%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU750^2 : 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 : n006.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 08:31:07 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 824 ( 232 equ; 0 cnn)
% Maximal formula atoms : 12 ( 13 avg)
% Number of connectives : 936 ( 115 ~; 86 |; 58 &; 610 @)
% ( 11 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 19 con; 0-2 aty)
% Number of variables : 159 ( 0 ^; 127 !; 32 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
setminusER: $o ).
thf(func_def_7,type,
binunionTIRcontra: $o ).
thf(f1,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( setminusER
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f3,axiom,
( binunionTIRcontra
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f4,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a2) ).
thf(f5,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
=> ( $true
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f16,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f17,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f18,plain,
( ( setminusER = $true )
& ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
& ( binunionTIRcontra = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f20,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f22,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f24,plain,
( ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X2 )
= $true )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ? [X4: $i,X5: $i] :
( ? [X6: $i] :
( ? [X7: $i] :
( ( $true
!= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
& ( $true
= ( in @ X7 @ X6 ) )
& ( $true
= ( in @ X7 @ X4 ) ) )
& ( $true
= ( in @ X6 @ ( powerset @ X4 ) ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X4 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) )
& ( ( binunionTIRcontra = $true )
| ( ( ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f25]) ).
thf(f27,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f20]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X5 ) )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( $true
!= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( $true
= ( in @ sK4 @ sK6 ) )
& ( $true
!= ( in @ sK4 @ sK5 ) )
& ( $true
!= ( in @ sK4 @ ( setminus @ sK6 @ sK5 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f28]) ).
thf(f30,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
| ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( $true
= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f30]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK9 @ sK7 ) )
& ( $true
= ( in @ sK9 @ ( setminus @ sK8 @ sK7 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f31]) ).
thf(f33,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) )
& ( binunionTIRcontra = $true )
& ( setminusI = $true ) ),
inference(rectify,[],[f18]) ).
thf(f34,plain,
( ( setminusER = $true )
& ( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) )
& ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) )
& ( $true
= ( in @ sK13 @ sK10 ) )
& ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ sK12 ) ) )
& ( $true
= ( in @ sK12 @ ( powerset @ sK10 ) ) )
& ( binunionTIRcontra = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f33]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( binunionTIRcontra != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( setminusI != $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setminusER != $true )
| ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f48,plain,
setminusI = $true,
inference(cnf_transformation,[],[f34]) ).
thf(f49,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[],[f34]) ).
thf(f50,plain,
( $true
= ( in @ sK12 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f51,plain,
( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ sK12 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f52,plain,
( $true
= ( in @ sK13 @ sK10 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f53,plain,
( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f54,plain,
( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f55,plain,
setminusER = $true,
inference(cnf_transformation,[],[f34]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f47,f55]) ).
thf(f61,plain,
( ( $true
!= ( in @ sK13 @ ( binunion @ sK11 @ sK12 ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f60,f53]) ).
thf(f62,plain,
( $true
!= ( in @ sK13 @ ( binunion @ sK11 @ sK12 ) ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(forward_subsumption_resolution,[],[f44,f48]) ).
thf(f65,plain,
( ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
= ( in @ sK13 @ sK12 ) )
| ( $true != $true ) ),
inference(superposition,[],[f51,f63]) ).
thf(f66,plain,
( ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
= ( in @ sK13 @ sK12 ) ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f67,plain,
( $true
= ( in @ sK13 @ sK12 ) ),
inference(forward_subsumption_resolution,[],[f66,f52]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f40,f49]) ).
thf(f69,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ sK10 ) ) )
| ( $true
= ( in @ X0 @ ( binunion @ sK11 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ sK10 ) ) ),
inference(superposition,[],[f68,f54]) ).
thf(f72,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ sK11 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ sK10 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ sK10 ) ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f73,plain,
( ( $true
!= ( in @ sK13 @ sK12 ) )
| ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f62,f72]) ).
thf(f74,plain,
( ( $true
!= ( in @ sK13 @ sK12 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) )
| ( $true
!= ( in @ sK13 @ sK10 ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f75,plain,
( ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) ) ),
inference(forward_subsumption_resolution,[],[f74,f67]) ).
thf(f76,plain,
( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) ),
inference(forward_subsumption_resolution,[],[f75,f52]) ).
thf(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU750^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.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 14:21:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (795643)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (795652)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=479209826:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (795652) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-795643-795652"...
% 0.22/0.29 % (795652)...printing done.
% 0.22/0.29 % (795654)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 % (795652)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 % (795652)------------------------------
% 0.22/0.29 % (795652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (795652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (795652)CaDiCaL version: 2.1.3
% 0.22/0.29 % (795652)Termination reason: Refutation
% 0.22/0.29 % (795652)Time elapsed: 0.003 s
% 0.22/0.29 % (795652)Peak memory usage: 12 MB
% 0.22/0.29 % (795652)Instructions burned: 10 (million)
% 0.22/0.29 % (795643)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------