%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU508^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:29:51 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 22 unt; 0 typ; 9 def)
% Number of atoms : 581 ( 143 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 613 ( 117 ~; 106 |; 27 &; 325 @)
% ( 17 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 19 con; 0-4 aty)
% Number of variables : 136 ( 0 sgn 81 !; 21 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
dsetconstrER: $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK1: $i > $o ).
thf(func_def_13,type,
sK4: $i > $o ).
thf(func_def_16,type,
sK7: $i > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f3,conjecture,
( dsetconstrI
=> ( dsetconstrER
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
<=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrER
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
<=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( dsetconstrI = $true )
<=> ! [X1: $i,X2: $i,X0: $i > $o] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( X0 @ X1 )
= $true )
=> ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( dsetconstrI
=> ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
<=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( dsetconstrI = $true )
=> ( ( dsetconstrER = $true )
=> ! [X2: $i > $o,X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= ( X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X2: $i > $o,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= ( X2 @ X0 ) ) )
& ( dsetconstrER = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ? [X1: $i,X2: $i > $o,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= ( X2 @ X0 ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
<=> ! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ( dsetconstrI = $true )
<=> ! [X1: $i,X2: $i,X0: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f15,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f17,plain,
( ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( ( sK1 @ sK2 )
!= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
thf(f18,plain,
( ( ( dsetconstrER = $true )
| ? [X2: $i,X1: $i > $o,X0: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f19,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK4 @ sK3 )
!= $true )
& ( ( in @ sK3
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f19]) ).
thf(f21,plain,
( ( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( ( sK7 @ sK8 )
= $true )
& ( ( in @ sK8 @ sK6 )
= $true )
& ( ( in @ sK8
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f22]) ).
thf(f24,plain,
( ( sK1 @ sK2 )
!= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( X4 @ X3 )
= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f34,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
!= $true )
| ( dsetconstrI != $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
= $true )
| ( dsetconstrI != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f39,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f24]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f24]) ).
thf(f41,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f43,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( dsetconstrER != $true )
| ( ( X4 @ X3 )
= $true )
| ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f45,definition,
( spl9_1
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f48,plain,
spl9_1,
inference(avatar_split_clause,[],[f26,f45]) ).
thf(f64,definition,
( spl9_5
<=> ( dsetconstrI = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f69,definition,
( spl9_6
<=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
= $true )
| ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f70,plain,
( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f71,plain,
( spl9_6
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f38,f64,f69]) ).
thf(f73,definition,
( spl9_7
<=> ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f75,plain,
( ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f77,definition,
( spl9_8
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f79,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
( spl9_7
| spl9_8 ),
inference(avatar_split_clause,[],[f41,f77,f73]) ).
thf(f82,definition,
( spl9_9
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f84,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl9_10
<=> ( ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f88,plain,
( ( ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f89,plain,
( spl9_9
| spl9_10 ),
inference(avatar_split_clause,[],[f42,f86,f82]) ).
thf(f95,plain,
spl9_5,
inference(avatar_split_clause,[],[f27,f64]) ).
thf(f97,definition,
( spl9_12
<=> ! [X4: $i > $o,X5: $i,X3: $i] :
( ( ( X4 @ X3 )
= $true )
| ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
thf(f98,plain,
( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) )
!= $true )
| ( ( X4 @ X3 )
= $true ) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f99,plain,
( ~ spl9_1
| spl9_12 ),
inference(avatar_split_clause,[],[f43,f97,f45]) ).
thf(f101,definition,
( spl9_13
<=> ( ( in @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f103,plain,
( ( ( in @ sK2 @ sK0 )
= $true )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f104,plain,
spl9_13,
inference(avatar_split_clause,[],[f25,f101]) ).
thf(f114,plain,
( ( ( in @ sK2 @ sK0 )
!= $true )
| ( ( sK1 @ sK2 )
!= $true )
| ( $false = $true )
| ~ spl9_6
| ~ spl9_7 ),
inference(superposition,[],[f75,f70]) ).
thf(f117,plain,
( ( ( in @ sK2 @ sK0 )
!= $true )
| ( ( sK1 @ sK2 )
!= $true )
| ~ spl9_6
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f119,plain,
( ( ( sK1 @ sK2 )
!= $true )
| ~ spl9_6
| ~ spl9_7
| ~ spl9_13 ),
inference(forward_subsumption_resolution,[],[f117,f103]) ).
thf(f122,plain,
( $false
| ~ spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_13 ),
inference(forward_subsumption_resolution,[],[f119,f84]) ).
thf(f123,plain,
( ~ spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f126,plain,
( ( $false = $true )
| ~ spl9_8
| ~ spl9_9 ),
inference(superposition,[],[f84,f79]) ).
thf(f129,plain,
( $false
| ~ spl9_8
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f130,plain,
( ~ spl9_8
| ~ spl9_9 ),
inference(avatar_contradiction_clause,[],[f129]) ).
thf(f133,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $true != $true )
| ~ spl9_10
| ~ spl9_12 ),
inference(superposition,[],[f98,f88]) ).
thf(f134,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl9_10
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f135,plain,
( ( $false = $true )
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(forward_demodulation,[],[f134,f79]) ).
thf(f136,plain,
( $false
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f137,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f136]) ).
thf(f138,plain,
( spl9_9
| ~ spl9_10
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f134,f97,f86,f82]) ).
cnf(s1,plain,
spl9_1,
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
( ~ spl9_5
| spl9_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
( spl9_7
| spl9_8 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( spl9_9
| spl9_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s9,plain,
spl9_5,
inference(sat_conversion,[],[f95]) ).
cnf(s10,plain,
( ~ spl9_1
| spl9_12 ),
inference(sat_conversion,[],[f99]) ).
cnf(s11,plain,
spl9_13,
inference(sat_conversion,[],[f104]) ).
cnf(s14,plain,
( ~ spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s16,plain,
( ~ spl9_8
| ~ spl9_9 ),
inference(sat_conversion,[],[f130]) ).
cnf(s17,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl9_9
| ~ spl9_10
| ~ spl9_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
spl9_6,
inference(rat,[],[s5,s9]) ).
cnf(s20,plain,
spl9_12,
inference(rat,[],[s10,s1]) ).
cnf(s21,plain,
~ spl9_8,
inference(rat,[],[s7,s16,s17,s20]) ).
cnf(s22,plain,
spl9_7,
inference(rat,[],[s6,s21]) ).
cnf(s23,plain,
~ spl9_9,
inference(rat,[],[s14,s11,s19,s22]) ).
cnf(s24,plain,
~ spl9_10,
inference(rat,[],[s18,s20,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s7,s24,s23]) ).
thf(f139,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU508^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:47:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.28 % (788604)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (788612)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=990073757: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)
% 0.21/0.28 % (788612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-788604-788612"...
% 0.21/0.28 % (788615)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (788615)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
% 0.21/0.28 % (788612)...printing done.
% 0.21/0.28 % (788612)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (788612)------------------------------
% 0.21/0.28 % (788612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (788612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (788612)CaDiCaL version: 2.1.3
% 0.21/0.28 % (788612)Termination reason: Refutation
% 0.21/0.28 % (788612)Time elapsed: 0.003 s
% 0.21/0.28 % (788612)Peak memory usage: 13 MB
% 0.21/0.28 % (788612)Instructions burned: 8 (million)
% 0.21/0.28 % (788604)Success in time 0.038 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------