%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU512^2 : 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 : n026.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 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 270 ( 84 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 297 ( 47 ~; 46 |; 23 &; 170 @)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 15 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 38 !; 13 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setadjoinAx: $o ).
thf(f1,axiom,
( setadjoinAx
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( X2 = X0 )
| ( in @ X2 @ X1 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( in @ X0 @ X2 ) )
<=> ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
<=> ( ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setadjoinAx = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( setadjoinAx = $true )
& ? [X1: $i,X0: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( setadjoinAx = $true )
& ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( setadjoinAx = $true )
& ( $true
!= ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
thf(f11,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X0 @ X2 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( ( X0 != X1 )
& ( $true
!= ( in @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f12,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X0 @ X2 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( ( X0 != X1 )
& ( $true
!= ( in @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( X1 != X2 )
& ( $true
!= ( in @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( X4 != X5 )
& ( $true
!= ( in @ X5 @ X3 ) ) )
| ( $true
!= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) ) )
& ( ( X4 = X5 )
| ( $true
= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( X1 != X2 )
& ( $true
!= ( in @ X2 @ X0 ) ) ) )
& ( ( X1 = X2 )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( sK4 != sK3 )
& ( $true
!= ( in @ sK4 @ sK2 ) ) )
| ( $true
!= ( in @ sK4 @ ( setadjoin @ sK3 @ sK2 ) ) ) )
& ( ( sK4 = sK3 )
| ( $true
= ( in @ sK4 @ sK2 ) )
| ( $true
= ( in @ sK4 @ ( setadjoin @ sK3 @ sK2 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4)],[f13]) ).
thf(f15,plain,
( $true
!= ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( X1 != X2 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
! [X2: $i,X0: $i] :
( ( setadjoinAx != $true )
| ( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X0 ) ) ) ),
inference(equality_resolution,[],[f22]) ).
thf(f30,definition,
( spl5_2
<=> ( setadjoinAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f48,definition,
( spl5_6
<=> ( $true
= ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
!= ( in @ sK0 @ ( setadjoin @ sK0 @ sK1 ) ) )
| spl5_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
~ spl5_6,
inference(avatar_split_clause,[],[f15,f48]) ).
thf(f53,plain,
spl5_2,
inference(avatar_split_clause,[],[f16,f30]) ).
thf(f59,definition,
( spl5_8
<=> ! [X2: $i,X0: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f60,plain,
( ! [X2: $i,X0: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X0 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f61,plain,
( spl5_8
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f24,f30,f59]) ).
thf(f64,plain,
( $false
| spl5_6
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f50,f60]) ).
thf(f65,plain,
( spl5_6
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s4,plain,
~ spl5_6,
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
spl5_2,
inference(sat_conversion,[],[f53]) ).
cnf(s8,plain,
( ~ spl5_2
| spl5_8 ),
inference(sat_conversion,[],[f61]) ).
cnf(s9,plain,
( spl5_6
| ~ spl5_8 ),
inference(sat_conversion,[],[f65]) ).
cnf(s10,plain,
spl5_8,
inference(rat,[],[s8,s6]) ).
cnf(s12,plain,
spl5_6,
inference(rat,[],[s9,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12]) ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU512^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.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 13:50:13 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.08/0.26 % (617848)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (617856)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=1576778833: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)
% 0.08/0.26 % (617856) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-617848-617856"...
% 0.08/0.26 % (617856)...printing done.
% 0.08/0.26 % (617856)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (617856)------------------------------
% 0.08/0.26 % (617856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (617856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (617856)CaDiCaL version: 2.1.3
% 0.08/0.26 % (617856)Termination reason: Refutation
% 0.08/0.26 % (617856)Time elapsed: 0.002 s
% 0.08/0.26 % (617856)Peak memory usage: 13 MB
% 0.08/0.26 % (617856)Instructions burned: 4 (million)
% 0.08/0.26 % (617848)Success in time 0.016 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------