%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU684^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:25:02 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 35 equ; 0 cnn)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 699 ( 29 ~; 27 |; 29 &; 574 @)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 155 ( 75 ^; 67 !; 13 ?; 155 :)
% 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,
setunion: $i > $i ).
thf(decl_27,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_28,type,
dsetconstrER: $o ).
thf(decl_29,type,
subset: $i > $i > $o ).
thf(decl_30,type,
kpair: $i > $i > $i ).
thf(decl_31,type,
cartprod: $i > $i > $i ).
thf(decl_32,type,
singleton: $i > $o ).
thf(decl_33,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_34,type,
theprop: $o ).
thf(decl_35,type,
breln: $i > $i > $i > $o ).
thf(decl_36,type,
func: $i > $i > $i > $o ).
thf(decl_37,type,
funcImageSingleton: $o ).
thf(decl_38,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_39,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_40,type,
esk2_4: $i > $i > $i > $i > $i ).
thf(decl_41,type,
esk3_0: $i ).
thf(decl_42,type,
esk4_0: $i ).
thf(decl_43,type,
esk5_0: $i ).
thf(decl_44,type,
esk6_1: $i > $i ).
thf(decl_45,type,
esk7_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X1: $i,X6: $i,X8: $i] :
( ( breln @ X1 @ X6 @ X8 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ex1 @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X6: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',breln) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',funcImageSingleton) ).
thf(funcGraphProp1,conjecture,
( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X6 @ X9 @ X3 ) ) @ X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',funcGraphProp1) ).
thf(ap,axiom,
( ap
= ( ^ [X1: $i,X6: $i,X9: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X6
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X9 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',ap) ).
thf(theprop,axiom,
( theprop
<=> ! [X5: $i] :
( ( singleton @ X5 )
=> ( in @ ( setunion @ X5 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',theprop) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TE3yxzqmoA/E---3.1_775276.p',dsetconstrER) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_10,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_11,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_12,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_13,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
( funcImageSingleton
<=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_15,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X3 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [X1: $i,X6: $i,X9: $i] :
( ( func @ X1 @ X6 @ X9 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X6 @ X9 @ X3 ) ) @ X9 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcGraphProp1]) ).
thf(c_0_17,plain,
( ap
= ( ^ [Z0: $i,Z1: $i,Z2: $i,Z3: $i] :
( setunion
@ ( dsetconstr @ Z1
@ ^ [Z4: $i] : ( in @ ( kpair @ Z3 @ Z4 ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ap]) ).
thf(c_0_18,plain,
( funcImageSingleton
= ( ! [X1: $i,X6: $i,X9: $i] :
( ( ( subset @ X9 @ ( cartprod @ X1 @ X6 ) )
& ! [X25: $i] :
( ( in @ X25 @ X1 )
=> ? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X25 @ Z0 ) @ X9 ) ) )
& ( ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X25 @ Z0 ) @ X9 ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X27: $i] :
( ( in @ X27
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) )
& ( ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) )
= ( setadjoin @ X27 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_10]),c_0_15]) ).
thf(c_0_19,axiom,
( theprop
= ( ! [X5: $i] :
( ? [X23: $i] :
( ( in @ X23 @ X5 )
& ( X5
= ( setadjoin @ X23 @ emptyset ) ) )
=> ( in @ ( setunion @ X5 ) @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_10]) ).
thf(c_0_20,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_21,negated_conjecture,
~ ( ! [X28: $i,X29: $i > $o,X30: $i] :
( ( in @ X30 @ ( dsetconstr @ X28 @ X29 ) )
=> ( X29 @ X30 ) )
=> ( ! [X31: $i] :
( ? [X32: $i] :
( ( in @ X32 @ X31 )
& ( X31
= ( setadjoin @ X32 @ emptyset ) ) )
=> ( in @ ( setunion @ X31 ) @ X31 ) )
=> ( ! [X33: $i,X34: $i,X35: $i] :
( ( ( subset @ X35 @ ( cartprod @ X33 @ X34 ) )
& ! [X36: $i] :
( ( in @ X36 @ X33 )
=> ? [X37: $i] :
( ( in @ X37
@ ( dsetconstr @ X34
@ ^ [Z0: $i] : ( in @ ( kpair @ X36 @ Z0 ) @ X35 ) ) )
& ( ( dsetconstr @ X34
@ ^ [Z0: $i] : ( in @ ( kpair @ X36 @ Z0 ) @ X35 ) )
= ( setadjoin @ X37 @ emptyset ) ) ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X33 )
=> ? [X39: $i] :
( ( in @ X39
@ ( dsetconstr @ X34
@ ^ [Z0: $i] : ( in @ ( kpair @ X38 @ Z0 ) @ X35 ) ) )
& ( ( dsetconstr @ X34
@ ^ [Z0: $i] : ( in @ ( kpair @ X38 @ Z0 ) @ X35 ) )
= ( setadjoin @ X39 @ emptyset ) ) ) ) )
=> ! [X1: $i,X6: $i,X9: $i] :
( ( ( subset @ X9 @ ( cartprod @ X1 @ X6 ) )
& ! [X40: $i] :
( ( in @ X40 @ X1 )
=> ? [X41: $i] :
( ( in @ X41
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X40 @ Z0 ) @ X9 ) ) )
& ( ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X40 @ Z0 ) @ X9 ) )
= ( setadjoin @ X41 @ emptyset ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in
@ ( kpair @ X3
@ ( setunion
@ ( dsetconstr @ X6
@ ^ [Z0: $i] : ( in @ ( kpair @ X3 @ Z0 ) @ X9 ) ) ) )
@ X9 ) ) ) ) ) ),
inference(fool_unroll,[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)],[c_0_16,c_0_17]),c_0_18]),c_0_15]),c_0_19]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
! [X42: $i,X43: $i > $o,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X51: $i,X52: $i,X57: $i] :
( ( ~ ( in @ X44 @ ( dsetconstr @ X42 @ X43 ) )
| ( X43 @ X44 ) )
& ( ~ ( in @ X46 @ X45 )
| ( X45
!= ( setadjoin @ X46 @ emptyset ) )
| ( in @ ( setunion @ X45 ) @ X45 ) )
& ( ( in @ ( esk2_4 @ X47 @ X48 @ X49 @ X52 )
@ ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ X52 @ Z0 ) @ X49 ) ) )
| ~ ( in @ X52 @ X47 )
| ( in @ ( esk1_3 @ X47 @ X48 @ X49 ) @ X47 )
| ~ ( subset @ X49 @ ( cartprod @ X47 @ X48 ) ) )
& ( ( ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ X52 @ Z0 ) @ X49 ) )
= ( setadjoin @ ( esk2_4 @ X47 @ X48 @ X49 @ X52 ) @ emptyset ) )
| ~ ( in @ X52 @ X47 )
| ( in @ ( esk1_3 @ X47 @ X48 @ X49 ) @ X47 )
| ~ ( subset @ X49 @ ( cartprod @ X47 @ X48 ) ) )
& ( ( in @ ( esk2_4 @ X47 @ X48 @ X49 @ X52 )
@ ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ X52 @ Z0 ) @ X49 ) ) )
| ~ ( in @ X52 @ X47 )
| ~ ( in @ X51
@ ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X47 @ X48 @ X49 ) @ Z0 ) @ X49 ) ) )
| ( ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X47 @ X48 @ X49 ) @ Z0 ) @ X49 ) )
!= ( setadjoin @ X51 @ emptyset ) )
| ~ ( subset @ X49 @ ( cartprod @ X47 @ X48 ) ) )
& ( ( ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ X52 @ Z0 ) @ X49 ) )
= ( setadjoin @ ( esk2_4 @ X47 @ X48 @ X49 @ X52 ) @ emptyset ) )
| ~ ( in @ X52 @ X47 )
| ~ ( in @ X51
@ ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X47 @ X48 @ X49 ) @ Z0 ) @ X49 ) ) )
| ( ( dsetconstr @ X48
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X47 @ X48 @ X49 ) @ Z0 ) @ X49 ) )
!= ( setadjoin @ X51 @ emptyset ) )
| ~ ( subset @ X49 @ ( cartprod @ X47 @ X48 ) ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( in @ ( esk6_1 @ X57 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X57 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X57 @ esk3_0 ) )
& ( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X57 @ Z0 ) @ esk5_0 ) )
= ( setadjoin @ ( esk6_1 @ X57 ) @ emptyset ) )
| ~ ( in @ X57 @ esk3_0 ) )
& ( in @ esk7_0 @ esk3_0 )
& ~ ( in
@ ( kpair @ esk7_0
@ ( setunion
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk7_0 @ Z0 ) @ esk5_0 ) ) ) )
@ esk5_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])])]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( setunion @ X3 ) @ X3 )
| ~ ( in @ X1 @ X3 )
| ( X3
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( in @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(er,[status(thm)],[c_0_23]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) )
= ( setadjoin @ ( esk6_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_1 @ X1 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( in
@ ( setunion
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) ) )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_29,negated_conjecture,
~ ( in
@ ( kpair @ esk7_0
@ ( setunion
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ esk7_0 @ Z0 ) @ esk5_0 ) ) ) )
@ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( in
@ ( kpair @ X1
@ ( setunion
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) ) ) )
@ esk5_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_31,negated_conjecture,
in @ esk7_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU684^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:08:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.TE3yxzqmoA/E---3.1_775276.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % partial match(1): HSSSSLSSMLMNSFA
% 0.23/0.27 % Preprocessing class: HSSSSLSSMLMNHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.27 % sh5l with pid 775290 completed with status 0
% 0.23/0.27 % Result found by sh5l
% 0.23/0.27 % partial match(1): HSSSSLSSMLMNSFA
% 0.23/0.27 % Preprocessing class: HSSSSLSSMLMNHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HGUSF-FFMF32-DHFSMFBN
% 0.23/0.27 % partial match(4): HGUSM-FFMF32-SHFFMSBN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 775294 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % partial match(1): HSSSSLSSMLMNSFA
% 0.23/0.27 % Preprocessing class: HSSSSLSSMLMNHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HGUSF-FFMF32-DHFSMFBN
% 0.23/0.27 % partial match(4): HGUSM-FFMF32-SHFFMSBN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% See solution above
% 0.23/0.27 % Parsed axioms : 25
% 0.23/0.27 % Removed by relevancy pruning/SinE : 16
% 0.23/0.27 % Initial clauses : 11
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 11
% 0.23/0.27 % Processed clauses : 16
% 0.23/0.27 % ...of these trivial : 0
% 0.23/0.27 % ...subsumed : 0
% 0.23/0.27 % ...remaining for further processing : 16
% 0.23/0.27 % Other redundant clauses eliminated : 1
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 0
% 0.23/0.27 % Generated clauses : 9
% 0.23/0.27 % ...of the previous two non-redundant : 8
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 1
% 0.23/0.27 % Paramodulations : 8
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 1
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 1
% 0.23/0.27 % ...of those cached : 0
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 15
% 0.23/0.27 % Positive orientable unit clauses : 2
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 1
% 0.23/0.27 % Non-unit-clauses : 12
% 0.23/0.27 % Current number of unprocessed clauses: 3
% 0.23/0.27 % ...number of literals in the above : 14
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 0
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 28
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 23
% 0.23/0.27 % Non-unit clause-clause subsumptions : 1
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 0
% 0.23/0.27 % BW rewrite match successes : 0
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 2510
% 0.23/0.27 % Search garbage collected termcells : 669
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.005 s
% 0.23/0.27 % System time : 0.003 s
% 0.23/0.27 % Total time : 0.007 s
% 0.23/0.27 % Maximum resident set size: 3652 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.008 s
% 0.23/0.27 % System time : 0.006 s
% 0.23/0.27 % Total time : 0.014 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------