%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU680^2 : 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 : n015.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 08:27:12 AM UTC 2026
% Result : Theorem 0.49s 0.43s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 200 ( 30 equ; 0 cnn)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 1011 ( 36 ~; 51 |; 26 &; 865 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 181 ( 61 ^; 110 !; 10 ?; 181 :)
% 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_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/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.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/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.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/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.p',lamp) ).
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/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.p',lam2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ( in @ X8 @ ( funcSet @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i1e5W85l10/E---3.1_3585431.p',funcinfuncset) ).
thf(c_0_7,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_8,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_9,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_10,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_7,c_0_8]) ).
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,
( 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_9,c_0_10]),c_0_11]) ).
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,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_15,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_12]) ).
thf(c_0_16,plain,
( lamp
= ( ! [X1: $i,X4: $i,X10: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X10 @ X2 ) @ X4 ) )
=> ( ( subset
@ ( lam @ X1 @ X4
@ ^ [Z0: $i] : ( X10 @ Z0 ) )
@ ( cartprod @ X1 @ X4 ) )
& ! [X27: $i] :
( ( in @ X27 @ X1 )
=> ? [X28: $i] :
( ( in @ X28
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( in @ ( kpair @ X27 @ Z0 )
@ ( lam @ X1 @ X4
@ ^ [Z1: $i] : ( X10 @ Z1 ) ) ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( in @ ( kpair @ X27 @ Z0 )
@ ( lam @ X1 @ X4
@ ^ [Z1: $i] : ( X10 @ Z1 ) ) ) )
= ( setadjoin @ X28 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,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 @ ( lam @ X34 @ X35 @ X36 ) @ ( cartprod @ X34 @ X35 ) )
& ! [X38: $i] :
( ( in @ X38 @ X34 )
=> ? [X39: $i] :
( ( in @ X39
@ ( dsetconstr @ X35
@ ^ [Z0: $i] : ( in @ ( kpair @ X38 @ Z0 ) @ ( lam @ X34 @ X35 @ X36 ) ) ) )
& ( ( dsetconstr @ X35
@ ^ [Z0: $i] : ( in @ ( kpair @ X38 @ Z0 ) @ ( lam @ X34 @ X35 @ X36 ) ) )
= ( setadjoin @ X39 @ emptyset ) ) ) ) ) )
=> ! [X1: $i,X4: $i,X11: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( X11 @ X2 ) @ X4 ) )
=> ( in @ ( lam @ X1 @ X4 @ X11 ) @ ( funcSet @ X1 @ X4 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14]),c_0_15]),c_0_16])]) ).
thf(c_0_18,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 @ ( lam @ X45 @ X46 @ X47 ) @ ( 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 ) @ ( lam @ X45 @ X46 @ X47 ) ) ) )
| ~ ( in @ X49 @ X45 )
| ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 ) )
& ( ( ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X49 @ Z0 ) @ ( lam @ X45 @ X46 @ X47 ) ) )
= ( setadjoin @ ( esk3_4 @ X45 @ X46 @ X47 @ X49 ) @ emptyset ) )
| ~ ( in @ X49 @ X45 )
| ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 ) )
& ( ( subset @ ( lam @ X45 @ X46 @ X47 ) @ ( 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 ) @ ( lam @ X45 @ X46 @ X47 ) ) ) )
| ~ ( in @ X49 @ X45 )
| ~ ( in @ ( X47 @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X46 ) )
& ( ( ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X49 @ Z0 ) @ ( lam @ X45 @ X46 @ X47 ) ) )
= ( 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 @ ( lam @ esk4_0 @ esk5_0 @ esk6_0 ) @ ( 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_17])])])])])]) ).
thf(c_0_19,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_18]) ).
thf(c_0_20,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( subset @ ( lam @ X1 @ X2 @ X9 ) @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i,X9: $i > $i,X4: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ ( lam @ X4 @ X1 @ X9 ) ) )
= ( 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_18]) ).
thf(c_0_22,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ ( lam @ X1 @ X2 @ X9 ) ) @ X1 )
| ( in @ ( lam @ X1 @ X2 @ X9 ) @ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X9: $i > $i,X2: $i] :
( ( subset @ ( lam @ X1 @ X2 @ X9 ) @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_0 @ X1 ) @ esk5_0 )
| ~ ( in @ X1 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,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_18]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X4: $i,X9: $i > $i,X10: $i > $i,X2: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X2 @ X4 @ ( lam @ X2 @ X4 @ X9 ) ) @ Z0 ) @ ( lam @ X2 @ X1 @ X10 ) ) )
= ( setadjoin @ ( esk3_4 @ X2 @ X1 @ X10 @ ( esk1_3 @ X2 @ X4 @ ( lam @ X2 @ X4 @ X9 ) ) ) @ emptyset ) )
| ( in @ ( lam @ X2 @ X4 @ X9 ) @ ( funcSet @ X2 @ X4 ) )
| ( in @ ( esk2_3 @ X2 @ X4 @ X9 ) @ X2 )
| ( in @ ( esk2_3 @ X2 @ X1 @ X10 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_27,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 ) @ ( lam @ X1 @ X2 @ X9 ) ) ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 )
| ~ ( in @ X4 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,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 ) @ ( lam @ X1 @ X2 @ X9 ) ) ) )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_29,negated_conjecture,
! [X4: $i,X9: $i > $i,X2: $i,X1: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ ( lam @ X4 @ X1 @ X9 ) ) )
= ( 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_18]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( subset @ ( lam @ X1 @ esk5_0 @ esk6_0 ) @ ( cartprod @ X1 @ esk5_0 ) )
| ~ ( in @ ( esk2_3 @ X1 @ esk5_0 @ esk6_0 ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X9: $i > $i] :
( ( in @ ( lam @ X1 @ X2 @ X9 ) @ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 )
| ( ( setadjoin @ ( esk3_4 @ X1 @ X2 @ X9 @ ( esk1_3 @ X1 @ X2 @ ( lam @ X1 @ X2 @ X9 ) ) ) @ emptyset )
!= ( setadjoin @ X4 @ emptyset ) )
| ~ ( in @ X4 @ ( setadjoin @ ( esk3_4 @ X1 @ X2 @ X9 @ ( esk1_3 @ X1 @ X2 @ ( lam @ X1 @ X2 @ X9 ) ) ) @ emptyset ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_20]) ).
thf(c_0_32,negated_conjecture,
! [X2: $i,X10: $i > $i,X9: $i > $i,X4: $i,X1: $i] :
( ( in @ ( esk3_4 @ X1 @ X2 @ X9 @ ( esk1_3 @ X1 @ X4 @ ( lam @ X1 @ X4 @ X10 ) ) ) @ ( setadjoin @ ( esk3_4 @ X1 @ X2 @ X9 @ ( esk1_3 @ X1 @ X4 @ ( lam @ X1 @ X4 @ X10 ) ) ) @ emptyset ) )
| ( in @ ( lam @ X1 @ X4 @ X10 ) @ ( 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_27,c_0_26]),c_0_22]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X9: $i > $i,X4: $i,X2: $i] :
( ( in @ ( lam @ X1 @ X2 @ X9 ) @ ( funcSet @ X4 @ X2 ) )
| ~ ( in @ ( esk1_3 @ X4 @ X2 @ ( lam @ X1 @ X2 @ X9 ) ) @ X1 )
| ~ ( subset @ ( lam @ X1 @ X2 @ X9 ) @ ( cartprod @ X4 @ X2 ) )
| ~ ( in @ ( X9 @ ( esk2_3 @ X1 @ X2 @ X9 ) ) @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_29]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_3 @ X1 @ esk5_0 @ ( lam @ X1 @ esk5_0 @ esk6_0 ) ) @ X1 )
| ( in @ ( lam @ X1 @ esk5_0 @ esk6_0 ) @ ( funcSet @ X1 @ esk5_0 ) )
| ~ ( in @ ( esk2_3 @ X1 @ esk5_0 @ esk6_0 ) @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
thf(c_0_35,negated_conjecture,
~ ( in @ ( lam @ esk4_0 @ esk5_0 @ esk6_0 ) @ ( funcSet @ esk4_0 @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_36,negated_conjecture,
! [X9: $i > $i,X2: $i,X1: $i] :
( ( in @ ( lam @ X1 @ X2 @ X9 ) @ ( funcSet @ X1 @ X2 ) )
| ( in @ ( esk2_3 @ X1 @ X2 @ X9 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i] :
( ( in @ ( lam @ X1 @ esk5_0 @ esk6_0 ) @ ( 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_33,c_0_34]),c_0_24]),c_0_30]) ).
thf(c_0_38,negated_conjecture,
in @ ( esk2_3 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU680^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n015.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 14:12:47 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.35 Running higher-order theorem proving
% 0.28/0.39 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.i1e5W85l10/E---3.1_3585431.p
% 0.49/0.43 % Version: 3.5.1-ho
% 0.49/0.43 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.49/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.43 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.49/0.43 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.49/0.43 % Starting pre_casc_5 with 300s (1) cores
% 0.49/0.43 % Starting additional_ho_6 with 300s (1) cores
% 0.49/0.43 % ho_unfolding_6 with pid 3585444 completed with status 0
% 0.49/0.43 % Result found by ho_unfolding_6
% 0.49/0.43 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.49/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.43 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.49/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.43 % No SInE strategy applied
% 0.49/0.43 % Search class: HGUSF-FFMF32-DHSFMFNN
% 0.49/0.43 % partial match(3): HGUSF-FFMF32-SFFFMFNN
% 0.49/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.43 % Starting ho_unfolding_6 with 151s (1) cores
% 0.49/0.43 % Starting lpo1_def_fix with 136s (1) cores
% 0.49/0.43 % Starting post_as_ho9 with 136s (1) cores
% 0.49/0.43 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.49/0.43 % SubtermCWHack with pid 3585449 completed with status 0
% 0.49/0.43 % Result found by SubtermCWHack
% 0.49/0.43 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.49/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.43 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.49/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.43 % No SInE strategy applied
% 0.49/0.43 % Search class: HGUSF-FFMF32-DHSFMFNN
% 0.49/0.43 % partial match(3): HGUSF-FFMF32-SFFFMFNN
% 0.49/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.43 % Preprocessing time : 0.001 s
% 0.49/0.43
% 0.49/0.43 % Proof found!
% 0.49/0.43 % SZS status Theorem
% 0.49/0.43 % SZS output start CNFRefutation
% See solution above
% 0.49/0.43 % Parsed axioms : 24
% 0.49/0.43 % Removed by relevancy pruning/SinE : 0
% 0.49/0.43 % Initial clauses : 27
% 0.49/0.43 % Removed in clause preprocessing : 16
% 0.49/0.43 % Initial clauses in saturation : 11
% 0.49/0.43 % Processed clauses : 51
% 0.49/0.43 % ...of these trivial : 3
% 0.49/0.43 % ...subsumed : 7
% 0.49/0.43 % ...remaining for further processing : 41
% 0.49/0.43 % Other redundant clauses eliminated : 0
% 0.49/0.43 % Clauses deleted for lack of memory : 0
% 0.49/0.43 % Backward-subsumed : 11
% 0.49/0.43 % Backward-rewritten : 0
% 0.49/0.43 % Generated clauses : 75
% 0.49/0.43 % ...of the previous two non-redundant : 73
% 0.49/0.43 % ...aggressively subsumed : 0
% 0.49/0.43 % Contextual simplify-reflections : 11
% 0.49/0.43 % Paramodulations : 69
% 0.49/0.43 % Factorizations : 0
% 0.49/0.43 % NegExts : 0
% 0.49/0.43 % Equation resolutions : 0
% 0.49/0.43 % Disequality decompositions : 0
% 0.49/0.43 % Total rewrite steps : 6
% 0.49/0.43 % ...of those cached : 2
% 0.49/0.43 % Propositional unsat checks : 0
% 0.49/0.43 % Propositional check models : 0
% 0.49/0.43 % Propositional check unsatisfiable : 0
% 0.49/0.43 % Propositional clauses : 0
% 0.49/0.43 % Propositional clauses after purity: 0
% 0.49/0.43 % Propositional unsat core size : 0
% 0.49/0.43 % Propositional preprocessing time : 0.000
% 0.49/0.43 % Propositional encoding time : 0.000
% 0.49/0.43 % Propositional solver time : 0.000
% 0.49/0.43 % Success case prop preproc time : 0.000
% 0.49/0.43 % Success case prop encoding time : 0.000
% 0.49/0.43 % Success case prop solver time : 0.000
% 0.49/0.43 % Current number of processed clauses : 30
% 0.49/0.43 % Positive orientable unit clauses : 5
% 0.49/0.43 % Positive unorientable unit clauses: 0
% 0.49/0.43 % Negative unit clauses : 1
% 0.49/0.43 % Non-unit-clauses : 24
% 0.49/0.43 % Current number of unprocessed clauses: 30
% 0.49/0.43 % ...number of literals in the above : 144
% 0.49/0.43 % Current number of archived formulas : 0
% 0.49/0.43 % Current number of archived clauses : 11
% 0.49/0.43 % Clause-clause subsumption calls (NU) : 335
% 0.49/0.43 % Rec. Clause-clause subsumption calls : 201
% 0.49/0.43 % Non-unit clause-clause subsumptions : 29
% 0.49/0.43 % Unit Clause-clause subsumption calls : 7
% 0.49/0.43 % Rewrite failures with RHS unbound : 0
% 0.49/0.43 % BW rewrite match attempts : 3
% 0.49/0.43 % BW rewrite match successes : 0
% 0.49/0.43 % Condensation attempts : 0
% 0.49/0.43 % Condensation successes : 0
% 0.49/0.43 % Termbank termtop insertions : 13646
% 0.49/0.43 % Search garbage collected termcells : 590
% 0.49/0.43
% 0.49/0.43 % -------------------------------------------------
% 0.49/0.43 % User time : 0.013 s
% 0.49/0.43 % System time : 0.006 s
% 0.49/0.43 % Total time : 0.019 s
% 0.49/0.43 % Maximum resident set size: 3656 pages
% 0.49/0.43
% 0.49/0.43 % -------------------------------------------------
% 0.49/0.43 % User time : 0.042 s
% 0.49/0.43 % System time : 0.021 s
% 0.49/0.43 % Total time : 0.063 s
% 0.49/0.43 % Maximum resident set size: 4608 pages
% 0.49/0.43 % E exiting
%------------------------------------------------------------------------------