%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU764^2 : 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 : n012.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 08:31:13 AM UTC 2026
% Result : Theorem 0.06s 0.17s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 789 ( 211 equ; 0 cnn)
% Maximal formula atoms : 8 ( 13 avg)
% Number of connectives : 1320 ( 98 ~; 75 |; 55 &;1040 @)
% ( 6 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 19 con; 0-2 aty)
% Number of variables : 134 ( 0 ^; 101 !; 33 ?; 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,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_5,type,
binunionT_lem: $o ).
thf(func_def_7,type,
demorgan1: $o ).
thf(func_def_8,type,
demorgan2: $o ).
thf(f1,axiom,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(f2,axiom,
( demorgan1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
thf(f3,axiom,
( demorgan2
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).
thf(f4,conjecture,
( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_2) ).
thf(f5,negated_conjecture,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( binunionT_lem = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
=> ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
<=> ( binunionT_lem = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( demorgan1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( demorgan1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( demorgan2
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X0 @ X2 ) )
= ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ( demorgan2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( setminus @ X1 @ ( binunion @ X0 @ X2 ) )
= ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( setminus @ X1 @ ( binunion @ X0 @ X2 ) )
= ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
<=> ( demorgan2 = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ( binunionT_lem = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
<=> ( demorgan1 = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f17,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
!= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( demorgan2 = $true )
& ( demorgan1 = $true )
& ( binunionT_lem = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f18,plain,
( ( demorgan1 = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
& ? [X4: $i] :
( ( ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) )
!= ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( ( setminus @ X1 @ ( binunion @ X0 @ X2 ) )
= ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( ( setminus @ X1 @ ( binunion @ X0 @ X2 ) )
!= ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ? [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
& ? [X5: $i] :
( ( ( binintersect @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) )
!= ( setminus @ X3 @ ( binunion @ X4 @ X5 ) ) )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan2 != $true ) )
& ( ( demorgan2 = $true )
| ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= ( binintersect @ ( setminus @ sK0 @ sK1 ) @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f20]) ).
thf(f22,plain,
( ( demorgan1 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ? [X4: $i] :
( ( ( setminus @ X0 @ ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) @ ( binintersect @ ( setminus @ X0 @ X3 ) @ ( setminus @ X0 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true ) ),
inference(rectify,[],[f18]) ).
thf(f23,plain,
( ( demorgan1 = $true )
& ( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true )
& ( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) @ ( binintersect @ ( setminus @ sK3 @ sK6 ) @ ( setminus @ sK3 @ sK7 ) ) ) )
& ( ( in @ sK7 @ ( powerset @ sK3 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ( binunionT_lem = $true )
& ( demorgan2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7)],[f22]) ).
thf(f24,plain,
( ( ( binunionT_lem = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f25,plain,
( ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ( $true
!= ( in @ ( binunion @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) ) )
| ( binunionT_lem != $true ) ) ),
inference(rectify,[],[f24]) ).
thf(f26,plain,
( ( ( binunionT_lem = $true )
| ( ( ( in @ sK10 @ ( powerset @ sK9 ) )
= $true )
& ( $true
!= ( in @ ( binunion @ sK8 @ sK10 ) @ ( powerset @ sK9 ) ) )
& ( $true
= ( in @ sK8 @ ( powerset @ sK9 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) ) )
| ( binunionT_lem != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
!= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) )
& ( ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) )
!= ( binunion @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) ) ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ( ( $true
= ( in @ sK12 @ ( powerset @ sK11 ) ) )
& ( ( in @ sK13 @ ( powerset @ sK11 ) )
= $true )
& ( ( binunion @ ( setminus @ sK11 @ sK12 ) @ ( setminus @ sK11 @ sK13 ) )
!= ( setminus @ sK11 @ ( binintersect @ sK12 @ sK13 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11),skolemize(X4,sK12),skolemize(X5,sK13)],[f28]) ).
thf(f33,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( demorgan2 != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
demorgan2 = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f35,plain,
binunionT_lem = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f36,plain,
( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f37,plain,
( ( in @ sK5 @ ( powerset @ sK3 ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
( ( in @ sK7 @ ( powerset @ sK3 ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f39,plain,
( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) @ ( binintersect @ ( setminus @ sK3 @ sK6 ) @ ( setminus @ sK3 @ sK7 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f40,plain,
( ( in @ sK6 @ ( powerset @ sK3 ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f41,plain,
demorgan1 = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f42,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( binunionT_lem != $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( demorgan1 != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f54,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( binunion @ X3 @ X5 ) @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X4 ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f42,f35]) ).
thf(f55,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f33,f34]) ).
thf(f56,plain,
( ( ( in @ sK6 @ ( powerset @ sK3 ) )
!= $true )
| ( ( in @ sK7 @ ( powerset @ sK3 ) )
!= $true )
| ( ( binunion @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) )
!= ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) ) ) ),
inference(superposition,[],[f39,f55]) ).
thf(f58,plain,
( ( ( in @ sK7 @ ( powerset @ sK3 ) )
!= $true )
| ( ( binunion @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) )
!= ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) ) ) ),
inference(forward_subsumption_resolution,[],[f56,f40]) ).
thf(f60,plain,
( ( binunion @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) )
!= ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) ) ),
inference(forward_subsumption_resolution,[],[f58,f38]) ).
thf(f62,plain,
( ( ( in @ sK5 @ ( powerset @ sK3 ) )
!= $true )
| ( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( binunion @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ),
inference(superposition,[],[f60,f55]) ).
thf(f63,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( binunion @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) ) ) ),
inference(forward_subsumption_resolution,[],[f62,f37]) ).
thf(f64,plain,
( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( binunion @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) @ ( setminus @ sK3 @ ( binunion @ sK6 @ sK7 ) ) ) ),
inference(forward_subsumption_resolution,[],[f63,f36]) ).
thf(f66,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) )
= ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f49,f41]) ).
thf(f67,plain,
( ( $true
!= ( in @ ( binunion @ sK6 @ sK7 ) @ ( powerset @ sK3 ) ) )
| ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true )
| ( ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) )
!= ( setminus @ sK3 @ ( binintersect @ ( binunion @ sK4 @ sK5 ) @ ( binunion @ sK6 @ sK7 ) ) ) ) ),
inference(superposition,[],[f64,f66]) ).
thf(f69,plain,
( ( $true
!= ( in @ ( binunion @ sK6 @ sK7 ) @ ( powerset @ sK3 ) ) )
| ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f70,plain,
( ( ( in @ sK7 @ ( powerset @ sK3 ) )
!= $true )
| ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK6 @ ( powerset @ sK3 ) )
!= $true ) ),
inference(superposition,[],[f69,f54]) ).
thf(f71,plain,
( ( ( in @ sK7 @ ( powerset @ sK3 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ sK3 ) )
!= $true )
| ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f72,plain,
( ( ( in @ sK6 @ ( powerset @ sK3 ) )
!= $true )
| ( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f71,f38]) ).
thf(f73,plain,
( ( in @ ( binunion @ sK4 @ sK5 ) @ ( powerset @ sK3 ) )
!= $true ),
inference(forward_subsumption_resolution,[],[f72,f40]) ).
thf(f74,plain,
( ( ( in @ sK5 @ ( powerset @ sK3 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ),
inference(superposition,[],[f73,f54]) ).
thf(f75,plain,
( ( ( in @ sK5 @ ( powerset @ sK3 ) )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) ),
inference(forward_subsumption_resolution,[],[f75,f37]) ).
thf(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU764^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:23:04 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.17 % (176239)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.17 % (176250)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.17 % (176250)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
% 0.06/0.17 % (176250)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=1848705398:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.17 % (176245)lrs+10_16_si=on:nwc=1.5:random_seed=2472999886:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.17 % (176246)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1632839753:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.17 % (176244)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1211175928:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.17 % (176248)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4065307062:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.17 % (176247)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=770720003: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)
% 0.06/0.17 % (176249)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1916486834:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.17 % (176246)Instruction limit reached!
% 0.06/0.17 % (176246)------------------------------
% 0.06/0.17 % (176246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (176246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (176246)CaDiCaL version: 2.1.3
% 0.06/0.17 % (176246)Termination reason: Instruction limit
% 0.06/0.17 % (176246)Termination phase: Saturation
% 0.06/0.17 % (176246)Time elapsed: 0.001 s
% 0.06/0.17 % (176246)Peak memory usage: 11 MB
% 0.06/0.17 % (176246)Instructions burned: 3 (million)
% 0.06/0.17 % (176248) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-176239-176248"...
% 0.06/0.17 % (176245) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-176239-176245"...
% 0.06/0.17 % (176248)...printing done.
% 0.06/0.17 % (176248)Refutation found. Thanks to Tanya!
% 0.06/0.17 % SZS status Theorem for theBenchmark
% 0.06/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.17 % (176248)------------------------------
% 0.06/0.17 % (176248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (176248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (176248)CaDiCaL version: 2.1.3
% 0.06/0.17 % (176248)Termination reason: Refutation
% 0.06/0.17 % (176248)Time elapsed: 0.004 s
% 0.06/0.17 % (176248)Peak memory usage: 12 MB
% 0.06/0.17 % (176248)Instructions burned: 14 (million)
% 0.06/0.17 % (176239)Success in time 0.026 s
% 0.06/0.17 % Vampire exiting
%------------------------------------------------------------------------------