TSTP Solution File: SET013^7 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 09:17:19 EDT 2024
% Result : Theorem 4.05s 1.07s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 101 ( 32 unt; 18 typ; 0 def)
% Number of atoms : 287 ( 17 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1446 ( 163 ~; 134 |; 10 &;1124 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 130 ( 52 ^ 78 !; 0 ?; 130 :)
% 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_33,type,
mequiv: ( $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_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_57,type,
subset: mu > mu > $i > $o ).
thf(decl_58,type,
member: mu > mu > $i > $o ).
thf(decl_59,type,
equal_set: mu > mu > $i > $o ).
thf(decl_60,type,
power_set: mu > mu ).
thf(decl_68,type,
intersection: mu > mu > mu ).
thf(decl_70,type,
esk2_3: $i > mu > mu > mu ).
thf(decl_73,type,
esk5_0: $i ).
thf(decl_74,type,
esk6_0: mu ).
thf(decl_75,type,
esk7_0: mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mand @ ( mimplies @ X4 @ X5 ) @ ( mimplies @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mequiv) ).
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.uwQJOMpTIm/E---3.1_8419.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mvalid) ).
thf(thI06,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( equal_set @ ( intersection @ X28 @ X29 ) @ ( intersection @ X29 @ X28 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',thI06) ).
thf(equal_set,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( mequiv @ ( equal_set @ X28 @ X29 ) @ ( mand @ ( subset @ X28 @ X29 ) @ ( subset @ X29 @ X28 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',equal_set) ).
thf(existence_of_intersection_ax,axiom,
! [X7: $i,X21: mu,X20: mu] : ( exists_in_world @ ( intersection @ X21 @ X20 ) @ X7 ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',existence_of_intersection_ax) ).
thf(power_set,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X32: mu] :
( mforall_ind
@ ^ [X28: mu] : ( mequiv @ ( member @ X32 @ ( power_set @ X28 ) ) @ ( subset @ X32 @ X28 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',power_set) ).
thf(subset,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mequiv @ ( subset @ X28 @ X29 )
@ ( mforall_ind
@ ^ [X31: mu] : ( mimplies @ ( member @ X31 @ X28 ) @ ( member @ X31 @ X29 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',subset) ).
thf(intersection,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X33: mu] :
( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( mequiv @ ( member @ X33 @ ( intersection @ X28 @ X29 ) ) @ ( mand @ ( member @ X33 @ X28 ) @ ( member @ X33 @ X29 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',intersection) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_14,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_15,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_16,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_17,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_18,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_13,c_0_14]),c_0_15]) ).
thf(c_0_19,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_16,c_0_14]),c_0_15]) ).
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,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_22,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
thf(c_0_23,negated_conjecture,
~ ! [X195: $i,X194: mu] :
( ( exists_in_world @ X194 @ X195 )
=> ! [X193: mu] :
( ( exists_in_world @ X193 @ X195 )
=> ( equal_set @ ( intersection @ X194 @ X193 ) @ ( intersection @ X193 @ X194 ) @ X195 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thI06])]),c_0_20]),c_0_21]) ).
thf(c_0_24,plain,
! [X160: $i,X159: mu] :
( ( exists_in_world @ X159 @ X160 )
=> ! [X158: mu] :
( ( exists_in_world @ X158 @ X160 )
=> ~ ( ~ ( ~ ( equal_set @ X159 @ X158 @ X160 )
| ~ ( ~ ( subset @ X159 @ X158 @ X160 )
| ~ ( subset @ X158 @ X159 @ X160 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X159 @ X158 @ X160 )
| ~ ( subset @ X158 @ X159 @ X160 ) )
| ( equal_set @ X159 @ X158 @ X160 ) ) ) ) ),
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)],[equal_set]),c_0_18]),c_0_22]),c_0_20]),c_0_21])]) ).
thf(c_0_25,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk5_0 )
& ( exists_in_world @ esk7_0 @ esk5_0 )
& ~ ( equal_set @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
thf(c_0_26,plain,
! [X308: $i,X309: mu,X310: mu] :
( ( ( subset @ X309 @ X310 @ X308 )
| ~ ( equal_set @ X309 @ X310 @ X308 )
| ~ ( exists_in_world @ X310 @ X308 )
| ~ ( exists_in_world @ X309 @ X308 ) )
& ( ( subset @ X310 @ X309 @ X308 )
| ~ ( equal_set @ X309 @ X310 @ X308 )
| ~ ( exists_in_world @ X310 @ X308 )
| ~ ( exists_in_world @ X309 @ X308 ) )
& ( ~ ( subset @ X309 @ X310 @ X308 )
| ~ ( subset @ X310 @ X309 @ X308 )
| ( equal_set @ X309 @ X310 @ X308 )
| ~ ( exists_in_world @ X310 @ X308 )
| ~ ( exists_in_world @ X309 @ X308 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])]) ).
thf(c_0_27,plain,
! [X223: $i,X224: mu,X225: mu] : ( exists_in_world @ ( intersection @ X224 @ X225 ) @ X223 ),
inference(variable_rename,[status(thm)],[existence_of_intersection_ax]) ).
thf(c_0_28,plain,
! [X163: $i,X162: mu] :
( ( exists_in_world @ X162 @ X163 )
=> ! [X161: mu] :
( ( exists_in_world @ X161 @ X163 )
=> ~ ( ~ ( ~ ( member @ X162 @ ( power_set @ X161 ) @ X163 )
| ( subset @ X162 @ X161 @ X163 ) )
| ~ ( ~ ( subset @ X162 @ X161 @ X163 )
| ( member @ X162 @ ( power_set @ X161 ) @ X163 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[power_set]),c_0_22]),c_0_20]),c_0_21])]) ).
thf(c_0_29,negated_conjecture,
~ ( equal_set @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( equal_set @ X10 @ X12 @ X3 )
| ~ ( subset @ X10 @ X12 @ X3 )
| ~ ( subset @ X12 @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,plain,
! [X12: mu,X10: mu,X3: $i] : ( exists_in_world @ ( intersection @ X10 @ X12 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
! [X311: $i,X312: mu,X313: mu] :
( ( ~ ( member @ X312 @ ( power_set @ X313 ) @ X311 )
| ( subset @ X312 @ X313 @ X311 )
| ~ ( exists_in_world @ X313 @ X311 )
| ~ ( exists_in_world @ X312 @ X311 ) )
& ( ~ ( subset @ X312 @ X313 @ X311 )
| ( member @ X312 @ ( power_set @ X313 ) @ X311 )
| ~ ( exists_in_world @ X313 @ X311 )
| ~ ( exists_in_world @ X312 @ X311 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).
thf(c_0_33,plain,
! [X157: $i,X156: mu] :
( ( exists_in_world @ X156 @ X157 )
=> ! [X155: mu] :
( ( exists_in_world @ X155 @ X157 )
=> ~ ( ~ ( ~ ( subset @ X156 @ X155 @ X157 )
| ! [X154: mu] :
( ( exists_in_world @ X154 @ X157 )
=> ( ~ ( member @ X154 @ X156 @ X157 )
| ( member @ X154 @ X155 @ X157 ) ) ) )
| ~ ( ~ ! [X154: mu] :
( ( exists_in_world @ X154 @ X157 )
=> ( ~ ( member @ X154 @ X156 @ X157 )
| ( member @ X154 @ X155 @ X157 ) ) )
| ( subset @ X156 @ X155 @ X157 ) ) ) ) ),
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)],[subset]),c_0_19]),c_0_22]),c_0_20]),c_0_21])]) ).
thf(c_0_34,plain,
! [X167: $i,X166: mu] :
( ( exists_in_world @ X166 @ X167 )
=> ! [X165: mu] :
( ( exists_in_world @ X165 @ X167 )
=> ! [X164: mu] :
( ( exists_in_world @ X164 @ X167 )
=> ~ ( ~ ( ~ ( member @ X166 @ ( intersection @ X165 @ X164 ) @ X167 )
| ~ ( ~ ( member @ X166 @ X165 @ X167 )
| ~ ( member @ X166 @ X164 @ X167 ) ) )
| ~ ( ~ ~ ( ~ ( member @ X166 @ X165 @ X167 )
| ~ ( member @ X166 @ X164 @ X167 ) )
| ( member @ X166 @ ( intersection @ X165 @ X164 ) @ X167 ) ) ) ) ) ),
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)],[intersection]),c_0_18]),c_0_22]),c_0_20]),c_0_21])]) ).
thf(c_0_35,negated_conjecture,
( ~ ( subset @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31])]) ).
thf(c_0_36,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( subset @ X10 @ X12 @ X3 )
| ~ ( member @ X10 @ ( power_set @ X12 ) @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
! [X303: $i,X304: mu,X305: mu,X306: mu] :
( ( ~ ( subset @ X304 @ X305 @ X303 )
| ~ ( exists_in_world @ X306 @ X303 )
| ~ ( member @ X306 @ X304 @ X303 )
| ( member @ X306 @ X305 @ X303 )
| ~ ( exists_in_world @ X305 @ X303 )
| ~ ( exists_in_world @ X304 @ X303 ) )
& ( ( exists_in_world @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X303 )
| ( subset @ X304 @ X305 @ X303 )
| ~ ( exists_in_world @ X305 @ X303 )
| ~ ( exists_in_world @ X304 @ X303 ) )
& ( ( member @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X304 @ X303 )
| ( subset @ X304 @ X305 @ X303 )
| ~ ( exists_in_world @ X305 @ X303 )
| ~ ( exists_in_world @ X304 @ X303 ) )
& ( ~ ( member @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X305 @ X303 )
| ( subset @ X304 @ X305 @ X303 )
| ~ ( exists_in_world @ X305 @ X303 )
| ~ ( exists_in_world @ X304 @ X303 ) ) ),
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_38,plain,
! [X314: $i,X315: mu,X316: mu,X317: mu] :
( ( ( member @ X315 @ X316 @ X314 )
| ~ ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
| ~ ( exists_in_world @ X317 @ X314 )
| ~ ( exists_in_world @ X316 @ X314 )
| ~ ( exists_in_world @ X315 @ X314 ) )
& ( ( member @ X315 @ X317 @ X314 )
| ~ ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
| ~ ( exists_in_world @ X317 @ X314 )
| ~ ( exists_in_world @ X316 @ X314 )
| ~ ( exists_in_world @ X315 @ X314 ) )
& ( ~ ( member @ X315 @ X316 @ X314 )
| ~ ( member @ X315 @ X317 @ X314 )
| ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
| ~ ( exists_in_world @ X317 @ X314 )
| ~ ( exists_in_world @ X316 @ X314 )
| ~ ( exists_in_world @ X315 @ X314 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])]) ).
thf(c_0_39,negated_conjecture,
( ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
| ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]),c_0_31])]) ).
thf(c_0_40,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( member @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X10 @ X3 )
| ( subset @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_41,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( exists_in_world @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X3 )
| ( subset @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( subset @ X10 @ X12 @ X3 )
| ~ ( member @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,plain,
! [X12: mu,X14: mu,X10: mu,X3: $i] :
( ( member @ X10 @ X12 @ X3 )
| ~ ( member @ X10 @ ( intersection @ X14 @ X12 ) @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_44,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]),c_0_31])]) ).
thf(c_0_45,negated_conjecture,
exists_in_world @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_46,negated_conjecture,
exists_in_world @ esk7_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_47,negated_conjecture,
( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_31]),c_0_31])]) ).
thf(c_0_48,plain,
! [X14: mu,X12: mu,X10: mu,X3: $i] :
( ( member @ X10 @ X12 @ X3 )
| ~ ( member @ X10 @ ( intersection @ X12 @ X14 ) @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_49,negated_conjecture,
( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_31]),c_0_31])]) ).
thf(c_0_50,plain,
! [X14: mu,X12: mu,X10: mu,X3: $i] :
( ( member @ X10 @ ( intersection @ X12 @ X14 ) @ X3 )
| ~ ( member @ X10 @ X12 @ X3 )
| ~ ( member @ X10 @ X14 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_51,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 )
| ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_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_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
thf(c_0_52,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0 )
| ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_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_48,c_0_44]),c_0_46]),c_0_45])]),c_0_47]) ).
thf(c_0_53,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( member @ X10 @ ( power_set @ X12 ) @ X3 )
| ~ ( subset @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_54,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
| ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_31]),c_0_31])]) ).
thf(c_0_55,negated_conjecture,
( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
| ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_41]),c_0_31]),c_0_31])]) ).
thf(c_0_56,negated_conjecture,
( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_42]),c_0_31]),c_0_31])]) ).
thf(c_0_57,negated_conjecture,
~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]),c_0_46])]),c_0_47]),c_0_51]),c_0_52]) ).
thf(c_0_58,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( exists_in_world @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X3 )
| ( member @ X10 @ ( power_set @ X12 ) @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_41]) ).
thf(c_0_59,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_36]),c_0_31]),c_0_31])]) ).
thf(c_0_60,negated_conjecture,
( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_31]),c_0_31])]) ).
thf(c_0_61,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_31]),c_0_31])]) ).
thf(c_0_62,negated_conjecture,
( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_42]),c_0_31]),c_0_31])]) ).
thf(c_0_63,negated_conjecture,
( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_31]),c_0_31])]) ).
thf(c_0_64,negated_conjecture,
exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31]),c_0_31])]) ).
thf(c_0_65,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk6_0 @ esk5_0 )
| ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ 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_43,c_0_59]),c_0_46]),c_0_45])]),c_0_60]) ).
thf(c_0_66,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_0 @ esk5_0 )
| ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ 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_48,c_0_59]),c_0_45]),c_0_46])]),c_0_60]) ).
thf(c_0_67,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_31]),c_0_31])]) ).
thf(c_0_68,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_31]),c_0_31])]) ).
thf(c_0_69,negated_conjecture,
( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_31]),c_0_31])]) ).
thf(c_0_70,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk6_0 @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ 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_43,c_0_61]),c_0_46]),c_0_45])]),c_0_62]) ).
thf(c_0_71,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_0 @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ 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_48,c_0_61]),c_0_45]),c_0_46])]),c_0_62]) ).
thf(c_0_72,negated_conjecture,
~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_65]),c_0_66]) ).
thf(c_0_73,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_31]),c_0_31])]) ).
thf(c_0_74,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ 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_43,c_0_67]),c_0_46]),c_0_45])]),c_0_68]) ).
thf(c_0_75,negated_conjecture,
( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
| ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_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_48,c_0_67]),c_0_45]),c_0_46])]),c_0_68]) ).
thf(c_0_76,negated_conjecture,
~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_70]),c_0_71]) ).
thf(c_0_77,negated_conjecture,
exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_58]),c_0_31]),c_0_31])]) ).
thf(c_0_78,negated_conjecture,
member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_74]),c_0_75]) ).
thf(c_0_79,negated_conjecture,
( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0 )
| ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_50]),c_0_45]),c_0_46]),c_0_77])]) ).
thf(c_0_80,negated_conjecture,
member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_78]),c_0_46]),c_0_45]),c_0_77])]) ).
thf(c_0_81,negated_conjecture,
~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
thf(c_0_82,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_78]),c_0_45]),c_0_46]),c_0_77])]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 10:22:13 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.23/0.52 Running higher-order theorem proving
% 0.23/0.52 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.uwQJOMpTIm/E---3.1_8419.p
% 4.05/1.07 # Version: 3.1.0-ho
% 4.05/1.07 # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07 # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07 # Starting sh10 with 300s (1) cores
% 4.05/1.07 # Starting new_ho_16 with 300s (1) cores
% 4.05/1.07 # Starting post_as_ho11 with 300s (1) cores
% 4.05/1.07 # new_ho_16 with pid 8564 completed with status 8
% 4.05/1.07 # almost_fo_3 with pid 8562 completed with status 0
% 4.05/1.07 # Result found by almost_fo_3
% 4.05/1.07 # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07 # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07 # No SInE strategy applied
% 4.05/1.07 # Search class: HGHNM-FFMF31-SHSSMFNN
% 4.05/1.07 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.05/1.07 # Starting new_ho_10 with 811s (1) cores
% 4.05/1.07 # Starting almost_fo_3 with 151s (1) cores
% 4.05/1.07 # Starting full_lambda_9 with 136s (1) cores
% 4.05/1.07 # Starting new_ho_14 with 136s (1) cores
% 4.05/1.07 # Starting pre_casc_4 with 136s (1) cores
% 4.05/1.07 # new_ho_14 with pid 8584 completed with status 0
% 4.05/1.07 # Result found by new_ho_14
% 4.05/1.07 # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07 # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07 # No SInE strategy applied
% 4.05/1.07 # Search class: HGHNM-FFMF31-SHSSMFNN
% 4.05/1.07 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.05/1.07 # Starting new_ho_10 with 811s (1) cores
% 4.05/1.07 # Starting almost_fo_3 with 151s (1) cores
% 4.05/1.07 # Starting full_lambda_9 with 136s (1) cores
% 4.05/1.07 # Starting new_ho_14 with 136s (1) cores
% 4.05/1.07 # Preprocessing time : 0.006 s
% 4.05/1.07 # Presaturation interreduction done
% 4.05/1.07
% 4.05/1.07 # Proof found!
% 4.05/1.07 # SZS status Theorem
% 4.05/1.07 # SZS output start CNFRefutation
% See solution above
% 4.05/1.07 # Parsed axioms : 126
% 4.05/1.07 # Removed by relevancy pruning/SinE : 0
% 4.05/1.07 # Initial clauses : 117
% 4.05/1.07 # Removed in clause preprocessing : 48
% 4.05/1.07 # Initial clauses in saturation : 69
% 4.05/1.07 # Processed clauses : 1756
% 4.05/1.07 # ...of these trivial : 0
% 4.05/1.07 # ...subsumed : 622
% 4.05/1.07 # ...remaining for further processing : 1133
% 4.05/1.07 # Other redundant clauses eliminated : 0
% 4.05/1.07 # Clauses deleted for lack of memory : 0
% 4.05/1.07 # Backward-subsumed : 46
% 4.05/1.07 # Backward-rewritten : 52
% 4.05/1.07 # Generated clauses : 37171
% 4.05/1.07 # ...of the previous two non-redundant : 35054
% 4.05/1.07 # ...aggressively subsumed : 0
% 4.05/1.07 # Contextual simplify-reflections : 28
% 4.05/1.07 # Paramodulations : 37169
% 4.05/1.07 # Factorizations : 0
% 4.05/1.07 # NegExts : 0
% 4.05/1.07 # Equation resolutions : 0
% 4.05/1.07 # Disequality decompositions : 0
% 4.05/1.07 # Total rewrite steps : 52176
% 4.05/1.07 # ...of those cached : 51477
% 4.05/1.07 # Propositional unsat checks : 0
% 4.05/1.07 # Propositional check models : 0
% 4.05/1.07 # Propositional check unsatisfiable : 0
% 4.05/1.07 # Propositional clauses : 0
% 4.05/1.07 # Propositional clauses after purity: 0
% 4.05/1.07 # Propositional unsat core size : 0
% 4.05/1.07 # Propositional preprocessing time : 0.000
% 4.05/1.07 # Propositional encoding time : 0.000
% 4.05/1.07 # Propositional solver time : 0.000
% 4.05/1.07 # Success case prop preproc time : 0.000
% 4.05/1.07 # Success case prop encoding time : 0.000
% 4.05/1.07 # Success case prop solver time : 0.000
% 4.05/1.07 # Current number of processed clauses : 964
% 4.05/1.07 # Positive orientable unit clauses : 18
% 4.05/1.07 # Positive unorientable unit clauses: 0
% 4.05/1.07 # Negative unit clauses : 7
% 4.05/1.07 # Non-unit-clauses : 939
% 4.05/1.07 # Current number of unprocessed clauses: 33373
% 4.05/1.07 # ...number of literals in the above : 129255
% 4.05/1.07 # Current number of archived formulas : 0
% 4.05/1.07 # Current number of archived clauses : 169
% 4.05/1.07 # Clause-clause subsumption calls (NU) : 133218
% 4.05/1.07 # Rec. Clause-clause subsumption calls : 26959
% 4.05/1.07 # Non-unit clause-clause subsumptions : 573
% 4.05/1.07 # Unit Clause-clause subsumption calls : 753
% 4.05/1.07 # Rewrite failures with RHS unbound : 0
% 4.05/1.07 # BW rewrite match attempts : 15
% 4.05/1.07 # BW rewrite match successes : 5
% 4.05/1.07 # Condensation attempts : 0
% 4.05/1.07 # Condensation successes : 0
% 4.05/1.07 # Termbank termtop insertions : 1036018
% 4.05/1.07 # Search garbage collected termcells : 8249
% 4.05/1.07
% 4.05/1.07 # -------------------------------------------------
% 4.05/1.07 # User time : 0.496 s
% 4.05/1.07 # System time : 0.034 s
% 4.05/1.07 # Total time : 0.530 s
% 4.05/1.07 # Maximum resident set size: 3264 pages
% 4.05/1.07
% 4.05/1.07 # -------------------------------------------------
% 4.05/1.07 # User time : 2.502 s
% 4.05/1.07 # System time : 0.154 s
% 4.05/1.07 # Total time : 2.656 s
% 4.05/1.07 # Maximum resident set size: 1868 pages
% 4.05/1.07 % E---3.1 exiting
% 4.05/1.08 % E exiting
%------------------------------------------------------------------------------