%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU639^2 : 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 : n019.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 08:24:50 AM UTC 2026
% Result : Theorem 73.80s 11.01s
% Output : CNFRefutation 73.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 56 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 718 ( 43 ~; 61 |; 17 &; 531 @)
% ( 9 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 139 ( 21 ^; 113 !; 5 ?; 139 :)
% 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,
dsetconstrI: $o ).
thf(decl_28,type,
dsetconstrEL: $o ).
thf(decl_29,type,
dsetconstrER: $o ).
thf(decl_30,type,
setext: $o ).
thf(decl_31,type,
uniqinunit: $o ).
thf(decl_32,type,
eqinunit: $o ).
thf(decl_33,type,
singleton: $i > $o ).
thf(decl_34,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_35,type,
esk1_2: $i > $i > $i ).
thf(decl_36,type,
esk2_2: $i > $i > $i ).
thf(decl_37,type,
esk3_0: $i ).
thf(decl_38,type,
epred1_0: $i > $o ).
thf(decl_39,type,
esk4_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',singleton) ).
thf(ex1I,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X4 )
=> ( X4 = X3 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',ex1I) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',dsetconstrER) ).
thf(setext,axiom,
( setext
<=> ! [X1: $i,X5: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X5 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',setext) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X3: $i,X4: $i] :
( ( in @ X3 @ ( setadjoin @ X4 @ emptyset ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',uniqinunit) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( in @ X3 @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MfR4xrKweo/E---3.1_814895.p',eqinunit) ).
thf(c_0_9,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X27: $i] :
( ( in @ X27
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X27 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_10,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_11,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X4 )
=> ( X4 = X3 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ex1I]) ).
thf(c_0_12,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_13,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_14,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_15,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X27: $i] :
( ( in @ X27
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X27 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_16,negated_conjecture,
~ ( ! [X28: $i,X29: $i > $o,X30: $i] :
( ( in @ X30 @ X28 )
=> ( ( X29 @ X30 )
=> ( in @ X30 @ ( dsetconstr @ X28 @ X29 ) ) ) )
=> ( ! [X31: $i,X32: $i > $o,X33: $i] :
( ( in @ X33 @ ( dsetconstr @ X31 @ X32 ) )
=> ( in @ X33 @ X31 ) )
=> ( ! [X34: $i,X35: $i > $o,X36: $i] :
( ( in @ X36 @ ( dsetconstr @ X34 @ X35 ) )
=> ( X35 @ X36 ) )
=> ( ! [X37: $i,X38: $i] :
( ! [X39: $i] :
( ( in @ X39 @ X37 )
=> ( in @ X39 @ X38 ) )
=> ( ! [X40: $i] :
( ( in @ X40 @ X38 )
=> ( in @ X40 @ X37 ) )
=> ( X37 = X38 ) ) )
=> ( ! [X41: $i,X42: $i] :
( ( in @ X41 @ ( setadjoin @ X42 @ emptyset ) )
=> ( X41 = X42 ) )
=> ( ! [X43: $i,X44: $i] :
( ( X43 = X44 )
=> ( in @ X43 @ ( setadjoin @ X44 @ emptyset ) ) )
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X4 )
=> ( X4 = X3 ) ) )
=> ? [X45: $i] :
( ( in @ X45 @ ( dsetconstr @ X1 @ X2 ) )
& ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X45 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ),
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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11]),c_0_12]),c_0_13]),c_0_14]),setext]),uniqinunit]),eqinunit]),c_0_15])]) ).
thf(c_0_17,negated_conjecture,
! [X46: $i,X47: $i > $o,X48: $i,X49: $i,X50: $i > $o,X51: $i,X52: $i,X53: $i > $o,X54: $i,X55: $i,X56: $i,X59: $i,X60: $i,X61: $i,X62: $i,X66: $i,X67: $i] :
( ( ~ ( in @ X48 @ X46 )
| ~ ( X47 @ X48 )
| ( in @ X48 @ ( dsetconstr @ X46 @ X47 ) ) )
& ( ~ ( in @ X51 @ ( dsetconstr @ X49 @ X50 ) )
| ( in @ X51 @ X49 ) )
& ( ~ ( in @ X54 @ ( dsetconstr @ X52 @ X53 ) )
| ( X53 @ X54 ) )
& ( ( in @ ( esk2_2 @ X55 @ X56 ) @ X56 )
| ( X55 = X56 )
| ( in @ ( esk1_2 @ X55 @ X56 ) @ X55 ) )
& ( ~ ( in @ ( esk2_2 @ X55 @ X56 ) @ X55 )
| ( X55 = X56 )
| ( in @ ( esk1_2 @ X55 @ X56 ) @ X55 ) )
& ( ( in @ ( esk2_2 @ X55 @ X56 ) @ X56 )
| ( X55 = X56 )
| ~ ( in @ ( esk1_2 @ X55 @ X56 ) @ X56 ) )
& ( ~ ( in @ ( esk2_2 @ X55 @ X56 ) @ X55 )
| ( X55 = X56 )
| ~ ( in @ ( esk1_2 @ X55 @ X56 ) @ X56 ) )
& ( ~ ( in @ X59 @ ( setadjoin @ X60 @ emptyset ) )
| ( X59 = X60 ) )
& ( ( X61 != X62 )
| ( in @ X61 @ ( setadjoin @ X62 @ emptyset ) ) )
& ( in @ esk4_0 @ esk3_0 )
& ( epred1_0 @ esk4_0 )
& ( ~ ( in @ X66 @ esk3_0 )
| ~ ( epred1_0 @ X66 )
| ( X66 = esk4_0 ) )
& ( ~ ( in @ X67 @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( ( dsetconstr @ esk3_0 @ epred1_0 )
!= ( setadjoin @ X67 @ emptyset ) ) ) ),
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,X3: $i] :
( ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( esk2_2 @ X1 @ X3 ) @ X3 )
| ( X1 = X3 )
| ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i,X1: $i] :
( ( ( esk2_2 @ X1 @ ( setadjoin @ X3 @ emptyset ) )
= X3 )
| ( X1
= ( setadjoin @ X3 @ emptyset ) )
| ( in @ ( esk1_2 @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i,X1: $i] :
( ( X1 = X3 )
| ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 )
| ~ ( in @ ( esk2_2 @ X1 @ X3 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X3 @ emptyset ) )
= X3 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X3 @ emptyset ) )
| ( X2 @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,negated_conjecture,
epred1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X3 @ emptyset ) )
= X3 )
| ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X3 @ emptyset ) )
| ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X3 @ emptyset ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( ( dsetconstr @ X1 @ X2 )
= ( setadjoin @ X3 @ emptyset ) )
| ( X2 @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ ( setadjoin @ X3 @ emptyset ) ) )
| ~ ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( in @ esk4_0 @ ( dsetconstr @ X1 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ X2 ) @ ( setadjoin @ X1 @ emptyset ) )
= esk4_0 )
| ( ( esk2_2 @ ( dsetconstr @ esk3_0 @ X2 ) @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( ( dsetconstr @ esk3_0 @ X2 )
= ( setadjoin @ X1 @ emptyset ) )
| ~ ( epred1_0 @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ X2 ) @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ X1 @ epred1_0 )
= ( setadjoin @ esk4_0 @ emptyset ) )
| ( epred1_0 @ ( esk1_2 @ ( dsetconstr @ X1 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) ) )
| ~ ( in @ esk4_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_33,negated_conjecture,
in @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_34,negated_conjecture,
( ( ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ( ( setadjoin @ esk4_0 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( ( dsetconstr @ esk3_0 @ epred1_0 )
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_36,negated_conjecture,
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ( in @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) ) @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_35]) ).
thf(c_0_37,negated_conjecture,
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ( in @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) ) @ esk3_0 )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
thf(c_0_38,negated_conjecture,
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ( epred1_0 @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) ) )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) )
| ( X1 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk2_2 @ X1 @ X3 ) @ X3 )
| ( X1 = X3 )
| ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ~ ( in @ ( esk2_2 @ X1 @ X3 ) @ X1 )
| ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_42,negated_conjecture,
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_38]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ),
inference(er,[status(thm)],[c_0_39]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X3: $i] :
( ( ( esk2_2 @ X1 @ ( setadjoin @ X3 @ emptyset ) )
= X3 )
| ( X1
= ( setadjoin @ X3 @ emptyset ) )
| ~ ( in @ ( esk1_2 @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
thf(c_0_45,negated_conjecture,
( ~ ( in @ ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) ) @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_35]) ).
thf(c_0_46,negated_conjecture,
( ( ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ esk4_0 @ emptyset ) )
= esk4_0 )
| ~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_43])]),c_0_35]) ).
thf(c_0_47,negated_conjecture,
~ ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU639^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:01:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.MfR4xrKweo/E---3.1_814895.p
% 73.80/11.01 % Version: 3.5.1-ho
% 73.80/11.01 % partial match(1): HSSSSLSSSLMNHSA
% 73.80/11.01 % Preprocessing class: HSSSSLSSMLMNHSA.
% 73.80/11.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.80/11.01 % Starting new_ho_10 with 1500s (5) cores
% 73.80/11.01 % Starting new_ho_7 with 300s (1) cores
% 73.80/11.01 % Starting lpo8_lambda_fix with 300s (1) cores
% 73.80/11.01 % Starting lpo9_lambda_fix with 300s (1) cores
% 73.80/11.01 % new_ho_10 with pid 814908 completed with status 0
% 73.80/11.01 % Result found by new_ho_10
% 73.80/11.01 % partial match(1): HSSSSLSSSLMNHSA
% 73.80/11.01 % Preprocessing class: HSSSSLSSMLMNHSA.
% 73.80/11.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.80/11.01 % Starting new_ho_10 with 1500s (5) cores
% 73.80/11.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.80/11.01 % No SInE strategy applied
% 73.80/11.01 % Search class: HGHSF-FFSF22-SHSSMSBN
% 73.80/11.01 % partial match(2): HGHNF-FFSF22-SHSSMMBN
% 73.80/11.01 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 73.80/11.01 % Starting SubtermCWHack with 151s (1) cores
% 73.80/11.01 % Starting new_ho_10 with 901s (1) cores
% 73.80/11.01 % Starting sh5l with 151s (1) cores
% 73.80/11.01 % Starting new_bool_1 with 151s (1) cores
% 73.80/11.01 % Starting new_bool_2 with 146s (1) cores
% 73.80/11.01 % sh5l with pid 814916 completed with status 0
% 73.80/11.01 % Result found by sh5l
% 73.80/11.01 % partial match(1): HSSSSLSSSLMNHSA
% 73.80/11.01 % Preprocessing class: HSSSSLSSMLMNHSA.
% 73.80/11.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.80/11.01 % Starting new_ho_10 with 1500s (5) cores
% 73.80/11.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.80/11.01 % No SInE strategy applied
% 73.80/11.01 % Search class: HGHSF-FFSF22-SHSSMSBN
% 73.80/11.01 % partial match(2): HGHNF-FFSF22-SHSSMMBN
% 73.80/11.01 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 73.80/11.01 % Starting SubtermCWHack with 151s (1) cores
% 73.80/11.01 % Starting new_ho_10 with 901s (1) cores
% 73.80/11.01 % Starting sh5l with 151s (1) cores
% 73.80/11.01 % Preprocessing time : 0.001 s
% 73.80/11.01 % Presaturation interreduction done
% 73.80/11.01
% 73.80/11.01 % Proof found!
% 73.80/11.01 % SZS status Theorem
% 73.80/11.01 % SZS output start CNFRefutation
% See solution above
% 73.80/11.01 % Parsed axioms : 21
% 73.80/11.01 % Removed by relevancy pruning/SinE : 0
% 73.80/11.01 % Initial clauses : 25
% 73.80/11.01 % Removed in clause preprocessing : 12
% 73.80/11.01 % Initial clauses in saturation : 13
% 73.80/11.01 % Processed clauses : 6337
% 73.80/11.01 % ...of these trivial : 0
% 73.80/11.01 % ...subsumed : 4592
% 73.80/11.01 % ...remaining for further processing : 1745
% 73.80/11.01 % Other redundant clauses eliminated : 1
% 73.80/11.01 % Clauses deleted for lack of memory : 0
% 73.80/11.01 % Backward-subsumed : 249
% 73.80/11.01 % Backward-rewritten : 0
% 73.80/11.01 % Generated clauses : 130272
% 73.80/11.01 % ...of the previous two non-redundant : 126388
% 73.80/11.01 % ...aggressively subsumed : 0
% 73.80/11.01 % Contextual simplify-reflections : 94
% 73.80/11.01 % Paramodulations : 130072
% 73.80/11.01 % Factorizations : 0
% 73.80/11.01 % NegExts : 0
% 73.80/11.01 % Equation resolutions : 1
% 73.80/11.01 % Disequality decompositions : 0
% 73.80/11.01 % Total rewrite steps : 2672
% 73.80/11.01 % ...of those cached : 2626
% 73.80/11.01 % Propositional unsat checks : 0
% 73.80/11.01 % Propositional check models : 0
% 73.80/11.01 % Propositional check unsatisfiable : 0
% 73.80/11.01 % Propositional clauses : 0
% 73.80/11.01 % Propositional clauses after purity: 0
% 73.80/11.01 % Propositional unsat core size : 0
% 73.80/11.01 % Propositional preprocessing time : 0.000
% 73.80/11.01 % Propositional encoding time : 0.000
% 73.80/11.01 % Propositional solver time : 0.000
% 73.80/11.01 % Success case prop preproc time : 0.000
% 73.80/11.01 % Success case prop encoding time : 0.000
% 73.80/11.01 % Success case prop solver time : 0.000
% 73.80/11.01 % Current number of processed clauses : 1283
% 73.80/11.01 % Positive orientable unit clauses : 3
% 73.80/11.01 % Positive unorientable unit clauses: 0
% 73.80/11.01 % Negative unit clauses : 1
% 73.80/11.01 % Non-unit-clauses : 1279
% 73.80/11.01 % Current number of unprocessed clauses: 119244
% 73.80/11.01 % ...number of literals in the above : 830558
% 73.80/11.01 % Current number of archived formulas : 0
% 73.80/11.01 % Current number of archived clauses : 461
% 73.80/11.01 % Clause-clause subsumption calls (NU) : 561187
% 73.80/11.01 % Rec. Clause-clause subsumption calls : 46843
% 73.80/11.01 % Non-unit clause-clause subsumptions : 5003
% 73.80/11.01 % Unit Clause-clause subsumption calls : 49
% 73.80/11.01 % Rewrite failures with RHS unbound : 0
% 73.80/11.01 % BW rewrite match attempts : 1
% 73.80/11.01 % BW rewrite match successes : 0
% 73.80/11.01 % Condensation attempts : 6337
% 73.80/11.01 % Condensation successes : 71
% 73.80/11.01 % Termbank termtop insertions : 26621893
% 73.80/11.01 % Search garbage collected termcells : 788
% 73.80/11.01
% 73.80/11.01 % -------------------------------------------------
% 73.80/11.01 % User time : 9.972 s
% 73.80/11.01 % System time : 0.156 s
% 73.80/11.01 % Total time : 10.128 s
% 73.80/11.01 % Maximum resident set size: 3648 pages
% 73.80/11.01
% 73.80/11.01 % -------------------------------------------------
% 73.80/11.01 % User time : 51.443 s
% 73.80/11.01 % System time : 1.071 s
% 73.80/11.01 % Total time : 52.514 s
% 73.80/11.01 % Maximum resident set size: 4864 pages
% 73.80/11.01 % E exiting
%------------------------------------------------------------------------------