%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU709^2 : 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 : 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 08:30:53 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 88 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 950 ( 311 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 1012 ( 122 ~; 123 |; 67 &; 632 @)
% ( 13 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 28 con; 0-4 aty)
% Number of variables : 243 ( 0 ^; 199 !; 44 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(func_def_5,type,
in__Cong: $o ).
thf(func_def_6,type,
secondinupair: $o ).
thf(func_def_7,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_8,type,
iftrue: $o ).
thf(func_def_9,type,
iffalse: $o ).
thf(func_def_14,type,
sK2: $o ).
thf(func_def_17,type,
sK5: $o ).
thf(func_def_23,type,
sK11: $o ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( in__Cong
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(f3,axiom,
! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= secondinupair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(f4,axiom,
( iftrue
= ( ! [X2: $i,X0: $i,X1: $o] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(f5,axiom,
! [X1: $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) )
= iffalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(f6,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2: $i,X1: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X2: $i,X1: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( if @ X2 @ X1 @ X0 @ X3 ) @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in__Cong = $true )
=> ( ( secondinupair = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ! [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( if @ X2 @ X1 @ X0 @ X3 ) @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( setadjoinIL = $true )
<=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X0
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) )
= iffalse ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( ! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) )
<=> ( iffalse = $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( iftrue
= ( ! [X0: $i,X1: $i,X2: $o] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( X2
=> ( ( if @ X1 @ X2 @ X0 @ X3 )
= X0 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
( ( iftrue = $true )
<=> ! [X1: $i,X2: $o,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true = X2 )
=> ( ( if @ X1 @ X2 @ X0 @ X3 )
= X0 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( in__Cong
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
<=> ( in @ X3 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
= ( in @ X3 @ X1 ) ) ) )
<=> ( in__Cong = $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= secondinupair ),
inference(rectify,[],[f3]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
<=> ( secondinupair = $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( iffalse = $true )
<=> ! [X0: $o,X2: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f21,plain,
( ? [X2: $i,X1: $o,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( if @ X2 @ X1 @ X0 @ X3 ) @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) )
& ( iffalse = $true )
& ( iftrue = $true )
& ( secondinupair = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f22,plain,
( ( secondinupair = $true )
& ( iffalse = $true )
& ( setadjoinIL = $true )
& ? [X2: $i,X1: $o,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( if @ X2 @ X1 @ X0 @ X3 ) @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) )
& ( iftrue = $true )
& ( in__Cong = $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
( ( iffalse = $true )
<=> ! [X0: $o,X2: $i,X1: $i] :
( ! [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( $true = X0 )
| ( $true
!= ( in @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f24,plain,
( ( iffalse = $true )
<=> ! [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( $true = X0 )
| ( $true
!= ( in @ X3 @ X2 ) ) ) ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
( ( iftrue = $true )
<=> ! [X1: $i,X2: $o,X0: $i] :
( ! [X3: $i] :
( ( ( if @ X1 @ X2 @ X0 @ X3 )
= X0 )
| ( $true != X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f26,plain,
( ( iftrue = $true )
<=> ! [X0: $i,X1: $i,X2: $o] :
( ! [X3: $i] :
( ( ( if @ X1 @ X2 @ X0 @ X3 )
= X0 )
| ( $true != X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f25]) ).
thf(f27,plain,
( ( in__Cong = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ X0 )
= ( in @ X3 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f28,plain,
( ( ( iftrue = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( if @ X1 @ X2 @ X0 @ X3 )
!= X0 )
& ( $true = X2 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $o] :
( ! [X3: $i] :
( ( ( if @ X1 @ X2 @ X0 @ X3 )
= X0 )
| ( $true != X2 )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( iftrue != $true ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f29,plain,
( ( ( iftrue = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( if @ X1 @ X2 @ X0 @ X3 )
!= X0 )
& ( $true = X2 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ! [X7: $i] :
( ( ( if @ X5 @ X6 @ X4 @ X7 )
= X4 )
| ( $true != X6 )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( iftrue != $true ) ) ),
inference(rectify,[],[f28]) ).
thf(f30,plain,
( ( ( iftrue = $true )
| ( ( sK0
!= ( if @ sK1 @ sK2 @ sK0 @ sK3 ) )
& ( $true = sK2 )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK0 @ sK1 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ! [X7: $i] :
( ( ( if @ X5 @ X6 @ X4 @ X7 )
= X4 )
| ( $true != X6 )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( iftrue != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f29]) ).
thf(f31,plain,
( ( secondinupair = $true )
& ( iffalse = $true )
& ( setadjoinIL = $true )
& ? [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( if @ X0 @ X1 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
!= $true ) ) )
& ( iftrue = $true )
& ( in__Cong = $true ) ),
inference(rectify,[],[f22]) ).
thf(f32,plain,
( ( secondinupair = $true )
& ( iffalse = $true )
& ( setadjoinIL = $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( $true
= ( in @ sK7 @ sK4 ) )
& ( $true
!= ( in @ ( if @ sK4 @ sK5 @ sK6 @ sK7 ) @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
& ( iftrue = $true )
& ( in__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f31]) ).
thf(f33,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f34,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f33]) ).
thf(f35,plain,
( ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK8 @ ( setadjoin @ sK8 @ sK9 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f34]) ).
thf(f36,plain,
( ( ( iffalse = $true )
| ? [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X3 )
& ( $true != X0 )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) )
& ( ! [X1: $i,X0: $o,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 )
| ( $true = X0 )
| ( $true
!= ( in @ X3 @ X2 ) ) ) )
| ( iffalse != $true ) ) ),
inference(nnf_transformation,[],[f24]) ).
thf(f37,plain,
( ( ( iffalse = $true )
| ? [X0: $i,X1: $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( if @ X2 @ X1 @ X0 @ X3 )
!= X3 )
& ( $true != X1 )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ! [X7: $i] :
( ( ( if @ X6 @ X5 @ X4 @ X7 )
= X7 )
| ( $true = X5 )
| ( $true
!= ( in @ X7 @ X6 ) ) ) )
| ( iffalse != $true ) ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( ( ( iffalse = $true )
| ( ( $true
= ( in @ sK10 @ sK12 ) )
& ( sK13
!= ( if @ sK12 @ sK11 @ sK10 @ sK13 ) )
& ( $true != sK11 )
& ( $true
= ( in @ sK13 @ sK12 ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ! [X7: $i] :
( ( ( if @ X6 @ X5 @ X4 @ X7 )
= X7 )
| ( $true = X5 )
| ( $true
!= ( in @ X7 @ X6 ) ) ) )
| ( iffalse != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f37]) ).
thf(f39,plain,
( ( ( in__Cong = $true )
| ? [X1: $i,X0: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X2 @ X0 )
!= ( in @ X3 @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( in @ X2 @ X0 )
= ( in @ X3 @ X1 ) ) ) )
| ( in__Cong != $true ) ) ),
inference(nnf_transformation,[],[f27]) ).
thf(f40,plain,
( ( ( in__Cong = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( in @ X3 @ X0 )
!= ( in @ X2 @ X1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( X4 != X5 )
| ! [X6: $i,X7: $i] :
( ( X6 != X7 )
| ( ( in @ X7 @ X4 )
= ( in @ X6 @ X5 ) ) ) )
| ( in__Cong != $true ) ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( ( in__Cong = $true )
| ( ( sK14 = sK15 )
& ( sK16 = sK17 )
& ( ( in @ sK16 @ sK15 )
!= ( in @ sK17 @ sK14 ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( X4 != X5 )
| ! [X6: $i,X7: $i] :
( ( X6 != X7 )
| ( ( in @ X7 @ X4 )
= ( in @ X6 @ X5 ) ) ) )
| ( in__Cong != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X3,sK17)],[f40]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f44,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) )
& ( ( secondinupair = $true )
| ( $true
!= ( in @ sK18 @ ( setadjoin @ sK19 @ ( setadjoin @ sK18 @ emptyset ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19]),skolemize(X2,sK18),skolemize(X3,sK19)],[f43]) ).
thf(f45,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( if @ X5 @ X6 @ X4 @ X7 )
= X4 )
| ( $true != X6 )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( iftrue != $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f50,plain,
in__Cong = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f51,plain,
iftrue = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f52,plain,
( $true
!= ( in @ ( if @ sK4 @ sK5 @ sK6 @ sK7 ) @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f53,plain,
( $true
= ( in @ sK7 @ sK4 ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f54,plain,
( ( in @ sK6 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f55,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f56,plain,
iffalse = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f57,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f32]) ).
thf(f58,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f60,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ( ( if @ X6 @ X5 @ X4 @ X7 )
= X7 )
| ( $true = X5 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( iffalse != $true ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f65,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( X4 != X5 )
| ( X6 != X7 )
| ( ( in @ X7 @ X4 )
= ( in @ X6 @ X5 ) )
| ( in__Cong != $true ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f77,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( if @ X5 @ X6 @ X4 @ X7 )
= X4 )
| ( $true != X6 )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f45,f51]) ).
thf(f79,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f58,f55]) ).
thf(f84,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( if @ X6 @ X5 @ X4 @ X7 )
= X7 )
| ( $true = X5 )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( $true != $true )
| ( $true
!= ( in @ X4 @ X6 ) ) ),
inference(definition_unfolding,[],[f60,f56]) ).
thf(f88,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( X4 != X5 )
| ( X6 != X7 )
| ( ( in @ X7 @ X4 )
= ( in @ X6 @ X5 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f65,f50]) ).
thf(f89,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ) ),
inference(definition_unfolding,[],[f70,f57]) ).
thf(f91,plain,
! [X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true != $true )
| ( ( if @ X5 @ $true @ X4 @ X7 )
= X4 )
| ( $true
!= ( in @ X4 @ X5 ) ) ),
inference(equality_resolution,[],[f77]) ).
thf(f92,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( X6 != X7 )
| ( ( in @ X7 @ X5 )
= ( in @ X6 @ X5 ) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f88]) ).
thf(f93,plain,
! [X7: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X7 @ X5 )
= ( in @ X7 @ X5 ) ) ),
inference(equality_resolution,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X3: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f95,plain,
! [X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( ( if @ X5 @ $true @ X4 @ X7 )
= X4 ) ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f97,plain,
! [X7: $i,X5: $i] :
( ( $false
= ( in @ X7 @ X5 ) )
| ( $true != $true )
| ( $true
= ( in @ X7 @ X5 ) ) ),
inference(iff_proxy_clausification,[],[f93]) ).
thf(f98,plain,
! [X7: $i,X5: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
| ( $false
= ( in @ X7 @ X5 ) ) ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f103,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( if @ X6 @ X5 @ X4 @ X7 )
= X7 )
| ( $true = X5 )
| ( $true
!= ( in @ X4 @ X6 ) ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f105,plain,
! [X0: $i] :
( ( ( if @ sK4 @ $true @ X0 @ sK7 )
= X0 )
| ( $true
!= ( in @ X0 @ sK4 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f95,f53]) ).
thf(f110,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK4 ) )
| ( ( if @ sK4 @ $true @ X0 @ sK7 )
= X0 ) ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f115,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ sK4 )
!= $true )
| ( $true != $true )
| ( $true = X0 )
| ( sK7
= ( if @ sK4 @ X0 @ X1 @ sK7 ) ) ),
inference(constrained_superposition,[],[f103,f53]) ).
thf(f121,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ sK4 )
!= $true )
| ( $true = X0 )
| ( sK7
= ( if @ sK4 @ X0 @ X1 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f126,plain,
( ( $true != $true )
| ( sK6
= ( if @ sK4 @ $true @ sK6 @ sK7 ) ) ),
inference(constrained_superposition,[],[f110,f54]) ).
thf(f130,plain,
( sK6
= ( if @ sK4 @ $true @ sK6 @ sK7 ) ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f131,plain,
( ( $false
= ( in @ ( if @ sK4 @ sK5 @ sK6 @ sK7 ) @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f52,f98]) ).
thf(f132,plain,
( $false
= ( in @ ( if @ sK4 @ sK5 @ sK6 @ sK7 ) @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f147,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( sK7
= ( if @ sK4 @ X0 @ sK6 @ sK7 ) ) ),
inference(constrained_superposition,[],[f121,f54]) ).
thf(f150,plain,
! [X0: $o] :
( ( sK7
= ( if @ sK4 @ X0 @ sK6 @ sK7 ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f294,plain,
( ( $true = sK5 )
| ( $false
= ( in @ sK7 @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) ) ),
inference(constrained_superposition,[],[f132,f150]) ).
thf(f306,plain,
( ( $true = sK5 )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f294,f102]) ).
thf(f307,plain,
$true = sK5,
inference(trivial_inequality_removal,[],[f306]) ).
thf(f310,plain,
( $false
= ( in @ ( if @ sK4 @ $true @ sK6 @ sK7 ) @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) ),
inference(backward_demodulation,[],[f132,f307]) ).
thf(f311,plain,
( $false
= ( in @ sK6 @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) ) ),
inference(forward_demodulation,[],[f310,f130]) ).
thf(f312,plain,
$false = $true,
inference(forward_demodulation,[],[f311,f94]) ).
thf(f313,plain,
$false,
inference(trivial_inequality_removal,[],[f312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n004.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:13:07 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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 % (1346015)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1346028)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4209197138:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1346029)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 % (1346029)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 % (1346023)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=979233759:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1346025)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4188236259:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1346024)lrs+10_16_si=on:nwc=1.5:random_seed=3811424827:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1346027)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2241966742:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1346026)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=4220423678: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 % (1346025)Instruction limit reached!
% 0.21/0.29 % (1346025)------------------------------
% 0.21/0.29 % (1346025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1346025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1346025)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1346025)Termination reason: Instruction limit
% 0.21/0.29 % (1346025)Termination phase: Saturation
% 0.21/0.29 % (1346025)Time elapsed: 0.002 s
% 0.21/0.29 % (1346025)Peak memory usage: 11 MB
% 0.21/0.29 % (1346025)Instructions burned: 3 (million)
% 0.21/0.29 % (1346028) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1346015-1346028"...
% 0.21/0.29 % (1346029)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=1106463883:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1346027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1346015-1346027"...
% 0.21/0.29 % (1346023) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1346015-1346023"...
% 0.21/0.29 % (1346028)...printing done.
% 0.21/0.29 % (1346028)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 % (1346028)------------------------------
% 0.21/0.29 % (1346028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1346028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1346028)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1346028)Termination reason: Refutation
% 0.21/0.29 % (1346028)Time elapsed: 0.012 s
% 0.21/0.29 % (1346028)Peak memory usage: 13 MB
% 0.21/0.29 % (1346028)Instructions burned: 42 (million)
% 0.21/0.29 % (1346015)Success in time 0.043 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------