%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU539^2 : 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 : n001.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 08:29:59 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 119 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 124 ( 30 ~; 10 |; 11 &; 61 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 19 !; 11 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(f1,conjecture,
! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ~ ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( X1 @ X3 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ~ ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( X1 @ X3 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X1: $i > $o,X0: $i] :
( ! [X3: $i] :
( ( $true
= ( X1 @ X3 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( X0 @ X3 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X2: $i] :
( ( ( sK0 @ X2 )
= $true )
| ( $true
!= ( in @ X2 @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( ( sK0 @ sK2 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f7]) ).
thf(f9,plain,
( ( sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( ( sK0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,definition,
( spl3_1
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f9,f14]) ).
thf(f19,definition,
( spl3_2
<=> ( $true
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ( $true
= ( in @ sK2 @ sK1 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
spl3_2,
inference(avatar_split_clause,[],[f10,f19]) ).
thf(f23,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $true != $true )
| ~ spl3_2 ),
inference(superposition,[],[f11,f21]) ).
thf(f24,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f24,f19,f14]) ).
cnf(s1,plain,
~ spl3_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s4,plain,
spl3_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
thf(f26,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU539^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:54:51 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.27 % (1275885)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1275893)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=2293177971: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)
% 0.20/0.27 % (1275893) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1275885-1275893"...
% 0.20/0.27 % (1275893)...printing done.
% 0.20/0.27 % (1275893)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1275893)------------------------------
% 0.20/0.27 % (1275893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1275893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1275893)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1275893)Termination reason: Refutation
% 0.20/0.27 % (1275893)Time elapsed: 0.001 s
% 0.20/0.27 % (1275893)Peak memory usage: 13 MB
% 0.20/0.27 % (1275893)Instructions burned: 1 (million)
% 0.20/0.27 % (1275885)Success in time 0.029 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------