negated_conjecture,
! [X10: mu,X7: $i,X3: $i] :
( ( exists_in_world @ esk6_0 @ esk5_0 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_132,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ ( esk9_3 @ esk8_0 @ ( esk1_1 @ esk8_0 ) @ esk10_0 ) ) )
| ( exists_in_world @ esk6_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
thf(c_0_133,negated_conjecture,
! [X10: mu] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_130,c_0_95]) ).
thf(c_0_134,negated_conjecture,
exists_in_world @ esk6_0 @ esk5_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_51]),c_0_83])]),c_0_118]) ).
thf(c_0_135,negated_conjecture,
! [X3: $i,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ( f @ esk6_0 @ X7 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_136,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( rel_s4 @ esk7_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
thf(c_0_137,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
thf(c_0_138,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ~ ( rel_s4 @ X3 @ esk10_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_127]) ).
thf(c_0_139,negated_conjecture,
! [X3: $i,X10: mu,X7: $i] :
( ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 )
| ~ ( f @ X10 @ ( esk4_2 @ X7 @ X10 ) )
| ~ ( exists_in_world @ X10 @ X7 )
| ~ ( rel_s4 @ esk3_0 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_140,negated_conjecture,
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ esk6_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_54])]) ).
thf(c_0_141,negated_conjecture,
! [X3: $i,X7: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X7 @ esk5_0 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_92]) ).
thf(c_0_142,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
thf(c_0_143,negated_conjecture,
! [X3: $i] :
( ( rel_s4 @ X3 @ esk7_0 )
| ~ ( rel_s4 @ X3 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_141,c_0_63]) ).
thf(c_0_144,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_54])]) ).
thf(c_0_145,negated_conjecture,
! [X3: $i] :
( ( f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ) )
| ( f @ esk11_0 @ X3 )
| ~ ( rel_s4 @ esk10_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_95]),c_0_134])]) ).
thf(c_0_146,negated_conjecture,
! [X3: $i,X10: mu,X7: $i,X16: $i] :
( ( f @ esk6_0 @ X16 )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_147,negated_conjecture,
f @ esk11_0 @ ( esk9_3 @ esk10_0 @ esk11_0 @ esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_138]),c_0_54])]) ).
thf(c_0_148,negated_conjecture,
! [X3: $i,X10: mu,X7: $i,X12: mu,X16: $i] :
( ( rel_s4 @ X16 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_149,negated_conjecture,
! [X3: $i,X7: $i,X10: mu,X12: mu,X16: $i] :
( ~ ( f @ X10 @ ( esk9_3 @ X3 @ X10 @ X7 ) )
| ~ ( rel_s4 @ X3 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ esk8_0 @ X3 )
| ~ ( f @ X12 @ ( esk4_2 @ X16 @ X12 ) )
| ~ ( exists_in_world @ X12 @ X16 )
| ~ ( rel_s4 @ esk3_0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_150,negated_conjecture,
! [X3: $i] :
( ( f @ esk6_0 @ X3 )
| ~ ( rel_s4 @ esk7_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_51]),c_0_54]),c_0_83])]) ).
thf(c_0_151,negated_conjecture,
! [X10: mu,X3: $i] :
( ( rel_s4 @ X3 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_147]),c_0_51]),c_0_54]),c_0_83])]) ).
thf(c_0_152,negated_conjecture,
! [X10: mu,X3: $i] :
( ~ ( f @ X10 @ ( esk4_2 @ X3 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_147]),c_0_51]),c_0_54]),c_0_83])]) ).
thf(c_0_153,negated_conjecture,
! [X10: mu] :
( ( f @ esk6_0 @ ( esk4_2 @ esk7_0 @ X10 ) )
| ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ X10 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
thf(c_0_154,negated_conjecture,
( ~ ( rel_s4 @ esk3_0 @ esk7_0 )
| ~ ( exists_in_world @ esk6_0 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
thf(c_0_155,negated_conjecture,
~ ( rel_s4 @ esk3_0 @ esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_95]),c_0_134])]) ).
thf(c_0_156,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_143]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN397^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:17:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.fJlLEjAUJw/E---3.1_1240290.p
% 3.76/0.82 % Version: 3.5.1-ho
% 3.76/0.82 % Preprocessing class: HSMSSMSSMLMNHSN.
% 3.76/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/0.82 % Starting ho_unfolding_3 with 1500s (5) cores
% 3.76/0.82 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 3.76/0.82 % Starting almost_fo_3_lam with 300s (1) cores
% 3.76/0.82 % Starting post_as_ho1 with 300s (1) cores
% 3.76/0.82 % ho_unfolding_3 with pid 1240303 completed with status 0
% 3.76/0.82 % Result found by ho_unfolding_3
% 3.76/0.82 % Preprocessing class: HSMSSMSSMLMNHSN.
% 3.76/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/0.82 % Starting ho_unfolding_3 with 1500s (5) cores
% 3.76/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.76/0.82 % No SInE strategy applied
% 3.76/0.82 % Search class: HGHNS-FFMM32-SHSSMFNN
% 3.76/0.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.76/0.82 % Starting SubtermCWHack with 136s (1) cores
% 3.76/0.82 % Starting ho_unfolding_3 with 151s (1) cores
% 3.76/0.82 % Starting ho_unfolding_6 with 136s (1) cores
% 3.76/0.82 % Starting sh4l with 136s (1) cores
% 3.76/0.82 % Starting lpo8_s with 136s (1) cores
% 3.76/0.82 % ho_unfolding_3 with pid 1240309 completed with status 0
% 3.76/0.82 % Result found by ho_unfolding_3
% 3.76/0.82 % Preprocessing class: HSMSSMSSMLMNHSN.
% 3.76/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/0.82 % Starting ho_unfolding_3 with 1500s (5) cores
% 3.76/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.76/0.82 % No SInE strategy applied
% 3.76/0.82 % Search class: HGHNS-FFMM32-SHSSMFNN
% 3.76/0.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.76/0.82 % Starting SubtermCWHack with 136s (1) cores
% 3.76/0.82 % Starting ho_unfolding_3 with 151s (1) cores
% 3.76/0.82 % Preprocessing time : 0.002 s
% 3.76/0.82 % Presaturation interreduction done
% 3.76/0.82
% 3.76/0.82 % Proof found!
% 3.76/0.82 % SZS status Theorem
% 3.76/0.82 % SZS output start CNFRefutation
% See solution above
% 3.76/0.82 % Parsed axioms : 74
% 3.76/0.82 % Removed by relevancy pruning/SinE : 0
% 3.76/0.82 % Initial clauses : 83
% 3.76/0.82 % Removed in clause preprocessing : 37
% 3.76/0.82 % Initial clauses in saturation : 46
% 3.76/0.82 % Processed clauses : 5096
% 3.76/0.82 % ...of these trivial : 0
% 3.76/0.82 % ...subsumed : 2191
% 3.76/0.82 % ...remaining for further processing : 2905
% 3.76/0.82 % Other redundant clauses eliminated : 0
% 3.76/0.82 % Clauses deleted for lack of memory : 0
% 3.76/0.82 % Backward-subsumed : 269
% 3.76/0.82 % Backward-rewritten : 1141
% 3.76/0.82 % Generated clauses : 10207
% 3.76/0.82 % ...of the previous two non-redundant : 10135
% 3.76/0.82 % ...aggressively subsumed : 0
% 3.76/0.82 % Contextual simplify-reflections : 18
% 3.76/0.82 % Paramodulations : 10207
% 3.76/0.82 % Factorizations : 0
% 3.76/0.82 % NegExts : 0
% 3.76/0.82 % Equation resolutions : 0
% 3.76/0.82 % Disequality decompositions : 0
% 3.76/0.82 % Total rewrite steps : 1410
% 3.76/0.82 % ...of those cached : 1391
% 3.76/0.82 % Propositional unsat checks : 0
% 3.76/0.82 % Propositional check models : 0
% 3.76/0.82 % Propositional check unsatisfiable : 0
% 3.76/0.82 % Propositional clauses : 0
% 3.76/0.82 % Propositional clauses after purity: 0
% 3.76/0.82 % Propositional unsat core size : 0
% 3.76/0.82 % Propositional preprocessing time : 0.000
% 3.76/0.82 % Propositional encoding time : 0.000
% 3.76/0.82 % Propositional solver time : 0.000
% 3.76/0.82 % Success case prop preproc time : 0.000
% 3.76/0.82 % Success case prop encoding time : 0.000
% 3.76/0.82 % Success case prop solver time : 0.000
% 3.76/0.82 % Current number of processed clauses : 1449
% 3.76/0.82 % Positive orientable unit clauses : 21
% 3.76/0.82 % Positive unorientable unit clauses: 0
% 3.76/0.82 % Negative unit clauses : 1
% 3.76/0.82 % Non-unit-clauses : 1427
% 3.76/0.82 % Current number of unprocessed clauses: 3617
% 3.76/0.82 % ...number of literals in the above : 16684
% 3.76/0.82 % Current number of archived formulas : 0
% 3.76/0.82 % Current number of archived clauses : 1456
% 3.76/0.82 % Clause-clause subsumption calls (NU) : 123754
% 3.76/0.82 % Rec. Clause-clause subsumption calls : 46731
% 3.76/0.82 % Non-unit clause-clause subsumptions : 2469
% 3.76/0.82 % Unit Clause-clause subsumption calls : 2595
% 3.76/0.82 % Rewrite failures with RHS unbound : 0
% 3.76/0.82 % BW rewrite match attempts : 16
% 3.76/0.82 % BW rewrite match successes : 14
% 3.76/0.82 % Condensation attempts : 5096
% 3.76/0.82 % Condensation successes : 0
% 3.76/0.82 % Termbank termtop insertions : 254380
% 3.76/0.82 % Search garbage collected termcells : 1323
% 3.76/0.82
% 3.76/0.82 % -------------------------------------------------
% 3.76/0.82 % User time : 0.545 s
% 3.76/0.82 % System time : 0.018 s
% 3.76/0.82 % Total time : 0.563 s
% 3.76/0.82 % Maximum resident set size: 3960 pages
% 3.76/0.82
% 3.76/0.82 % -------------------------------------------------
% 3.76/0.82 % User time : 2.464 s
% 3.76/0.82 % System time : 0.064 s
% 3.76/0.82 % Total time : 2.528 s
% 3.76/0.82 % Maximum resident set size: 4864 pages
% 3.76/0.82 % E exiting
%------------------------------------------------------------------------------