%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU513^2 : 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 : n013.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 08:29:52 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 144 ( 29 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 128 ( 21 ~; 15 |; 4 &; 80 @)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 18 !; 4 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,conjecture,
( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(f3,negated_conjecture,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ( setadjoinIL = $true )
<=> ! [X1: $i,X0: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X1: $i,X0: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f10,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( setadjoinIL = $true )
| ( ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,definition,
( spl2_1
<=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f20,plain,
( ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f13,f18]) ).
thf(f23,definition,
( spl2_2
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,definition,
( spl2_4
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f33,plain,
( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X3 ) )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f34,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_split_clause,[],[f14,f32,f23]) ).
thf(f35,plain,
spl2_2,
inference(avatar_split_clause,[],[f12,f23]) ).
thf(f37,plain,
( $false
| spl2_1
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f20,f33]) ).
thf(f38,plain,
( spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
~ spl2_1,
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
spl2_2,
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s6,plain,
spl2_4,
inference(rat,[],[s3,s4]) ).
cnf(s7,plain,
spl2_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
thf(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU513^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n013.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:46:51 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.20 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
% 0.09/0.24 % (2138764)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.24 % (2138772)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=2695181161: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)
% 0.09/0.24 % (2138772) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2138764-2138772"...
% 0.09/0.24 % (2138772)...printing done.
% 0.09/0.24 % (2138772)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (2138772)------------------------------
% 0.09/0.24 % (2138772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (2138772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (2138772)CaDiCaL version: 2.1.3
% 0.09/0.24 % (2138772)Termination reason: Refutation
% 0.09/0.24 % (2138772)Time elapsed: 0.002 s
% 0.09/0.24 % (2138772)Peak memory usage: 13 MB
% 0.09/0.24 % (2138772)Instructions burned: 2 (million)
% 0.09/0.24 % (2138764)Success in time 0.032 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------