%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU813^2 : 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 : n001.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 08:31:38 AM UTC 2026
% Result : Theorem 0.26s 0.34s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 80 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 866 ( 261 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 915 ( 114 ~; 116 |; 48 &; 572 @)
% ( 9 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 20 con; 0-4 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 185 ( 12 ^; 147 !; 26 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
binintersectSubset5: $o ).
thf(func_def_5,type,
binintersectEL: $o ).
thf(func_def_6,type,
binintersectER: $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
transitivesetOp1: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
sK13: $i > $i ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectSubset5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= binintersectEL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(f3,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) )
= binintersectER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f4,axiom,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(f5,axiom,
! [X0: $i] :
( ( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitivesetOp1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp1) ).
thf(f6,conjecture,
( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(f7,negated_conjecture,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X2 ) )
= binintersectER ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( ( binintersectER = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
~ ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectER = $true )
=> ( ( transitivesetOp1 = $true )
=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X1 ) )
= binintersectEL ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( binintersectEL = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= binintersectSubset5 ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitivesetOp1 ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) )
<=> ( transitivesetOp1 = $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[],[f4]) ).
thf(f19,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( binintersectSubset5 = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) )
<=> ( transitivesetOp1 = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f23,plain,
( ( binintersectER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f24,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
& ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f25,plain,
( ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
& ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( binintersectSubset5 = $true ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( binintersectEL = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f27,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) )
| ( transitivesetOp1 != $true ) )
& ( ( transitivesetOp1 = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( ( transitiveset @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f28,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) )
| ( transitivesetOp1 != $true ) )
& ( ( transitivesetOp1 = $true )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( subset @ X3 @ X2 ) ) )
& ( ( transitiveset @ X2 )
= $true ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) )
| ( transitivesetOp1 != $true ) )
& ( ( transitivesetOp1 = $true )
| ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( subset @ sK1 @ sK0 )
!= $true )
& ( $true
= ( transitiveset @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f28]) ).
thf(f30,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( binintersectER != $true ) ) ),
inference(nnf_transformation,[],[f23]) ).
thf(f31,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(rectify,[],[f30]) ).
thf(f32,plain,
( ( ( binintersectER = $true )
| ( ( ( in @ sK2 @ sK3 )
!= $true )
& ( ( in @ sK2 @ ( binintersect @ sK4 @ sK3 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f31]) ).
thf(f33,plain,
( ( ( binintersectEL = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f34,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[],[f33]) ).
thf(f35,plain,
( ( ( binintersectEL = $true )
| ( ( ( in @ sK7 @ sK5 )
!= $true )
& ( ( in @ sK7 @ ( binintersect @ sK5 @ sK6 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) ) )
| ( binintersectEL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f34]) ).
thf(f36,plain,
( ( transitivesetOp1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( $true
= ( transitiveset @ sK9 ) )
& ( ( transitiveset @ ( binintersect @ sK8 @ sK9 ) )
!= $true )
& ( ( transitiveset @ sK8 )
= $true )
& ( binintersectSubset5 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f25]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
& ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f21]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X4 @ X5 ) )
& ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
& ( $true
= ( subset @ X4 @ X3 ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ( ( ( subset @ sK11 @ sK12 )
= $true )
& ( $true
!= ( subset @ sK11 @ ( binintersect @ sK10 @ sK12 ) ) )
& ( $true
= ( subset @ sK11 @ sK10 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f38]) ).
thf(f43,plain,
! [X0: $i,X1: $i] :
( ( transitivesetOp1 != $true )
| ( ( transitiveset @ X0 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f45,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
!= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f48,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f51,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f52,plain,
( ( transitiveset @ sK8 )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f53,plain,
( ( transitiveset @ ( binintersect @ sK8 @ sK9 ) )
!= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f54,plain,
( $true
= ( transitiveset @ sK9 ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f55,plain,
binintersectEL = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f56,plain,
binintersectER = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f57,plain,
transitivesetOp1 = $true,
inference(cnf_transformation,[],[f36]) ).
thf(f61,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersectSubset5 != $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f67,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( transitiveset @ X0 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f43,f57]) ).
thf(f68,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binintersect @ X5 @ X4 ) )
!= $true )
| ( ( in @ X3 @ X4 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f45,f56]) ).
thf(f69,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binintersect @ X3 @ X4 ) ) )
| ( ( in @ X5 @ X3 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f48,f55]) ).
thf(f70,plain,
! [X1: $i] :
( ( transitiveset @ X1 )
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f44]) ).
thf(f71,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $false )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f70]) ).
thf(f77,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) ) ) )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f78,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( subset @ Y0 @ X1 ) )
@ ( sK13 @ X1 ) ) )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( $false
= ( ( in @ ( sK13 @ X1 ) @ X1 )
=> ( subset @ ( sK13 @ X1 ) @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( $false
= ( subset @ ( sK13 @ X1 ) @ X1 ) )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( in @ ( sK13 @ X1 ) @ X1 )
= $true )
| ( ( transitiveset @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f61,f51]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( $true
!= ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f80,f84]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( $true
!= ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f89,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( $true
!= ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) )
| ( ( transitiveset @ X0 )
!= $true ) ),
inference(superposition,[],[f87,f67]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 ) )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( ( transitiveset @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
!= $true )
| ( $true != $true )
| ( ( transitiveset @ X1 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X0 )
!= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true ) ),
inference(superposition,[],[f91,f67]) ).
thf(f96,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( ( transitiveset @ X1 )
!= $true )
| ( ( transitiveset @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f125,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
= $true ) ),
inference(superposition,[],[f69,f81]) ).
thf(f126,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f68,f81]) ).
thf(f127,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f128,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X1 )
= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f150,plain,
! [X0: $i,X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X0 )
!= $true )
| ( ( transitiveset @ X1 )
!= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( $true != $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ),
inference(superposition,[],[f96,f128]) ).
thf(f157,plain,
! [X0: $i,X1: $i] :
( ( ( transitiveset @ X0 )
!= $true )
| ( ( transitiveset @ X1 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[],[f150]) ).
thf(f158,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK13 @ ( binintersect @ X0 @ X1 ) ) @ X0 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X1 )
!= $true )
| ( ( transitiveset @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f167,plain,
! [X0: $i,X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X0 )
!= $true )
| ( ( transitiveset @ X1 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f158,f127]) ).
thf(f176,plain,
( ( $true != $true )
| ( ( transitiveset @ sK8 )
!= $true )
| ( $true
!= ( transitiveset @ sK9 ) ) ),
inference(superposition,[],[f53,f167]) ).
thf(f177,plain,
( ( $true
!= ( transitiveset @ sK9 ) )
| ( ( transitiveset @ sK8 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
( ( transitiveset @ sK8 )
!= $true ),
inference(forward_subsumption_resolution,[],[f177,f54]) ).
thf(f179,plain,
$false,
inference(forward_subsumption_resolution,[],[f178,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU813^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n001.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 14:39:36 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running higher-order theorem proving
% 0.26/0.30 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
% 0.26/0.34 % (1331548)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.34 % (1331562)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.34 % (1331562)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
% 0.26/0.34 % (1331560)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1265714442:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.34 % (1331562)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=2238206334:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.34 % (1331560) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1331548-1331560"...
% 0.26/0.34 % (1331560)...printing done.
% 0.26/0.34 % (1331557)lrs+10_16_si=on:nwc=1.5:random_seed=2998154756:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.34 % (1331556)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1229537045:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.34 % (1331560)Refutation found. Thanks to Tanya!
% 0.26/0.34 % SZS status Theorem for theBenchmark
% 0.26/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.34 % (1331560)------------------------------
% 0.26/0.34 % (1331560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (1331560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (1331560)CaDiCaL version: 2.1.3
% 0.26/0.34 % (1331560)Termination reason: Refutation
% 0.26/0.34 % (1331560)Time elapsed: 0.009 s
% 0.26/0.34 % (1331560)Peak memory usage: 12 MB
% 0.26/0.34 % (1331560)Instructions burned: 18 (million)
% 0.26/0.34 % (1331548)Success in time 0.035 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------