%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU687^2 : 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 : n003.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 0.20s 0.28s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 254 ( 49 equ; 0 cnn)
% Maximal formula atoms : 42 ( 6 avg)
% Number of connectives : 1072 ( 62 ~; 64 |; 35 &; 855 @)
% ( 2 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 10 con; 0-4 aty)
% Number of variables : 180 ( 61 ^; 107 !; 12 ?; 180 :)
% 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,
funcGraphProp1: $o ).
thf(decl_36,type,
funcGraphProp2: $o ).
thf(decl_37,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_38,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_39,type,
esk3_0: $i ).
thf(decl_40,type,
esk4_0: $i ).
thf(decl_41,type,
esk5_0: $i ).
thf(decl_42,type,
esk6_1: $i > $i ).
thf(decl_43,type,
esk7_0: $i ).
thf(decl_44,type,
esk8_1: $i > $i ).
thf(decl_45,type,
esk9_0: $i ).
thf(decl_46,type,
esk10_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.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.0o2je2L90z/E---3.1_2561624.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p',breln) ).
thf(funcextLem,conjecture,
( funcGraphProp1
=> ( funcGraphProp2
=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X9: $i] :
( ( func @ X1 @ X4 @ X9 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= ( ap @ X1 @ X4 @ X9 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X9 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p',funcextLem) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [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/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p',funcGraphProp2) ).
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/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p',funcGraphProp1) ).
thf(c_0_7,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_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 )
=> ? [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_10,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
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_7,c_0_8]) ).
thf(c_0_12,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_9,c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
~ ( funcGraphProp1
=> ( funcGraphProp2
=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X9: $i] :
( ( func @ X1 @ X4 @ X9 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= ( ap @ X1 @ X4 @ X9 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X9 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcextLem]) ).
thf(c_0_14,axiom,
( funcGraphProp2
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X30: $i] :
( ( in @ X30 @ X1 )
=> ? [X31: $i] :
( ( in @ X31
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X30 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X30 @ Z0 ) @ X8 ) )
= ( setadjoin @ X31 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp2,c_0_12]) ).
thf(c_0_15,axiom,
( funcGraphProp1
= ( ! [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 @ ( kpair @ X2 @ ( ap @ X1 @ X4 @ X8 @ X2 ) ) @ X8 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp1,c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( ! [X32: $i,X33: $i,X34: $i] :
( ( ( subset @ X34 @ ( cartprod @ X32 @ X33 ) )
& ! [X35: $i] :
( ( in @ X35 @ X32 )
=> ? [X36: $i] :
( ( in @ X36
@ ( dsetconstr @ X33
@ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X34 ) ) )
& ( ( dsetconstr @ X33
@ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X34 ) )
= ( setadjoin @ X36 @ emptyset ) ) ) ) )
=> ! [X37: $i] :
( ( in @ X37 @ X32 )
=> ( in @ ( kpair @ X37 @ ( ap @ X32 @ X33 @ X34 @ X37 ) ) @ X34 ) ) )
=> ( ! [X38: $i,X39: $i,X40: $i] :
( ( ( subset @ X40 @ ( cartprod @ X38 @ X39 ) )
& ! [X41: $i] :
( ( in @ X41 @ X38 )
=> ? [X42: $i] :
( ( in @ X42
@ ( dsetconstr @ X39
@ ^ [Z0: $i] : ( in @ ( kpair @ X41 @ Z0 ) @ X40 ) ) )
& ( ( dsetconstr @ X39
@ ^ [Z0: $i] : ( in @ ( kpair @ X41 @ Z0 ) @ X40 ) )
= ( setadjoin @ X42 @ emptyset ) ) ) ) )
=> ! [X43: $i] :
( ( in @ X43 @ X38 )
=> ! [X44: $i] :
( ( in @ X44 @ X39 )
=> ( ( in @ ( kpair @ X43 @ X44 ) @ X40 )
=> ( ( ap @ X38 @ X39 @ X40 @ X43 )
= X44 ) ) ) ) )
=> ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X45: $i] :
( ( in @ X45 @ X1 )
=> ? [X46: $i] :
( ( in @ X46
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X45 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X45 @ Z0 ) @ X8 ) )
= ( setadjoin @ X46 @ emptyset ) ) ) ) )
=> ! [X9: $i] :
( ( ( subset @ X9 @ ( cartprod @ X1 @ X4 ) )
& ! [X47: $i] :
( ( in @ X47 @ X1 )
=> ? [X48: $i] :
( ( in @ X48
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X47 @ Z0 ) @ X9 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X47 @ Z0 ) @ X9 ) )
= ( setadjoin @ X48 @ emptyset ) ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= ( ap @ X1 @ X4 @ X9 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X9 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_12]) ).
thf(c_0_17,negated_conjecture,
! [X49: $i,X50: $i,X51: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X59: $i,X60: $i,X61: $i,X65: $i,X68: $i,X70: $i] :
( ( ( in @ ( esk1_3 @ X49 @ X50 @ X51 ) @ X49 )
| ~ ( subset @ X51 @ ( cartprod @ X49 @ X50 ) )
| ~ ( in @ X54 @ X49 )
| ( in @ ( kpair @ X54 @ ( ap @ X49 @ X50 @ X51 @ X54 ) ) @ X51 ) )
& ( ~ ( in @ X53
@ ( dsetconstr @ X50
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X49 @ X50 @ X51 ) @ Z0 ) @ X51 ) ) )
| ( ( dsetconstr @ X50
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X49 @ X50 @ X51 ) @ Z0 ) @ X51 ) )
!= ( setadjoin @ X53 @ emptyset ) )
| ~ ( subset @ X51 @ ( cartprod @ X49 @ X50 ) )
| ~ ( in @ X54 @ X49 )
| ( in @ ( kpair @ X54 @ ( ap @ X49 @ X50 @ X51 @ X54 ) ) @ X51 ) )
& ( ( in @ ( esk2_3 @ X55 @ X56 @ X57 ) @ X55 )
| ~ ( subset @ X57 @ ( cartprod @ X55 @ X56 ) )
| ~ ( in @ X60 @ X55 )
| ~ ( in @ X61 @ X56 )
| ~ ( in @ ( kpair @ X60 @ X61 ) @ X57 )
| ( ( ap @ X55 @ X56 @ X57 @ X60 )
= X61 ) )
& ( ~ ( in @ X59
@ ( dsetconstr @ X56
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X55 @ X56 @ X57 ) @ Z0 ) @ X57 ) ) )
| ( ( dsetconstr @ X56
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X55 @ X56 @ X57 ) @ Z0 ) @ X57 ) )
!= ( setadjoin @ X59 @ emptyset ) )
| ~ ( subset @ X57 @ ( cartprod @ X55 @ X56 ) )
| ~ ( in @ X60 @ X55 )
| ~ ( in @ X61 @ X56 )
| ~ ( in @ ( kpair @ X60 @ X61 ) @ X57 )
| ( ( ap @ X55 @ X56 @ X57 @ X60 )
= X61 ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( in @ ( esk6_1 @ X65 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X65 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X65 @ esk3_0 ) )
& ( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X65 @ Z0 ) @ esk5_0 ) )
= ( setadjoin @ ( esk6_1 @ X65 ) @ emptyset ) )
| ~ ( in @ X65 @ esk3_0 ) )
& ( subset @ esk7_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( in @ ( esk8_1 @ X68 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X68 @ Z0 ) @ esk7_0 ) ) )
| ~ ( in @ X68 @ esk3_0 ) )
& ( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X68 @ Z0 ) @ esk7_0 ) )
= ( setadjoin @ ( esk8_1 @ X68 ) @ emptyset ) )
| ~ ( in @ X68 @ esk3_0 ) )
& ( ~ ( in @ X70 @ esk3_0 )
| ( ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X70 )
= ( ap @ esk3_0 @ esk4_0 @ esk7_0 @ X70 ) ) )
& ( in @ esk9_0 @ esk3_0 )
& ( in @ esk10_0 @ esk4_0 )
& ( in @ ( kpair @ esk9_0 @ esk10_0 ) @ esk7_0 )
& ~ ( in @ ( kpair @ esk9_0 @ esk10_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_16])])])])])]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X7: $i,X6: $i,X5: $i] :
( ( ( ap @ X4 @ X2 @ X5 @ X6 )
= X7 )
| ~ ( 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 )
| ~ ( in @ X7 @ X2 )
| ~ ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk8_1 @ X1 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk7_0 ) ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk7_0 ) )
= ( setadjoin @ ( esk8_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i,X6: $i,X5: $i,X4: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( ( ap @ X1 @ X2 @ X4 @ X5 )
= X6 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
subset @ esk7_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X4: $i,X2: $i,X1: $i] :
( ( ( ap @ X1 @ esk4_0 @ esk7_0 @ X2 )
= X4 )
| ~ ( in @ ( esk2_3 @ X1 @ esk4_0 @ esk7_0 ) @ esk3_0 )
| ~ ( subset @ esk7_0 @ ( cartprod @ X1 @ esk4_0 ) )
| ~ ( in @ ( kpair @ X2 @ X4 ) @ esk7_0 )
| ~ ( in @ X4 @ esk4_0 )
| ~ ( in @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk3_0 @ esk4_0 @ esk7_0 @ X1 )
= X2 )
| ( in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk7_0 ) @ esk3_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk7_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,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 @ ( 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_17]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_1 @ X1 )
@ ( dsetconstr @ esk4_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk5_0 ) ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,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_17]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk1_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_17]) ).
thf(c_0_29,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk3_0 @ esk4_0 @ esk7_0 @ X1 )
= X2 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk7_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
thf(c_0_31,negated_conjecture,
in @ ( kpair @ esk9_0 @ esk10_0 ) @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_32,negated_conjecture,
in @ esk10_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_33,negated_conjecture,
in @ esk9_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ X2 @ esk4_0 @ esk5_0 @ X1 ) ) @ esk5_0 )
| ~ ( in @ ( esk1_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_25,c_0_26]),c_0_27]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) ) @ esk5_0 )
| ( in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 )
= ( ap @ esk3_0 @ esk4_0 @ esk7_0 @ X1 ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_37,negated_conjecture,
( ( ap @ esk3_0 @ esk4_0 @ esk7_0 @ esk9_0 )
= esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) ) @ esk5_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_35]) ).
thf(c_0_39,negated_conjecture,
( ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk9_0 )
= esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]) ).
thf(c_0_40,negated_conjecture,
~ ( in @ ( kpair @ esk9_0 @ esk10_0 ) @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU687^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:10:43 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.0o2je2L90z/E---3.1_2561624.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.28 % Preprocessing class: HSMSSLSSSLMNHFN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.28 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.28 % Starting pre_casc_5 with 300s (1) cores
% 0.20/0.28 % Starting ehoh_best_sine with 300s (1) cores
% 0.20/0.28 % ehoh_best_sine_rwall with pid 2561638 completed with status 0
% 0.20/0.28 % Result found by ehoh_best_sine_rwall
% 0.20/0.28 % partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.28 % Preprocessing class: HSMSSLSSSLMNHFN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.28 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.28 % Search class: HGUSF-FFMS32-MHFFMFNN
% 0.20/0.28 % partial match(2): HGUSF-FFSF32-MHFFMFNN
% 0.20/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.28 % SubtermCWHack with pid 2561641 completed with status 0
% 0.20/0.28 % Result found by SubtermCWHack
% 0.20/0.28 % partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.28 % Preprocessing class: HSMSSLSSSLMNHFN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.28 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.20/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.28 % Search class: HGUSF-FFMS32-MHFFMFNN
% 0.20/0.28 % partial match(2): HGUSF-FFSF32-MHFFMFNN
% 0.20/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.20/0.28 % Preprocessing time : 0.001 s
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% See solution above
% 0.20/0.28 % Parsed axioms : 21
% 0.20/0.28 % Removed by relevancy pruning/SinE : 14
% 0.20/0.28 % Initial clauses : 15
% 0.20/0.28 % Removed in clause preprocessing : 0
% 0.20/0.28 % Initial clauses in saturation : 15
% 0.20/0.28 % Processed clauses : 32
% 0.20/0.28 % ...of these trivial : 0
% 0.20/0.28 % ...subsumed : 2
% 0.20/0.28 % ...remaining for further processing : 30
% 0.20/0.28 % Other redundant clauses eliminated : 0
% 0.20/0.28 % Clauses deleted for lack of memory : 0
% 0.20/0.28 % Backward-subsumed : 4
% 0.20/0.28 % Backward-rewritten : 1
% 0.20/0.28 % Generated clauses : 22
% 0.20/0.28 % ...of the previous two non-redundant : 19
% 0.20/0.28 % ...aggressively subsumed : 0
% 0.20/0.28 % Contextual simplify-reflections : 6
% 0.20/0.28 % Paramodulations : 22
% 0.20/0.28 % Factorizations : 0
% 0.20/0.28 % NegExts : 0
% 0.20/0.28 % Equation resolutions : 0
% 0.20/0.28 % Disequality decompositions : 0
% 0.20/0.28 % Total rewrite steps : 11
% 0.20/0.28 % ...of those cached : 7
% 0.20/0.28 % Propositional unsat checks : 0
% 0.20/0.28 % Propositional check models : 0
% 0.20/0.28 % Propositional check unsatisfiable : 0
% 0.20/0.28 % Propositional clauses : 0
% 0.20/0.28 % Propositional clauses after purity: 0
% 0.20/0.28 % Propositional unsat core size : 0
% 0.20/0.28 % Propositional preprocessing time : 0.000
% 0.20/0.28 % Propositional encoding time : 0.000
% 0.20/0.28 % Propositional solver time : 0.000
% 0.20/0.28 % Success case prop preproc time : 0.000
% 0.20/0.28 % Success case prop encoding time : 0.000
% 0.20/0.28 % Success case prop solver time : 0.000
% 0.20/0.28 % Current number of processed clauses : 25
% 0.20/0.28 % Positive orientable unit clauses : 7
% 0.20/0.28 % Positive unorientable unit clauses: 0
% 0.20/0.28 % Negative unit clauses : 1
% 0.20/0.28 % Non-unit-clauses : 17
% 0.20/0.28 % Current number of unprocessed clauses: 2
% 0.20/0.28 % ...number of literals in the above : 10
% 0.20/0.28 % Current number of archived formulas : 0
% 0.20/0.28 % Current number of archived clauses : 5
% 0.20/0.28 % Clause-clause subsumption calls (NU) : 50
% 0.20/0.28 % Rec. Clause-clause subsumption calls : 20
% 0.20/0.28 % Non-unit clause-clause subsumptions : 12
% 0.20/0.28 % Unit Clause-clause subsumption calls : 4
% 0.20/0.28 % Rewrite failures with RHS unbound : 0
% 0.20/0.28 % BW rewrite match attempts : 6
% 0.20/0.28 % BW rewrite match successes : 1
% 0.20/0.28 % Condensation attempts : 0
% 0.20/0.28 % Condensation successes : 0
% 0.20/0.28 % Termbank termtop insertions : 3803
% 0.20/0.28 % Search garbage collected termcells : 910
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.005 s
% 0.20/0.28 % System time : 0.001 s
% 0.20/0.28 % Total time : 0.006 s
% 0.20/0.28 % Maximum resident set size: 3904 pages
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.008 s
% 0.20/0.28 % System time : 0.005 s
% 0.20/0.28 % Total time : 0.013 s
% 0.20/0.28 % Maximum resident set size: 4608 pages
% 0.20/0.28 % E exiting
%------------------------------------------------------------------------------