%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU733^2 : 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 : n014.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 08:31:01 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 693 ( 192 equ; 0 cnn)
% Maximal formula atoms : 12 ( 14 avg)
% Number of connectives : 846 ( 98 ~; 79 |; 42 &; 571 @)
% ( 8 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 15 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 106 !; 22 ?; 128 :)
% 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,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
complementTnotintersectT: $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
= complementTnotintersectT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(f3,conjecture,
( setminusI
=> ( complementTnotintersectT
=> ! [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 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( complementTnotintersectT
=> ! [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 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setminusI
=> ( complementTnotintersectT
=> ! [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 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setminusI = $true )
=> ( ( complementTnotintersectT = $true )
=> ! [X0: $i,X1: $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 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) )
= complementTnotintersectT ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) ) ) ) )
<=> ( complementTnotintersectT = $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) ) ) ) )
<=> ( complementTnotintersectT = $true ) ),
inference(flattening,[],[f8]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f10]) ).
thf(f13,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( complementTnotintersectT = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f16,plain,
( ( complementTnotintersectT = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( complementTnotintersectT = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( complementTnotintersectT = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ( complementTnotintersectT = $true )
| ? [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( complementTnotintersectT != $true ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f20,plain,
( ( ( complementTnotintersectT = $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 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
!= $true ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
| ( complementTnotintersectT != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( complementTnotintersectT = $true )
| ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
!= $true ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ) )
| ( complementTnotintersectT != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
thf(f22,plain,
( ( ( in @ sK7 @ ( setminus @ sK4 @ ( binintersect @ sK5 @ sK6 ) ) )
!= $true )
& ( $true
= ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) ) )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( $true
= ( in @ sK6 @ ( powerset @ sK4 ) ) )
& ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ( complementTnotintersectT = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f18]) ).
thf(f23,plain,
( ( ( setminusI = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( $true
= ( in @ X0 @ X1 ) ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f24,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK10 @ sK8 )
= $true )
& ( $true
!= ( in @ sK10 @ ( setminus @ sK8 @ sK9 ) ) )
& ( ( in @ sK10 @ sK9 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true )
| ( ( in @ X5 @ X4 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f24]) ).
thf(f26,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
!= $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( complementTnotintersectT != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
setminusI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
complementTnotintersectT = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
( $true
= ( in @ sK6 @ ( powerset @ sK4 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
( ( in @ sK7 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
( $true
= ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f38,plain,
( ( in @ sK7 @ ( setminus @ sK4 @ ( binintersect @ sK5 @ sK6 ) ) )
!= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f50,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ),
inference(definition_unfolding,[],[f26,f33]) ).
thf(f54,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true )
| ( $true != $true )
| ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(definition_unfolding,[],[f39,f32]) ).
thf(f55,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X7 @ ( binintersect @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f56,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK7 @ X0 )
= $true )
| ( ( in @ sK7 @ ( setminus @ sK4 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f56,f36]) ).
thf(f61,plain,
! [X0: $i] :
( ( ( in @ sK7 @ ( setminus @ sK4 @ X0 ) )
= $true )
| ( ( in @ sK7 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f66,plain,
( ( $true
= ( in @ sK7 @ ( binintersect @ sK5 @ sK6 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f38,f61]) ).
thf(f68,plain,
( $true
= ( in @ sK7 @ ( binintersect @ sK5 @ sK6 ) ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f99,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK4 ) ) )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ( ( in @ sK7 @ ( binintersect @ sK5 @ X0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) ) ),
inference(constrained_superposition,[],[f55,f37]) ).
thf(f115,plain,
! [X0: $i] :
( ( ( in @ sK7 @ ( binintersect @ sK5 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ sK4 ) ) )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f131,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK4 ) ) )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ( ( in @ sK7 @ ( binintersect @ sK5 @ X0 ) )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f115,f36]) ).
thf(f147,plain,
! [X0: $i] :
( ( ( in @ sK7 @ ( binintersect @ sK5 @ X0 ) )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ sK4 ) ) ) ),
inference(forward_subsumption_resolution,[],[f131,f34]) ).
thf(f148,plain,
( ( $true
!= ( in @ sK6 @ ( powerset @ sK4 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f147,f68]) ).
thf(f149,plain,
( $true
!= ( in @ sK6 @ ( powerset @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f150,plain,
$false,
inference(forward_subsumption_resolution,[],[f149,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU733^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n014.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:18:15 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running higher-order theorem proving
% 0.22/0.27 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
% 0.22/0.33 % (2730567)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (2730572)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3274939992:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (2730574)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3941429625:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (2730578)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (2730578)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.33 % (2730574)Refutation not found, incomplete strategy
% 0.22/0.33 % (2730574)------------------------------
% 0.22/0.33 % (2730574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2730574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2730574)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2730574)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (2730574)Time elapsed: 0.002 s
% 0.22/0.33 % (2730574)Peak memory usage: 12 MB
% 0.22/0.33 % (2730574)Instructions burned: 3 (million)
% 0.22/0.33 % (2730574)------------------------------
% 0.22/0.33 % (2730574)------------------------------
% 0.22/0.33 % (2730578)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=4103847082:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (2730572) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2730567-2730572"...
% 0.22/0.33 % (2730573)lrs+10_16_si=on:nwc=1.5:random_seed=2380288170:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (2730572)...printing done.
% 0.22/0.33 % (2730572)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (2730572)------------------------------
% 0.22/0.33 % (2730572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (2730572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (2730572)CaDiCaL version: 2.1.3
% 0.22/0.33 % (2730572)Termination reason: Refutation
% 0.22/0.33 % (2730572)Time elapsed: 0.013 s
% 0.22/0.33 % (2730572)Peak memory usage: 12 MB
% 0.22/0.33 % (2730572)Instructions burned: 22 (million)
% 0.22/0.33 % (2730567)Success in time 0.046 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------