%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU566^2 : 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 : n007.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 08:30:06 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 18 unt; 0 typ; 5 def)
% Number of atoms : 363 ( 87 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 336 ( 74 ~; 53 |; 18 &; 162 @)
% ( 8 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 50 !; 12 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
subsetE: $o ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(f2,conjecture,
( subsetE
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(f3,negated_conjecture,
~ ( subsetE
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( subsetE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ~ ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( subsetE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
!= ( subset @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( subsetE = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( $true
!= ( subset @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f10,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( subsetE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( subsetE = $true )
& ( $true
= ( subset @ sK1 @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ sK0 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
thf(f14,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( ( subset @ X5 @ X4 )
= $true )
& ( $true
= ( in @ X3 @ X5 ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( in @ sK3 @ sK4 )
!= $true )
& ( ( subset @ sK5 @ sK4 )
= $true )
& ( ( in @ sK3 @ sK5 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f15]) ).
thf(f17,plain,
( ( in @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
subsetE = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( subsetE != $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,definition,
( spl6_1
<=> ( subsetE = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f30,plain,
spl6_1,
inference(avatar_split_clause,[],[f20,f27]) ).
thf(f32,definition,
( spl6_2
<=> ( $true
= ( subset @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( subset @ sK1 @ sK0 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
spl6_2,
inference(avatar_split_clause,[],[f19,f32]) ).
thf(f47,definition,
( spl6_5
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f48,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f49,plain,
( ~ spl6_1
| spl6_5 ),
inference(avatar_split_clause,[],[f24,f47,f27]) ).
thf(f51,definition,
( spl6_6
<=> ( ( in @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f53,plain,
( ( ( in @ sK2 @ sK1 )
= $true )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
spl6_6,
inference(avatar_split_clause,[],[f18,f51]) ).
thf(f56,definition,
( spl6_7
<=> ( ( in @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f58,plain,
( ( ( in @ sK2 @ sK0 )
!= $true )
| spl6_7 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f59,plain,
~ spl6_7,
inference(avatar_split_clause,[],[f17,f56]) ).
thf(f66,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ sK0 )
!= $true )
| ( ( in @ sK2 @ X0 )
!= $true ) )
| ~ spl6_5
| spl6_7 ),
inference(superposition,[],[f58,f48]) ).
thf(f67,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK0 )
!= $true )
| ( ( in @ sK2 @ X0 )
!= $true ) )
| ~ spl6_5
| spl6_7 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
( ( ( in @ sK2 @ sK1 )
!= $true )
| ( $true != $true )
| ~ spl6_2
| ~ spl6_5
| spl6_7 ),
inference(superposition,[],[f67,f34]) ).
thf(f69,plain,
( ( ( in @ sK2 @ sK1 )
!= $true )
| ~ spl6_2
| ~ spl6_5
| spl6_7 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f70,plain,
( $false
| ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f69,f53]) ).
thf(f71,plain,
( ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(avatar_contradiction_clause,[],[f70]) ).
cnf(s1,plain,
spl6_1,
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
spl6_2,
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( ~ spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
spl6_6,
inference(sat_conversion,[],[f54]) ).
cnf(s7,plain,
~ spl6_7,
inference(sat_conversion,[],[f59]) ).
cnf(s9,plain,
( ~ spl6_2
| ~ spl6_5
| ~ spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f71]) ).
cnf(s10,plain,
~ spl6_5,
inference(rat,[],[s9,s7,s6,s2]) ).
cnf(s11,plain,
~ spl6_1,
inference(rat,[],[s5,s10]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s11]) ).
thf(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU566^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 13:48:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.28 % (3393046)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (3393054)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=1802366366: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)
% 0.19/0.28 % (3393054) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3393046-3393054"...
% 0.19/0.28 % (3393054)...printing done.
% 0.19/0.28 % (3393054)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3393054)------------------------------
% 0.19/0.28 % (3393054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3393054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3393054)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3393054)Termination reason: Refutation
% 0.19/0.28 % (3393054)Time elapsed: 0.002 s
% 0.19/0.28 % (3393054)Peak memory usage: 13 MB
% 0.19/0.28 % (3393054)Instructions burned: 4 (million)
% 0.19/0.28 % (3393046)Success in time 0.045 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------