%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU817^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:31:40 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 648 ( 139 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 968 ( 50 ~; 57 |; 68 &; 618 @)
% ( 3 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 12 con; 0-4 aty)
% ( 54 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 177 ( 93 ^; 70 !; 14 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetE: $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_9,type,
wellorderedByIn: $i > $o ).
thf(func_def_10,type,
ordinal: $i > $o ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_31,type,
sK6: $i > $i ).
thf(f1,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(f2,axiom,
( subsetE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(f3,axiom,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(f4,axiom,
( ( ^ [X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X2 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 = X3 )
| ( in @ X3 @ X2 )
| ( in @ X2 @ X3 ) ) ) )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ( in @ X1 @ X2 )
& ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) )
= stricttotalorderedByIn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(f5,axiom,
( wellorderedByIn
= ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ( in @ X2 @ X1 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(f6,axiom,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(f7,conjecture,
( subsetE
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(f8,negated_conjecture,
~ ( subsetE
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( wellorderedByIn
= ( ^ [X0: $i] :
( ( stricttotalorderedByIn @ X0 )
& ! [X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( nonempty @ X1 )
=> ? [X2: $i] :
( ( in @ X2 @ X1 )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
| ( X2 = X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( subsetE
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f12,plain,
~ ( ( subsetE = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ^ [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) )
& ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 = X3 )
| ( in @ X3 @ X2 )
| ( in @ X2 @ X3 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ( ( ( in @ X4 @ X5 )
& ( in @ X5 @ X6 ) )
=> ( in @ X4 @ X6 ) ) ) ) ) ) )
= stricttotalorderedByIn ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f16,plain,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
inference(rectify,[],[f6]) ).
thf(f17,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f23,plain,
( ( subsetE = $true )
& ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
!= ( subset @ X2 @ X0 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f25,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( subset @ X2 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( subset @ X2 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 ) )
& ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
& ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
= ( subset @ sK1 @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
!= ( in @ sK2 @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f27]) ).
thf(f29,plain,
( ( subsetE = $true )
& ( ( ordinal @ sK3 )
= $true )
& ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK4 @ sK5 )
= $true )
& ( ( in @ sK4 @ sK3 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f23]) ).
thf(f30,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( stricttotalorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f31,plain,
( stricttotalorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( in @ Y2 @ Y1 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ~ ( in @ Y1 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f36,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f37,plain,
( ( in @ sK4 @ sK3 )
!= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f38,plain,
( ( in @ sK4 @ sK5 )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
( ( ordinal @ sK3 )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
subsetE = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f42,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f43,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f46,plain,
( wellorderedByIn
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( ^ [Y2: $i] : ( emptyset != Y2 )
@ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y2 = Y3 )
| ( in @ Y2 @ Y3 ) ) ) )
& ( in @ Y2 @ Y1 ) ) ) ) ) )
& ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( ( in @ Y3 @ Y4 )
& ( in @ Y2 @ Y3 ) )
=> ( in @ Y2 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( in @ Y3 @ Y2 )
| ( Y2 = Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ~ ( in @ Y2 @ Y2 ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f30,f42,f31]) ).
thf(f47,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) )
& ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 )
| ( Y3 = Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 ) )
@ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f43,f46,f36]) ).
thf(f48,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true != $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f35,f41]) ).
thf(f52,plain,
( ( ^ [Y0: $i] :
( ( ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( ^ [Y3: $i] : ( emptyset != Y3 )
@ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y3 = Y4 )
| ( in @ Y3 @ Y4 ) ) ) )
& ( in @ Y3 @ Y2 ) ) ) ) ) )
& ( ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y2 )
=> ( ( ( in @ Y4 @ Y5 )
& ( in @ Y3 @ Y4 ) )
=> ( in @ Y3 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( in @ Y3 @ Y4 )
| ( in @ Y4 @ Y3 )
| ( Y3 = Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ~ ( in @ Y3 @ Y3 ) ) ) )
@ Y1 ) )
@ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK3 )
= $true ),
inference(definition_unfolding,[],[f40,f47]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f54,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ sK3 ) )
=> ( ( emptyset != Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 = Y2 )
| ( in @ Y1 @ Y2 ) ) ) )
& ( in @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK3 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK3 )
=> ( ( in @ Y0 @ Y1 )
| ( in @ Y1 @ Y0 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ~ ( in @ Y0 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( subset @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f55,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( subset @ Y0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f102,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( subset @ Y0 @ sK3 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f103,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK3 )
=> ( subset @ X1 @ sK3 ) )
= $true ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( ( subset @ X1 @ sK3 )
= $true )
| ( $false
= ( in @ X1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ sK3 ) )
| ( $true != $true )
| ( $false
= ( in @ X0 @ sK3 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f53,f104]) ).
thf(f106,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ sK3 ) )
| ( $false
= ( in @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f107,plain,
( ( ( in @ sK4 @ sK3 )
= $true )
| ( $true != $true )
| ( $false
= ( in @ sK5 @ sK3 ) ) ),
inference(constrained_superposition,[],[f106,f38]) ).
thf(f108,plain,
( ( ( in @ sK4 @ sK3 )
= $true )
| ( $false
= ( in @ sK5 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f109,plain,
( $false
= ( in @ sK5 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f108,f37]) ).
thf(f110,plain,
$false = $true,
inference(backward_demodulation,[],[f39,f109]) ).
thf(f111,plain,
$false,
inference(trivial_inequality_removal,[],[f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU817^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.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 14:34:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.29 % (1370056)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (1370066)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4232393228:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (1370066) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1370056-1370066"...
% 0.23/0.29 % (1370066)...printing done.
% 0.23/0.29 % (1370066)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (1370066)------------------------------
% 0.23/0.30 % (1370066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1370066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1370066)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1370066)Termination reason: Refutation
% 0.23/0.30 % (1370066)Time elapsed: 0.004 s
% 0.23/0.30 % (1370066)Peak memory usage: 13 MB
% 0.23/0.30 % (1370066)Instructions burned: 13 (million)
% 0.23/0.30 % (1370056)Success in time 0.033 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------