%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU704^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:25:16 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 110 equ; 0 cnn)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 627 ( 93 ~; 82 |; 69 &; 320 @)
% ( 8 <=>; 54 =>; 0 <=; 1 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 151 ( 42 ^; 106 !; 3 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
singleton: $i > $o ).
thf(decl_28,type,
iffalseProp1: $o ).
thf(decl_29,type,
iffalseProp2: $o ).
thf(decl_30,type,
iftrueProp1: $o ).
thf(decl_31,type,
iftrueProp2: $o ).
thf(decl_32,type,
esk1_0: $i ).
thf(decl_33,type,
epred1_0: $o ).
thf(decl_34,type,
esk2_0: $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(decl_40,type,
esk6_1: $i > $i ).
thf(ifSingleton,conjecture,
( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',ifSingleton) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',iftrueProp2) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X3
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',iffalseProp2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X3
=> ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',iffalseProp1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GLyYrh1xOi/E---3.1_4064314.p',singleton) ).
thf(c_0_6,negated_conjecture,
~ ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ifSingleton]) ).
thf(c_0_7,plain,
( iftrueProp1
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_8,plain,
( iftrueProp2
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
=> ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp2]) ).
thf(c_0_9,plain,
( iffalseProp2
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X3
=> ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp2]) ).
thf(c_0_10,plain,
( iffalseProp1
<=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X3
=> ( in @ X4
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp1]) ).
thf(c_0_11,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_12,negated_conjecture,
~ ( ! [X26: $i,X27: $o,X28: $i] :
( ( in @ X28 @ X26 )
=> ! [X29: $i] :
( ( in @ X29 @ X26 )
=> ( ~ X27
=> ( in @ X29
@ ( dsetconstr @ X26
@ ^ [Z0: $i] :
( ( X27
& ( Z0 = X28 ) )
| ( ~ X27
& ( Z0 = X29 ) ) ) ) ) ) ) )
=> ( ! [X30: $i,X31: $o,X32: $i] :
( ( in @ X32 @ X30 )
=> ! [X33: $i] :
( ( in @ X33 @ X30 )
=> ( ~ X31
=> ( ( dsetconstr @ X30
@ ^ [Z0: $i] :
( ( X31
& ( Z0 = X32 ) )
| ( ~ X31
& ( Z0 = X33 ) ) ) )
= ( setadjoin @ X33 @ emptyset ) ) ) ) )
=> ( ! [X34: $i,X35: $o,X36: $i] :
( ( in @ X36 @ X34 )
=> ! [X37: $i] :
( ( in @ X37 @ X34 )
=> ( X35
=> ( in @ X36
@ ( dsetconstr @ X34
@ ^ [Z0: $i] :
( ( X35
& ( Z0 = X36 ) )
| ( ~ X35
& ( Z0 = X37 ) ) ) ) ) ) ) )
=> ( ! [X38: $i,X39: $o,X40: $i] :
( ( in @ X40 @ X38 )
=> ! [X41: $i] :
( ( in @ X41 @ X38 )
=> ( X39
=> ( ( dsetconstr @ X38
@ ^ [Z0: $i] :
( ( X39
& ( Z0 = X40 ) )
| ( ~ X39
& ( Z0 = X41 ) ) ) )
= ( setadjoin @ X40 @ emptyset ) ) ) ) )
=> ! [X1: $i,X3: $o,X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ? [X42: $i] :
( ( in @ X42
@ ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) ) )
& ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X4 ) ) ) )
= ( setadjoin @ X42 @ emptyset ) ) ) ) ) ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_6]),c_0_7]),c_0_8]),c_0_9]),c_0_10]),c_0_11])]) ).
thf(c_0_13,negated_conjecture,
! [X43: $i,X44: $o,X45: $i,X46: $i,X47: $i,X48: $o,X49: $i,X50: $i,X51: $i,X52: $o,X53: $i,X54: $i,X55: $i,X56: $o,X57: $i,X58: $i,X63: $i] :
( ( ~ ( in @ X45 @ X43 )
| ~ ( in @ X46 @ X43 )
| X44
| ( in @ X46
@ ( dsetconstr @ X43
@ ^ [Z0: $i] :
( ( X44
& ( Z0 = X45 ) )
| ( ~ X44
& ( Z0 = X46 ) ) ) ) ) )
& ( ~ ( in @ X49 @ X47 )
| ~ ( in @ X50 @ X47 )
| X48
| ( ( dsetconstr @ X47
@ ^ [Z0: $i] :
( ( X48
& ( Z0 = X49 ) )
| ( ~ X48
& ( Z0 = X50 ) ) ) )
= ( setadjoin @ X50 @ emptyset ) ) )
& ( ~ ( in @ X53 @ X51 )
| ~ ( in @ X54 @ X51 )
| ~ X52
| ( in @ X53
@ ( dsetconstr @ X51
@ ^ [Z0: $i] :
( ( X52
& ( Z0 = X53 ) )
| ( ~ X52
& ( Z0 = X54 ) ) ) ) ) )
& ( ~ ( in @ X57 @ X55 )
| ~ ( in @ X58 @ X55 )
| ~ X56
| ( ( dsetconstr @ X55
@ ^ [Z0: $i] :
( ( X56
& ( Z0 = X57 ) )
| ( ~ X56
& ( Z0 = X58 ) ) ) )
= ( setadjoin @ X57 @ emptyset ) ) )
& ( in @ esk2_0 @ esk1_0 )
& ( in @ esk3_0 @ esk1_0 )
& ( ~ ( in @ X63
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) ) )
| ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( setadjoin @ X63 @ emptyset ) ) ) ),
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_12])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( dsetconstr @ X2
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = X1 ) )
| ( ~ $true
& ( Z0 = X4 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_13])])]) ).
thf(c_0_15,negated_conjecture,
! [X4: $i,X2: $i,X1: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( Z0 = X2 ) )
= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ X2 @ X1 ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1
@ ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) ) )
| ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( Z0 = X2 ) )
= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ X1 ) ),
inference(condense,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( in @ X4
@ ( dsetconstr @ X2
@ ^ [Z0: $i] :
( ( ~ $true
& ( Z0 = X1 ) )
| ( ~ ~ $true
& ( Z0 = X4 ) ) ) ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_13])])]) ).
thf(c_0_19,plain,
! [X1: $i,X2: $i] :
( ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( ( ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( ^ [Z0: $i] : ( Z0 = X2 ) ) )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( Z0 = X1 ) ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference(cn,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_22,plain,
! [X1: $i,X2: $i] :
( ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] :
( ( epred1_0
& ( Z0 = esk2_0 ) )
| ( ~ epred1_0
& ( Z0 = esk3_0 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( ( ( epred1_0
& ( ( esk6_1 @ X2 )
= esk2_0 ) )
| ( ~ epred1_0
& ( ( esk6_1 @ X2 )
= esk3_0 ) ) )
<~> ( ( esk6_1 @ X2 )
= X2 ) )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(neg_ext,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( Z0 = X1 ) ) )
| ~ ( in @ X1 @ X2 ) ),
inference(condense,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
= ( setadjoin @ esk2_0 @ emptyset ) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
thf(c_0_25,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_26,plain,
! [X1: $i,X2: $i] :
( ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( ( esk6_1 @ X2 )
!= esk2_0 )
| ( ( esk6_1 @ X2 )
!= X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ esk1_0 )
| ~ epred1_0 ),
inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_27,negated_conjecture,
in @ esk2_0 @ ( setadjoin @ esk2_0 @ emptyset ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).
thf(c_0_28,negated_conjecture,
( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
= ( setadjoin @ esk3_0 @ emptyset ) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
thf(c_0_29,plain,
! [X2: $i,X1: $i] :
( ( ( esk6_1 @ X1 )
= esk2_0 )
| ( ( esk6_1 @ X1 )
= X1 )
| ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ esk1_0 )
| ~ epred1_0 ),
inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_30,negated_conjecture,
( ( ( esk6_1 @ esk2_0 )
!= esk2_0 )
| ~ epred1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]),c_0_21])]) ).
thf(c_0_31,plain,
! [X1: $i,X2: $i] :
( epred1_0
| ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ( ( esk6_1 @ X2 )
!= esk3_0 )
| ( ( esk6_1 @ X2 )
!= X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_32,negated_conjecture,
in @ esk3_0 @ ( setadjoin @ esk3_0 @ emptyset ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_25])]) ).
thf(c_0_33,plain,
! [X2: $i,X1: $i] :
( ( ( esk6_1 @ X1 )
= esk3_0 )
| ( ( esk6_1 @ X1 )
= X1 )
| epred1_0
| ( ( dsetconstr @ esk1_0
@ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_34,negated_conjecture,
~ epred1_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_24]),c_0_21])]),c_0_30]) ).
thf(c_0_35,negated_conjecture,
( epred1_0
| ( ( esk6_1 @ esk3_0 )
!= esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28]),c_0_25])]) ).
thf(c_0_36,negated_conjecture,
( ( esk6_1 @ esk3_0 )
= esk3_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_28]),c_0_25])]),c_0_34]) ).
thf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU704^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n009.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 14:12:45 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.24 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.GLyYrh1xOi/E---3.1_4064314.p
% 0.21/0.28 % Version: 3.5.1-ho
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting full_lambda_10 with 1500s (5) cores
% 0.21/0.28 % Starting lpo4_fix with 300s (1) cores
% 0.21/0.28 % Starting new_bool_6 with 300s (1) cores
% 0.21/0.28 % Starting lpo8_s with 300s (1) cores
% 0.21/0.28 % full_lambda_10 with pid 4064352 completed with status 0
% 0.21/0.28 % Result found by full_lambda_10
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting full_lambda_10 with 1500s (5) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.21/0.28 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.21/0.28 % Search class: HHHSF-FFSF22-MSSFMFNN
% 0.21/0.28 % partial match(3): HHUSF-FFSF22-SSSFFFNN
% 0.21/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.28 % Starting full_lambda_10 with 151s (1) cores
% 0.21/0.28 % Starting sh5l with 136s (1) cores
% 0.21/0.28 % Starting new_bool_1 with 136s (1) cores
% 0.21/0.28 % Starting new_bool_2 with 136s (1) cores
% 0.21/0.28 % full_lambda_10 with pid 4064360 completed with status 0
% 0.21/0.28 % Result found by full_lambda_10
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNSSN.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting full_lambda_10 with 1500s (5) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.21/0.28 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.21/0.28 % Search class: HHHSF-FFSF22-MSSFMFNN
% 0.21/0.28 % partial match(3): HHUSF-FFSF22-SSSFFFNN
% 0.21/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.28 % Starting full_lambda_10 with 151s (1) cores
% 0.21/0.28 % Preprocessing time : 0.001 s
% 0.21/0.28 % Presaturation interreduction done
% 0.21/0.28
% 0.21/0.28 % Proof found!
% 0.21/0.28 % SZS status Theorem
% 0.21/0.28 % SZS output start CNFRefutation
% See solution above
% 0.21/0.28 % Parsed axioms : 15
% 0.21/0.28 % Removed by relevancy pruning/SinE : 9
% 0.21/0.28 % Initial clauses : 7
% 0.21/0.28 % Removed in clause preprocessing : 0
% 0.21/0.28 % Initial clauses in saturation : 7
% 0.21/0.28 % Processed clauses : 59
% 0.21/0.28 % ...of these trivial : 5
% 0.21/0.28 % ...subsumed : 1
% 0.21/0.28 % ...remaining for further processing : 53
% 0.21/0.28 % Other redundant clauses eliminated : 6
% 0.21/0.28 % Clauses deleted for lack of memory : 0
% 0.21/0.28 % Backward-subsumed : 9
% 0.21/0.28 % Backward-rewritten : 2
% 0.21/0.28 % Generated clauses : 116
% 0.21/0.28 % ...of the previous two non-redundant : 101
% 0.21/0.28 % ...aggressively subsumed : 0
% 0.21/0.28 % Contextual simplify-reflections : 3
% 0.21/0.28 % Paramodulations : 77
% 0.21/0.28 % Factorizations : 0
% 0.21/0.28 % NegExts : 5
% 0.21/0.28 % Equation resolutions : 7
% 0.21/0.28 % Disequality decompositions : 0
% 0.21/0.28 % Total rewrite steps : 52
% 0.21/0.28 % ...of those cached : 43
% 0.21/0.28 % Propositional unsat checks : 0
% 0.21/0.28 % Propositional check models : 0
% 0.21/0.28 % Propositional check unsatisfiable : 0
% 0.21/0.28 % Propositional clauses : 0
% 0.21/0.28 % Propositional clauses after purity: 0
% 0.21/0.28 % Propositional unsat core size : 0
% 0.21/0.28 % Propositional preprocessing time : 0.000
% 0.21/0.28 % Propositional encoding time : 0.000
% 0.21/0.28 % Propositional solver time : 0.000
% 0.21/0.28 % Success case prop preproc time : 0.000
% 0.21/0.28 % Success case prop encoding time : 0.000
% 0.21/0.28 % Success case prop solver time : 0.000
% 0.21/0.28 % Current number of processed clauses : 32
% 0.21/0.28 % Positive orientable unit clauses : 9
% 0.21/0.28 % Positive unorientable unit clauses: 0
% 0.21/0.28 % Negative unit clauses : 1
% 0.21/0.28 % Non-unit-clauses : 22
% 0.21/0.28 % Current number of unprocessed clauses: 52
% 0.21/0.28 % ...number of literals in the above : 247
% 0.21/0.28 % Current number of archived formulas : 0
% 0.21/0.28 % Current number of archived clauses : 21
% 0.21/0.28 % Clause-clause subsumption calls (NU) : 195
% 0.21/0.28 % Rec. Clause-clause subsumption calls : 30
% 0.21/0.28 % Non-unit clause-clause subsumptions : 7
% 0.21/0.28 % Unit Clause-clause subsumption calls : 20
% 0.21/0.28 % Rewrite failures with RHS unbound : 0
% 0.21/0.28 % BW rewrite match attempts : 1
% 0.21/0.28 % BW rewrite match successes : 1
% 0.21/0.28 % Condensation attempts : 59
% 0.21/0.28 % Condensation successes : 2
% 0.21/0.28 % Termbank termtop insertions : 11917
% 0.21/0.28 % Search garbage collected termcells : 595
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.014 s
% 0.21/0.28 % System time : 0.004 s
% 0.21/0.28 % Total time : 0.018 s
% 0.21/0.28 % Maximum resident set size: 3592 pages
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.072 s
% 0.21/0.28 % System time : 0.016 s
% 0.21/0.28 % Total time : 0.088 s
% 0.21/0.28 % Maximum resident set size: 4864 pages
% 0.21/0.28 % E exiting
%------------------------------------------------------------------------------