%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU731^2 : 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 : n013.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 08:25:24 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 227 ( 36 equ; 0 cnn)
% Maximal formula atoms : 57 ( 6 avg)
% Number of connectives : 1132 ( 105 ~; 131 |; 13 &; 834 @)
% ( 4 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 109 ( 0 ^; 109 !; 0 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
setminus: $i > $i > $i ).
thf(decl_26,type,
complementT_lem: $o ).
thf(decl_27,type,
setextT: $o ).
thf(decl_28,type,
doubleComplementI1: $o ).
thf(decl_29,type,
doubleComplementE1: $o ).
thf(decl_30,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(doubleComplementEq,conjecture,
( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( X2
= ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.S8GD2Ry1wL/E---3.1_2183847.p',doubleComplementEq) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.S8GD2Ry1wL/E---3.1_2183847.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/sandbox/tmp/tmp.S8GD2Ry1wL/E---3.1_2183847.p',setextT) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.S8GD2Ry1wL/E---3.1_2183847.p',doubleComplementI1) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X4 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.S8GD2Ry1wL/E---3.1_2183847.p',doubleComplementE1) ).
thf(c_0_5,negated_conjecture,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( X2
= ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[doubleComplementEq]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X20: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X20 ) )
=> ( in @ ( setminus @ X20 @ X21 ) @ ( powerset @ X20 ) ) )
=> ( ! [X22: $i,X23: $i] :
( ( in @ X23 @ ( powerset @ X22 ) )
=> ! [X24: $i] :
( ( in @ X24 @ ( powerset @ X22 ) )
=> ( ! [X25: $i] :
( ( in @ X25 @ X22 )
=> ( ( in @ X25 @ X23 )
=> ( in @ X25 @ X24 ) ) )
=> ( ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( in @ X26 @ X24 )
=> ( in @ X26 @ X23 ) ) )
=> ( X23 = X24 ) ) ) ) )
=> ( ! [X27: $i,X28: $i] :
( ( in @ X28 @ ( powerset @ X27 ) )
=> ! [X29: $i] :
( ( in @ X29 @ X27 )
=> ( ( in @ X29 @ X28 )
=> ( in @ X29 @ ( setminus @ X27 @ ( setminus @ X27 @ X28 ) ) ) ) ) )
=> ( ! [X30: $i,X31: $i] :
( ( in @ X31 @ ( powerset @ X30 ) )
=> ! [X32: $i] :
( ( in @ X32 @ X30 )
=> ( ( in @ X32 @ ( setminus @ X30 @ ( setminus @ X30 @ X31 ) ) )
=> ( in @ X32 @ X31 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( X2
= ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,complementT_lem]),setextT]),doubleComplementI1]),doubleComplementE1]) ).
thf(c_0_7,negated_conjecture,
! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i] :
( ( ~ ( in @ X34 @ ( powerset @ X33 ) )
| ( in @ ( setminus @ X33 @ X34 ) @ ( powerset @ X33 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
| ( X36 = X37 )
| ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
| ( X36 = X37 )
| ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
| ( X36 = X37 )
| ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
| ( X36 = X37 )
| ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ~ ( in @ X36 @ ( powerset @ X35 ) ) )
& ( ~ ( in @ X41 @ ( powerset @ X40 ) )
| ~ ( in @ X42 @ X40 )
| ~ ( in @ X42 @ X41 )
| ( in @ X42 @ ( setminus @ X40 @ ( setminus @ X40 @ X41 ) ) ) )
& ( ~ ( in @ X44 @ ( powerset @ X43 ) )
| ~ ( in @ X45 @ X43 )
| ~ ( in @ X45 @ ( setminus @ X43 @ ( setminus @ X43 @ X44 ) ) )
| ( in @ X45 @ X44 ) )
& ( in @ esk4_0 @ ( powerset @ esk3_0 ) )
& ( esk4_0
!= ( setminus @ esk3_0 @ ( setminus @ esk3_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_6])])])])])]) ).
thf(c_0_8,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_7]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,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_7]) ).
thf(c_0_11,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_7]) ).
thf(c_0_12,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,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_7]) ).
thf(c_0_14,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X4 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_15,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_7]) ).
thf(c_0_16,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ~ ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X3 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_17,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_7]) ).
thf(c_0_18,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
| ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
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 ) @ X2 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,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_7]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X3 )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X3 )
| ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,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_7]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X1 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X2 )
| ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X2 )
| ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ X1 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X2 )
| ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X2 )
| ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_30,negated_conjecture,
( esk4_0
!= ( setminus @ esk3_0 @ ( setminus @ esk3_0 @ esk4_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
= X2 )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
thf(c_0_32,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU731^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:17:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.S8GD2Ry1wL/E---3.1_2183847.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 2183860 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 2183866 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 : 12
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 21
% 0.21/0.29 % Removed in clause preprocessing : 7
% 0.21/0.29 % Initial clauses in saturation : 14
% 0.21/0.29 % Processed clauses : 126
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 64
% 0.21/0.29 % ...remaining for further processing : 62
% 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 : 7
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 257
% 0.21/0.29 % ...of the previous two non-redundant : 193
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 4
% 0.21/0.29 % Paramodulations : 257
% 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 : 1
% 0.21/0.29 % ...of those cached : 0
% 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 : 41
% 0.21/0.29 % Positive orientable unit clauses : 1
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 1
% 0.21/0.29 % Non-unit-clauses : 39
% 0.21/0.29 % Current number of unprocessed clauses: 95
% 0.21/0.29 % ...number of literals in the above : 666
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 21
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 1646
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 138
% 0.21/0.29 % Non-unit clause-clause subsumptions : 75
% 0.21/0.29 % Unit Clause-clause subsumption calls : 0
% 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 : 12233
% 0.21/0.29 % Search garbage collected termcells : 583
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.012 s
% 0.21/0.29 % System time : 0.003 s
% 0.21/0.29 % Total time : 0.015 s
% 0.21/0.29 % Maximum resident set size: 3636 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.087 s
% 0.21/0.29 % System time : 0.014 s
% 0.21/0.29 % Total time : 0.101 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------