%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU750^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:33:15 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 51 unt; 0 typ; 6 def)
% Number of atoms : 785 ( 159 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1187 ( 100 ~; 77 |; 21 &; 812 @)
% ( 6 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 30 ( 26 usr; 16 con; 0-4 aty)
% ( 57 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 195 ( 0 sgn 120 !; 8 ?; 195 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
setminusER: $o ).
thf(func_def_7,type,
binunionTIRcontra: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f3,axiom,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f4,conjecture,
( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a2) ).
thf(f5,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( binunionTIRcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( binunionTIRcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( setminusI
=> ( setminusER
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTIRcontra = $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 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( binunionTIRcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( binunionTIRcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
setminusI = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
setminusER = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( $true
= ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( $true
!= ( in @ sK3 @ ( setminus @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f19,f22]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ ( binunion @ Y0 @ Y2 ) )
=> ~ ( in @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ ( binunion @ X1 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ ( binunion @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X3 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X3 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ Y0 @ X3 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( ~ ( in @ X4 @ ( binunion @ X1 @ X3 ) )
=> ~ ( in @ X4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( ~ ( in @ X4 @ ( binunion @ X1 @ X3 ) ) ) )
| ( $true
= ( ~ ( in @ X4 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $true
= ( in @ X4 @ ( binunion @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( in @ X4 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ X4 @ ( binunion @ X1 @ X3 ) ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setminus @ X3 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( ~ ( in @ X1 @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f62]) ).
thf(f66,plain,
( ( $true = $false )
| ( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f26,f54]) ).
thf(f67,plain,
( $false
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f71,plain,
( ( $true != $true )
| ( $true
= ( in @ sK3 @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f27,f63]) ).
thf(f72,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ( ( in @ sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f76,definition,
( spl4_1
<=> ( ( in @ sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f78,plain,
( ( ( in @ sK3 @ sK0 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f80,definition,
( spl4_2
<=> ( $true
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f82,plain,
( ( $true
= ( in @ sK3 @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f80]) ).
thf(f83,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f72,f80,f76]) ).
thf(f117,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK2 ) ) ),
inference(constrained_superposition,[],[f46,f67]) ).
thf(f138,plain,
! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f151,definition,
( spl4_3
<=> ( $false
= ( in @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f153,plain,
( ( $false
= ( in @ sK3 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f155,definition,
( spl4_4
<=> ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f156,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK3 @ X0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f138,f155,f151]) ).
thf(f159,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(constrained_superposition,[],[f153,f82]) ).
thf(f165,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f166,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f165]) ).
thf(f172,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f156,f25]) ).
thf(f192,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f207,definition,
( spl4_7
<=> ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f209,plain,
( ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f211,definition,
( spl4_8
<=> ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f213,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f226,plain,
( spl4_7
| spl4_8
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f192,f155,f211,f207]) ).
thf(f228,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f78,f25]) ).
thf(f234,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f235,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f234]) ).
thf(f266,plain,
( ( $true = $false )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f209,f24]) ).
thf(f272,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f273,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f272]) ).
thf(f280,plain,
( ( $true = $false )
| ~ spl4_8 ),
inference(constrained_superposition,[],[f213,f23]) ).
thf(f286,plain,
( $false
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f287,plain,
~ spl4_8,
inference(avatar_contradiction_clause,[],[f286]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f83]) ).
cnf(s3,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f158]) ).
cnf(s5,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f166]) ).
cnf(s12,plain,
( ~ spl4_4
| spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f226]) ).
cnf(s15,plain,
~ spl4_1,
inference(sat_conversion,[],[f235]) ).
cnf(s23,plain,
~ spl4_7,
inference(sat_conversion,[],[f273]) ).
cnf(s25,plain,
~ spl4_8,
inference(sat_conversion,[],[f287]) ).
cnf(s26,plain,
~ spl4_4,
inference(rat,[],[s12,s25,s23]) ).
cnf(s27,plain,
spl4_3,
inference(rat,[],[s3,s26]) ).
cnf(s28,plain,
~ spl4_2,
inference(rat,[],[s5,s27]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s28,s15]) ).
thf(f288,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU750^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:22:21 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 % (1123527)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (1123538)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=481099871:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.25 % (1123533)% WARNING: option uhcvi not known.
% 0.08/0.25 % (1123536)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1327821453:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (1123538) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1123527-1123538"...
% 0.08/0.25 % (1123535)dis+10_1_sil=32000:sp=arity:random_seed=1998023819:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (1123534)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1621639189:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (1123533)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=115871899:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (1123537)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=866586128:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (1123536)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (1123533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (1123533)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (1123538)...printing done.
% 0.08/0.25 % (1123538)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (1123538)------------------------------
% 0.08/0.26 % (1123538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (1123538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (1123538)CaDiCaL version: 2.1.3
% 0.08/0.26 % (1123538)Termination reason: Refutation
% 0.08/0.26 % (1123538)Time elapsed: 0.008 s
% 0.08/0.26 % (1123538)Peak memory usage: 13 MB
% 0.08/0.26 % (1123538)Instructions burned: 23 (million)
% 0.08/0.26 % (1123527)Success in time 0.039 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------