%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU637^2 : 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 : n005.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 08:24:49 AM UTC 2026
% Result : Theorem 207.17s 30.49s
% Output : CNFRefutation 207.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 249 ( 63 equ; 0 cnn)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 996 ( 66 ~; 104 |; 18 &; 739 @)
% ( 9 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 180 ( 10 ^; 164 !; 6 ?; 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,
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,
esk1_2: $i > $i > $i ).
thf(decl_35,type,
esk2_2: $i > $i > $i ).
thf(decl_36,type,
esk3_0: $i ).
thf(decl_37,type,
epred1_0: $i > $o ).
thf(decl_38,type,
esk4_0: $i ).
thf(singletonprop,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) )
=> ( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',singletonprop) ).
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/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.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/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',dsetconstrER) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',singleton) ).
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/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',dsetconstrI) ).
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/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',setext) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X3: $i,X4: $i] :
( ( in @ X3 @ ( setadjoin @ X4 @ emptyset ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',uniqinunit) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( in @ X3 @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t21i0TbfrB/E---3.1_1714232.p',eqinunit) ).
thf(c_0_8,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) )
=> ( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ X3 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[singletonprop]) ).
thf(c_0_9,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_10,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_11,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
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,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 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 )
=> ( ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) )
=> ( ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X2 @ 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_8]),setext]),c_0_9]),c_0_10]),uniqinunit]),eqinunit]),c_0_11]),c_0_12])]) ).
thf(c_0_14,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,X65: $i,X66: $i,X68: $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 @ X65 @ esk3_0 )
| ~ ( in @ X66 @ esk3_0 )
| ~ ( epred1_0 @ X65 )
| ~ ( epred1_0 @ X66 )
| ( X65 = X66 ) )
& ( in @ esk4_0 @ esk3_0 )
& ( epred1_0 @ esk4_0 )
& ( ~ ( in @ X68 @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( ( dsetconstr @ esk3_0 @ epred1_0 )
!= ( setadjoin @ X68 @ 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_13])])])])])]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_16,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_14]) ).
thf(c_0_17,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_14]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( X1
= ( dsetconstr @ X3 @ X2 ) )
| ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X1 )
| ( in @ ( esk2_2 @ X1 @ ( dsetconstr @ X3 @ X2 ) ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X1 )
| ( in @ ( esk1_2 @ X1 @ ( dsetconstr @ X1 @ X2 ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,negated_conjecture,
! [X7: $i > $o,X2: $i > $o,X1: $i] :
( ( ( dsetconstr @ ( dsetconstr @ X1 @ X2 ) @ X7 )
= ( dsetconstr @ X1 @ X2 ) )
| ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ ( dsetconstr @ ( dsetconstr @ X1 @ X2 ) @ X7 ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X7: $i > $o,X2: $i > $o] :
( ( ( esk1_2 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) @ ( dsetconstr @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) @ X7 ) )
= X1 )
| ( ( dsetconstr @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) @ X7 )
= ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i,X7: $i > $o,X2: $i > $o] :
( ( ( dsetconstr @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) @ X7 )
= ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) )
| ( in @ X1 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X3: $i] :
( ( X1 = X3 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X3 @ esk3_0 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_26,negated_conjecture,
in @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_27,negated_conjecture,
epred1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X3 )
| ( in @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X3 )
| ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X7: $i > $o,X3: $i,X2: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) )
| ( X7 @ X3 )
| ~ ( in @ X3 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_30,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_14]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) )
| ( X1 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( X1 = esk4_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
thf(c_0_33,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_20,c_0_28]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X3 )
| ( in @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X3 )
| ( X2 @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X2: $i > $o,X7: $i > $o,X3: $i] :
( ( in @ X1 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) )
| ( X7 @ X3 )
| ~ ( in @ X3 @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ),
inference(er,[status(thm)],[c_0_31]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X3 )
| ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ ( dsetconstr @ X1 @ X2 ) )
| ~ ( in @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 )
| ~ ( X2 @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
thf(c_0_38,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_32,c_0_33]) ).
thf(c_0_39,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_34]) ).
thf(c_0_40,negated_conjecture,
! [X7: $i > $o,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ ( setadjoin @ X1 @ emptyset ) @ X2 ) )
| ( X7 @ X1 )
| ~ ( X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X3 )
| ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 )
| ~ ( X2 @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i] :
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= esk4_0 )
| ( ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( ( dsetconstr @ X1 @ X2 )
= X3 )
| ( X2 @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) )
| ~ ( in @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 )
| ~ ( X2 @ ( esk2_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X2: $i > $o,X7: $i > $o,X3: $i] :
( ( in @ ( dsetconstr @ X1 @ X2 ) @ ( dsetconstr @ ( setadjoin @ ( dsetconstr @ X1 @ X2 ) @ emptyset ) @ ( in @ X3 ) ) )
| ( X7 @ ( dsetconstr @ X1 @ X2 ) )
| ~ ( in @ X3 @ X1 )
| ~ ( X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i] :
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= esk4_0 )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( in @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) ) @ esk3_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i] :
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= esk4_0 )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( epred1_0 @ ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
thf(c_0_47,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_14]) ).
thf(c_0_48,negated_conjecture,
! [X7: $i > $o,X2: $i > $o] :
( ( in @ ( dsetconstr @ esk3_0 @ X2 ) @ ( dsetconstr @ ( setadjoin @ ( dsetconstr @ esk3_0 @ X2 ) @ emptyset ) @ ( in @ esk4_0 ) ) )
| ( X7 @ ( dsetconstr @ esk3_0 @ X2 ) )
| ~ ( X2 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
thf(c_0_49,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_14]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( ( esk1_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= esk4_0 )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_46]) ).
thf(c_0_51,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_20,c_0_47]) ).
thf(c_0_52,negated_conjecture,
! [X2: $i > $o] :
( ( in @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( dsetconstr @ ( setadjoin @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ emptyset ) @ ( in @ esk4_0 ) ) )
| ( X2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_48,c_0_27]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) ) @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i] :
( ( ( esk2_2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( ( setadjoin @ X1 @ emptyset )
= ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
thf(c_0_55,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_14]) ).
thf(c_0_56,negated_conjecture,
! [X2: $i > $o] :
( ( in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ( X2 @ ( dsetconstr @ esk3_0 @ epred1_0 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ ( dsetconstr @ esk3_0 @ epred1_0 ) )
| ~ ( in @ esk4_0 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_23]),c_0_15]),c_0_55]) ).
thf(c_0_58,negated_conjecture,
in @ esk4_0 @ ( dsetconstr @ esk3_0 @ epred1_0 ),
inference(ef,[status(thm)],[c_0_56]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_36]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU637^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.20 % Computer : n005.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 14:01:01 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 Running higher-order theorem proving
% 0.12/0.30 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.t21i0TbfrB/E---3.1_1714232.p
% 207.17/30.49 % Version: 3.5.1-ho
% 207.17/30.49 % partial match(1): HSSSSLSSSLMNSSA
% 207.17/30.49 % Preprocessing class: HSMSSLSSSLMNSSA.
% 207.17/30.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 207.17/30.49 % Starting new_ho_10 with 1500s (5) cores
% 207.17/30.49 % Starting new_bool_2 with 300s (1) cores
% 207.17/30.49 % Starting new_bool_9 with 300s (1) cores
% 207.17/30.49 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 207.17/30.49 % new_bool_9 with pid 1714247 completed with status 0
% 207.17/30.49 % Result found by new_bool_9
% 207.17/30.49 % partial match(1): HSSSSLSSSLMNSSA
% 207.17/30.49 % Preprocessing class: HSMSSLSSSLMNSSA.
% 207.17/30.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 207.17/30.49 % Starting new_ho_10 with 1500s (5) cores
% 207.17/30.49 % Starting new_bool_2 with 300s (1) cores
% 207.17/30.49 % Starting new_bool_9 with 300s (1) cores
% 207.17/30.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 207.17/30.49 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 207.17/30.49 % Search class: HGHSF-FFSF22-SSSFMSBN
% 207.17/30.49 % partial match(1): HGHSF-FFSF22-SSFFMSBN
% 207.17/30.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 207.17/30.49 % Starting SubtermCWHack with 31s (1) cores
% 207.17/30.49 % SubtermCWHack with pid 1714253 completed with status 0
% 207.17/30.49 % Result found by SubtermCWHack
% 207.17/30.49 % partial match(1): HSSSSLSSSLMNSSA
% 207.17/30.49 % Preprocessing class: HSMSSLSSSLMNSSA.
% 207.17/30.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 207.17/30.49 % Starting new_ho_10 with 1500s (5) cores
% 207.17/30.49 % Starting new_bool_2 with 300s (1) cores
% 207.17/30.49 % Starting new_bool_9 with 300s (1) cores
% 207.17/30.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 207.17/30.49 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 207.17/30.49 % Search class: HGHSF-FFSF22-SSSFMSBN
% 207.17/30.49 % partial match(1): HGHSF-FFSF22-SSFFMSBN
% 207.17/30.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 207.17/30.49 % Starting SubtermCWHack with 31s (1) cores
% 207.17/30.49 % Preprocessing time : 0.001 s
% 207.17/30.49
% 207.17/30.49 % Proof found!
% 207.17/30.49 % SZS status Theorem
% 207.17/30.49 % SZS output start CNFRefutation
% See solution above
% 207.17/30.49 % Parsed axioms : 19
% 207.17/30.49 % Removed by relevancy pruning/SinE : 11
% 207.17/30.49 % Initial clauses : 13
% 207.17/30.49 % Removed in clause preprocessing : 0
% 207.17/30.49 % Initial clauses in saturation : 13
% 207.17/30.49 % Processed clauses : 12836
% 207.17/30.49 % ...of these trivial : 48
% 207.17/30.49 % ...subsumed : 10094
% 207.17/30.49 % ...remaining for further processing : 2694
% 207.17/30.49 % Other redundant clauses eliminated : 5144
% 207.17/30.49 % Clauses deleted for lack of memory : 0
% 207.17/30.49 % Backward-subsumed : 237
% 207.17/30.49 % Backward-rewritten : 81
% 207.17/30.49 % Generated clauses : 1037864
% 207.17/30.49 % ...of the previous two non-redundant : 1021186
% 207.17/30.49 % ...aggressively subsumed : 0
% 207.17/30.49 % Contextual simplify-reflections : 52
% 207.17/30.49 % Paramodulations : 1032601
% 207.17/30.49 % Factorizations : 119
% 207.17/30.49 % NegExts : 0
% 207.17/30.49 % Equation resolutions : 5144
% 207.17/30.49 % Disequality decompositions : 0
% 207.17/30.49 % Total rewrite steps : 20728
% 207.17/30.49 % ...of those cached : 20595
% 207.17/30.49 % Propositional unsat checks : 0
% 207.17/30.49 % Propositional check models : 0
% 207.17/30.49 % Propositional check unsatisfiable : 0
% 207.17/30.49 % Propositional clauses : 0
% 207.17/30.49 % Propositional clauses after purity: 0
% 207.17/30.49 % Propositional unsat core size : 0
% 207.17/30.49 % Propositional preprocessing time : 0.000
% 207.17/30.49 % Propositional encoding time : 0.000
% 207.17/30.49 % Propositional solver time : 0.000
% 207.17/30.49 % Success case prop preproc time : 0.000
% 207.17/30.49 % Success case prop encoding time : 0.000
% 207.17/30.49 % Success case prop solver time : 0.000
% 207.17/30.49 % Current number of processed clauses : 2375
% 207.17/30.49 % Positive orientable unit clauses : 9
% 207.17/30.49 % Positive unorientable unit clauses: 0
% 207.17/30.49 % Negative unit clauses : 0
% 207.17/30.49 % Non-unit-clauses : 2366
% 207.17/30.49 % Current number of unprocessed clauses: 1003148
% 207.17/30.49 % ...number of literals in the above : 6815340
% 207.17/30.49 % Current number of archived formulas : 0
% 207.17/30.49 % Current number of archived clauses : 318
% 207.17/30.49 % Clause-clause subsumption calls (NU) : 1455915
% 207.17/30.49 % Rec. Clause-clause subsumption calls : 69062
% 207.17/30.49 % Non-unit clause-clause subsumptions : 10354
% 207.17/30.49 % Unit Clause-clause subsumption calls : 851
% 207.17/30.49 % Rewrite failures with RHS unbound : 0
% 207.17/30.49 % BW rewrite match attempts : 56
% 207.17/30.49 % BW rewrite match successes : 24
% 207.17/30.49 % Condensation attempts : 0
% 207.17/30.49 % Condensation successes : 0
% 207.17/30.49 % Termbank termtop insertions : 42609996
% 207.17/30.49 % Search garbage collected termcells : 791
% 207.17/30.49
% 207.17/30.49 % -------------------------------------------------
% 207.17/30.49 % User time : 28.800 s
% 207.17/30.49 % System time : 0.787 s
% 207.17/30.49 % Total time : 29.587 s
% 207.17/30.49 % Maximum resident set size: 3644 pages
% 207.17/30.49
% 207.17/30.49 % -------------------------------------------------
% 207.17/30.49 % User time : 28.802 s
% 207.17/30.49 % System time : 0.797 s
% 207.17/30.49 % Total time : 29.599 s
% 207.17/30.49 % Maximum resident set size: 4608 pages
% 207.17/30.49 % E exiting
%------------------------------------------------------------------------------