%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL588^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:14:24 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 47 unt; 0 typ; 2 def)
% Number of atoms : 431 ( 74 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 526 ( 47 ~; 51 |; 15 &; 358 @)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 37 usr; 8 con; 0-4 aty)
% ( 20 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 146 ( 0 sgn 17 !; 2 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
a: $i > $o ).
thf(func_def_21,type,
b: $i > $o ).
thf(func_def_22,type,
r: $i > $i > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_34,type,
vOR: $o > $o > $o ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f9,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mdia) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X0 @ X2 @ X3 )
& ( X1 @ X3 ) ) )
= mdia ),
inference(rectify,[],[f9]) ).
thf(f19,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f23,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f25,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f26,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f32,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f33,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f35,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f40,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f43,plain,
~ ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f44,plain,
( ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f46,plain,
( ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(flattening,[],[f44]) ).
thf(f48,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f49,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f50,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f51,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f54,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f56,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f60,plain,
( ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f65,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f54,f49,f56]) ).
thf(f67,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 @ Y3 ) ) )
@ r
@ a )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ b ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ a
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f60,f51,f65,f65,f50,f48,f48,f65]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( a @ Y1 )
& ( r @ Y0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ~ ( ?? @ $i
@ ^ [Y1: $i] :
( ( a @ Y1 )
& ( r @ Y0 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( $false
= ( ( r @ sK0 @ sK1 )
=> ( ( b @ sK1 )
| ~ ( a @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
( $false
= ( ( b @ sK1 )
| ~ ( a @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $true
= ( r @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f77,plain,
( $false
= ( ~ ( a @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( $false
= ( b @ sK1 ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f79,plain,
( ( a @ sK1 )
= $true ),
inference(not_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f71]) ).
thf(f81,plain,
( ( ( ~ ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( a @ Y0 )
& ( r @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( a @ X1 )
& ( r @ sK0 @ X1 ) ) )
| ( ( ( r @ sK0 @ X2 )
=> ( b @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X1: $i] :
( ( ( ( r @ sK0 @ X2 )
=> ( b @ X2 ) )
= $true )
| ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( a @ X1 ) ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK0 @ X2 )
= $false )
| ( $false
= ( a @ X1 ) )
| ( $false
= ( r @ sK0 @ X1 ) )
| ( $true
= ( b @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f89,definition,
( spl2_1
<=> ! [X1: $i] :
( ( $false
= ( a @ X1 ) )
| ( $false
= ( r @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f90,plain,
( ! [X1: $i] :
( ( $false
= ( r @ sK0 @ X1 ) )
| ( $false
= ( a @ X1 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f92,definition,
( spl2_2
<=> ! [X2: $i] :
( ( ( r @ sK0 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f93,plain,
( ! [X2: $i] :
( ( ( r @ sK0 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f94,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f87,f92,f89]) ).
thf(f96,plain,
( ( $true
= ( b @ sK1 ) )
| ( $false = $true )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f93,f76]) ).
thf(f98,plain,
( ( $true
= ( b @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f102,plain,
( ( $false = $true )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f98,f78]) ).
thf(f103,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f104,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f103]) ).
thf(f106,plain,
( ( $false = $true )
| ( ( a @ sK1 )
= $false )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f76,f90]) ).
thf(f108,plain,
( ( ( a @ sK1 )
= $false )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f112,plain,
( ( $false = $true )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f108,f79]) ).
thf(f113,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f114,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f114]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL588^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 09:07:57 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.09/0.28 % (323568)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.28 % (323576)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1580523011:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.28 % (323576)Refutation not found, incomplete strategy
% 0.09/0.28 % (323576)------------------------------
% 0.09/0.28 % (323576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (323576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (323576)CaDiCaL version: 2.1.3
% 0.09/0.28 % (323576)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.28 % (323576)Time elapsed: 0.001 s
% 0.09/0.28 % (323576)Peak memory usage: 12 MB
% 0.09/0.28 % (323576)Instructions burned: 4 (million)
% 0.09/0.28 % (323576)------------------------------
% 0.09/0.28 % (323576)------------------------------
% 0.09/0.28 % (323574)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2265108057:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.28 % (323575)lrs+10_16_si=on:nwc=1.5:random_seed=3608406409:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.28 % (323574) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-323568-323574"...
% 0.09/0.28 % (323580)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.28 % (323580)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
% 0.09/0.28 % (323574)...printing done.
% 0.09/0.28 % (323574)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.29 % (323574)------------------------------
% 0.09/0.29 % (323574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.29 % (323574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.29 % (323574)CaDiCaL version: 2.1.3
% 0.09/0.29 % (323574)Termination reason: Refutation
% 0.09/0.29 % (323574)Time elapsed: 0.014 s
% 0.09/0.29 % (323574)Peak memory usage: 13 MB
% 0.09/0.29 % (323574)Instructions burned: 9 (million)
% 0.09/0.29 % (323568)Success in time 0.057 s
% 0.09/0.29 % Vampire exiting
%------------------------------------------------------------------------------