%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU789^2 : 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 : n004.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 08:25:38 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 11 equ; 0 cnn)
% Maximal formula atoms : 33 ( 6 avg)
% Number of connectives : 1149 ( 113 ~; 117 |; 9 &; 853 @)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 126 ( 0 ^; 126 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
setextsub: $o ).
thf(decl_26,type,
kpair: $i > $i > $i ).
thf(decl_27,type,
breln1: $i > $i > $o ).
thf(decl_28,type,
subbreln1: $o ).
thf(decl_29,type,
breln1invset: $i > $i > $i ).
thf(decl_30,type,
breln1invprop: $o ).
thf(decl_31,type,
breln1invI: $o ).
thf(decl_32,type,
breln1invE: $o ).
thf(decl_33,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_34,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(decl_36,type,
esk4_0: $i ).
thf(woz2Ex,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ( X3
= ( breln1invset @ X1 @ ( breln1invset @ X1 @ X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',woz2Ex) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',setextsub) ).
thf(subbreln1,axiom,
( subbreln1
<=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',subbreln1) ).
thf(breln1invprop,axiom,
( breln1invprop
<=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ( breln1 @ X1 @ ( breln1invset @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',breln1invprop) ).
thf(breln1invI,axiom,
( breln1invI
<=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X6 @ X5 ) @ ( breln1invset @ X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',breln1invI) ).
thf(breln1invE,axiom,
( breln1invE
<=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ ( breln1invset @ X1 @ X3 ) )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0sybVFWrRW/E---3.1_1364791.p',breln1invE) ).
thf(c_0_6,negated_conjecture,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ( X3
= ( breln1invset @ X1 @ ( breln1invset @ X1 @ X3 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[woz2Ex]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X26: $i,X27: $i] :
( ( subset @ X26 @ X27 )
=> ( ( subset @ X27 @ X26 )
=> ( X26 = X27 ) ) )
=> ( ! [X28: $i,X29: $i] :
( ( breln1 @ X28 @ X29 )
=> ! [X30: $i] :
( ( breln1 @ X28 @ X30 )
=> ( ! [X31: $i] :
( ( in @ X31 @ X28 )
=> ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( in @ ( kpair @ X31 @ X32 ) @ X29 )
=> ( in @ ( kpair @ X31 @ X32 ) @ X30 ) ) ) )
=> ( subset @ X29 @ X30 ) ) ) )
=> ( ! [X33: $i,X34: $i] :
( ( breln1 @ X33 @ X34 )
=> ( breln1 @ X33 @ ( breln1invset @ X33 @ X34 ) ) )
=> ( ! [X35: $i,X36: $i] :
( ( breln1 @ X35 @ X36 )
=> ! [X37: $i] :
( ( in @ X37 @ X35 )
=> ! [X38: $i] :
( ( in @ X38 @ X35 )
=> ( ( in @ ( kpair @ X37 @ X38 ) @ X36 )
=> ( in @ ( kpair @ X38 @ X37 ) @ ( breln1invset @ X35 @ X36 ) ) ) ) ) )
=> ( ! [X39: $i,X40: $i] :
( ( breln1 @ X39 @ X40 )
=> ! [X41: $i] :
( ( in @ X41 @ X39 )
=> ! [X42: $i] :
( ( in @ X42 @ X39 )
=> ( ( in @ ( kpair @ X42 @ X41 ) @ ( breln1invset @ X39 @ X40 ) )
=> ( in @ ( kpair @ X41 @ X42 ) @ X40 ) ) ) ) )
=> ! [X1: $i,X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ( X3
= ( breln1invset @ X1 @ ( breln1invset @ 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)],[c_0_6,setextsub]),subbreln1]),breln1invprop]),breln1invI]),breln1invE]) ).
thf(c_0_8,negated_conjecture,
! [X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i] :
( ( ~ ( subset @ X43 @ X44 )
| ~ ( subset @ X44 @ X43 )
| ( X43 = X44 ) )
& ( ( in @ ( esk1_3 @ X45 @ X46 @ X47 ) @ X45 )
| ( subset @ X46 @ X47 )
| ~ ( breln1 @ X45 @ X47 )
| ~ ( breln1 @ X45 @ X46 ) )
& ( ( in @ ( esk2_3 @ X45 @ X46 @ X47 ) @ X45 )
| ( subset @ X46 @ X47 )
| ~ ( breln1 @ X45 @ X47 )
| ~ ( breln1 @ X45 @ X46 ) )
& ( ( in @ ( kpair @ ( esk1_3 @ X45 @ X46 @ X47 ) @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X46 )
| ( subset @ X46 @ X47 )
| ~ ( breln1 @ X45 @ X47 )
| ~ ( breln1 @ X45 @ X46 ) )
& ( ~ ( in @ ( kpair @ ( esk1_3 @ X45 @ X46 @ X47 ) @ ( esk2_3 @ X45 @ X46 @ X47 ) ) @ X47 )
| ( subset @ X46 @ X47 )
| ~ ( breln1 @ X45 @ X47 )
| ~ ( breln1 @ X45 @ X46 ) )
& ( ~ ( breln1 @ X50 @ X51 )
| ( breln1 @ X50 @ ( breln1invset @ X50 @ X51 ) ) )
& ( ~ ( breln1 @ X52 @ X53 )
| ~ ( in @ X54 @ X52 )
| ~ ( in @ X55 @ X52 )
| ~ ( in @ ( kpair @ X54 @ X55 ) @ X53 )
| ( in @ ( kpair @ X55 @ X54 ) @ ( breln1invset @ X52 @ X53 ) ) )
& ( ~ ( breln1 @ X56 @ X57 )
| ~ ( in @ X58 @ X56 )
| ~ ( in @ X59 @ X56 )
| ~ ( in @ ( kpair @ X59 @ X58 ) @ ( breln1invset @ X56 @ X57 ) )
| ( in @ ( kpair @ X58 @ X59 ) @ X57 ) )
& ( breln1 @ esk3_0 @ esk4_0 )
& ( esk4_0
!= ( breln1invset @ esk3_0 @ ( breln1invset @ 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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( kpair @ ( esk1_3 @ X1 @ X2 @ X3 ) @ ( esk2_3 @ X1 @ X2 @ X3 ) ) @ X3 )
| ~ ( breln1 @ X1 @ X3 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X1 @ X2 ) )
| ~ ( breln1 @ X1 @ X2 )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ X3 ) )
| ~ ( in @ ( kpair @ ( esk2_3 @ X4 @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ ( esk1_3 @ X4 @ X1 @ ( breln1invset @ X2 @ X3 ) ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X4 @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X4 @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X2 )
| ~ ( breln1 @ X4 @ ( breln1invset @ X2 @ X3 ) )
| ~ ( breln1 @ X4 @ X1 )
| ~ ( breln1 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i,X1: $i,X3: $i,X5: $i,X4: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) )
| ~ ( in @ ( kpair @ ( esk1_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) @ ( esk2_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) ) @ X4 )
| ~ ( in @ ( esk1_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X5 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) ) @ X3 )
| ~ ( breln1 @ X5 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) )
| ~ ( breln1 @ X2 @ ( breln1invset @ X3 @ X4 ) )
| ~ ( breln1 @ X5 @ X1 )
| ~ ( breln1 @ X3 @ X4 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk1_3 @ X1 @ X2 @ X3 ) @ ( esk2_3 @ X1 @ X2 @ X3 ) ) @ X2 )
| ( subset @ X2 @ X3 )
| ~ ( breln1 @ X1 @ X3 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ~ ( breln1 @ X1 @ X2 )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ ( kpair @ X4 @ X3 ) @ ( breln1invset @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) )
| ~ ( in @ ( esk1_3 @ X4 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X4 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X4 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X4 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( breln1 @ X4 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) )
| ~ ( breln1 @ X2 @ ( breln1invset @ X3 @ X1 ) )
| ~ ( breln1 @ X4 @ X1 )
| ~ ( breln1 @ X3 @ X1 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( breln1 @ X1 @ X3 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ ( breln1invset @ X1 @ X2 ) )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i] :
( ( in @ ( kpair @ ( esk2_3 @ X1 @ ( breln1invset @ X2 @ X3 ) @ X4 ) @ ( esk1_3 @ X1 @ ( breln1invset @ X2 @ X3 ) @ X4 ) ) @ X3 )
| ( subset @ ( breln1invset @ X2 @ X3 ) @ X4 )
| ~ ( in @ ( esk1_3 @ X1 @ ( breln1invset @ X2 @ X3 ) @ X4 ) @ X2 )
| ~ ( in @ ( esk2_3 @ X1 @ ( breln1invset @ X2 @ X3 ) @ X4 ) @ X2 )
| ~ ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) )
| ~ ( breln1 @ X2 @ X3 )
| ~ ( breln1 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X2 )
| ~ ( in @ ( esk2_3 @ X2 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X3 @ X1 ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X3 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( breln1 @ X1 @ X3 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i,X1: $i,X4: $i,X3: $i,X5: $i] :
( ( in @ ( kpair @ ( esk1_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) @ ( esk2_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) ) @ X4 )
| ( subset @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 )
| ~ ( in @ ( esk2_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) @ X2 )
| ~ ( in @ ( esk2_3 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) @ X5 ) @ X2 )
| ~ ( breln1 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X4 ) ) )
| ~ ( breln1 @ X2 @ ( breln1invset @ X3 @ X4 ) )
| ~ ( breln1 @ X3 @ X4 )
| ~ ( breln1 @ X1 @ X5 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) )
| ~ ( in @ ( esk2_3 @ X2 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X3 @ X1 ) ) ) @ X3 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X3 @ X1 ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X3 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 )
| ~ ( in @ ( esk2_3 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( esk1_3 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X2 )
| ~ ( in @ ( esk1_3 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X1 )
| ~ ( breln1 @ X4 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) )
| ~ ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) )
| ~ ( breln1 @ X4 @ X3 )
| ~ ( breln1 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X1: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
| ~ ( breln1 @ X2 @ ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_17]),c_0_20]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 )
| ~ ( in @ ( esk1_3 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) @ X3 ) @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ ( breln1invset @ X2 @ X3 ) ) )
| ~ ( breln1 @ X1 @ ( breln1invset @ X2 @ X3 ) )
| ~ ( breln1 @ X2 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( subset @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i,X1: $i] :
( ( subset @ X1 @ ( breln1invset @ X2 @ ( breln1invset @ X2 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) ) @ X2 )
| ~ ( breln1 @ X1 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) ) )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_17]),c_0_20]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) )
= X2 )
| ~ ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) ) @ X2 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) ) @ X2 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_17]) ).
thf(c_0_31,negated_conjecture,
( esk4_0
!= ( breln1invset @ esk3_0 @ ( breln1invset @ esk3_0 @ esk4_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X2 ) )
= X2 )
| ~ ( breln1 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_33,negated_conjecture,
breln1 @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU789^2 : 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 : n004.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 14:28:52 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.0sybVFWrRW/E---3.1_1364791.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.26 % lpo6_lambda_fix with pid 1364804 completed with status 0
% 0.08/0.26 % Result found by lpo6_lambda_fix
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HGUSF-FFSF32-SFFFMFNN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.26 % Starting sh5l with 151s (1) cores
% 0.08/0.26 % Starting sh3l with 151s (1) cores
% 0.08/0.26 % Starting ehoh_best3_rw with 146s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 1364808 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HGUSF-FFSF32-SFFFMFNN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 16
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 20
% 0.08/0.26 % Removed in clause preprocessing : 10
% 0.08/0.26 % Initial clauses in saturation : 10
% 0.08/0.26 % Processed clauses : 32
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 1
% 0.08/0.26 % ...remaining for further processing : 31
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 5
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 54
% 0.08/0.26 % ...of the previous two non-redundant : 26
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 11
% 0.08/0.26 % Paramodulations : 54
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 1
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 26
% 0.08/0.26 % Positive orientable unit clauses : 2
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 23
% 0.08/0.26 % Current number of unprocessed clauses: 4
% 0.08/0.26 % ...number of literals in the above : 44
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 5
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 581
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 63
% 0.08/0.26 % Non-unit clause-clause subsumptions : 17
% 0.08/0.26 % Unit Clause-clause subsumption calls : 5
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 4312
% 0.08/0.26 % Search garbage collected termcells : 627
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.007 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.009 s
% 0.08/0.26 % Maximum resident set size: 3576 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.024 s
% 0.08/0.26 % System time : 0.013 s
% 0.08/0.26 % Total time : 0.036 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------