%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU686^2 : 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 : n002.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 0.21s 0.28s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 50 equ; 0 cnn)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 1079 ( 72 ~; 75 |; 32 &; 835 @)
% ( 4 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 10 con; 0-4 aty)
% Number of variables : 192 ( 59 ^; 120 !; 13 ?; 192 :)
% 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,
func: $i > $i > $i > $o ).
thf(decl_34,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_35,type,
app: $o ).
thf(decl_36,type,
ex1E2: $o ).
thf(decl_37,type,
funcGraphProp1: $o ).
thf(decl_38,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_39,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_40,type,
esk3_0: $i ).
thf(decl_41,type,
esk4_0: $i ).
thf(decl_42,type,
esk5_0: $i ).
thf(decl_43,type,
esk6_1: $i > $i ).
thf(decl_44,type,
esk7_0: $i ).
thf(decl_45,type,
esk8_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.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.aqNkJekw5P/E---3.1_1345711.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',breln) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X1: $i,X3: $i > $o] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X7 )
=> ( X2 = X7 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',ex1E2) ).
thf(funcGraphProp2,conjecture,
( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',funcGraphProp2) ).
thf(app,axiom,
( app
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',app) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( kpair @ X2 @ ( ap @ X1 @ X4 @ X8 @ X2 ) ) @ X8 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqNkJekw5P/E---3.1_1345711.p',funcGraphProp1) ).
thf(c_0_8,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X26 @ 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 )
=> ? [X27: $i] :
( ( in @ X27
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X27 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_11,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
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,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X27: $i] :
( ( in @ X27
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X27 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_14,plain,
( ex1E2
<=> ! [X1: $i,X3: $i > $o] :
( ( ex1 @ X1
@ ^ [Z0: $i] : ( X3 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X7 )
=> ( X2 = X7 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_15,negated_conjecture,
~ ( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcGraphProp2]) ).
thf(c_0_16,axiom,
( app
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X28: $i] :
( ( in @ X28 @ X1 )
=> ? [X29: $i] :
( ( in @ X29
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X28 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X28 @ Z0 ) @ X8 ) )
= ( setadjoin @ X29 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_13]) ).
thf(c_0_17,plain,
( ex1E2
= ( ! [X1: $i,X3: $i > $o] :
( ? [X30: $i] :
( ( in @ X30
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X3 @ Z0 ) ) )
& ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X3 @ Z0 ) )
= ( setadjoin @ X30 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( X3 @ X2 )
=> ( ( X3 @ X7 )
=> ( X2 = X7 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_11]) ).
thf(c_0_18,axiom,
( funcGraphProp1
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X31: $i] :
( ( in @ X31 @ X1 )
=> ? [X32: $i] :
( ( in @ X32
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X31 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X31 @ Z0 ) @ X8 ) )
= ( setadjoin @ X32 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( kpair @ X2 @ ( ap @ X1 @ X4 @ X8 @ X2 ) ) @ X8 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp1,c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ( ! [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 )
=> ( in @ ( ap @ X33 @ X34 @ X35 @ X38 ) @ X34 ) ) )
=> ( ! [X39: $i,X40: $i > $o] :
( ? [X41: $i] :
( ( in @ X41 @ ( dsetconstr @ X39 @ X40 ) )
& ( ( dsetconstr @ X39 @ X40 )
= ( setadjoin @ X41 @ emptyset ) ) )
=> ! [X42: $i] :
( ( in @ X42 @ X39 )
=> ! [X43: $i] :
( ( in @ X43 @ X39 )
=> ( ( X40 @ X42 )
=> ( ( X40 @ X43 )
=> ( X42 = X43 ) ) ) ) ) )
=> ( ! [X44: $i,X45: $i,X46: $i] :
( ( ( subset @ X46 @ ( cartprod @ X44 @ X45 ) )
& ! [X47: $i] :
( ( in @ X47 @ X44 )
=> ? [X48: $i] :
( ( in @ X48
@ ( dsetconstr @ X45
@ ^ [Z0: $i] : ( in @ ( kpair @ X47 @ Z0 ) @ X46 ) ) )
& ( ( dsetconstr @ X45
@ ^ [Z0: $i] : ( in @ ( kpair @ X47 @ Z0 ) @ X46 ) )
= ( setadjoin @ X48 @ emptyset ) ) ) ) )
=> ! [X49: $i] :
( ( in @ X49 @ X44 )
=> ( in @ ( kpair @ X49 @ ( ap @ X44 @ X45 @ X46 @ X49 ) ) @ X46 ) ) )
=> ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X50: $i] :
( ( in @ X50 @ X1 )
=> ? [X51: $i] :
( ( in @ X51
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X50 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X50 @ Z0 ) @ X8 ) )
= ( setadjoin @ X51 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ) ) ),
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)],[c_0_15,c_0_13]),c_0_16]),c_0_17]),c_0_18])]) ).
thf(c_0_20,negated_conjecture,
! [X52: $i,X53: $i,X54: $i,X56: $i,X57: $i,X58: $i,X59: $i > $o,X60: $i,X61: $i,X62: $i,X63: $i,X64: $i,X65: $i,X67: $i,X68: $i,X72: $i] :
( ( ( in @ ( esk1_3 @ X52 @ X53 @ X54 ) @ X52 )
| ~ ( subset @ X54 @ ( cartprod @ X52 @ X53 ) )
| ~ ( in @ X57 @ X52 )
| ( in @ ( ap @ X52 @ X53 @ X54 @ X57 ) @ X53 ) )
& ( ~ ( in @ X56
@ ( dsetconstr @ X53
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X52 @ X53 @ X54 ) @ Z0 ) @ X54 ) ) )
| ( ( dsetconstr @ X53
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X52 @ X53 @ X54 ) @ Z0 ) @ X54 ) )
!= ( setadjoin @ X56 @ emptyset ) )
| ~ ( subset @ X54 @ ( cartprod @ X52 @ X53 ) )
| ~ ( in @ X57 @ X52 )
| ( in @ ( ap @ X52 @ X53 @ X54 @ X57 ) @ X53 ) )
& ( ~ ( in @ X60 @ ( dsetconstr @ X58 @ X59 ) )
| ( ( dsetconstr @ X58 @ X59 )
!= ( setadjoin @ X60 @ emptyset ) )
| ~ ( in @ X61 @ X58 )
| ~ ( in @ X62 @ X58 )
| ~ ( X59 @ X61 )
| ~ ( X59 @ X62 )
| ( X61 = X62 ) )
& ( ( in @ ( esk2_3 @ X63 @ X64 @ X65 ) @ X63 )
| ~ ( subset @ X65 @ ( cartprod @ X63 @ X64 ) )
| ~ ( in @ X68 @ X63 )
| ( in @ ( kpair @ X68 @ ( ap @ X63 @ X64 @ X65 @ X68 ) ) @ X65 ) )
& ( ~ ( in @ X67
@ ( dsetconstr @ X64
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X63 @ X64 @ X65 ) @ Z0 ) @ X65 ) ) )
| ( ( dsetconstr @ X64
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X63 @ X64 @ X65 ) @ Z0 ) @ X65 ) )
!= ( setadjoin @ X67 @ emptyset ) )
| ~ ( subset @ X65 @ ( cartprod @ X63 @ X64 ) )
| ~ ( in @ X68 @ X63 )
| ( in @ ( kpair @ X68 @ ( ap @ X63 @ X64 @ X65 @ X68 ) ) @ X65 ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( in @ ( esk6_1 @ X72 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X72 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X72 @ esk3_0 ) )
& ( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X72 @ Z0 ) @ esk5_0 ) )
= ( setadjoin @ ( esk6_1 @ X72 ) @ emptyset ) )
| ~ ( in @ X72 @ esk3_0 ) )
& ( in @ esk7_0 @ esk3_0 )
& ( in @ esk8_0 @ esk4_0 )
& ( in @ ( kpair @ esk7_0 @ esk8_0 ) @ esk5_0 )
& ( ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk7_0 )
!= esk8_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,X2: $i,X3: $i > $o,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
| ( ( dsetconstr @ X2 @ X3 )
!= ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X5 @ X2 )
| ~ ( X3 @ X4 )
| ~ ( X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_22,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_20]) ).
thf(c_0_23,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_20]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( in @ ( kpair @ X5 @ ( ap @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_25,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X6: $i,X4: $i] :
( ( in @ ( ap @ X4 @ X2 @ X5 @ X6 ) @ 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 ) )
| ~ ( in @ X6 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X2: $i,X4: $i] :
( ( X1 = X2 )
| ~ ( in @ ( kpair @ X4 @ X2 ) @ esk5_0 )
| ~ ( in @ ( kpair @ X4 @ X1 ) @ esk5_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ X1 @ esk4_0 )
| ~ ( in @ X4 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) ) @ esk5_0 )
| ( in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( ap @ X1 @ esk4_0 @ esk5_0 @ X2 ) @ esk4_0 )
| ~ ( in @ ( esk1_3 @ X1 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ esk4_0 ) )
| ~ ( in @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i] :
( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
| ( in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
thf(c_0_32,negated_conjecture,
in @ ( kpair @ esk7_0 @ esk8_0 ) @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_33,negated_conjecture,
in @ esk8_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_34,negated_conjecture,
in @ esk7_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X6: $i,X4: $i] :
( ( in @ ( kpair @ X6 @ ( ap @ X4 @ X2 @ X5 @ X6 ) ) @ X5 )
| ~ ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ~ ( subset @ X5 @ ( cartprod @ X4 @ X2 ) )
| ~ ( in @ X6 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1
= ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X2 ) )
| ( in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X2 ) @ esk4_0 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ esk5_0 )
| ~ ( in @ X1 @ esk4_0 )
| ~ ( in @ X2 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i] :
( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_31]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( X1 = esk8_0 )
| ~ ( in @ ( kpair @ esk7_0 @ X1 ) @ esk5_0 )
| ~ ( in @ X1 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_33]),c_0_34])]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ X2 @ esk4_0 @ esk5_0 @ X1 ) ) @ esk5_0 )
| ~ ( in @ ( esk2_3 @ X2 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X2 @ esk4_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_23]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1
= ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X2 ) )
| ( in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ esk5_0 )
| ~ ( in @ X1 @ esk4_0 )
| ~ ( in @ X2 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_41,negated_conjecture,
( ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk7_0 )
!= esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk4_0 @ esk5_0 @ esk7_0 )
= esk8_0 )
| ~ ( in @ ( ap @ X1 @ esk4_0 @ esk5_0 @ esk7_0 ) @ esk4_0 )
| ~ ( in @ ( esk2_3 @ X1 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ esk4_0 ) )
| ~ ( in @ esk7_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_43,negated_conjecture,
in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_33]),c_0_34])]),c_0_41]) ).
thf(c_0_44,negated_conjecture,
~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk7_0 ) @ esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_25]),c_0_43]),c_0_34])]),c_0_41]) ).
thf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU686^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:11:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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.aqNkJekw5P/E---3.1_1345711.p
% 0.21/0.28 % Version: 3.5.1-ho
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.21/0.28 % Starting pre_casc_5 with 300s (1) cores
% 0.21/0.28 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.28 % Starting sh11_fix with 300s (1) cores
% 0.21/0.28 % ho_unfolding_6 with pid 1345738 completed with status 0
% 0.21/0.28 % Result found by ho_unfolding_6
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.28 % No SInE strategy applied
% 0.21/0.28 % Search class: HGUSF-FFMS32-MHFFMFBN
% 0.21/0.28 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.21/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.28 % Starting ho_unfolding_6 with 151s (1) cores
% 0.21/0.28 % Starting sh5l with 136s (1) cores
% 0.21/0.28 % Starting new_bool_1 with 136s (1) cores
% 0.21/0.28 % Starting new_bool_2 with 136s (1) cores
% 0.21/0.28 % SubtermCWHack with pid 1345742 completed with status 0
% 0.21/0.28 % Result found by SubtermCWHack
% 0.21/0.28 % Preprocessing class: HSSSSLSSSLMNHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.28 % No SInE strategy applied
% 0.21/0.28 % Search class: HGUSF-FFMS32-MHFFMFBN
% 0.21/0.28 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.21/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.28 % Preprocessing time : 0.001 s
% 0.21/0.28
% 0.21/0.28 % Proof found!
% 0.21/0.28 % SZS status Theorem
% 0.21/0.28 % SZS output start CNFRefutation
% See solution above
% 0.21/0.28 % Parsed axioms : 23
% 0.21/0.28 % Removed by relevancy pruning/SinE : 0
% 0.21/0.28 % Initial clauses : 27
% 0.21/0.28 % Removed in clause preprocessing : 15
% 0.21/0.28 % Initial clauses in saturation : 12
% 0.21/0.28 % Processed clauses : 28
% 0.21/0.28 % ...of these trivial : 0
% 0.21/0.28 % ...subsumed : 1
% 0.21/0.28 % ...remaining for further processing : 27
% 0.21/0.28 % Other redundant clauses eliminated : 0
% 0.21/0.28 % Clauses deleted for lack of memory : 0
% 0.21/0.28 % Backward-subsumed : 3
% 0.21/0.28 % Backward-rewritten : 2
% 0.21/0.28 % Generated clauses : 20
% 0.21/0.28 % ...of the previous two non-redundant : 18
% 0.21/0.28 % ...aggressively subsumed : 0
% 0.21/0.28 % Contextual simplify-reflections : 5
% 0.21/0.28 % Paramodulations : 19
% 0.21/0.28 % Factorizations : 0
% 0.21/0.28 % NegExts : 0
% 0.21/0.28 % Equation resolutions : 0
% 0.21/0.28 % Disequality decompositions : 0
% 0.21/0.28 % Total rewrite steps : 10
% 0.21/0.28 % ...of those cached : 7
% 0.21/0.28 % Propositional unsat checks : 0
% 0.21/0.28 % Propositional check models : 0
% 0.21/0.28 % Propositional check unsatisfiable : 0
% 0.21/0.28 % Propositional clauses : 0
% 0.21/0.28 % Propositional clauses after purity: 0
% 0.21/0.28 % Propositional unsat core size : 0
% 0.21/0.28 % Propositional preprocessing time : 0.000
% 0.21/0.28 % Propositional encoding time : 0.000
% 0.21/0.28 % Propositional solver time : 0.000
% 0.21/0.28 % Success case prop preproc time : 0.000
% 0.21/0.28 % Success case prop encoding time : 0.000
% 0.21/0.28 % Success case prop solver time : 0.000
% 0.21/0.28 % Current number of processed clauses : 21
% 0.21/0.28 % Positive orientable unit clauses : 5
% 0.21/0.28 % Positive unorientable unit clauses: 0
% 0.21/0.28 % Negative unit clauses : 2
% 0.21/0.28 % Non-unit-clauses : 14
% 0.21/0.28 % Current number of unprocessed clauses: 1
% 0.21/0.28 % ...number of literals in the above : 8
% 0.21/0.28 % Current number of archived formulas : 0
% 0.21/0.28 % Current number of archived clauses : 6
% 0.21/0.28 % Clause-clause subsumption calls (NU) : 58
% 0.21/0.28 % Rec. Clause-clause subsumption calls : 16
% 0.21/0.28 % Non-unit clause-clause subsumptions : 8
% 0.21/0.28 % Unit Clause-clause subsumption calls : 9
% 0.21/0.28 % Rewrite failures with RHS unbound : 0
% 0.21/0.28 % BW rewrite match attempts : 1
% 0.21/0.28 % BW rewrite match successes : 1
% 0.21/0.28 % Condensation attempts : 0
% 0.21/0.28 % Condensation successes : 0
% 0.21/0.28 % Termbank termtop insertions : 3740
% 0.21/0.28 % Search garbage collected termcells : 926
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.008 s
% 0.21/0.28 % System time : 0.001 s
% 0.21/0.28 % Total time : 0.009 s
% 0.21/0.28 % Maximum resident set size: 3652 pages
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.017 s
% 0.21/0.28 % System time : 0.011 s
% 0.21/0.28 % Total time : 0.028 s
% 0.21/0.28 % Maximum resident set size: 4864 pages
% 0.21/0.28 % E exiting
%------------------------------------------------------------------------------