%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV238^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:35:15 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 0 equ; 0 cnn)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 855 ( 46 ~; 50 |; 95 &; 557 @)
% ( 3 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 100 ( 100 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 281 ( 74 ^; 127 !; 80 ?; 281 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_0: ( $i > $o ) > $i > $o ).
thf(decl_24,type,
esk1_1: ( $i > $o ) > $i ).
thf(decl_25,type,
esk2_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_26,type,
esk3_0: $i ).
thf(decl_27,type,
epred2_0: $i > $o ).
thf(decl_28,type,
esk4_0: $i ).
thf(decl_29,type,
esk5_0: $i ).
thf(cTHM2D_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) )
@ X3 ) ) )
& ( ! [X7: $i] :
( ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X1 @ X4 @ X3 ) )
& ( X4 @ X7 ) )
=> ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X7 ) )
=> ! [X8: $i] :
( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X8 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) ) )
@ X8 ) ) ) )
=> ! [X9: $i] :
( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X9 )
<=> ( ! [X3: $i] :
( ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) ) )
@ X3 ) )
& ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ilk5vabzQI/E---3.1_916103.p',cTHM2D_pme) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) )
@ X3 ) ) )
& ( ! [X7: $i] :
( ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X1 @ X4 @ X3 ) )
& ( X4 @ X7 ) )
=> ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X7 ) )
=> ! [X8: $i] :
( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X8 )
=> ( X1
@ ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) ) )
@ X8 ) ) ) )
=> ! [X9: $i] :
( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X9 )
<=> ( ! [X3: $i] :
( ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [X5: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ X5 ) ) )
@ X3 ) )
& ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) )
@ X9 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2D_pme]) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X3 ) ) )
& ( ! [X7: $i] :
( ? [X4: $i > $o] :
( ! [X3: $i] :
( ( X4 @ X3 )
=> ( X1 @ X4 @ X3 ) )
& ( X4 @ X7 ) )
=> ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X7 ) )
=> ! [X8: $i] :
( ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X8 )
=> ( X1
@ ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ Z0 ) ) )
@ X8 ) ) ) )
=> ! [X9: $i] :
( ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X9 )
<=> ( ! [X3: $i] :
( ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X3 )
=> ( X1
@ ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X1 @ X4 @ X6 ) )
& ( X4 @ Z0 ) ) )
@ X3 ) )
& ( X1
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X9 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X23: $i > $o,X25: $i > $o,X27: $i,X30: $i,X31: $i,X34: $i] :
( ( ( X23 @ ( esk1_1 @ X23 ) )
| ~ ( epred1_0 @ X23 @ X27 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X27 ) )
& ( ( X25 @ ( esk2_2 @ X23 @ X25 ) )
| ~ ( X25 @ ( esk1_1 @ X23 ) )
| ~ ( epred1_0 @ X23 @ X27 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X27 ) )
& ( ~ ( epred1_0 @ X25 @ ( esk2_2 @ X23 @ X25 ) )
| ~ ( X25 @ ( esk1_1 @ X23 ) )
| ~ ( epred1_0 @ X23 @ X27 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X27 ) )
& ( ~ ( epred2_0 @ X30 )
| ( epred1_0 @ epred2_0 @ X30 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X31 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) ) )
@ X31 ) )
& ( ( epred2_0 @ esk3_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X31 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) ) )
@ X31 ) )
& ( ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk3_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ X31 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) ) )
@ X31 ) )
& ( ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ esk5_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 ) )
& ( ~ ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) ) )
@ esk5_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 ) )
& ( ~ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) )
@ X34 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X6: $i] :
( ( X4 @ X6 )
=> ( epred1_0 @ X4 @ X6 ) )
& ( X4 @ Z0 ) ) )
@ X34 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 ) )
& ( ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( epred1_0 @ X4 @ X5 ) )
& ( X4 @ Z0 ) )
@ esk4_0 ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
thf(c_0_4,negated_conjecture,
( ( epred1_0
@ ^ [Z0: $i] :
? [X35: $i > $o] :
( ! [X36: $i] :
( ( X35 @ X36 )
=> ( epred1_0 @ X35 @ X36 ) )
& ( X35 @ Z0 ) )
@ esk5_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X37: $i > $o] :
( ! [X38: $i] :
( ( X37 @ X38 )
=> ( epred1_0 @ X37 @ X38 ) )
& ( X37 @ Z0 ) )
@ esk4_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X39: $i > $o] :
( ! [X40: $i] :
( ( X39 @ X40 )
=> ( epred1_0 @ X39 @ X40 ) )
& ( X39 @ Z0 ) )
@ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( epred1_0
@ ^ [Z0: $i] :
? [X41: $i > $o] :
( ! [X42: $i] :
( ( X41 @ X42 )
=> ( epred1_0 @ X41 @ X42 ) )
& ( X41 @ Z0 ) )
@ esk4_0 )
| ( epred1_0
@ ^ [Z0: $i] :
? [X43: $i > $o] :
( ! [X44: $i] :
( ( X43 @ X44 )
=> ( epred1_0 @ X43 @ X44 ) )
& ( X43 @ Z0 ) )
@ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
( ~ ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X45: $i > $o] :
( ! [X46: $i] :
( ( X45 @ X46 )
=> ( epred1_0 @ X45 @ X46 ) )
& ( X45 @ Z0 ) ) )
@ esk5_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X47: $i > $o] :
( ! [X48: $i] :
( ( X47 @ X48 )
=> ( epred1_0 @ X47 @ X48 ) )
& ( X47 @ Z0 ) )
@ esk4_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X49: $i > $o] :
( ! [X50: $i] :
( ( X49 @ X50 )
=> ( epred1_0 @ X49 @ X50 ) )
& ( X49 @ Z0 ) )
@ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
( ( epred1_0
@ ^ [Z0: $i] :
? [X51: $i > $o] :
( ! [X52: $i] :
( ( X51 @ X52 )
=> ( epred1_0 @ X51 @ X52 ) )
& ( X51 @ Z0 ) )
@ esk5_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X53: $i > $o] :
( ! [X54: $i] :
( ( X53 @ X54 )
=> ( epred1_0 @ X53 @ X54 ) )
& ( X53 @ Z0 ) )
@ esk4_0 ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_8,negated_conjecture,
( epred1_0
@ ^ [Z0: $i] :
? [X55: $i > $o] :
( ! [X56: $i] :
( ( X55 @ X56 )
=> ( epred1_0 @ X55 @ X56 ) )
& ( X55 @ Z0 ) )
@ esk4_0 ),
inference(cn,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ~ ( epred1_0
@ ^ [Z0: $i] :
? [X57: $i > $o] :
( ! [X58: $i] :
( ( X57 @ X58 )
=> ( epred1_0 @ X57 @ X58 ) )
& ( X57 @ Z0 ) )
@ esk4_0 )
| ~ ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X59: $i > $o] :
( ! [X60: $i] :
( ( X59 @ X60 )
=> ( epred1_0 @ X59 @ X60 ) )
& ( X59 @ Z0 ) ) )
@ esk5_0 ) ),
inference(cn,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X6: $i] :
( ( epred1_0 @ epred2_0 @ X3 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X61: $i > $o] :
( ! [X62: $i] :
( ( X61 @ X62 )
=> ( epred1_0 @ X61 @ X62 ) )
& ( X61 @ Z0 ) ) )
@ X6 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X63: $i > $o] :
( ! [X64: $i] :
( ( X63 @ X64 )
=> ( epred1_0 @ X63 @ X64 ) )
& ( X63 @ Z0 ) )
@ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_11,negated_conjecture,
( epred1_0
@ ^ [Z0: $i] :
? [X65: $i > $o] :
( ! [X66: $i] :
( ( X65 @ X66 )
=> ( epred1_0 @ X65 @ X66 ) )
& ( X65 @ Z0 ) )
@ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]) ).
thf(c_0_12,negated_conjecture,
~ ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X67: $i > $o] :
( ! [X68: $i] :
( ( X67 @ X68 )
=> ( epred1_0 @ X67 @ X68 ) )
& ( X67 @ Z0 ) ) )
@ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_8])]) ).
thf(c_0_13,negated_conjecture,
! [X5: $i] :
( ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X69: $i > $o] :
( ! [X70: $i] :
( ( X69 @ X70 )
=> ( epred1_0 @ X69 @ X70 ) )
& ( X69 @ Z0 ) ) )
@ X5 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X71: $i > $o] :
( ! [X72: $i] :
( ( X71 @ X72 )
=> ( epred1_0 @ X71 @ X72 ) )
& ( X71 @ Z0 ) )
@ esk3_0 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X73: $i > $o] :
( ! [X74: $i] :
( ( X73 @ X74 )
=> ( epred1_0 @ X73 @ X74 ) )
& ( X73 @ Z0 ) )
@ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( X2 @ ( esk1_1 @ X2 ) )
| ( epred1_0
@ ^ [Z0: $i] :
? [X75: $i > $o] :
( ! [X76: $i] :
( ( X75 @ X76 )
=> ( epred1_0 @ X75 @ X76 ) )
& ( X75 @ Z0 ) )
@ X3 )
| ~ ( epred1_0 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ epred2_0 @ X3 )
| ~ ( epred2_0 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X5: $i] :
( ( epred2_0 @ esk3_0 )
| ( epred1_0
@ ( epred1_0
@ ^ [Z0: $i] :
? [X77: $i > $o] :
( ! [X78: $i] :
( ( X77 @ X78 )
=> ( epred1_0 @ X77 @ X78 ) )
& ( X77 @ Z0 ) ) )
@ X5 )
| ~ ( epred1_0
@ ^ [Z0: $i] :
? [X79: $i > $o] :
( ! [X80: $i] :
( ( X79 @ X80 )
=> ( epred1_0 @ X79 @ X80 ) )
& ( X79 @ Z0 ) )
@ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i > $o,X4: $i > $o,X3: $i] :
( ( epred1_0
@ ^ [Z0: $i] :
? [X81: $i > $o] :
( ! [X82: $i] :
( ( X81 @ X82 )
=> ( epred1_0 @ X81 @ X82 ) )
& ( X81 @ Z0 ) )
@ X3 )
| ~ ( epred1_0 @ X2 @ ( esk2_2 @ X4 @ X2 ) )
| ~ ( X2 @ ( esk1_1 @ X4 ) )
| ~ ( epred1_0 @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_18,negated_conjecture,
! [X2: $i > $o,X4: $i > $o,X3: $i] :
( ( X2 @ ( esk2_2 @ X4 @ X2 ) )
| ( epred1_0
@ ^ [Z0: $i] :
? [X83: $i > $o] :
( ! [X84: $i] :
( ( X83 @ X84 )
=> ( epred1_0 @ X83 @ X84 ) )
& ( X83 @ Z0 ) )
@ X3 )
| ~ ( X2 @ ( esk1_1 @ X4 ) )
| ~ ( epred1_0 @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_19,negated_conjecture,
~ ( epred1_0
@ ^ [Z0: $i] :
? [X85: $i > $o] :
( ! [X86: $i] :
( ( X85 @ X86 )
=> ( epred1_0 @ X85 @ X86 ) )
& ( X85 @ Z0 ) )
@ esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11])]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i] :
( ( epred1_0
@ ^ [Z0: $i] :
? [X87: $i > $o] :
( ! [X88: $i] :
( ( X87 @ X88 )
=> ( epred1_0 @ X87 @ X88 ) )
& ( X87 @ Z0 ) )
@ X3 )
| ( epred2_0 @ ( esk1_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,negated_conjecture,
epred2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_11])]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( epred1_0
@ ^ [Z0: $i] :
? [X89: $i > $o] :
( ! [X90: $i] :
( ( X89 @ X90 )
=> ( epred1_0 @ X89 @ X90 ) )
& ( X89 @ Z0 ) )
@ X3 )
| ~ ( epred2_0 @ ( esk1_1 @ X2 ) )
| ~ ( epred1_0 @ X2 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).
thf(c_0_23,negated_conjecture,
epred2_0 @ ( esk1_1 @ epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i] :
( ( epred1_0
@ ^ [Z0: $i] :
? [X91: $i > $o] :
( ! [X92: $i] :
( ( X91 @ X92 )
=> ( epred1_0 @ X91 @ X92 ) )
& ( X91 @ Z0 ) )
@ X3 )
| ~ ( epred1_0 @ epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_25,negated_conjecture,
~ ( epred1_0 @ epred2_0 @ esk3_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV238^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.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 15:26:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.ilk5vabzQI/E---3.1_916103.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSMSSMSSSSLNHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting sh5l with 900s (3) cores
% 0.07/0.25 % Starting new_bool_2 with 900s (3) cores
% 0.07/0.25 % Starting full_lambda_3 with 300s (1) cores
% 0.07/0.25 % Starting pre_casc_2 with 300s (1) cores
% 0.07/0.25 % new_bool_2 with pid 916134 completed with status 0
% 0.07/0.25 % Result found by new_bool_2
% 0.07/0.25 % Preprocessing class: HSMSSMSSSSLNHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting sh5l with 900s (3) cores
% 0.07/0.25 % Starting new_bool_2 with 900s (3) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HGHNF-FFMF21-DHHFFSBN
% 0.07/0.25 % partial match(3): HGHNF-FFMF00-SHHFFSBN
% 0.07/0.25 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.07/0.25 % Starting SubtermCWHack with 82s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 91s (1) cores
% 0.07/0.25 % Starting new_bool_3 with 184s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 916139 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSMSSMSSSSLNHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting sh5l with 900s (3) cores
% 0.07/0.25 % Starting new_bool_2 with 900s (3) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HGHNF-FFMF21-DHHFFSBN
% 0.07/0.25 % partial match(3): HGHNF-FFMF00-SHHFFSBN
% 0.07/0.25 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.07/0.25 % Starting SubtermCWHack with 82s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 1
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 10
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 10
% 0.07/0.25 % Processed clauses : 21
% 0.07/0.25 % ...of these trivial : 1
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 20
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 2
% 0.07/0.25 % Backward-rewritten : 3
% 0.07/0.25 % Generated clauses : 39
% 0.07/0.25 % ...of the previous two non-redundant : 28
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 2
% 0.07/0.25 % Paramodulations : 39
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 16
% 0.07/0.25 % ...of those cached : 11
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 15
% 0.07/0.25 % Positive orientable unit clauses : 5
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 3
% 0.07/0.25 % Non-unit-clauses : 7
% 0.07/0.25 % Current number of unprocessed clauses: 16
% 0.07/0.25 % ...number of literals in the above : 69
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 5
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 42
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 33
% 0.07/0.25 % Non-unit clause-clause subsumptions : 3
% 0.07/0.25 % Unit Clause-clause subsumption calls : 14
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 3
% 0.07/0.25 % BW rewrite match successes : 3
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 7815
% 0.07/0.25 % Search garbage collected termcells : 532
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.004 s
% 0.07/0.25 % Total time : 0.009 s
% 0.07/0.25 % Maximum resident set size: 3640 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.011 s
% 0.07/0.25 % System time : 0.011 s
% 0.07/0.25 % Total time : 0.022 s
% 0.07/0.25 % Maximum resident set size: 4608 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------