%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET649^3 : 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 : n018.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 08:23:26 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 47 unt; 0 typ; 2 def)
% Number of atoms : 347 ( 75 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 394 ( 19 ~; 16 |; 21 &; 280 @)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 57 usr; 8 con; 0-4 aty)
% ( 16 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 133 ( 0 sgn 30 !; 10 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_17,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_18,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_20,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_22,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_29,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_30,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_31,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_32,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_33,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $o ).
thf(func_def_53,type,
sK1: $i > $o ).
thf(func_def_54,type,
sK2: $i > $i > $o ).
thf(f12,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subset ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f15,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ( X1 @ X3 ) ) )
= cartesian_product ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',cartesian_product) ).
thf(f18,axiom,
( sub_rel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X3: $i,X2: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',sub_rel) ).
thf(f28,axiom,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_codomain) ).
thf(f29,axiom,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(f36,conjecture,
! [X2: $i > $o,X1: $i > $o,X0: $i > $i > $o] :
( ( ( subset @ ( rel_domain @ X0 ) @ X1 )
& ( subset @ ( rel_codomain @ X0 ) @ X2 ) )
=> ( sub_rel @ X0 @ ( cartesian_product @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X2: $i > $o,X1: $i > $o,X0: $i > $i > $o] :
( ( ( subset @ ( rel_domain @ X0 ) @ X1 )
& ( subset @ ( rel_codomain @ X0 ) @ X2 ) )
=> ( sub_rel @ X0 @ ( cartesian_product @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f54,plain,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f55,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f62,plain,
( ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= subset ),
inference(rectify,[],[f12]) ).
thf(f63,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ( X1 @ X3 ) ) )
= cartesian_product ),
inference(rectify,[],[f15]) ).
thf(f65,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f69,plain,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f29]) ).
thf(f70,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f90,plain,
( sub_rel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f91,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f95,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $i > $o] :
( ( ( subset @ ( rel_domain @ X2 ) @ X1 )
& ( subset @ ( rel_codomain @ X2 ) @ X0 ) )
=> ( sub_rel @ X2 @ ( cartesian_product @ X1 @ X0 ) ) ),
inference(rectify,[],[f37]) ).
thf(f96,plain,
~ ! [X1: $i > $o,X0: $i > $o,X2: $i > $i > $o] :
( ( ( ( subset @ ( rel_domain @ X2 ) @ X1 )
= $true )
& ( ( subset @ ( rel_codomain @ X2 ) @ X0 )
= $true ) )
=> ( ( sub_rel @ X2 @ ( cartesian_product @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f95]) ).
thf(f101,plain,
? [X1: $i > $o,X0: $i > $o,X2: $i > $i > $o] :
( ( ( sub_rel @ X2 @ ( cartesian_product @ X1 @ X0 ) )
!= $true )
& ( ( subset @ ( rel_domain @ X2 ) @ X1 )
= $true )
& ( ( subset @ ( rel_codomain @ X2 ) @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f96]) ).
thf(f102,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $i > $o] :
( ( ( sub_rel @ X2 @ ( cartesian_product @ X1 @ X0 ) )
!= $true )
& ( ( subset @ ( rel_domain @ X2 ) @ X1 )
= $true )
& ( ( subset @ ( rel_codomain @ X2 ) @ X0 )
= $true ) ),
inference(flattening,[],[f101]) ).
thf(f103,plain,
( ( ( sub_rel @ sK2 @ ( cartesian_product @ sK1 @ sK0 ) )
!= $true )
& ( ( subset @ ( rel_domain @ sK2 ) @ sK1 )
= $true )
& ( ( subset @ ( rel_codomain @ sK2 ) @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f102]) ).
thf(f119,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f121,plain,
( ( subset @ ( rel_codomain @ sK2 ) @ sK0 )
= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f122,plain,
( ( subset @ ( rel_domain @ sK2 ) @ sK1 )
= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f123,plain,
( ( sub_rel @ sK2 @ ( cartesian_product @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f126,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f130,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f134,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f138,plain,
( cartesian_product
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f147,plain,
( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y2 ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[],[f123,f134,f138]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK2 )
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f122,f130,f119]) ).
thf(f149,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ sK2 )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f121,f130,f126]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK2 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( sK2 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK2 @ Y0 @ X1 ) )
=> ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] : ( sK2 @ Y0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 )
= $true )
| ( ( ^ [Y0: $i] : ( sK2 @ Y0 @ X1 )
@ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X2 @ X1 ) )
| ( ( sK0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK0 @ Y1 )
& ( sK1 @ Y0 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f157,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( ( sK0 @ Y1 )
& ( sK1 @ Y0 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ sK3 @ Y0 )
=> ( ( sK0 @ Y0 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK2 @ sK3 @ Y0 )
=> ( ( sK0 @ Y0 )
& ( sK1 @ sK3 ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( ( sK2 @ sK3 @ sK4 )
=> ( ( sK0 @ sK4 )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( $false
= ( ( sK0 @ sK4 )
& ( sK1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( sK2 @ sK3 @ sK4 )
= $true ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( sK2 @ Y0 ) )
=> ( sK1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f165,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ?? @ $i @ ( sK2 @ Y0 ) )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( ?? @ $i @ ( sK2 @ X1 ) )
=> ( sK1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i @ ( sK2 @ X1 ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f170,definition,
( spl5_1
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f172,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f174,definition,
( spl5_2
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f176,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f177,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f163,f174,f170]) ).
thf(f179,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f155,f162]) ).
thf(f181,plain,
( $true
= ( sK0 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f185,plain,
( ( $false = $true )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f181,f176]) ).
thf(f186,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f187,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f186]) ).
thf(f190,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f162,f168]) ).
thf(f192,plain,
( ( sK1 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f196,plain,
( ( $false = $true )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f192,f172]) ).
thf(f197,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f198,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f197]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f187]) ).
cnf(s5,plain,
~ spl5_1,
inference(sat_conversion,[],[f198]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f199,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET649^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.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 13:42:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.29 % (82573)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (82581)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=936705118: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)
% 0.21/0.29 % (82578)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3672853611:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (82579)lrs+10_16_si=on:nwc=1.5:random_seed=897066341:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (82580)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2912191957:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (82582)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3527977042:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (82584)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (82584)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
% 0.21/0.29 % (82583)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=828666136:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (82580)Instruction limit reached!
% 0.21/0.29 % (82580)------------------------------
% 0.21/0.29 % (82580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (82580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (82580)CaDiCaL version: 2.1.3
% 0.21/0.29 % (82580)Termination reason: Instruction limit
% 0.21/0.29 % (82580)Termination phase: Function definition elimination
% 0.21/0.29 % (82580)Time elapsed: 0.003 s
% 0.21/0.29 % (82580)Peak memory usage: 10 MB
% 0.21/0.29 % (82580)Instructions burned: 6 (million)
% 0.21/0.29 % (82584)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=2377568232:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (82579) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-82573-82579"...
% 0.21/0.29 % (82578) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-82573-82578"...
% 0.21/0.29 % (82583) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-82573-82583"...
% 0.21/0.29 % (82579)...printing done.
% 0.21/0.29 % (82578)...printing done.
% 0.21/0.29 % (82578)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (82578)------------------------------
% 0.21/0.29 % (82578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (82578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (82578)CaDiCaL version: 2.1.3
% 0.21/0.29 % (82578)Termination reason: Refutation
% 0.21/0.29 % (82578)Time elapsed: 0.008 s
% 0.21/0.29 % (82578)Peak memory usage: 13 MB
% 0.21/0.29 % (82578)Instructions burned: 13 (million)
% 0.21/0.29 % (82573)Success in time 0.051 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------