%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU680^2 : 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 : n016.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 08:25:00 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 245 ( 37 equ; 0 cnn)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 1095 ( 36 ~; 51 |; 26 &; 949 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 232 ( 112 ^; 110 !; 10 ?; 232 :)
% 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,
subset: $i > $i > $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
cartprod: $i > $i > $i ).
thf(decl_30,type,
singleton: $i > $o ).
thf(decl_31,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_32,type,
breln: $i > $i > $i > $o ).
thf(decl_33,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_34,type,
func: $i > $i > $i > $o ).
thf(decl_35,type,
funcSet: $i > $i > $i ).
thf(decl_36,type,
funcinfuncset: $o ).
thf(decl_37,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_38,type,
lamp: $o ).
thf(decl_39,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_40,type,
esk2_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_41,type,
esk3_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_42,type,
esk4_0: $i ).
thf(decl_43,type,
esk5_0: $i ).
thf(decl_44,type,
esk6_0: $i > $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X1: $i,X4: $i,X6: $i] :
( ( breln @ X1 @ X4 @ X6 )
& ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ex1 @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',breln) ).
thf(lamp,axiom,
( lamp
<=> ! [X1: $i,X4: $i,X10: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X10 @ X2 ) @ X4 ) )
=> ( func @ X1 @ X4
@ ( lam @ X1 @ X4
@ ^ [X2: $i] : ( X10 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',lamp) ).
thf(lam,axiom,
( lam
= ( ^ [X1: $i,X4: $i,X9: $i > $i] :
( dpsetconstr @ X1 @ X4
@ ^ [X2: $i,X7: $i] :
( ( X9 @ X2 )
= X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',lam) ).
thf(lam2p,conjecture,
( funcinfuncset
=> ( lamp
=> ! [X1: $i,X4: $i,X11: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X11 @ X2 ) @ X4 ) )
=> ( in
@ ( lam @ X1 @ X4
@ ^ [X2: $i] : ( X11 @ X2 ) )
@ ( funcSet @ X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',lam2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ( in @ X8 @ ( funcSet @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Qf5SlzlcJF/E---3.1_415061.p',funcinfuncset) ).
thf(c_0_8,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X23: $i] :
( ( in @ X23
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X23 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_9,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_10,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_11,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_12,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X23: $i] :
( ( in @ X23
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X23 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,plain,
( lamp
<=> ! [X1: $i,X4: $i,X10: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X10 @ X2 ) @ X4 ) )
=> ( func @ X1 @ X4
@ ( lam @ X1 @ X4
@ ^ [Z0: $i] : ( X10 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_14,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( 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_15,plain,
( lam
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( dpsetconstr @ Z0 @ Z1
@ ^ [Z3: $i,Z4: $i] :
( ( Z2 @ Z3 )
= Z4 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam]) ).
thf(c_0_16,negated_conjecture,
~ ( funcinfuncset
=> ( lamp
=> ! [X1: $i,X4: $i,X11: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X11 @ X2 ) @ X4 ) )
=> ( in
@ ( lam @ X1 @ X4
@ ^ [X2: $i] : ( X11 @ X2 ) )
@ ( funcSet @ X1 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[lam2p]) ).
thf(c_0_17,plain,
( lamp
= ( ! [X1: $i,X4: $i,X10: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X10 @ X2 ) @ X4 ) )
=> ( ( subset
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z0: $i,Z1: $i] :
( ( X10 @ Z0 )
= Z1 ) )
@ ( cartprod @ X1 @ X4 ) )
& ! [X27: $i] :
( ( in @ X27 @ X1 )
=> ? [X28: $i] :
( ( in @ X28
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( in @ ( kpair @ X27 @ Z0 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z1: $i,Z2: $i] :
( ( X10 @ Z1 )
= Z2 ) ) ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( in @ ( kpair @ X27 @ Z0 )
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z1: $i,Z2: $i] :
( ( X10 @ Z1 )
= Z2 ) ) ) )
= ( setadjoin @ X28 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_18,axiom,
( funcinfuncset
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X25: $i] :
( ( in @ X25 @ X1 )
=> ? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X25 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X25 @ Z0 ) @ X8 ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) )
=> ( in @ X8 @ ( funcSet @ X1 @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_14]) ).
thf(c_0_19,negated_conjecture,
~ ( ! [X29: $i,X30: $i,X31: $i] :
( ( ( subset @ X31 @ ( cartprod @ X29 @ X30 ) )
& ! [X32: $i] :
( ( in @ X32 @ X29 )
=> ? [X33: $i] :
( ( in @ X33
@ ( dsetconstr @ X30
@ ^ [Z0: $i] : ( in @ ( kpair @ X32 @ Z0 ) @ X31 ) ) )
& ( ( dsetconstr @ X30
@ ^ [Z0: $i] : ( in @ ( kpair @ X32 @ Z0 ) @ X31 ) )
= ( setadjoin @ X33 @ emptyset ) ) ) ) )
=> ( in @ X31 @ ( funcSet @ X29 @ X30 ) ) )
=> ( ! [X34: $i,X35: $i,X36: $i > $i] :
( ! [X37: $i] :
( ( in @ X37 @ X34 )
=> ( in @ ( X36 @ X37 ) @ X35 ) )
=> ( ( subset
@ ( dpsetconstr @ X34 @ X35
@ ^ [Z0: $i] : ( $eq @ ( X36 @ Z0 ) ) )
@ ( cartprod @ X34 @ X35 ) )
& ! [X38: $i] :
( ( in @ X38 @ X34 )
=> ? [X39: $i] :
( ( in @ X39
@ ( dsetconstr @ X35
@ ^ [Z0: $i] :
( in @ ( kpair @ X38 @ Z0 )
@ ( dpsetconstr @ X34 @ X35
@ ^ [Z1: $i] : ( $eq @ ( X36 @ Z1 ) ) ) ) ) )
& ( ( dsetconstr @ X35
@ ^ [Z0: $i] :
( in @ ( kpair @ X38 @ Z0 )
@ ( dpsetconstr @ X34 @ X35
@ ^ [Z1: $i] : ( $eq @ ( X36 @ Z1 ) ) ) ) )
= ( setadjoin @ X39 @ emptyset ) ) ) ) ) )
=> ! [X1: $i,X4: $i,X11: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X11 @ X2 ) @ X4 ) )
=> ( in
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X11 @ Z0 ) ) )
@ ( funcSet @ X1 @ X4 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_16]),c_0_15]),c_0_17]),c_0_18])]) ).
thf(c_0_20,negated_conjecture,
! [X40: $i,X41: $i,X42: $i,X44: $i,X45: $i,X46: $i,X47: $i > $i,X49: $i,X54: $i] :
( ( ( in @ ( esk1_3 @ X40 @ X41 @ X42 ) @ X40 )
| ~ ( subset @ X42 @ ( cartprod @ X40 @ X41 ) )
| ( in @ X42 @ ( funcSet @ X40 @ X41 ) ) )
& ( ~ ( in @ X44
@ ( dsetconstr @ X41
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X40 @ X41 @ X42 ) @ Z0 ) @ X42 ) ) )
| ( ( dsetconstr @ X41
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X40 @ X41 @ X42 ) @ Z0 ) @ X42 ) )
!= ( setadjoin @ X44 @ emptyset ) )
| ~ ( subset @ X42 @ ( cartprod @ X40 @ X41 ) )
| ( in @ X42 @ ( funcSet @ X40 @ X41 ) ) )
& ( ( subset
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z0: $i] : ( $eq @ ( X47 @ Z0 ) ) )
@ ( cartprod @ X45 @ X46 ) )
| ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 ) )
& ( ( in @ ( esk3_4 @ X45 @ X46 @ X47 @ X49 )
@ ( dsetconstr @ X46
@ ^ [Z0: $i] :
( in @ ( kpair @ X49 @ Z0 )
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z1: $i] : ( $eq @ ( X47 @ Z1 ) ) ) ) ) )
| ~ ( in @ X49 @ X45 )
| ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 ) )
& ( ( ( dsetconstr @ X46
@ ^ [Z0: $i] :
( in @ ( kpair @ X49 @ Z0 )
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z1: $i] : ( $eq @ ( X47 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk3_4 @ X45 @ X46 @ X47 @ X49 ) @ emptyset ) )
| ~ ( in @ X49 @ X45 )
| ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 ) )
& ( ( subset
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z0: $i] : ( $eq @ ( X47 @ Z0 ) ) )
@ ( cartprod @ X45 @ X46 ) )
| ~ ( in @ ( X47 @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X46 ) )
& ( ( in @ ( esk3_4 @ X45 @ X46 @ X47 @ X49 )
@ ( dsetconstr @ X46
@ ^ [Z0: $i] :
( in @ ( kpair @ X49 @ Z0 )
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z1: $i] : ( $eq @ ( X47 @ Z1 ) ) ) ) ) )
| ~ ( in @ X49 @ X45 )
| ~ ( in @ ( X47 @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X46 ) )
& ( ( ( dsetconstr @ X46
@ ^ [Z0: $i] :
( in @ ( kpair @ X49 @ Z0 )
@ ( dpsetconstr @ X45 @ X46
@ ^ [Z1: $i] : ( $eq @ ( X47 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk3_4 @ X45 @ X46 @ X47 @ X49 ) @ emptyset ) )
| ~ ( in @ X49 @ X45 )
| ~ ( in @ ( X47 @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X46 ) )
& ( ~ ( in @ X54 @ esk4_0 )
| ( in @ ( esk6_0 @ X54 ) @ esk5_0 ) )
& ~ ( in
@ ( dpsetconstr @ esk4_0 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) )
@ ( funcSet @ esk4_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_19])])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( cartprod @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i,X9: $i > $i,X4: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( in @ ( kpair @ X2 @ Z0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Z1: $i] : ( $eq @ ( X9 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk3_4 @ X4 @ X1 @ X9 @ X2 ) @ emptyset ) )
| ( in @ ( esk2_3 @ X4 @ X1 @ X9 ) @ X4 )
| ~ ( in @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( in
@ ( esk1_3 @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) ) )
@ X1 )
| ( in
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X9: $i > $i,X2: $i] :
( ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ X1 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ X5 @ ( funcSet @ X4 @ X2 ) )
| ~ ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ~ ( subset @ X5 @ ( cartprod @ X4 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X4: $i,X9: $i > $i,X10: $i > $i,X2: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( in
@ ( kpair
@ ( esk1_3 @ X2 @ X4
@ ( dpsetconstr @ X2 @ X4
@ ^ [Z1: $i] : ( $eq @ ( X9 @ Z1 ) ) ) )
@ Z0 )
@ ( dpsetconstr @ X2 @ X1
@ ^ [Z1: $i] : ( $eq @ ( X10 @ Z1 ) ) ) ) )
= ( setadjoin
@ ( esk3_4 @ X2 @ X1 @ X10
@ ( esk1_3 @ X2 @ X4
@ ( dpsetconstr @ X2 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) ) ) )
@ emptyset ) )
| ( in
@ ( dpsetconstr @ X2 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( funcSet @ X2 @ X4 ) )
| ( in @ ( esk2_3 @ X2 @ X4 @ X9 ) @ X2 )
| ( in @ ( esk2_3 @ X2 @ X1 @ X10 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,negated_conjecture,
! [X2: $i,X9: $i > $i,X4: $i,X1: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X9 @ X4 )
@ ( dsetconstr @ X2
@ ^ [Z0: $i] :
( in @ ( kpair @ X4 @ Z0 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z1: $i] : ( $eq @ ( X9 @ Z1 ) ) ) ) ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 )
| ~ ( in @ X4 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X4: $i,X9: $i > $i,X2: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X9 @ X4 )
@ ( dsetconstr @ X2
@ ^ [Z0: $i] :
( in @ ( kpair @ X4 @ Z0 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z1: $i] : ( $eq @ ( X9 @ Z1 ) ) ) ) ) )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X4: $i,X9: $i > $i,X2: $i,X1: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] :
( in @ ( kpair @ X2 @ Z0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Z1: $i] : ( $eq @ ( X9 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk3_4 @ X4 @ X1 @ X9 @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ X4 )
| ~ ( in @ ( X9 @ ( esk2_3 @ X4 @ X1 @ X9 ) ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( subset
@ ( dpsetconstr @ X1 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) )
@ ( cartprod @ X1 @ esk5_0 ) )
| ~ ( in @ ( esk2_3 @ X1 @ esk5_0 @ esk6_0 ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X9: $i > $i] :
( ( in
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 )
| ( ( setadjoin
@ ( esk3_4 @ X1 @ X2 @ X9
@ ( esk1_3 @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) ) ) )
@ emptyset )
!= ( setadjoin @ X4 @ emptyset ) )
| ~ ( in @ X4
@ ( setadjoin
@ ( esk3_4 @ X1 @ X2 @ X9
@ ( esk1_3 @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) ) ) )
@ emptyset ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_22]) ).
thf(c_0_34,negated_conjecture,
! [X2: $i,X10: $i > $i,X9: $i > $i,X4: $i,X1: $i] :
( ( in
@ ( esk3_4 @ X1 @ X2 @ X9
@ ( esk1_3 @ X1 @ X4
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X10 @ Z0 ) ) ) ) )
@ ( setadjoin
@ ( esk3_4 @ X1 @ X2 @ X9
@ ( esk1_3 @ X1 @ X4
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X10 @ Z0 ) ) ) ) )
@ emptyset ) )
| ( in
@ ( dpsetconstr @ X1 @ X4
@ ^ [Z0: $i] : ( $eq @ ( X10 @ Z0 ) ) )
@ ( funcSet @ X1 @ X4 ) )
| ( in @ ( esk2_3 @ X1 @ X4 @ X10 ) @ X1 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_24]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X9: $i > $i,X4: $i,X2: $i] :
( ( in
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( funcSet @ X4 @ X2 ) )
| ~ ( in
@ ( esk1_3 @ X4 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) ) )
@ X1 )
| ~ ( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( cartprod @ X4 @ X2 ) )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_31]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( in
@ ( esk1_3 @ X1 @ esk5_0
@ ( dpsetconstr @ X1 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) ) )
@ X1 )
| ( in
@ ( dpsetconstr @ X1 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) )
@ ( funcSet @ X1 @ esk5_0 ) )
| ~ ( in @ ( esk2_3 @ X1 @ esk5_0 @ esk6_0 ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
thf(c_0_37,negated_conjecture,
~ ( in
@ ( dpsetconstr @ esk4_0 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) )
@ ( funcSet @ esk4_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_38,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( in
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X9 @ Z0 ) ) )
@ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i] :
( ( in
@ ( dpsetconstr @ X1 @ esk5_0
@ ^ [Z0: $i] : ( $eq @ ( esk6_0 @ Z0 ) ) )
@ ( funcSet @ X1 @ esk5_0 ) )
| ~ ( in @ ( esk2_3 @ X1 @ esk5_0 @ esk6_0 ) @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]),c_0_32]) ).
thf(c_0_40,negated_conjecture,
in @ ( esk2_3 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU680^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:14:19 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.Qf5SlzlcJF/E---3.1_415061.p
% 0.10/0.26 % Version: 3.5.1-ho
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % Starting additional_ho_6 with 300s (1) cores
% 0.10/0.26 % pre_casc_5 with pid 415076 completed with status 0
% 0.10/0.26 % Result found by pre_casc_5
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.10/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.10/0.26 % Search class: HGUSF-FFMF32-DHSFMFNN
% 0.10/0.26 % partial match(3): HGUSF-FFMF32-SFFFMFNN
% 0.10/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.26 % SubtermCWHack with pid 415078 completed with status 0
% 0.10/0.26 % Result found by SubtermCWHack
% 0.10/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.10/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.10/0.26 % Search class: HGUSF-FFMF32-DHSFMFNN
% 0.10/0.26 % partial match(3): HGUSF-FFMF32-SFFFMFNN
% 0.10/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.26 % Preprocessing time : 0.002 s
% 0.10/0.26
% 0.10/0.26 % Proof found!
% 0.10/0.26 % SZS status Theorem
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26 % Parsed axioms : 24
% 0.10/0.26 % Removed by relevancy pruning/SinE : 16
% 0.10/0.26 % Initial clauses : 10
% 0.10/0.26 % Removed in clause preprocessing : 0
% 0.10/0.26 % Initial clauses in saturation : 10
% 0.10/0.26 % Processed clauses : 41
% 0.10/0.26 % ...of these trivial : 0
% 0.10/0.26 % ...subsumed : 4
% 0.10/0.26 % ...remaining for further processing : 37
% 0.10/0.26 % Other redundant clauses eliminated : 0
% 0.10/0.26 % Clauses deleted for lack of memory : 0
% 0.10/0.26 % Backward-subsumed : 10
% 0.10/0.26 % Backward-rewritten : 0
% 0.10/0.26 % Generated clauses : 65
% 0.10/0.26 % ...of the previous two non-redundant : 63
% 0.10/0.26 % ...aggressively subsumed : 0
% 0.10/0.26 % Contextual simplify-reflections : 11
% 0.10/0.26 % Paramodulations : 65
% 0.10/0.26 % Factorizations : 0
% 0.10/0.26 % NegExts : 0
% 0.10/0.26 % Equation resolutions : 0
% 0.10/0.26 % Disequality decompositions : 0
% 0.10/0.26 % Total rewrite steps : 3
% 0.10/0.26 % ...of those cached : 2
% 0.10/0.26 % Propositional unsat checks : 0
% 0.10/0.26 % Propositional check models : 0
% 0.10/0.26 % Propositional check unsatisfiable : 0
% 0.10/0.26 % Propositional clauses : 0
% 0.10/0.26 % Propositional clauses after purity: 0
% 0.10/0.26 % Propositional unsat core size : 0
% 0.10/0.26 % Propositional preprocessing time : 0.000
% 0.10/0.26 % Propositional encoding time : 0.000
% 0.10/0.26 % Propositional solver time : 0.000
% 0.10/0.26 % Success case prop preproc time : 0.000
% 0.10/0.26 % Success case prop encoding time : 0.000
% 0.10/0.26 % Success case prop solver time : 0.000
% 0.10/0.26 % Current number of processed clauses : 27
% 0.10/0.26 % Positive orientable unit clauses : 1
% 0.10/0.26 % Positive unorientable unit clauses: 0
% 0.10/0.26 % Negative unit clauses : 1
% 0.10/0.26 % Non-unit-clauses : 25
% 0.10/0.26 % Current number of unprocessed clauses: 28
% 0.10/0.26 % ...number of literals in the above : 136
% 0.10/0.26 % Current number of archived formulas : 0
% 0.10/0.26 % Current number of archived clauses : 10
% 0.10/0.26 % Clause-clause subsumption calls (NU) : 400
% 0.10/0.26 % Rec. Clause-clause subsumption calls : 224
% 0.10/0.26 % Non-unit clause-clause subsumptions : 25
% 0.10/0.26 % Unit Clause-clause subsumption calls : 9
% 0.10/0.26 % Rewrite failures with RHS unbound : 0
% 0.10/0.26 % BW rewrite match attempts : 0
% 0.10/0.26 % BW rewrite match successes : 0
% 0.10/0.26 % Condensation attempts : 0
% 0.10/0.26 % Condensation successes : 0
% 0.10/0.26 % Termbank termtop insertions : 23727
% 0.10/0.26 % Search garbage collected termcells : 611
% 0.10/0.26
% 0.10/0.26 % -------------------------------------------------
% 0.10/0.26 % User time : 0.015 s
% 0.10/0.26 % System time : 0.004 s
% 0.10/0.26 % Total time : 0.019 s
% 0.10/0.26 % Maximum resident set size: 3656 pages
% 0.10/0.26
% 0.10/0.26 % -------------------------------------------------
% 0.10/0.26 % User time : 0.016 s
% 0.10/0.26 % System time : 0.010 s
% 0.10/0.26 % Total time : 0.026 s
% 0.10/0.26 % Maximum resident set size: 4864 pages
% 0.10/0.26 % E exiting
%------------------------------------------------------------------------------