%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU727^2 : 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 : n015.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 08:30:59 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 75 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 525 ( 33 ~; 12 |; 15 &; 381 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 8 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 105 ( 36 ^; 63 !; 6 ?; 105 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_3,type,
setminusI: $o ).
thf(func_def_5,type,
setminusER: $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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f3,conjecture,
( setminusI
=> ( setminusER
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
= setminusER ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,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,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( setminusER = $true )
& ( $true
!= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
thf(f14,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
setminusI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
!= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
setminusER = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f21,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,[],[f10]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f20]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f21,f15]) ).
thf(f26,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,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,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( in @ X1 @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f36,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setminus @ X3 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) )
| ( $true
= ( ~ ( in @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f45,plain,
( ( $true != $true )
| ( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f19,f34]) ).
thf(f47,plain,
( ( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false
= ( in @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f48,plain,
( ( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f47,f18]) ).
thf(f49,plain,
( ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f49,f42]) ).
thf(f52,plain,
( $false
= ( in @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f55,plain,
$false = $true,
inference(constrained_superposition,[],[f17,f52]) ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU727^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:20:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.28 % (3595705)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3595711)lrs+10_16_si=on:nwc=1.5:random_seed=2425294397:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (3595711) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3595705-3595711"...
% 0.20/0.28 % (3595711)...printing done.
% 0.20/0.28 % (3595711)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3595711)------------------------------
% 0.20/0.28 % (3595711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3595711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3595711)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3595711)Termination reason: Refutation
% 0.20/0.28 % (3595711)Time elapsed: 0.002 s
% 0.20/0.28 % (3595711)Peak memory usage: 12 MB
% 0.20/0.28 % (3595711)Instructions burned: 6 (million)
% 0.20/0.28 % (3595705)Success in time 0.039 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------