%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU611^2 : 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 : n007.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 08:30:19 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 104 ( 28 unt; 0 typ; 5 def)
% Number of atoms : 885 ( 236 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 910 ( 136 ~; 130 |; 45 &; 528 @)
% ( 12 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 21 con; 0-4 aty)
% Number of variables : 193 ( 0 sgn 119 !; 30 ?; 193 :)
% 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,
dsetconstrEL: $o ).
thf(func_def_4,type,
dsetconstrER: $o ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_6,type,
binunionE: $o ).
thf(func_def_7,type,
symdiff: $i > $i > $i ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK0: $i > $o ).
thf(func_def_21,type,
sK5: $i > $o ).
thf(func_def_25,type,
sK9: $o ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f3,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) )
= binunionE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiff) ).
thf(f5,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(f6,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X2 )
=> ( ( in @ X1 @ X0 )
=> X3 ) )
=> X3 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X2: $i,X1: $i > $o] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ X0 @ X1 )
| ( in @ X0 @ X2 ) ) )
= binunionE ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( ( in @ X0 @ X2 )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f14,plain,
( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ( in @ X2 @ X0 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(flattening,[],[f8]) ).
thf(f18,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
( ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 )
| ( $true
= ( in @ X1 @ X2 ) ) ) ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( dsetconstrEL = $true )
<=> ! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f21,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f22,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( binunionE = $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f24,plain,
( ( ( dsetconstrEL = $true )
| ? [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) )
& ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[],[f20]) ).
thf(f25,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X1 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X5 @ X4 ) )
& ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X1 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK5 @ sK4 ) )
& ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f28]) ).
thf(f30,plain,
( ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( ( in @ X2 @ X1 )
!= $true )
| ( $true = X3 )
| ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f31,plain,
( ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( binunionE = $true )
& ( $true
= ( in @ sK8 @ ( symdiff @ sK6 @ sK7 ) ) )
& ( sK9 != $true )
& ( ( sK9 = $true )
| ( $true
= ( in @ sK8 @ sK7 ) )
| ( $true
!= ( in @ sK8 @ sK6 ) ) )
& ( ( $true
!= ( in @ sK8 @ sK7 ) )
| ( sK9 = $true )
| ( $true
= ( in @ sK8 @ sK6 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f30]) ).
thf(f32,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
& ( $true
= ( in @ X4 @ ( binunion @ X5 @ X3 ) ) )
& ( $true
!= ( in @ X4 @ X3 ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( $true
!= ( in @ sK11 @ sK12 ) )
& ( $true
= ( in @ sK11 @ ( binunion @ sK12 @ sK10 ) ) )
& ( $true
!= ( in @ sK11 @ sK10 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f33]) ).
thf(f35,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f40,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( X2 @ X1 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f42,plain,
( ( $true
!= ( in @ sK8 @ sK7 ) )
| ( $true
= ( in @ sK8 @ sK6 ) )
| ( sK9 = $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f43,plain,
( ( $true
!= ( in @ sK8 @ sK6 ) )
| ( $true
= ( in @ sK8 @ sK7 ) )
| ( sK9 = $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
sK9 != $true,
inference(cnf_transformation,[],[f31]) ).
thf(f45,plain,
( $true
= ( in @ sK8 @ ( symdiff @ sK6 @ sK7 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f46,plain,
binunionE = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f47,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f48,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f31]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( binunionE != $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f57,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f35,f48]) ).
thf(f58,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(definition_unfolding,[],[f40,f47]) ).
thf(f61,plain,
( $true
= ( in @ sK8
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) )
@ sK6
@ sK7 ) ) ),
inference(definition_unfolding,[],[f45,f41]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true != $true )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(definition_unfolding,[],[f52,f46]) ).
thf(f66,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f67,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f68,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
!= $true )
| ( $true
= ( in @ X5 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f70,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $true
= ( in @ sK8
@ ( dsetconstr @ ( binunion @ sK6 @ sK7 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK7 )
| ~ ( in @ Y0 @ sK6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f73,definition,
( spl13_1
<=> ( $true
= ( in @ sK8 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
thf(f74,plain,
( ( $true
= ( in @ sK8 @ sK7 ) )
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,definition,
( spl13_2
<=> ( sK9 = $true ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
thf(f77,plain,
( ( sK9 = $true )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f79,definition,
( spl13_3
<=> ( $true
= ( in @ sK8 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
!= ( in @ sK8 @ sK6 ) )
| spl13_3 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f81,plain,
( spl13_1
| spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f43,f79,f76,f73]) ).
thf(f83,plain,
( ( $true
= ( in @ sK8 @ sK6 ) )
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f84,plain,
( spl13_2
| ~ spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f42,f79,f73,f76]) ).
thf(f85,plain,
( ( $true != $true )
| ( $true
= ( in @ sK8 @ ( binunion @ sK6 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f68,f71]) ).
thf(f86,plain,
( ( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK7 )
| ~ ( in @ Y0 @ sK6 ) )
@ sK8 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f70,f71]) ).
thf(f87,plain,
( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK7 )
| ~ ( in @ Y0 @ sK6 ) )
@ sK8 ) ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f88,plain,
( $true
= ( ~ ( in @ sK8 @ sK7 )
| ~ ( in @ sK8 @ sK6 ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
( ( ( ~ ( in @ sK8 @ sK6 ) )
= $true )
| ( ( ~ ( in @ sK8 @ sK7 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( ( in @ sK8 @ sK6 )
= $false )
| ( ( ~ ( in @ sK8 @ sK7 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( ( in @ sK8 @ sK6 )
= $false )
| ( $false
= ( in @ sK8 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( $true
= ( in @ sK8 @ ( binunion @ sK6 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f94,definition,
( spl13_4
<=> ( $false
= ( in @ sK8 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
thf(f95,plain,
( ( $false
= ( in @ sK8 @ sK7 ) )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,definition,
( spl13_5
<=> ( ( in @ sK8 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
thf(f98,plain,
( ( ( in @ sK8 @ sK6 )
= $false )
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f99,plain,
( spl13_4
| spl13_5 ),
inference(avatar_split_clause,[],[f91,f97,f94]) ).
thf(f101,plain,
( ( $true
= ( in @ sK8 @ sK7 ) )
| ( $true != $true )
| ( $true
= ( in @ sK8 @ sK6 ) ) ),
inference(constrained_superposition,[],[f66,f92]) ).
thf(f102,plain,
( ( $true
= ( in @ sK8 @ sK7 ) )
| ( $true
= ( in @ sK8 @ sK6 ) ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f103,plain,
( ( $true
= ( in @ sK8 @ sK7 ) )
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f102,f80]) ).
thf(f107,plain,
( spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f103,f79,f73]) ).
thf(f109,plain,
( ( $true = $false )
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_demodulation,[],[f83,f98]) ).
thf(f110,plain,
( $false
| ~ spl13_3
| ~ spl13_5 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f111,plain,
( ~ spl13_3
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f110]) ).
thf(f113,plain,
( $false
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f77,f44]) ).
thf(f114,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[],[f113]) ).
thf(f118,plain,
( ( $true = $false )
| ~ spl13_1
| ~ spl13_4 ),
inference(backward_demodulation,[],[f74,f95]) ).
thf(f119,plain,
( $false
| ~ spl13_1
| ~ spl13_4 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f120,plain,
( ~ spl13_1
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[],[f119]) ).
cnf(s1,plain,
( spl13_1
| spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
( ~ spl13_1
| spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
( spl13_4
| spl13_5 ),
inference(sat_conversion,[],[f99]) ).
cnf(s5,plain,
( spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f107]) ).
cnf(s6,plain,
( ~ spl13_3
| ~ spl13_5 ),
inference(sat_conversion,[],[f111]) ).
cnf(s7,plain,
~ spl13_2,
inference(sat_conversion,[],[f114]) ).
cnf(s9,plain,
( ~ spl13_1
| ~ spl13_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( ~ spl13_1
| spl13_3 ),
inference(rat,[],[s2,s7]) ).
cnf(s11,plain,
( spl13_1
| ~ spl13_3 ),
inference(rat,[],[s1,s7]) ).
cnf(s12,plain,
spl13_1,
inference(rat,[],[s11,s5]) ).
cnf(s13,plain,
~ spl13_4,
inference(rat,[],[s9,s12]) ).
cnf(s14,plain,
spl13_3,
inference(rat,[],[s10,s12]) ).
cnf(s15,plain,
spl13_5,
inference(rat,[],[s3,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s6,s15,s14]) ).
thf(f121,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU611^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n007.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:56:05 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.29 % (3405059)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (3405069)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3744189610:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (3405069) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3405059-3405069"...
% 0.22/0.29 % (3405070)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (3405070)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
% 0.22/0.29 % (3405069)...printing done.
% 0.22/0.29 % (3405069)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (3405069)------------------------------
% 0.22/0.29 % (3405069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (3405069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (3405069)CaDiCaL version: 2.1.3
% 0.22/0.29 % (3405069)Termination reason: Refutation
% 0.22/0.29 % (3405069)Time elapsed: 0.004 s
% 0.22/0.29 % (3405069)Peak memory usage: 13 MB
% 0.22/0.29 % (3405069)Instructions burned: 10 (million)
% 0.22/0.29 % (3405059)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------