%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU605^2 : 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 : n019.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 08:30:17 AM UTC 2026
% Result : Theorem 0.36s 0.42s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 29 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 303 ( 85 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 323 ( 42 ~; 28 |; 18 &; 208 @)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 0 ^; 53 !; 12 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setminus: $i > $i > $i ).
thf(func_def_2,type,
setminusI: $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,conjecture,
( setminusI
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(f3,negated_conjecture,
~ ( setminusI
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
= setminusI ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setminusI
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setminusI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f5]) ).
thf(f9,plain,
~ ( ( setminusI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( setminusI = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( ( in @ sK2 @ sK0 )
= $true )
& ( $true
!= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
!= ( in @ sK2 @ sK1 ) )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
!= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
& ( $true
!= ( in @ X5 @ ( setminus @ X4 @ X3 ) ) )
& ( $true
= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK5 @ sK3 ) )
& ( $true
!= ( in @ sK5 @ ( setminus @ sK4 @ sK3 ) ) )
& ( $true
= ( in @ sK5 @ sK4 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f16]) ).
thf(f18,plain,
setminusI = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( $true
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( $true
!= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( $true != $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(definition_unfolding,[],[f25,f18]) ).
thf(f32,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f33,plain,
! [X0: $i] :
( ( $true
= ( in @ sK2 @ X0 ) )
| ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ X0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f32,f21]) ).
thf(f34,plain,
! [X0: $i] :
( ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ X0 ) ) )
| ( $true
= ( in @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( ( $true != $true )
| ( $true
= ( in @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f20,f34]) ).
thf(f37,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU605^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n019.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 13:57:18 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.30/0.35 Running higher-order theorem proving
% 0.30/0.37 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
% 0.36/0.42 % (808449)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.42 % (808454)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1735432083:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.36/0.42 % (808454) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-808449-808454"...
% 0.36/0.42 % (808454)...printing done.
% 0.36/0.42 % (808454)Refutation found. Thanks to Tanya!
% 0.36/0.42 % SZS status Theorem for theBenchmark
% 0.36/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.42 % (808454)------------------------------
% 0.36/0.42 % (808454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.42 % (808454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.42 % (808454)CaDiCaL version: 2.1.3
% 0.36/0.42 % (808454)Termination reason: Refutation
% 0.36/0.42 % (808454)Time elapsed: 0.003 s
% 0.36/0.42 % (808454)Peak memory usage: 12 MB
% 0.36/0.42 % (808454)Instructions burned: 3 (million)
% 0.36/0.42 % (808449)Success in time 0.04 s
% 0.36/0.43 % Vampire exiting
%------------------------------------------------------------------------------