%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET013^7 : 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 : n005.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 08:21:51 AM UTC 2026
% Result : Theorem 5.29s 1.14s
% Output : CNFRefutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 17 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1456 ( 164 ~; 134 |; 10 &;1133 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 132 ( 54 ^; 78 !; 0 ?; 132 :)
% 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_34,type,
mequiv: ( $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_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_58,type,
subset: mu > mu > $i > $o ).
thf(decl_59,type,
member: mu > mu > $i > $o ).
thf(decl_60,type,
equal_set: mu > mu > $i > $o ).
thf(decl_61,type,
power_set: mu > mu ).
thf(decl_69,type,
intersection: mu > mu > mu ).
thf(decl_71,type,
esk2_3: $i > mu > mu > mu ).
thf(decl_74,type,
esk5_0: $i ).
thf(decl_75,type,
esk6_0: mu ).
thf(decl_76,type,
esk7_0: mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mand @ ( mimplies @ X4 @ X5 ) @ ( mimplies @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mequiv) ).
thf(thI06,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( equal_set @ ( intersection @ X28 @ X29 ) @ ( intersection @ X29 @ X28 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',thI06) ).
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.6KXVUz2ivP/E---3.1_1665804.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.p',mvalid) ).
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/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.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/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.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/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.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/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.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/sandbox/tmp/tmp.6KXVUz2ivP/E---3.1_1665804.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,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( equal_set @ ( intersection @ X28 @ X29 ) @ ( intersection @ X29 @ X28 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thI06]) ).
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,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_23,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_24,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)],[c_0_20]),c_0_21]),c_0_22]) ).
thf(c_0_25,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_23]),c_0_21]),c_0_22])]) ).
thf(c_0_26,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_24])])])]) ).
thf(c_0_27,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_25])])])])]) ).
thf(c_0_28,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_29,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_23]),c_0_21]),c_0_22])]) ).
thf(c_0_30,negated_conjecture,
~ ( equal_set @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,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_27]) ).
thf(c_0_32,plain,
! [X12: mu,X10: mu,X3: $i] : ( exists_in_world @ ( intersection @ X10 @ X12 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,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_29])])])])]) ).
thf(c_0_34,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_23]),c_0_21]),c_0_22])]) ).
thf(c_0_35,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_23]),c_0_21]),c_0_22])]) ).
thf(c_0_36,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_30,c_0_31]),c_0_32]),c_0_32])]) ).
thf(c_0_37,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_33]) ).
thf(c_0_38,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_34])])])])])]) ).
thf(c_0_39,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_35])])])])]) ).
thf(c_0_40,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_36,c_0_37]),c_0_32]),c_0_32])]) ).
thf(c_0_41,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_38]) ).
thf(c_0_42,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_38]) ).
thf(c_0_43,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_38]) ).
thf(c_0_44,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_39]) ).
thf(c_0_45,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_40,c_0_41]),c_0_32]),c_0_32])]) ).
thf(c_0_46,negated_conjecture,
exists_in_world @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_47,negated_conjecture,
exists_in_world @ esk7_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_48,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_40,c_0_42]),c_0_32]),c_0_32])]) ).
thf(c_0_49,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_39]) ).
thf(c_0_50,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_40,c_0_43]),c_0_32]),c_0_32])]) ).
thf(c_0_51,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_39]) ).
thf(c_0_52,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_44,c_0_45]),c_0_46]),c_0_47])]),c_0_48]) ).
thf(c_0_53,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_49,c_0_45]),c_0_47]),c_0_46])]),c_0_48]) ).
thf(c_0_54,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_33]) ).
thf(c_0_55,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_36,c_0_41]),c_0_32]),c_0_32])]) ).
thf(c_0_56,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_36,c_0_42]),c_0_32]),c_0_32])]) ).
thf(c_0_57,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_36,c_0_43]),c_0_32]),c_0_32])]) ).
thf(c_0_58,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_50,c_0_51]),c_0_46]),c_0_47])]),c_0_48]),c_0_52]),c_0_53]) ).
thf(c_0_59,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_54,c_0_42]) ).
thf(c_0_60,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_55,c_0_37]),c_0_32]),c_0_32])]) ).
thf(c_0_61,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_56,c_0_37]),c_0_32]),c_0_32])]) ).
thf(c_0_62,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_55,c_0_43]),c_0_32]),c_0_32])]) ).
thf(c_0_63,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_56,c_0_43]),c_0_32]),c_0_32])]) ).
thf(c_0_64,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_57,c_0_37]),c_0_32]),c_0_32])]) ).
thf(c_0_65,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_58,c_0_59]),c_0_32]),c_0_32])]) ).
thf(c_0_66,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_44,c_0_60]),c_0_47]),c_0_46])]),c_0_61]) ).
thf(c_0_67,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_49,c_0_60]),c_0_46]),c_0_47])]),c_0_61]) ).
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 )
| ( 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_55,c_0_41]),c_0_32]),c_0_32])]) ).
thf(c_0_69,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_56,c_0_41]),c_0_32]),c_0_32])]) ).
thf(c_0_70,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_57,c_0_43]),c_0_32]),c_0_32])]) ).
thf(c_0_71,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_44,c_0_62]),c_0_47]),c_0_46])]),c_0_63]) ).
thf(c_0_72,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_49,c_0_62]),c_0_46]),c_0_47])]),c_0_63]) ).
thf(c_0_73,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_64,c_0_51]),c_0_47]),c_0_46])]),c_0_65])]),c_0_66]),c_0_67]) ).
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 ) ) @ ( 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_41]),c_0_32]),c_0_32])]) ).
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 ) ) @ 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_44,c_0_68]),c_0_47]),c_0_46])]),c_0_69]) ).
thf(c_0_76,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_49,c_0_68]),c_0_46]),c_0_47])]),c_0_69]) ).
thf(c_0_77,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_70,c_0_51]),c_0_47]),c_0_46])]),c_0_65])]),c_0_71]),c_0_72]) ).
thf(c_0_78,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_73,c_0_59]),c_0_32]),c_0_32])]) ).
thf(c_0_79,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_74,c_0_51]),c_0_47]),c_0_46])]),c_0_65])]),c_0_75]),c_0_76]) ).
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 )
| ~ ( 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_77,c_0_51]),c_0_46]),c_0_47]),c_0_78])]) ).
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_79]),c_0_46]),c_0_47]),c_0_78])]) ).
thf(c_0_82,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)],[c_0_80,c_0_81])]) ).
thf(c_0_83,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_49,c_0_79]),c_0_47]),c_0_46]),c_0_78])]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:35:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.6KXVUz2ivP/E---3.1_1665804.p
% 5.29/1.14 % Version: 3.5.1-ho
% 5.29/1.14 % Preprocessing class: HSLSSMSSMLLNHSN.
% 5.29/1.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.29/1.14 % Starting almost_fo_3 with 1500s (5) cores
% 5.29/1.14 % Starting sh10 with 300s (1) cores
% 5.29/1.14 % Starting new_ho_16 with 300s (1) cores
% 5.29/1.14 % Starting post_as_ho11 with 300s (1) cores
% 5.29/1.14 % new_ho_16 with pid 1665834 completed with status 9
% 5.29/1.14 % almost_fo_3 with pid 1665832 completed with status 0
% 5.29/1.14 % Result found by almost_fo_3
% 5.29/1.14 % Preprocessing class: HSLSSMSSMLLNHSN.
% 5.29/1.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.29/1.14 % Starting almost_fo_3 with 1500s (5) cores
% 5.29/1.14 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.29/1.14 % No SInE strategy applied
% 5.29/1.14 % Search class: HGHNM-FFMF31-SHSSMFNN
% 5.29/1.14 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.29/1.14 % Starting SubtermCWHack with 136s (1) cores
% 5.29/1.14 % Starting almost_fo_3 with 151s (1) cores
% 5.29/1.14 % Starting full_lambda_10 with 136s (1) cores
% 5.29/1.14 % Starting full_lambda_9 with 136s (1) cores
% 5.29/1.14 % Starting new_ho_14 with 136s (1) cores
% 5.29/1.14 % new_ho_14 with pid 1665853 completed with status 0
% 5.29/1.14 % Result found by new_ho_14
% 5.29/1.14 % Preprocessing class: HSLSSMSSMLLNHSN.
% 5.29/1.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.29/1.14 % Starting almost_fo_3 with 1500s (5) cores
% 5.29/1.14 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.29/1.14 % No SInE strategy applied
% 5.29/1.14 % Search class: HGHNM-FFMF31-SHSSMFNN
% 5.29/1.14 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.29/1.14 % Starting SubtermCWHack with 136s (1) cores
% 5.29/1.14 % Starting almost_fo_3 with 151s (1) cores
% 5.29/1.14 % Starting full_lambda_10 with 136s (1) cores
% 5.29/1.14 % Starting full_lambda_9 with 136s (1) cores
% 5.29/1.14 % Starting new_ho_14 with 136s (1) cores
% 5.29/1.14 % Preprocessing time : 0.003 s
% 5.29/1.14 % Presaturation interreduction done
% 5.29/1.14
% 5.29/1.14 % Proof found!
% 5.29/1.14 % SZS status Theorem
% 5.29/1.14 % SZS output start CNFRefutation
% See solution above
% 5.29/1.14 % Parsed axioms : 126
% 5.29/1.14 % Removed by relevancy pruning/SinE : 0
% 5.29/1.14 % Initial clauses : 117
% 5.29/1.14 % Removed in clause preprocessing : 48
% 5.29/1.14 % Initial clauses in saturation : 69
% 5.29/1.14 % Processed clauses : 1756
% 5.29/1.14 % ...of these trivial : 0
% 5.29/1.14 % ...subsumed : 621
% 5.29/1.14 % ...remaining for further processing : 1134
% 5.29/1.14 % Other redundant clauses eliminated : 0
% 5.29/1.14 % Clauses deleted for lack of memory : 0
% 5.29/1.14 % Backward-subsumed : 49
% 5.29/1.14 % Backward-rewritten : 52
% 5.29/1.14 % Generated clauses : 36962
% 5.29/1.14 % ...of the previous two non-redundant : 34956
% 5.29/1.14 % ...aggressively subsumed : 0
% 5.29/1.14 % Contextual simplify-reflections : 28
% 5.29/1.14 % Paramodulations : 36960
% 5.29/1.14 % Factorizations : 0
% 5.29/1.14 % NegExts : 0
% 5.29/1.14 % Equation resolutions : 0
% 5.29/1.14 % Disequality decompositions : 0
% 5.29/1.14 % Total rewrite steps : 52033
% 5.29/1.14 % ...of those cached : 51334
% 5.29/1.14 % Propositional unsat checks : 0
% 5.29/1.14 % Propositional check models : 0
% 5.29/1.14 % Propositional check unsatisfiable : 0
% 5.29/1.14 % Propositional clauses : 0
% 5.29/1.14 % Propositional clauses after purity: 0
% 5.29/1.14 % Propositional unsat core size : 0
% 5.29/1.14 % Propositional preprocessing time : 0.000
% 5.29/1.14 % Propositional encoding time : 0.000
% 5.29/1.14 % Propositional solver time : 0.000
% 5.29/1.14 % Success case prop preproc time : 0.000
% 5.29/1.14 % Success case prop encoding time : 0.000
% 5.29/1.14 % Success case prop solver time : 0.000
% 5.29/1.14 % Current number of processed clauses : 962
% 5.29/1.14 % Positive orientable unit clauses : 18
% 5.29/1.14 % Positive unorientable unit clauses: 0
% 5.29/1.14 % Negative unit clauses : 7
% 5.29/1.14 % Non-unit-clauses : 937
% 5.29/1.14 % Current number of unprocessed clauses: 33275
% 5.29/1.14 % ...number of literals in the above : 129113
% 5.29/1.14 % Current number of archived formulas : 0
% 5.29/1.14 % Current number of archived clauses : 172
% 5.29/1.14 % Clause-clause subsumption calls (NU) : 91233
% 5.29/1.14 % Rec. Clause-clause subsumption calls : 16568
% 5.29/1.14 % Non-unit clause-clause subsumptions : 574
% 5.29/1.14 % Unit Clause-clause subsumption calls : 765
% 5.29/1.14 % Rewrite failures with RHS unbound : 0
% 5.29/1.14 % BW rewrite match attempts : 15
% 5.29/1.14 % BW rewrite match successes : 5
% 5.29/1.14 % Condensation attempts : 0
% 5.29/1.14 % Condensation successes : 0
% 5.29/1.14 % Termbank termtop insertions : 1029795
% 5.29/1.14 % Search garbage collected termcells : 8248
% 5.29/1.14
% 5.29/1.14 % -------------------------------------------------
% 5.29/1.14 % User time : 0.808 s
% 5.29/1.14 % System time : 0.044 s
% 5.29/1.14 % Total time : 0.852 s
% 5.29/1.14 % Maximum resident set size: 5064 pages
% 5.29/1.14
% 5.29/1.14 % -------------------------------------------------
% 5.29/1.14 % User time : 4.024 s
% 5.29/1.14 % System time : 0.187 s
% 5.29/1.14 % Total time : 4.210 s
% 5.29/1.14 % Maximum resident set size: 4864 pages
% 5.29/1.14 % E exiting
%------------------------------------------------------------------------------