%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU676^2 : 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 08:24:59 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 32 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 723 ( 37 ~; 36 |; 24 &; 596 @)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 8 con; 0-4 aty)
% Number of variables : 168 ( 68 ^; 90 !; 10 ?; 168 :)
% 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_27,type,
setunion: $i > $i ).
thf(decl_28,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_29,type,
subset: $i > $i > $o ).
thf(decl_30,type,
kpair: $i > $i > $i ).
thf(decl_31,type,
cartprod: $i > $i > $i ).
thf(decl_32,type,
singleton: $i > $o ).
thf(decl_33,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_34,type,
breln: $i > $i > $i > $o ).
thf(decl_35,type,
func: $i > $i > $i > $o ).
thf(decl_36,type,
funcSet: $i > $i > $i ).
thf(decl_37,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_38,type,
app: $o ).
thf(decl_39,type,
infuncsetfunc: $o ).
thf(decl_40,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_41,type,
esk2_4: $i > $i > $i > $i > $i ).
thf(decl_42,type,
esk3_0: $i ).
thf(decl_43,type,
esk4_0: $i ).
thf(decl_44,type,
esk5_0: $i ).
thf(decl_45,type,
esk6_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.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.6cLPkcuHic/E---3.1_3581906.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.p',breln) ).
thf(ap2p,conjecture,
( app
=> ( infuncsetfunc
=> ! [X1: $i,X4: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.p',ap2p) ).
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.6cLPkcuHic/E---3.1_3581906.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
=> ( func @ X1 @ X4 @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.p',infuncsetfunc) ).
thf(ap,axiom,
( ap
= ( ^ [X1: $i,X4: $i,X8: $i,X2: $i] :
( setunion
@ ( dsetconstr @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6cLPkcuHic/E---3.1_3581906.p',ap) ).
thf(c_0_8,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X20: $i] :
( ( in @ X20
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X20 @ 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 )
=> ? [X21: $i] :
( ( in @ X21
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X21 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_11,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X20: $i] :
( ( in @ X20
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X20 @ 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 )
=> ? [X21: $i] :
( ( in @ X21
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X21 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_14,negated_conjecture,
~ ( app
=> ( infuncsetfunc
=> ! [X1: $i,X4: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[ap2p]) ).
thf(c_0_15,axiom,
( app
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X22: $i] :
( ( in @ X22 @ X1 )
=> ? [X23: $i] :
( ( in @ X23
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X22 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X22 @ Z0 ) @ X8 ) )
= ( setadjoin @ X23 @ 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_16,axiom,
( infuncsetfunc
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
=> ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X24: $i] :
( ( in @ X24 @ X1 )
=> ? [X25: $i] :
( ( in @ X25
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X24 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X24 @ Z0 ) @ X8 ) )
= ( setadjoin @ X25 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_13]) ).
thf(c_0_17,plain,
( ap
= ( ^ [Z0: $i,Z1: $i,Z2: $i,Z3: $i] :
( setunion
@ ( dsetconstr @ Z1
@ ^ [Z4: $i] : ( in @ ( kpair @ Z3 @ Z4 ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ap]) ).
thf(c_0_18,negated_conjecture,
~ ( ! [X28: $i,X29: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X28 @ X29 ) )
& ! [X31: $i] :
( ( in @ X31 @ X28 )
=> ? [X32: $i] :
( ( in @ X32
@ ( dsetconstr @ X29
@ ^ [Z0: $i] : ( in @ ( kpair @ X31 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X29
@ ^ [Z0: $i] : ( in @ ( kpair @ X31 @ Z0 ) @ X30 ) )
= ( setadjoin @ X32 @ emptyset ) ) ) ) )
=> ! [X33: $i] :
( ( in @ X33 @ X28 )
=> ( in @ ( ap @ X28 @ X29 @ X30 @ X33 ) @ X29 ) ) )
=> ( ! [X34: $i,X35: $i,X36: $i] :
( ( in @ X36 @ ( funcSet @ X34 @ X35 ) )
=> ( ( subset @ X36 @ ( cartprod @ X34 @ X35 ) )
& ! [X37: $i] :
( ( in @ X37 @ X34 )
=> ? [X38: $i] :
( ( in @ X38
@ ( dsetconstr @ X35
@ ^ [Z0: $i] : ( in @ ( kpair @ X37 @ Z0 ) @ X36 ) ) )
& ( ( dsetconstr @ X35
@ ^ [Z0: $i] : ( in @ ( kpair @ X37 @ Z0 ) @ X36 ) )
= ( setadjoin @ X38 @ emptyset ) ) ) ) ) )
=> ! [X1: $i,X4: $i,X8: $i] :
( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
( ap
= ( ^ [Z0: $i,Z1: $i,Z2: $i,Z3: $i] :
( setunion
@ ( dsetconstr @ Z1
@ ^ [Z4: $i] : ( in @ ( kpair @ Z3 @ Z4 ) @ Z2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X39: $i,X40: $i,X41: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i] :
( ( ( in @ ( esk1_3 @ X39 @ X40 @ X41 ) @ X39 )
| ~ ( subset @ X41 @ ( cartprod @ X39 @ X40 ) )
| ~ ( in @ X44 @ X39 )
| ( in @ ( ap @ X39 @ X40 @ X41 @ X44 ) @ X40 ) )
& ( ~ ( in @ X43
@ ( dsetconstr @ X40
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X39 @ X40 @ X41 ) @ Z0 ) @ X41 ) ) )
| ( ( dsetconstr @ X40
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X39 @ X40 @ X41 ) @ Z0 ) @ X41 ) )
!= ( setadjoin @ X43 @ emptyset ) )
| ~ ( subset @ X41 @ ( cartprod @ X39 @ X40 ) )
| ~ ( in @ X44 @ X39 )
| ( in @ ( ap @ X39 @ X40 @ X41 @ X44 ) @ X40 ) )
& ( ( subset @ X47 @ ( cartprod @ X45 @ X46 ) )
| ~ ( in @ X47 @ ( funcSet @ X45 @ X46 ) ) )
& ( ( in @ ( esk2_4 @ X45 @ X46 @ X47 @ X48 )
@ ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X48 @ Z0 ) @ X47 ) ) )
| ~ ( in @ X48 @ X45 )
| ~ ( in @ X47 @ ( funcSet @ X45 @ X46 ) ) )
& ( ( ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X48 @ Z0 ) @ X47 ) )
= ( setadjoin @ ( esk2_4 @ X45 @ X46 @ X47 @ X48 ) @ emptyset ) )
| ~ ( in @ X48 @ X45 )
| ~ ( in @ X47 @ ( funcSet @ X45 @ X46 ) ) )
& ( in @ esk5_0 @ ( funcSet @ esk3_0 @ esk4_0 ) )
& ( in @ esk6_0 @ esk3_0 )
& ~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_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_18])])])])])]) ).
thf(c_0_21,plain,
! [X1: $i] :
( ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( setunion
@ ( dsetconstr @ Z0
@ ^ [Z3: $i] : ( in @ ( kpair @ Z2 @ Z3 ) @ Z1 ) ) ) )
= ( ap @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_19]) ).
thf(c_0_22,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_23,negated_conjecture,
! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X1 @ ( cartprod @ X2 @ X4 ) )
| ~ ( in @ X1 @ ( funcSet @ X2 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
! [X1: $i,X2: $i] :
( ( ap @ X1 )
= ( ap @ X2 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
in @ esk5_0 @ ( funcSet @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,negated_conjecture,
~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i] :
( ( ap @ X1 @ X2 @ X4 @ X5 )
= ( ap @ X6 @ X2 @ X4 @ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_24]) ).
thf(c_0_29,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_30,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ X4 @ X5 )
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ X5 @ Z0 ) @ X4 ) ) )
| ~ ( in @ X5 @ X1 )
| ~ ( in @ X4 @ ( funcSet @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( ( dsetconstr @ X1
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X4 ) )
= ( setadjoin @ ( esk2_4 @ X5 @ X1 @ X4 @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ X5 )
| ~ ( in @ X4 @ ( funcSet @ X5 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_32,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_25,c_0_26]) ).
thf(c_0_33,negated_conjecture,
in @ esk6_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i] :
~ ( in @ ( ap @ X1 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_35,negated_conjecture,
! [X4: $i,X6: $i,X5: $i,X2: $i,X1: $i] :
( ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X6 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X4 @ ( funcSet @ X6 @ X2 ) )
| ~ ( in @ X5 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_36,negated_conjecture,
in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i] :
( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26])]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_26])]) ).
thf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU676^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:10:47 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.6cLPkcuHic/E---3.1_3581906.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % partial match(1): HSSSSLSSSLMNHFN
% 0.22/0.27 % Preprocessing class: HSSSSLSSMLMNHFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.27 % Starting pre_casc_5 with 300s (1) cores
% 0.22/0.27 % Starting ehoh_best_sine with 300s (1) cores
% 0.22/0.27 % ho_unfolding_6 with pid 3581919 completed with status 0
% 0.22/0.27 % Result found by ho_unfolding_6
% 0.22/0.27 % partial match(1): HSSSSLSSSLMNHFN
% 0.22/0.27 % Preprocessing class: HSSSSLSSMLMNHFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUSF-FFSS32-DHFSMFNN
% 0.22/0.27 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.22/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 151s (1) cores
% 0.22/0.27 % Starting sh5l with 136s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 136s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 3581923 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % partial match(1): HSSSSLSSSLMNHFN
% 0.22/0.27 % Preprocessing class: HSSSSLSSMLMNHFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUSF-FFSS32-DHFSMFNN
% 0.22/0.27 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.22/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 26
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 27
% 0.22/0.27 % Removed in clause preprocessing : 17
% 0.22/0.27 % Initial clauses in saturation : 10
% 0.22/0.27 % Processed clauses : 68
% 0.22/0.27 % ...of these trivial : 1
% 0.22/0.27 % ...subsumed : 39
% 0.22/0.27 % ...remaining for further processing : 28
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 2
% 0.22/0.27 % Backward-rewritten : 1
% 0.22/0.27 % Generated clauses : 62
% 0.22/0.27 % ...of the previous two non-redundant : 59
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 1
% 0.22/0.27 % Paramodulations : 43
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 5
% 0.22/0.27 % ...of those cached : 1
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 25
% 0.22/0.27 % Positive orientable unit clauses : 7
% 0.22/0.27 % Positive unorientable unit clauses: 8
% 0.22/0.27 % Negative unit clauses : 2
% 0.22/0.27 % Non-unit-clauses : 8
% 0.22/0.27 % Current number of unprocessed clauses: 0
% 0.22/0.27 % ...number of literals in the above : 0
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 3
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 10
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 4
% 0.22/0.27 % Non-unit clause-clause subsumptions : 2
% 0.22/0.27 % Unit Clause-clause subsumption calls : 17
% 0.22/0.27 % Rewrite failures with RHS unbound : 176
% 0.22/0.27 % BW rewrite match attempts : 88
% 0.22/0.27 % BW rewrite match successes : 14
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 3049
% 0.22/0.27 % Search garbage collected termcells : 583
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.006 s
% 0.22/0.27 % System time : 0.003 s
% 0.22/0.27 % Total time : 0.009 s
% 0.22/0.27 % Maximum resident set size: 3652 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.015 s
% 0.22/0.27 % System time : 0.011 s
% 0.22/0.27 % Total time : 0.026 s
% 0.22/0.27 % Maximum resident set size: 4608 pages
% 0.22/0.27 % E exiting
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