%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU757^2 : 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 : 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 08:25:30 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 295 ( 37 equ; 0 cnn)
% Maximal formula atoms : 66 ( 7 avg)
% Number of connectives : 1761 ( 139 ~; 165 |; 16 &;1369 @)
% ( 6 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
binunion: $i > $i > $i ).
thf(decl_26,type,
binintersect: $i > $i > $i ).
thf(decl_27,type,
setminus: $i > $i > $i ).
thf(decl_28,type,
binintersectT_lem: $o ).
thf(decl_29,type,
binunionT_lem: $o ).
thf(decl_30,type,
complementT_lem: $o ).
thf(decl_31,type,
setextT: $o ).
thf(decl_32,type,
demorgan2a: $o ).
thf(decl_33,type,
demorgan2b: $o ).
thf(decl_34,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_35,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_36,type,
esk3_0: $i ).
thf(decl_37,type,
esk4_0: $i ).
thf(decl_38,type,
esk5_0: $i ).
thf(demorgan2,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan2a
=> ( demorgan2b
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',demorgan2) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',binunionT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X4 @ X2 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',setextT) ).
thf(demorgan2a,axiom,
( demorgan2a
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
=> ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',demorgan2a) ).
thf(demorgan2b,axiom,
( demorgan2b
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
=> ( in @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WNfY3OcqQy/E---3.1_849984.p',demorgan2b) ).
thf(c_0_7,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan2a
=> ( demorgan2b
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[demorgan2]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X29: $i,X30: $i] :
( ( in @ X30 @ ( powerset @ X29 ) )
=> ! [X31: $i] :
( ( in @ X31 @ ( powerset @ X29 ) )
=> ( in @ ( binintersect @ X30 @ X31 ) @ ( powerset @ X29 ) ) ) )
=> ( ! [X32: $i,X33: $i] :
( ( in @ X33 @ ( powerset @ X32 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( powerset @ X32 ) )
=> ( in @ ( binunion @ X33 @ X34 ) @ ( powerset @ X32 ) ) ) )
=> ( ! [X35: $i,X36: $i] :
( ( in @ X36 @ ( powerset @ X35 ) )
=> ( in @ ( setminus @ X35 @ X36 ) @ ( powerset @ X35 ) ) )
=> ( ! [X37: $i,X38: $i] :
( ( in @ X38 @ ( powerset @ X37 ) )
=> ! [X39: $i] :
( ( in @ X39 @ ( powerset @ X37 ) )
=> ( ! [X40: $i] :
( ( in @ X40 @ X37 )
=> ( ( in @ X40 @ X38 )
=> ( in @ X40 @ X39 ) ) )
=> ( ! [X41: $i] :
( ( in @ X41 @ X37 )
=> ( ( in @ X41 @ X39 )
=> ( in @ X41 @ X38 ) ) )
=> ( X38 = X39 ) ) ) ) )
=> ( ! [X42: $i,X43: $i] :
( ( in @ X43 @ ( powerset @ X42 ) )
=> ! [X44: $i] :
( ( in @ X44 @ ( powerset @ X42 ) )
=> ! [X45: $i] :
( ( in @ X45 @ X42 )
=> ( ( in @ X45 @ ( setminus @ X42 @ ( binunion @ X43 @ X44 ) ) )
=> ( in @ X45 @ ( binintersect @ ( setminus @ X42 @ X43 ) @ ( setminus @ X42 @ X44 ) ) ) ) ) ) )
=> ( ! [X46: $i,X47: $i] :
( ( in @ X47 @ ( powerset @ X46 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X46 ) )
=> ! [X49: $i] :
( ( in @ X49 @ X46 )
=> ( ( in @ X49 @ ( binintersect @ ( setminus @ X46 @ X47 ) @ ( setminus @ X46 @ X48 ) ) )
=> ( in @ X49 @ ( setminus @ X46 @ ( binunion @ X47 @ X48 ) ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
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)],[c_0_7,binintersectT_lem]),binunionT_lem]),complementT_lem]),setextT]),demorgan2a]),demorgan2b]) ).
thf(c_0_9,negated_conjecture,
! [X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X63: $i,X64: $i,X65: $i,X66: $i,X67: $i,X68: $i,X69: $i,X70: $i] :
( ( ~ ( in @ X51 @ ( powerset @ X50 ) )
| ~ ( in @ X52 @ ( powerset @ X50 ) )
| ( in @ ( binintersect @ X51 @ X52 ) @ ( powerset @ X50 ) ) )
& ( ~ ( in @ X54 @ ( powerset @ X53 ) )
| ~ ( in @ X55 @ ( powerset @ X53 ) )
| ( in @ ( binunion @ X54 @ X55 ) @ ( powerset @ X53 ) ) )
& ( ~ ( in @ X57 @ ( powerset @ X56 ) )
| ( in @ ( setminus @ X56 @ X57 ) @ ( powerset @ X56 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X58 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X58 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X60 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X58 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ~ ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X59 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X58 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X58 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X59 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X60 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X59 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ~ ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X59 )
| ( X59 = X60 )
| ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X59 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X58 )
| ( X59 = X60 )
| ~ ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X60 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X60 )
| ( X59 = X60 )
| ~ ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X60 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ~ ( in @ ( esk2_3 @ X58 @ X59 @ X60 ) @ X59 )
| ( X59 = X60 )
| ~ ( in @ ( esk1_3 @ X58 @ X59 @ X60 ) @ X60 )
| ~ ( in @ X60 @ ( powerset @ X58 ) )
| ~ ( in @ X59 @ ( powerset @ X58 ) ) )
& ( ~ ( in @ X64 @ ( powerset @ X63 ) )
| ~ ( in @ X65 @ ( powerset @ X63 ) )
| ~ ( in @ X66 @ X63 )
| ~ ( in @ X66 @ ( setminus @ X63 @ ( binunion @ X64 @ X65 ) ) )
| ( in @ X66 @ ( binintersect @ ( setminus @ X63 @ X64 ) @ ( setminus @ X63 @ X65 ) ) ) )
& ( ~ ( in @ X68 @ ( powerset @ X67 ) )
| ~ ( in @ X69 @ ( powerset @ X67 ) )
| ~ ( in @ X70 @ X67 )
| ~ ( in @ X70 @ ( binintersect @ ( setminus @ X67 @ X68 ) @ ( setminus @ X67 @ X69 ) ) )
| ( in @ X70 @ ( setminus @ X67 @ ( binunion @ X68 @ X69 ) ) ) )
& ( in @ esk4_0 @ ( powerset @ esk3_0 ) )
& ( in @ esk5_0 @ ( powerset @ esk3_0 ) )
& ( ( setminus @ esk3_0 @ ( binunion @ esk4_0 @ esk5_0 ) )
!= ( binintersect @ ( setminus @ esk3_0 @ esk4_0 ) @ ( setminus @ esk3_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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X4 @ ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( X2 = X3 )
| ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X2: $i,X5: $i] :
( ( X1
= ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
| ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( setminus @ X2 @ ( binunion @ X3 @ X4 ) ) )
| ~ ( in @ ( esk1_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
| ~ ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) @ ( powerset @ X5 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( X2 = X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X2: $i,X5: $i] :
( ( X1
= ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
| ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( setminus @ X2 @ ( binunion @ X3 @ X4 ) ) )
| ( in @ ( esk1_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X1 )
| ~ ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) @ ( powerset @ X5 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ X4 @ ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_22,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X2: $i,X5: $i] :
( ( X1
= ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) )
| ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ ( setminus @ X2 @ ( binunion @ X3 @ X4 ) ) )
| ( in @ ( esk1_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X5 )
| ~ ( in @ ( esk2_3 @ X5 @ X1 @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( binintersect @ ( setminus @ X2 @ X3 ) @ ( setminus @ X2 @ X4 ) ) @ ( powerset @ X5 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X5 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X4 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( X2 = X3 )
| ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) @ X1 )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( binintersect @ X1 @ X3 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_34,negated_conjecture,
( ( setminus @ esk3_0 @ ( binunion @ esk4_0 @ esk5_0 ) )
!= ( binintersect @ ( setminus @ esk3_0 @ esk4_0 ) @ ( setminus @ esk3_0 @ esk5_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_35,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) )
= ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X2 @ X3 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_33]) ).
thf(c_0_36,negated_conjecture,
in @ esk5_0 @ ( powerset @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_37,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_38,negated_conjecture,
~ ( in @ ( setminus @ esk3_0 @ ( binunion @ esk4_0 @ esk5_0 ) ) @ ( powerset @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).
thf(c_0_39,negated_conjecture,
~ ( in @ ( binunion @ esk4_0 @ esk5_0 ) @ ( powerset @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU757^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:22:32 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.WNfY3OcqQy/E---3.1_849984.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.29 % Starting post_as_ho8 with 300s (1) cores
% 0.21/0.29 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.29 % Starting post_as_ho2 with 300s (1) cores
% 0.21/0.29 % lpo6_lambda_fix with pid 849997 completed with status 0
% 0.21/0.29 % Result found by lpo6_lambda_fix
% 0.21/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HGUSF-FFMF32-SFFFMFNN
% 0.21/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.29 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.21/0.29 % Starting lpo1_def_fix with 136s (1) cores
% 0.21/0.29 % Starting post_as_ho9 with 136s (1) cores
% 0.21/0.29 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.21/0.29 % lpo1_def_fix with pid 850005 completed with status 0
% 0.21/0.29 % Result found by lpo1_def_fix
% 0.21/0.29 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HGUSF-FFMF32-SFFFMFNN
% 0.21/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.21/0.29 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.21/0.29 % Starting lpo1_def_fix with 136s (1) cores
% 0.21/0.29 % Preprocessing time : 0.001 s
% 0.21/0.29 % Presaturation interreduction done
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29 % Parsed axioms : 18
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 28
% 0.21/0.29 % Removed in clause preprocessing : 11
% 0.21/0.29 % Initial clauses in saturation : 17
% 0.21/0.29 % Processed clauses : 88
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 15
% 0.21/0.29 % ...remaining for further processing : 73
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 8
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 167
% 0.21/0.29 % ...of the previous two non-redundant : 163
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 3
% 0.21/0.29 % Paramodulations : 167
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 4
% 0.21/0.29 % ...of those cached : 2
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 48
% 0.21/0.29 % Positive orientable unit clauses : 2
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 3
% 0.21/0.29 % Non-unit-clauses : 43
% 0.21/0.29 % Current number of unprocessed clauses: 109
% 0.21/0.29 % ...number of literals in the above : 925
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 25
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 1848
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 81
% 0.21/0.29 % Non-unit clause-clause subsumptions : 26
% 0.21/0.29 % Unit Clause-clause subsumption calls : 1
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 0
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 18004
% 0.21/0.29 % Search garbage collected termcells : 840
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.028 s
% 0.21/0.29 % System time : 0.002 s
% 0.21/0.29 % Total time : 0.030 s
% 0.21/0.29 % Maximum resident set size: 3644 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.074 s
% 0.21/0.29 % System time : 0.017 s
% 0.21/0.29 % Total time : 0.091 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------