%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU601^2 : 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 : n012.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 08:30:16 AM UTC 2026
% Result : Theorem 0.09s 0.17s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 100 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 405 ( 62 ~; 33 |; 21 &; 265 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 111 ( 33 ^; 63 !; 15 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
setminus: $i > $i > $i ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: $i > $o ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminus) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( X1 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( ( X1 @ X0 )
= $true )
=> ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) )
<=> ( dsetconstrI = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f12,plain,
( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( dsetconstrI = $true )
<=> ! [X1: $i > $o,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( dsetconstrI = $true )
| ? [X1: $i > $o,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( ( X1 @ X0 )
= $true ) ) )
& ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X0 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f17,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
& ( $true
= ( X0 @ X2 ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( $true
!= ( X3 @ X5 ) ) )
| ( dsetconstrI != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( dsetconstrI = $true )
| ( ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
!= ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) )
& ( ( sK0 @ sK2 )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( $true
!= ( X3 @ X5 ) ) )
| ( dsetconstrI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(rectify,[],[f15]) ).
thf(f20,plain,
( ( ( in @ sK4 @ ( setminus @ sK3 @ sK5 ) )
!= $true )
& ( ( in @ sK4 @ sK5 )
!= $true )
& ( ( in @ sK4 @ sK3 )
= $true )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f19]) ).
thf(f21,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
!= ( X3 @ X5 ) )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f25,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( ( in @ sK4 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( ( in @ sK4 @ sK5 )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
( ( in @ sK4 @ ( setminus @ sK3 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f32,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
= $true )
| ( $true
!= ( X3 @ X5 ) )
| ( dsetconstrI != $true ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ X1 )
= ( setminus @ X1 ) ),
inference(argument_congruence,[],[f29]) ).
thf(f35,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( dsetconstr @ X1
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) ) )
= ( setminus @ X1 ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( setminus @ X1 @ X2 )
= ( ^ [Y0: $i] :
( dsetconstr @ X1
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
@ X2 ) ),
inference(argument_congruence,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( setminus @ X1 @ X2 )
= ( dsetconstr @ X1
@ ^ [Y0: $i] :
~ ( in @ Y0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
= $true )
| ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
!= ( X3 @ X5 ) ) ),
inference(forward_subsumption_resolution,[],[f32,f25]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ X1 )
@ X2 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(superposition,[],[f38,f37]) ).
thf(f40,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( $true
!= ( ~ ( in @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( ( in @ sK4 @ sK5 )
= $true )
| ( ( in @ sK4 @ sK3 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f28,f41]) ).
thf(f43,plain,
( ( ( in @ sK4 @ sK5 )
= $true )
| ( ( in @ sK4 @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
( ( in @ sK4 @ sK3 )
!= $true ),
inference(forward_subsumption_resolution,[],[f43,f27]) ).
thf(f45,plain,
$false,
inference(forward_subsumption_resolution,[],[f44,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU601^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:56:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.14 Running higher-order theorem proving
% 0.09/0.15 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
% 0.09/0.17 % (143917)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.17 % (143929)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2134657567:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.09/0.17 % (143929) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-143917-143929"...
% 0.09/0.17 % (143929)...printing done.
% 0.09/0.17 % (143929)Refutation found. Thanks to Tanya!
% 0.09/0.17 % SZS status Theorem for theBenchmark
% 0.09/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.17 % (143929)------------------------------
% 0.09/0.17 % (143929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (143929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (143929)CaDiCaL version: 2.1.3
% 0.09/0.17 % (143929)Termination reason: Refutation
% 0.09/0.17 % (143929)Time elapsed: 0.002 s
% 0.09/0.17 % (143929)Peak memory usage: 12 MB
% 0.09/0.17 % (143929)Instructions burned: 5 (million)
% 0.09/0.17 % (143917)Success in time 0.018 s
% 0.09/0.17 % Vampire exiting
%------------------------------------------------------------------------------