%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU645^2 : 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 : 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 08:24:51 AM UTC 2026
% Result : Theorem 0.28s 0.41s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 47 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 1102 ( 31 ~; 26 |; 26 &; 985 @)
% ( 7 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 137 ( 31 ^; 88 !; 18 ?; 137 :)
% 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,
iskpair: $i > $o ).
thf(decl_30,type,
kpair: $i > $i > $i ).
thf(decl_31,type,
kpairp: $o ).
thf(decl_32,type,
singleton: $i > $o ).
thf(decl_33,type,
setukpairinjL1: $o ).
thf(decl_34,type,
kfstsingleton: $o ).
thf(decl_35,type,
theprop: $o ).
thf(decl_36,type,
kfst: $i > $i ).
thf(decl_37,type,
esk1_2: $i > $i > $i ).
thf(decl_38,type,
esk2_2: $i > $i > $i ).
thf(decl_39,type,
esk3_1: $i > $i ).
thf(decl_40,type,
esk4_0: $i ).
thf(decl_41,type,
esk5_0: $i ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X6: $i] :
( ( iskpair @ X6 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',kfstsingleton) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',singleton) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ? [X4: $i] :
( ( in @ X4 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',iskpair) ).
thf(kpair,axiom,
( kpair
= ( ^ [X3: $i,X4: $i] : ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',kpair) ).
thf(kfstpairEq,conjecture,
( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X3: $i,X4: $i] :
( ( kfst @ ( kpair @ X3 @ X4 ) )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',kfstpairEq) ).
thf(theprop,axiom,
( theprop
<=> ! [X7: $i] :
( ( singleton @ X7 )
=> ( in @ ( setunion @ X7 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',theprop) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X3: $i,X4: $i] : ( iskpair @ ( kpair @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',kpairp) ).
thf(kfst,axiom,
( kfst
= ( ^ [X6: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',kfst) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',dsetconstrER) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o9kehR60mW/E---3.1_1714644.p',setukpairinjL1) ).
thf(c_0_10,plain,
( kfstsingleton
<=> ! [X6: $i] :
( ( iskpair @ X6 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_11,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_12,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ? [X4: $i] :
( ( in @ X4 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_13,plain,
( kpair
= ( ^ [Z0: $i,Z1: $i] : ( setadjoin @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[kpair]) ).
thf(c_0_14,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X3: $i,X4: $i] :
( ( kfst @ ( kpair @ X3 @ X4 ) )
= X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kfstpairEq]) ).
thf(c_0_15,plain,
( kfstsingleton
= ( ! [X6: $i] :
( ? [X22: $i] :
( ( in @ X22 @ ( setunion @ X6 ) )
& ? [X23: $i] :
( ( in @ X23 @ ( setunion @ X6 ) )
& ( X6
= ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X23 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) ) )
& ( ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_16,axiom,
( theprop
= ( ! [X7: $i] :
( ? [X25: $i] :
( ( in @ X25 @ X7 )
& ( X7
= ( setadjoin @ X25 @ emptyset ) ) )
=> ( in @ ( setunion @ X7 ) @ X7 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_11]) ).
thf(c_0_17,axiom,
( kpairp
= ( ! [X3: $i,X4: $i] :
? [X20: $i] :
( ( in @ X20 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X21: $i] :
( ( in @ X21 @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X20 @ ( setadjoin @ X21 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp,c_0_13]),c_0_12]) ).
thf(c_0_18,plain,
( kfst
= ( ^ [Z0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Z0 )
@ ^ [Z1: $i] : ( in @ ( setadjoin @ Z1 @ emptyset ) @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfst]) ).
thf(c_0_19,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_20,negated_conjecture,
~ ( ! [X26: $i,X27: $i > $o,X28: $i] :
( ( in @ X28
@ ( dsetconstr @ X26
@ ^ [Z0: $i] : ( X27 @ Z0 ) ) )
=> ( X27 @ X28 ) )
=> ( ! [X29: $i,X30: $i] :
? [X31: $i] :
( ( in @ X31 @ ( setunion @ ( setadjoin @ ( setadjoin @ X29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X29 @ ( setadjoin @ X30 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X32: $i] :
( ( in @ X32 @ ( setunion @ ( setadjoin @ ( setadjoin @ X29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X29 @ ( setadjoin @ X30 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X29 @ ( setadjoin @ X30 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X31 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X31 @ ( setadjoin @ X32 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X33: $i,X34: $i,X35: $i] :
( ( in @ ( setadjoin @ X35 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X33 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X33 @ ( setadjoin @ X34 @ emptyset ) ) @ emptyset ) ) )
=> ( X33 = X35 ) )
=> ( ! [X36: $i] :
( ? [X37: $i] :
( ( in @ X37 @ ( setunion @ X36 ) )
& ? [X38: $i] :
( ( in @ X38 @ ( setunion @ X36 ) )
& ( X36
= ( setadjoin @ ( setadjoin @ X37 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X37 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X39: $i] :
( ( in @ X39
@ ( dsetconstr @ ( setunion @ X36 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X36 ) ) )
& ( ( dsetconstr @ ( setunion @ X36 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X36 ) )
= ( setadjoin @ X39 @ emptyset ) ) ) )
=> ( ! [X40: $i] :
( ? [X41: $i] :
( ( in @ X41 @ X40 )
& ( X40
= ( setadjoin @ X41 @ emptyset ) ) )
=> ( in @ ( setunion @ X40 ) @ X40 ) )
=> ! [X3: $i,X4: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) )
= X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),setukpairinjL1]),c_0_16]),c_0_17]),c_0_13]),c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X42: $i,X43: $i > $o,X44: $i,X45: $i,X46: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X56: $i,X57: $i] :
( ( ~ ( in @ X44
@ ( dsetconstr @ X42
@ ^ [Z0: $i] : ( X43 @ Z0 ) ) )
| ( X43 @ X44 ) )
& ( in @ ( esk1_2 @ X45 @ X46 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X45 @ ( setadjoin @ X46 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk2_2 @ X45 @ X46 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X45 @ ( setadjoin @ X46 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X45 @ ( setadjoin @ X46 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X45 @ X46 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X45 @ X46 ) @ ( setadjoin @ ( esk2_2 @ X45 @ X46 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ ( setadjoin @ X51 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X49 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X49 @ ( setadjoin @ X50 @ emptyset ) ) @ emptyset ) ) )
| ( X49 = X51 ) )
& ( ( in @ ( esk3_1 @ X52 )
@ ( dsetconstr @ ( setunion @ X52 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X52 ) ) )
| ~ ( in @ X53 @ ( setunion @ X52 ) )
| ~ ( in @ X54 @ ( setunion @ X52 ) )
| ( X52
!= ( setadjoin @ ( setadjoin @ X53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X53 @ ( setadjoin @ X54 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X52 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X52 ) )
= ( setadjoin @ ( esk3_1 @ X52 ) @ emptyset ) )
| ~ ( in @ X53 @ ( setunion @ X52 ) )
| ~ ( in @ X54 @ ( setunion @ X52 ) )
| ( X52
!= ( setadjoin @ ( setadjoin @ X53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X53 @ ( setadjoin @ X54 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X57 @ X56 )
| ( X56
!= ( setadjoin @ X57 @ emptyset ) )
| ( in @ ( setunion @ X56 ) @ X56 ) )
& ( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) ) ) )
!= esk4_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1 ) )
= ( setadjoin @ ( esk3_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ X1 ) )
| ~ ( in @ X4 @ ( setunion @ X1 ) )
| ( X1
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X3: $i] :
( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(er,[status(thm)],[c_0_22]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i,X3: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X3 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X3 ) @ ( setadjoin @ ( esk2_2 @ X1 @ X3 ) @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk2_2 @ X1 @ X3 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk1_2 @ X1 @ X3 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ ( esk3_1 @ X1 )
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1 ) ) )
| ~ ( in @ X3 @ ( setunion @ X1 ) )
| ~ ( in @ X4 @ ( setunion @ X1 ) )
| ( X1
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1 @ ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_25]),c_0_26])]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( X3 = X1 )
| ~ ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_35,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( setunion @ X3 ) @ X3 )
| ~ ( in @ X1 @ X3 )
| ( X3
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_36,negated_conjecture,
! [X3: $i,X1: $i] :
( ( esk3_1 @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i] :
( ( in @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(er,[status(thm)],[c_0_35]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_36]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i] : ( in @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_40,negated_conjecture,
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) ) ) )
!= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( setadjoin @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_36]) ).
thf(c_0_42,negated_conjecture,
( ( setunion @ ( setadjoin @ ( esk3_1 @ ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
!= esk4_0 ),
inference(rw,[status(thm)],[c_0_40,c_0_28]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
thf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU645^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n005.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 14:01:31 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.35 Running higher-order theorem proving
% 0.28/0.37 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.o9kehR60mW/E---3.1_1714644.p
% 0.28/0.41 % Version: 3.5.1-ho
% 0.28/0.41 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.28/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.41 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.41 % Starting sh5l with 300s (1) cores
% 0.28/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.41 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.41 % new_bool_2 with pid 1714660 completed with status 0
% 0.28/0.41 % Result found by new_bool_2
% 0.28/0.41 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.28/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.41 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.41 % Starting sh5l with 300s (1) cores
% 0.28/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.41 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.41 % Search class: HHUSS-FFSF21-DSFSMSBN
% 0.28/0.41 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.28/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.41 % SubtermCWHack with pid 1714663 completed with status 0
% 0.28/0.41 % Result found by SubtermCWHack
% 0.28/0.41 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.28/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.41 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.41 % Starting sh5l with 300s (1) cores
% 0.28/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.41 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.41 % Search class: HHUSS-FFSF21-DSFSMSBN
% 0.28/0.41 % partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.28/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.41 % Preprocessing time : 0.001 s
% 0.28/0.41
% 0.28/0.41 % Proof found!
% 0.28/0.41 % SZS status Theorem
% 0.28/0.41 % SZS output start CNFRefutation
% See solution above
% 0.28/0.41 % Parsed axioms : 24
% 0.28/0.41 % Removed by relevancy pruning/SinE : 14
% 0.28/0.41 % Initial clauses : 9
% 0.28/0.41 % Removed in clause preprocessing : 0
% 0.28/0.41 % Initial clauses in saturation : 9
% 0.28/0.41 % Processed clauses : 65
% 0.28/0.41 % ...of these trivial : 3
% 0.28/0.41 % ...subsumed : 7
% 0.28/0.41 % ...remaining for further processing : 55
% 0.28/0.41 % Other redundant clauses eliminated : 3
% 0.28/0.41 % Clauses deleted for lack of memory : 0
% 0.28/0.41 % Backward-subsumed : 2
% 0.28/0.41 % Backward-rewritten : 26
% 0.28/0.41 % Generated clauses : 138
% 0.28/0.41 % ...of the previous two non-redundant : 148
% 0.28/0.41 % ...aggressively subsumed : 0
% 0.28/0.41 % Contextual simplify-reflections : 0
% 0.28/0.41 % Paramodulations : 135
% 0.28/0.41 % Factorizations : 0
% 0.28/0.41 % NegExts : 0
% 0.28/0.41 % Equation resolutions : 3
% 0.28/0.41 % Disequality decompositions : 0
% 0.28/0.41 % Total rewrite steps : 196
% 0.28/0.41 % ...of those cached : 157
% 0.28/0.41 % Propositional unsat checks : 0
% 0.28/0.41 % Propositional check models : 0
% 0.28/0.41 % Propositional check unsatisfiable : 0
% 0.28/0.41 % Propositional clauses : 0
% 0.28/0.41 % Propositional clauses after purity: 0
% 0.28/0.41 % Propositional unsat core size : 0
% 0.28/0.41 % Propositional preprocessing time : 0.000
% 0.28/0.41 % Propositional encoding time : 0.000
% 0.28/0.41 % Propositional solver time : 0.000
% 0.28/0.41 % Success case prop preproc time : 0.000
% 0.28/0.41 % Success case prop encoding time : 0.000
% 0.28/0.41 % Success case prop solver time : 0.000
% 0.28/0.41 % Current number of processed clauses : 24
% 0.28/0.41 % Positive orientable unit clauses : 19
% 0.28/0.41 % Positive unorientable unit clauses: 0
% 0.28/0.41 % Negative unit clauses : 0
% 0.28/0.41 % Non-unit-clauses : 5
% 0.28/0.41 % Current number of unprocessed clauses: 87
% 0.28/0.41 % ...number of literals in the above : 127
% 0.28/0.41 % Current number of archived formulas : 0
% 0.28/0.41 % Current number of archived clauses : 28
% 0.28/0.41 % Clause-clause subsumption calls (NU) : 108
% 0.28/0.41 % Rec. Clause-clause subsumption calls : 107
% 0.28/0.41 % Non-unit clause-clause subsumptions : 7
% 0.28/0.41 % Unit Clause-clause subsumption calls : 11
% 0.28/0.41 % Rewrite failures with RHS unbound : 0
% 0.28/0.41 % BW rewrite match attempts : 63
% 0.28/0.41 % BW rewrite match successes : 22
% 0.28/0.41 % Condensation attempts : 0
% 0.28/0.41 % Condensation successes : 0
% 0.28/0.41 % Termbank termtop insertions : 10020
% 0.28/0.41 % Search garbage collected termcells : 449
% 0.28/0.41
% 0.28/0.41 % -------------------------------------------------
% 0.28/0.41 % User time : 0.009 s
% 0.28/0.41 % System time : 0.008 s
% 0.28/0.41 % Total time : 0.017 s
% 0.28/0.41 % Maximum resident set size: 3648 pages
% 0.28/0.41
% 0.28/0.41 % -------------------------------------------------
% 0.28/0.41 % User time : 0.012 s
% 0.28/0.41 % System time : 0.013 s
% 0.28/0.41 % Total time : 0.025 s
% 0.28/0.41 % Maximum resident set size: 4608 pages
% 0.28/0.41 % E exiting
%------------------------------------------------------------------------------