%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV044^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:37:32 AM UTC 2026
% Result : Theorem 0.06s 0.19s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 6 unt; 0 typ; 8 def)
% Number of atoms : 566 ( 167 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1015 ( 147 ~; 157 |; 44 &; 615 @)
% ( 8 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 12 con; 0-3 aty)
% Number of variables : 161 ( 0 sgn 134 !; 27 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: b > a > a > $o ).
thf(func_def_4,type,
sK1: b > $o ).
thf(func_def_5,type,
sK2: b > a ).
thf(func_def_6,type,
sK3: b > a ).
thf(func_def_7,type,
sK4: b > a ).
thf(func_def_8,type,
sK5: b ).
thf(func_def_9,type,
sK6: b > a ).
thf(func_def_10,type,
sK7: b > a ).
thf(func_def_11,type,
sK8: b ).
thf(f1,conjecture,
! [X1: b > a > a > $o,X0: b > $o] :
( ! [X2: b] :
( ( X0 @ X2 )
=> ( ! [X5: a,X4: a,X3: a] :
( ( ( X1 @ X2 @ X4 @ X5 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) ) )
=> ( ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X2 @ X3 ) ) ) )
& ! [X2: b > a,X4: b > a,X5: b > a] :
( ( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
& ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X5 @ X3 ) ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X5 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM506_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: b > a > a > $o,X0: b > $o] :
( ! [X2: b] :
( ( X0 @ X2 )
=> ( ! [X5: a,X4: a,X3: a] :
( ( ( X1 @ X2 @ X4 @ X5 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) ) )
=> ( ! [X2: b > a,X4: b > a] :
( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X2 @ X3 ) ) ) )
& ! [X2: b > a,X4: b > a,X5: b > a] :
( ( ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X4 @ X3 ) ) )
& ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X4 @ X3 ) @ ( X5 @ X3 ) ) ) )
=> ! [X3: b] :
( ( X0 @ X3 )
=> ( X1 @ X3 @ ( X2 @ X3 ) @ ( X5 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: b > a > a > $o,X1: b > $o] :
( ! [X2: b] :
( ( X1 @ X2 )
=> ( ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X2 @ X4 @ X3 )
& ( X0 @ X2 @ X5 @ X4 ) )
=> ( X0 @ X2 @ X5 @ X3 ) )
& ! [X6: a,X7: a] :
( ( X0 @ X2 @ X6 @ X7 )
=> ( X0 @ X2 @ X7 @ X6 ) ) ) )
=> ( ! [X8: b > a,X9: b > a] :
( ! [X10: b] :
( ( X1 @ X10 )
=> ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) ) )
=> ! [X11: b] :
( ( X1 @ X11 )
=> ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) ) ) )
& ! [X12: b > a,X13: b > a,X14: b > a] :
( ( ! [X15: b] :
( ( X1 @ X15 )
=> ( X0 @ X15 @ ( X12 @ X15 ) @ ( X13 @ X15 ) ) )
& ! [X16: b] :
( ( X1 @ X16 )
=> ( X0 @ X16 @ ( X13 @ X16 ) @ ( X14 @ X16 ) ) ) )
=> ! [X17: b] :
( ( X1 @ X17 )
=> ( X0 @ X17 @ ( X12 @ X17 ) @ ( X14 @ X17 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: b > a > a > $o,X1: b > $o] :
( ! [X2: b] :
( ( ( X1 @ X2 )
= $true )
=> ( ! [X6: a,X7: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
= $true )
=> ( ( X0 @ X2 @ X7 @ X6 )
= $true ) )
& ! [X3: a,X5: a,X4: a] :
( ( ( ( X0 @ X2 @ X4 @ X3 )
= $true )
& ( ( X0 @ X2 @ X5 @ X4 )
= $true ) )
=> ( ( X0 @ X2 @ X5 @ X3 )
= $true ) ) ) )
=> ( ! [X14: b > a,X12: b > a,X13: b > a] :
( ( ! [X15: b] :
( ( ( X1 @ X15 )
= $true )
=> ( ( X0 @ X15 @ ( X12 @ X15 ) @ ( X13 @ X15 ) )
= $true ) )
& ! [X16: b] :
( ( ( X1 @ X16 )
= $true )
=> ( ( X0 @ X16 @ ( X13 @ X16 ) @ ( X14 @ X16 ) )
= $true ) ) )
=> ! [X17: b] :
( ( ( X1 @ X17 )
= $true )
=> ( ( X0 @ X17 @ ( X12 @ X17 ) @ ( X14 @ X17 ) )
= $true ) ) )
& ! [X9: b > a,X8: b > a] :
( ! [X10: b] :
( ( ( X1 @ X10 )
= $true )
=> ( $true
= ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) ) ) )
=> ! [X11: b] :
( ( ( X1 @ X11 )
= $true )
=> ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ( ? [X14: b > a,X12: b > a,X13: b > a] :
( ? [X17: b] :
( ( ( X0 @ X17 @ ( X12 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) )
& ! [X15: b] :
( ( ( X1 @ X15 )
!= $true )
| ( ( X0 @ X15 @ ( X12 @ X15 ) @ ( X13 @ X15 ) )
= $true ) )
& ! [X16: b] :
( ( ( X0 @ X16 @ ( X13 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) ) )
| ? [X8: b > a,X9: b > a] :
( ? [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
!= $true )
& ( ( X1 @ X11 )
= $true ) )
& ! [X10: b] :
( ( ( X1 @ X10 )
!= $true )
| ( $true
= ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) ) ) ) ) )
& ! [X2: b] :
( ( ! [X6: a,X7: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( ( X0 @ X2 @ X7 @ X6 )
= $true ) )
& ! [X3: a,X5: a,X4: a] :
( ( ( X0 @ X2 @ X5 @ X3 )
= $true )
| ( ( X0 @ X2 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X4 )
!= $true ) ) )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ! [X2: b] :
( ( ! [X5: a,X4: a,X3: a] :
( ( ( X0 @ X2 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X5 @ X3 )
= $true ) )
& ! [X6: a,X7: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( ( X0 @ X2 @ X7 @ X6 )
= $true ) ) )
| ( ( X1 @ X2 )
!= $true ) )
& ( ? [X14: b > a,X13: b > a,X12: b > a] :
( ! [X16: b] :
( ( ( X0 @ X16 @ ( X13 @ X16 ) @ ( X14 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true ) )
& ? [X17: b] :
( ( ( X0 @ X17 @ ( X12 @ X17 ) @ ( X14 @ X17 ) )
!= $true )
& ( ( X1 @ X17 )
= $true ) )
& ! [X15: b] :
( ( ( X1 @ X15 )
!= $true )
| ( ( X0 @ X15 @ ( X12 @ X15 ) @ ( X13 @ X15 ) )
= $true ) ) )
| ? [X8: b > a,X9: b > a] :
( ? [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
!= $true )
& ( ( X1 @ X11 )
= $true ) )
& ! [X10: b] :
( ( ( X1 @ X10 )
!= $true )
| ( $true
= ( X0 @ X10 @ ( X8 @ X10 ) @ ( X9 @ X10 ) ) ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: b > a > a > $o,X1: b > $o] :
( ! [X2: b] :
( ( ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X2 @ X4 @ X5 )
!= $true )
| ( ( X0 @ X2 @ X3 @ X4 )
!= $true )
| ( ( X0 @ X2 @ X3 @ X5 )
= $true ) )
& ! [X6: a,X7: a] :
( ( ( X0 @ X2 @ X6 @ X7 )
!= $true )
| ( ( X0 @ X2 @ X7 @ X6 )
= $true ) ) )
| ( ( X1 @ X2 )
!= $true ) )
& ( ? [X8: b > a,X9: b > a,X10: b > a] :
( ! [X11: b] :
( ( ( X0 @ X11 @ ( X9 @ X11 ) @ ( X8 @ X11 ) )
= $true )
| ( ( X1 @ X11 )
!= $true ) )
& ? [X12: b] :
( ( ( X0 @ X12 @ ( X10 @ X12 ) @ ( X8 @ X12 ) )
!= $true )
& ( ( X1 @ X12 )
= $true ) )
& ! [X13: b] :
( ( ( X1 @ X13 )
!= $true )
| ( ( X0 @ X13 @ ( X10 @ X13 ) @ ( X9 @ X13 ) )
= $true ) ) )
| ? [X14: b > a,X15: b > a] :
( ? [X16: b] :
( ( ( X0 @ X16 @ ( X15 @ X16 ) @ ( X14 @ X16 ) )
!= $true )
& ( ( X1 @ X16 )
= $true ) )
& ! [X17: b] :
( ( ( X1 @ X17 )
!= $true )
| ( ( X0 @ X17 @ ( X14 @ X17 ) @ ( X15 @ X17 ) )
= $true ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X2: b] :
( ( ! [X3: a,X4: a,X5: a] :
( ( $true
!= ( sK0 @ X2 @ X4 @ X5 ) )
| ( ( sK0 @ X2 @ X3 @ X4 )
!= $true )
| ( ( sK0 @ X2 @ X3 @ X5 )
= $true ) )
& ! [X6: a,X7: a] :
( ( ( sK0 @ X2 @ X6 @ X7 )
!= $true )
| ( ( sK0 @ X2 @ X7 @ X6 )
= $true ) ) )
| ( ( sK1 @ X2 )
!= $true ) )
& ( ( ! [X11: b] :
( ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true )
| ( ( sK1 @ X11 )
!= $true ) )
& ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
& ( ( sK1 @ sK5 )
= $true )
& ! [X13: b] :
( ( ( sK1 @ X13 )
!= $true )
| ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) ) ) )
| ( ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
& ( $true
= ( sK1 @ sK8 ) )
& ! [X17: b] :
( ( ( sK1 @ X17 )
!= $true )
| ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X8,sK2),skolemize(X9,sK3),skolemize(X10,sK4),skolemize(X12,sK5),skolemize(X14,sK6),skolemize(X15,sK7),skolemize(X16,sK8)],[f7]) ).
thf(f9,plain,
! [X17: b,X13: b] :
( ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true )
| ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) )
| ( ( sK1 @ X17 )
!= $true )
| ( ( sK1 @ X13 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X13: b] :
( ( $true
= ( sK1 @ sK8 ) )
| ( ( sK1 @ X13 )
!= $true )
| ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X13: b] :
( ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) )
| ( ( sK1 @ X13 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X17: b] :
( ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true )
| ( ( sK1 @ X17 )
!= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( $true
= ( sK1 @ sK8 ) )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X17: b] :
( ( ( sK1 @ X17 )
!= $true )
| ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true )
| ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
! [X11: b,X17: b] :
( ( ( sK1 @ X17 )
!= $true )
| ( ( sK1 @ X11 )
!= $true )
| ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true )
| ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f19,plain,
! [X11: b] :
( ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true )
| ( ( sK1 @ X11 )
!= $true )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
! [X11: b] :
( ( ( sK1 @ X11 )
!= $true )
| ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
! [X2: b,X6: a,X7: a] :
( ( ( sK0 @ X2 @ X7 @ X6 )
= $true )
| ( ( sK1 @ X2 )
!= $true )
| ( ( sK0 @ X2 @ X6 @ X7 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
! [X2: b,X3: a,X4: a,X5: a] :
( ( ( sK0 @ X2 @ X3 @ X5 )
= $true )
| ( ( sK0 @ X2 @ X3 @ X4 )
!= $true )
| ( $true
!= ( sK0 @ X2 @ X4 @ X5 ) )
| ( ( sK1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f25,definition,
( spl9_1
<=> ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f27,plain,
( ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| spl9_1 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f29,definition,
( spl9_2
<=> ! [X17: b] :
( ( ( sK1 @ X17 )
!= $true )
| ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f30,plain,
( ! [X17: b] :
( ( ( sK0 @ X17 @ ( sK6 @ X17 ) @ ( sK7 @ X17 ) )
= $true )
| ( ( sK1 @ X17 )
!= $true ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f31,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f15,f29,f25]) ).
thf(f33,definition,
( spl9_3
<=> ! [X13: b] :
( ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) )
| ( ( sK1 @ X13 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f34,plain,
( ! [X13: b] :
( ( $true
= ( sK0 @ X13 @ ( sK4 @ X13 ) @ ( sK3 @ X13 ) ) )
| ( ( sK1 @ X13 )
!= $true ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f35,plain,
( spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f9,f33,f29]) ).
thf(f37,definition,
( spl9_4
<=> ( $true
= ( sK1 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f39,plain,
( ( $true
= ( sK1 @ sK8 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f41,definition,
( spl9_5
<=> ! [X11: b] :
( ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true )
| ( ( sK1 @ X11 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f42,plain,
( ! [X11: b] :
( ( ( sK0 @ X11 @ ( sK3 @ X11 ) @ ( sK2 @ X11 ) )
= $true )
| ( ( sK1 @ X11 )
!= $true ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f43,plain,
( spl9_4
| spl9_5 ),
inference(avatar_split_clause,[],[f19,f41,f37]) ).
thf(f44,plain,
( spl9_4
| spl9_3 ),
inference(avatar_split_clause,[],[f10,f33,f37]) ).
thf(f46,definition,
( spl9_6
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f48,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl9_4
| spl9_6 ),
inference(avatar_split_clause,[],[f13,f46,f37]) ).
thf(f51,definition,
( spl9_7
<=> ( $true
= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
!= ( sK0 @ sK8 @ ( sK7 @ sK8 ) @ ( sK6 @ sK8 ) ) )
| spl9_7 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
( ~ spl9_7
| spl9_5 ),
inference(avatar_split_clause,[],[f20,f41,f51]) ).
thf(f55,plain,
( spl9_2
| spl9_6 ),
inference(avatar_split_clause,[],[f12,f46,f29]) ).
thf(f56,plain,
( spl9_2
| spl9_5 ),
inference(avatar_split_clause,[],[f18,f41,f29]) ).
thf(f57,plain,
( ~ spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f16,f37,f25]) ).
thf(f58,plain,
( spl9_3
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f11,f51,f33]) ).
thf(f59,plain,
( spl9_6
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f14,f51,f46]) ).
thf(f60,plain,
( ~ spl9_1
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f17,f51,f25]) ).
thf(f61,plain,
( ( ( sK0 @ sK8 @ ( sK6 @ sK8 ) @ ( sK7 @ sK8 ) )
!= $true )
| ( $true
!= ( sK1 @ sK8 ) )
| ( $true != $true )
| spl9_7 ),
inference(superposition,[],[f53,f21]) ).
thf(f62,plain,
( ( ( sK0 @ sK8 @ ( sK6 @ sK8 ) @ ( sK7 @ sK8 ) )
!= $true )
| ( $true
!= ( sK1 @ sK8 ) )
| spl9_7 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
( ( $true
!= ( sK1 @ sK8 ) )
| ~ spl9_2
| spl9_7 ),
inference(forward_subsumption_resolution,[],[f62,f30]) ).
thf(f64,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| spl9_7 ),
inference(forward_subsumption_resolution,[],[f63,f39]) ).
thf(f65,plain,
( ~ spl9_2
| ~ spl9_4
| spl9_7 ),
inference(avatar_contradiction_clause,[],[f64]) ).
thf(f85,plain,
( ! [X0: a] :
( ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ X0 )
!= $true )
| ( ( sK0 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true )
| ( $true != $true )
| ( ( sK1 @ sK5 )
!= $true ) )
| spl9_1 ),
inference(superposition,[],[f27,f22]) ).
thf(f88,plain,
( ! [X0: a] :
( ( ( sK1 @ sK5 )
!= $true )
| ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ X0 )
!= $true )
| ( ( sK0 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true ) )
| spl9_1 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f92,plain,
( ! [X0: a] :
( ( ( sK0 @ sK5 @ ( sK4 @ sK5 ) @ X0 )
!= $true )
| ( ( sK0 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true ) )
| spl9_1
| ~ spl9_6 ),
inference(forward_subsumption_resolution,[],[f88,f48]) ).
thf(f103,plain,
( ( ( sK0 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| ( ( sK1 @ sK5 )
!= $true )
| ( $true != $true )
| spl9_1
| ~ spl9_3
| ~ spl9_6 ),
inference(superposition,[],[f92,f34]) ).
thf(f106,plain,
( ( ( sK1 @ sK5 )
!= $true )
| ( ( sK0 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| spl9_1
| ~ spl9_3
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f109,plain,
( ( ( sK0 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| spl9_1
| ~ spl9_3
| ~ spl9_6 ),
inference(forward_subsumption_resolution,[],[f106,f48]) ).
thf(f111,definition,
( spl9_10
<=> ( ( sK0 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f113,plain,
( ( ( sK0 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) )
!= $true )
| spl9_10 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f114,plain,
( ~ spl9_10
| spl9_1
| ~ spl9_3
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f109,f46,f33,f25,f111]) ).
thf(f115,plain,
( ( $true != $true )
| ( ( sK1 @ sK5 )
!= $true )
| ~ spl9_5
| spl9_10 ),
inference(superposition,[],[f113,f42]) ).
thf(f119,plain,
( ( ( sK1 @ sK5 )
!= $true )
| ~ spl9_5
| spl9_10 ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f122,plain,
( $false
| ~ spl9_5
| ~ spl9_6
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f119,f48]) ).
thf(f123,plain,
( ~ spl9_5
| ~ spl9_6
| spl9_10 ),
inference(avatar_contradiction_clause,[],[f122]) ).
cnf(s1,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
( spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
( spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( spl9_4
| spl9_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
( spl9_5
| ~ spl9_7 ),
inference(sat_conversion,[],[f54]) ).
cnf(s7,plain,
( spl9_2
| spl9_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
( spl9_2
| spl9_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s9,plain,
( ~ spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
( spl9_3
| ~ spl9_7 ),
inference(sat_conversion,[],[f58]) ).
cnf(s11,plain,
( spl9_6
| ~ spl9_7 ),
inference(sat_conversion,[],[f59]) ).
cnf(s12,plain,
( ~ spl9_1
| ~ spl9_7 ),
inference(sat_conversion,[],[f60]) ).
cnf(s13,plain,
( ~ spl9_2
| ~ spl9_4
| spl9_7 ),
inference(sat_conversion,[],[f65]) ).
cnf(s16,plain,
( spl9_1
| ~ spl9_3
| ~ spl9_6
| ~ spl9_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s17,plain,
( ~ spl9_5
| ~ spl9_6
| spl9_10 ),
inference(sat_conversion,[],[f123]) ).
cnf(s19,plain,
( spl9_2
| spl9_1 ),
inference(rat,[],[s16,s17,s2,s7,s8]) ).
cnf(s20,plain,
( ~ spl9_6
| ~ spl9_5
| ~ spl9_3
| spl9_1 ),
inference(rat,[],[s16,s17]) ).
cnf(s21,plain,
( spl9_6
| ~ spl9_2 ),
inference(rat,[],[s13,s5,s11]) ).
cnf(s22,plain,
( spl9_5
| ~ spl9_2 ),
inference(rat,[],[s13,s3,s6]) ).
cnf(s23,plain,
spl9_1,
inference(rat,[],[s13,s4,s10,s20,s22,s21,s19]) ).
cnf(s24,plain,
~ spl9_7,
inference(rat,[],[s12,s23]) ).
cnf(s25,plain,
spl9_4,
inference(rat,[],[s9,s23]) ).
cnf(s26,plain,
spl9_2,
inference(rat,[],[s1,s23]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s13,s26,s24,s25]) ).
thf(f130,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV044^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 15:03:54 UTC 2026
% 0.06/0.11 % CPUTime :
% 0.06/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % (221941)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.19 % (221952)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.19 % (221952)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.06/0.19 % (221952)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2268993986:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.19 % (221951)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3278365725:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.19 % (221950)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=576163088:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.19 % (221946)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2246196755:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.19 % (221947)lrs+10_16_si=on:nwc=1.5:random_seed=3666226999:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.19 % (221948)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3233231733:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.19 % (221949)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=889712253:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.06/0.19 % (221948)Instruction limit reached!
% 0.06/0.19 % (221948)------------------------------
% 0.06/0.19 % (221948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (221948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (221948)CaDiCaL version: 2.1.3
% 0.06/0.19 % (221948)Termination reason: Instruction limit
% 0.06/0.19 % (221948)Termination phase: Saturation
% 0.06/0.19 % (221948)Time elapsed: 0.002 s
% 0.06/0.19 % (221948)Peak memory usage: 12 MB
% 0.06/0.19 % (221948)Instructions burned: 5 (million)
% 0.06/0.19 % (221949) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-221941-221949"...
% 0.06/0.19 % (221946) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-221941-221946"...
% 0.06/0.19 % (221949)...printing done.
% 0.06/0.19 % (221950) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-221941-221950"...
% 0.06/0.19 % (221949)Refutation found. Thanks to Tanya!
% 0.06/0.19 % SZS status Theorem for theBenchmark
% 0.06/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.19 % (221949)------------------------------
% 0.06/0.19 % (221949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (221949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (221949)CaDiCaL version: 2.1.3
% 0.06/0.19 % (221949)Termination reason: Refutation
% 0.06/0.19 % (221949)Time elapsed: 0.004 s
% 0.06/0.19 % (221949)Peak memory usage: 13 MB
% 0.06/0.19 % (221949)Instructions burned: 14 (million)
% 0.06/0.19 % (221941)Success in time 0.045 s
% 0.06/0.19 % Vampire exiting
%------------------------------------------------------------------------------