%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU627^2 : 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 : n002.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 08:30:23 AM UTC 2026
% Result : Theorem 0.22s 0.37s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 101 ( 55 unt; 0 typ; 2 def)
% Number of atoms : 852 ( 178 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 1348 ( 29 ~; 63 |; 24 &;1067 @)
% ( 2 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 14 con; 0-4 aty)
% ( 71 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 226 ( 0 sgn 130 !; 12 ?; 226 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
subsetI2: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
singletoninpowunion: $o ).
thf(func_def_9,type,
upairset2E: $o ).
thf(func_def_10,type,
upairinpowunion: $o ).
thf(func_def_13,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
sK4: $i > $i > $i ).
thf(f1,axiom,
( subsetI2
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(f2,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) )
= singletoninpowunion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(f3,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) )
= upairset2E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(f4,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
= upairinpowunion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(f5,conjecture,
( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(f6,negated_conjecture,
~ ( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( subsetI2
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairinpowunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( subsetI2 = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairinpowunion = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) )
= singletoninpowunion ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( singletoninpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X0 ) ) ) ) )
= upairinpowunion ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( upairinpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X0 = X1 ) ) )
= upairset2E ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( subsetI2 = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f18,plain,
( ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( subsetI2 = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X2 ) ) ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( upairinpowunion = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( subsetI2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( upairinpowunion = $true ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( subsetI2 = $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) ) )
& ( $true
= ( in @ sK0 @ sK2 ) )
& ( upairinpowunion = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19]) ).
thf(f21,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( singletoninpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( upairinpowunion
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f25,plain,
upairinpowunion = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( $true
= ( in @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( $true
!= ( subset @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
subsetI2 = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
singletoninpowunion = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f31,plain,
upairset2E = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f34,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f31]) ).
thf(f35,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f22,f30]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f23,f25]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f24,f29]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y2 = Y1 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( Y0 = X2 )
| ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X3 = X2 )
| ( X2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( X3 = X2 )
| ( X2 = X1 ) )
= $true )
| ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( X3 = X2 ) )
| ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(or_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( X2 = X3 ) ),
inference(equality_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ ( setadjoin @ Y3 @ emptyset ) ) @ ( powerset @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y1 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y1 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y1 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ Y0 ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) )
@ X4 )
= $true )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ X3 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X3 ) ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ ( setadjoin @ Y1 @ emptyset ) @ ( powerset @ ( binunion @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f59,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ ( binunion @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( powerset @ ( binunion @ Y1 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ Y0 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X3 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X3 @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK4 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $false )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f80,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= $true )
| ( ( sK4 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 )
| ( ( sK4 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 ) ),
inference(constrained_superposition,[],[f47,f73]) ).
thf(f82,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= $true )
| ( ( sK4 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X1 )
| ( ( sK4 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ X2 )
= X0 ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f84,plain,
( ( $true != $true )
| ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ emptyset ) )
| ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f27,f82]) ).
thf(f85,plain,
( ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f87,definition,
( spl5_1
<=> ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f89,plain,
( ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f91,definition,
( spl5_2
<=> ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f93,plain,
( ( ( sK4 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= ( setadjoin @ sK0 @ emptyset ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f94,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f85,f91,f87]) ).
thf(f96,plain,
( ( $true
= ( subset @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) ) )
| ( ( in @ ( setadjoin @ sK0 @ emptyset ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f72,f93]) ).
thf(f98,plain,
( ( ( in @ ( setadjoin @ sK0 @ emptyset ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= $false )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f96,f27]) ).
thf(f99,plain,
( ( $false
= ( in @ sK0 @ sK2 ) )
| ( $true = $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f98,f64]) ).
thf(f101,plain,
( ( $false
= ( in @ sK0 @ sK2 ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f26,f101]) ).
thf(f107,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f108,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f107]) ).
thf(f110,plain,
( ( ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= $false )
| ( $true
= ( subset @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f72,f89]) ).
thf(f113,plain,
( ( ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK2 @ sK1 ) ) )
= $false )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f110,f27]) ).
thf(f115,plain,
( ( $false
= ( in @ sK0 @ sK2 ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f57,f113]) ).
thf(f116,plain,
( ( $false
= ( in @ sK0 @ sK2 ) )
| ( ( in @ sK3 @ sK1 )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f118,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( $true = $false )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f116,f26]) ).
thf(f119,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f122,plain,
( ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f119,f28]) ).
thf(f126,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f127,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f126]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f108]) ).
cnf(s5,plain,
~ spl5_1,
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f128,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU627^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n002.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 14:01:52 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.29 Running higher-order theorem proving
% 0.22/0.30 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
% 0.22/0.37 % (1332804)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.37 % (1332815)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.37 % (1332815)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
% 0.22/0.37 % (1332814)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2913013101:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.37 % (1332815)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=1813489710:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.37 % (1332809)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4140985172:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.37 % (1332810)lrs+10_16_si=on:nwc=1.5:random_seed=1787127538:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.37 % (1332811)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=638376201:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.37 % (1332813)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3587510839:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.37 % (1332812)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=243472934: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)
% 0.22/0.37 % (1332811)Instruction limit reached!
% 0.22/0.37 % (1332811)------------------------------
% 0.22/0.37 % (1332811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1332811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1332811)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1332811)Termination reason: Instruction limit
% 0.22/0.37 % (1332811)Termination phase: Saturation
% 0.22/0.37 % (1332811)Time elapsed: 0.004 s
% 0.22/0.37 % (1332811)Peak memory usage: 11 MB
% 0.22/0.37 % (1332811)Instructions burned: 3 (million)
% 0.22/0.37 % (1332810) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1332804-1332810"...
% 0.22/0.37 % (1332812) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1332804-1332812"...
% 0.22/0.37 % (1332810)...printing done.
% 0.22/0.37 % (1332814)Instruction limit reached!
% 0.22/0.37 % (1332814)------------------------------
% 0.22/0.37 % (1332814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1332814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1332814)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1332814)Termination reason: Instruction limit
% 0.22/0.37 % (1332814)Termination phase: Saturation
% 0.22/0.37 % (1332814)Time elapsed: 0.035 s
% 0.22/0.37 % (1332814)Peak memory usage: 12 MB
% 0.22/0.37 % (1332814)Instructions burned: 76 (million)
% 0.22/0.37 % (1332810)Refutation found. Thanks to Tanya!
% 0.22/0.37 % SZS status Theorem for theBenchmark
% 0.22/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.37 % (1332810)------------------------------
% 0.22/0.37 % (1332810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1332810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1332810)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1332810)Termination reason: Refutation
% 0.22/0.37 % (1332810)Time elapsed: 0.019 s
% 0.22/0.37 % (1332810)Peak memory usage: 13 MB
% 0.22/0.37 % (1332810)Instructions burned: 19 (million)
% 0.22/0.37 % (1332804)Success in time 0.057 s
% 0.22/0.37 % Vampire exiting
%------------------------------------------------------------------------------