%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU574^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:32:30 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 84 ( 31 unt; 0 typ; 3 def)
% Number of atoms : 628 ( 155 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 749 ( 26 ~; 73 |; 12 &; 503 @)
% ( 3 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 10 con; 0-4 aty)
% ( 41 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 134 ( 0 sgn 78 !; 4 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setext: $o ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
subsetE: $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: $i > $i > $i ).
thf(func_def_18,type,
sK3: $i > $i > $i ).
thf(f1,axiom,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(f2,axiom,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f3,conjecture,
( setext
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(f4,negated_conjecture,
~ ( setext
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X0 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setext
=> ( subsetE
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setext = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( subsetE = $true )
& ( setext = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true ) )
& ( subsetE = $true )
& ( setext = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( sK0 != sK1 )
& ( $true
= ( subset @ sK1 @ sK0 ) )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( subsetE = $true )
& ( setext = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
setext = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
subsetE = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y2 @ Y1 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ Y0 @ X2 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X3 @ X2 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK3 @ X1 @ X2 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK3 @ X1 @ X2 ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) ) )
| ( $false
= ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) )
| ( X1 = X2 ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f44]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f53,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f18,f32]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f19,f32]) ).
thf(f56,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f124,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK2 @ X0 @ sK1 ) @ sK1 ) )
| ( sK1 = X0 ) ),
inference(constrained_superposition,[],[f57,f45]) ).
thf(f127,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK2 @ X0 @ sK1 ) @ sK1 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f156,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ sK1 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(constrained_superposition,[],[f57,f47]) ).
thf(f159,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK3 @ X0 @ sK1 ) @ sK0 ) )
| ( $false
= ( in @ ( sK2 @ X0 @ sK1 ) @ X0 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f186,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) )
| ( sK0 = sK1 )
| ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) )
| ( sK0 = sK1 ) ),
inference(constrained_superposition,[],[f127,f46]) ).
thf(f197,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) )
| ( sK0 = sK1 ) ),
inference(duplicate_literal_removal,[],[f186]) ).
thf(f198,plain,
( ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) )
| ( sK0 = sK1 ) ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f205,definition,
( spl4_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f207,plain,
( ( sK0 = sK1 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f209,definition,
( spl4_2
<=> ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f211,plain,
( ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f213,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f198,f209,f205]) ).
thf(f219,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f56,f211]) ).
thf(f220,plain,
( ( $true
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f321,plain,
( ( sK0 != sK0 )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f20,f207]) ).
thf(f332,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f333,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f332]) ).
thf(f377,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ( sK0 = sK1 )
| ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ( sK0 = sK1 ) ),
inference(constrained_superposition,[],[f159,f48]) ).
thf(f393,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ( sK0 = sK1 ) ),
inference(duplicate_literal_removal,[],[f377]) ).
thf(f394,plain,
( ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ( sK0 = sK1 ) ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f399,definition,
( spl4_4
<=> ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f401,plain,
( ( $false
= ( in @ ( sK2 @ sK0 @ sK1 ) @ sK0 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f399]) ).
thf(f403,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[],[f394,f399,f205]) ).
thf(f407,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f401,f220]) ).
thf(f425,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f426,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f425]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f213]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f333]) ).
cnf(s7,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f403]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f426]) ).
cnf(s10,plain,
spl4_4,
inference(rat,[],[s7,s5]) ).
cnf(s11,plain,
~ spl4_2,
inference(rat,[],[s9,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s11,s5]) ).
thf(f430,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU574^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n026.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:54:12 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.31 % (630575)Will run a generic schedule for satisfiability detection.
% 0.22/0.31 % (630586)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3444829171:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.22/0.31 % (630584)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3941902559:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.31 % (630581)% WARNING: option uhcvi not known.
% 0.22/0.31 % (630584)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % (630580)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1225178542_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.31 % (630581)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=802752128:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.31 % (630582)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1086475284:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.31 % (630581)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % Exception at run slice level
% 0.22/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.31 % (630581)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.31 % (630583)dis+10_1_sil=32000:sp=arity:random_seed=3804559064:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.31 % (630585)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3693518936:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.22/0.31 % (630586) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-630575-630586"...
% 0.22/0.31 % (630586)...printing done.
% 0.22/0.31 % (630586)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (630586)------------------------------
% 0.22/0.31 % (630586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (630586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (630586)CaDiCaL version: 2.1.3
% 0.22/0.31 % (630586)Termination reason: Refutation
% 0.22/0.31 % (630586)Time elapsed: 0.016 s
% 0.22/0.31 % (630586)Peak memory usage: 12 MB
% 0.22/0.31 % (630586)Instructions burned: 30 (million)
% 0.22/0.31 % (630575)Success in time 0.042 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------