%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU756^2 : 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 : n026.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 08:31:10 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 824 ( 223 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 1051 ( 105 ~; 97 |; 51 &; 742 @)
% ( 7 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 152 ( 0 ^; 124 !; 28 ?; 152 :)
% 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,
binintersectEL: $o ).
thf(func_def_6,type,
binintersectER: $o ).
thf(func_def_7,type,
setminus: $i > $i > $i ).
thf(func_def_8,type,
demorgan2b2: $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(f1,axiom,
( binintersectEL
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f2,axiom,
( binintersectER
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f3,axiom,
( demorgan2b2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
thf(f4,conjecture,
( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b) ).
thf(f5,negated_conjecture,
~ ( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( demorgan2b2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) ) )
<=> ( demorgan2b2 = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ( binintersectER = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
=> ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( binintersectEL
=> ( binintersectER
=> ( demorgan2b2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ( ( demorgan2b2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
=> ( $true
= ( in @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
<=> ( binintersectEL = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( demorgan2b2 = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f16,plain,
( ( demorgan2b2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( demorgan2b2 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f18,plain,
( ( binintersectER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectEL = $true )
& ( demorgan2b2 = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
<=> ( binintersectER = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f20,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true )
& ( $true
!= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binintersectER != $true ) )
& ( ( binintersectER = $true )
| ( ( $true
= ( in @ sK2 @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f21]) ).
thf(f23,plain,
( ( ( demorgan2b2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( demorgan2b2 != $true ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f24,plain,
( ( ( demorgan2b2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X6 ) ) )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
| ( demorgan2b2 != $true ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( ( demorgan2b2 = $true )
| ( ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) ) )
& ( $true
= ( in @ sK6 @ sK3 ) )
& ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) ) )
& ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X6 ) ) )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
| ( demorgan2b2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f24]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
& ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
| ( binintersectEL != $true ) )
& ( ( binintersectEL = $true )
| ( ( $true
!= ( in @ sK8 @ sK7 ) )
& ( $true
= ( in @ sK8 @ ( binintersect @ sK7 @ sK9 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f27]) ).
thf(f29,plain,
( ( binintersectER = $true )
& ( $true
= ( in @ sK13 @ ( binintersect @ ( setminus @ sK10 @ sK11 ) @ ( setminus @ sK10 @ sK12 ) ) ) )
& ( $true
= ( in @ sK13 @ sK10 ) )
& ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) )
& ( $true
= ( in @ sK12 @ ( powerset @ sK10 ) ) )
& ( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) )
& ( binintersectEL = $true )
& ( demorgan2b2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f18]) ).
thf(f32,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X6 ) ) )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( demorgan2b2 != $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f43,plain,
demorgan2b2 = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f45,plain,
( $true
= ( in @ sK11 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f46,plain,
( $true
= ( in @ sK12 @ ( powerset @ sK10 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f47,plain,
( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f48,plain,
( $true
= ( in @ sK13 @ sK10 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f49,plain,
( $true
= ( in @ sK13 @ ( binintersect @ ( setminus @ sK10 @ sK11 ) @ ( setminus @ sK10 @ sK12 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f50,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[],[f32,f50]) ).
thf(f62,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(definition_unfolding,[],[f33,f43]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(definition_unfolding,[],[f42,f44]) ).
thf(f66,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f67,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f68,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f69,plain,
( ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ sK11 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f67,f49]) ).
thf(f70,plain,
( ( $true != $true )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ sK12 ) ) ) ),
inference(constrained_superposition,[],[f66,f49]) ).
thf(f71,plain,
( $true
= ( in @ sK13 @ ( setminus @ sK10 @ sK12 ) ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f72,plain,
( $true
= ( in @ sK13 @ ( setminus @ sK10 @ sK11 ) ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f73,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) )
| ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK10 ) ) )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ X0 @ sK12 ) ) ) ) ),
inference(constrained_superposition,[],[f68,f71]) ).
thf(f74,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK10 ) ) )
| ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ X0 ) ) )
| ( $true
!= ( in @ sK13 @ sK10 ) )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ X0 @ sK12 ) ) ) )
| ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f75,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK12 @ ( powerset @ sK10 ) ) )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ X0 @ sK12 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK10 ) ) )
| ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ X0 ) ) ) ),
inference(forward_subsumption_resolution,[],[f74,f48]) ).
thf(f76,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK13 @ ( setminus @ sK10 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK10 ) ) )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ X0 @ sK12 ) ) ) ) ),
inference(forward_subsumption_resolution,[],[f75,f46]) ).
thf(f82,plain,
( ( $true
!= ( in @ sK11 @ ( powerset @ sK10 ) ) )
| ( $true != $true )
| ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) ) ),
inference(constrained_superposition,[],[f76,f72]) ).
thf(f83,plain,
( ( $true
= ( in @ sK13 @ ( setminus @ sK10 @ ( binunion @ sK11 @ sK12 ) ) ) )
| ( $true
!= ( in @ sK11 @ ( powerset @ sK10 ) ) ) ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f85,plain,
( $true
!= ( in @ sK11 @ ( powerset @ sK10 ) ) ),
inference(forward_subsumption_resolution,[],[f83,f47]) ).
thf(f87,plain,
$false,
inference(forward_subsumption_resolution,[],[f85,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU756^2 : 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 : n026.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 14:24:57 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 % (671420)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (671431)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 % (671431)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 % (671427)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3132683737:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (671425)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=938731046:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (671426)lrs+10_16_si=on:nwc=1.5:random_seed=4163038258:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (671431)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=585191785:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (671427)Instruction limit reached!
% 0.21/0.29 % (671427)------------------------------
% 0.21/0.29 % (671427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (671429)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3231954428:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (671427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (671427)CaDiCaL version: 2.1.3
% 0.21/0.29 % (671427)Termination reason: Instruction limit
% 0.21/0.29 % (671427)Termination phase: Saturation
% 0.21/0.29 % (671427)Time elapsed: 0.002 s
% 0.21/0.29 % (671427)Peak memory usage: 11 MB
% 0.21/0.29 % (671427)Instructions burned: 3 (million)
% 0.21/0.29 % (671430)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=378401134:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (671426) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-671420-671426"...
% 0.21/0.29 % (671425) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-671420-671425"...
% 0.21/0.29 % (671430) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-671420-671430"...
% 0.21/0.29 % (671429) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-671420-671429"...
% 0.21/0.29 % (671428)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=628294299: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 % (671430)...printing done.
% 0.21/0.29 % (671430)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 % (671430)------------------------------
% 0.21/0.29 % (671430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (671430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (671430)CaDiCaL version: 2.1.3
% 0.21/0.29 % (671430)Termination reason: Refutation
% 0.21/0.29 % (671430)Time elapsed: 0.004 s
% 0.21/0.29 % (671430)Peak memory usage: 13 MB
% 0.21/0.29 % (671430)Instructions burned: 11 (million)
% 0.21/0.29 % (671420)Success in time 0.045 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------