%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU552^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:30:02 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 51 ( 7 ~; 0 |; 6 &; 32 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 12 !; 8 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
setadjoin: $i > $i > $i ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
? [X1: $i,X0: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X0 @ X2 )
!= ( setadjoin @ X1 @ X3 ) ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X1 @ X2 )
!= ( setadjoin @ X0 @ X3 ) ) )
& ( X0 = X1 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ( sK2 = sK3 )
& ( ( setadjoin @ sK1 @ sK2 )
!= ( setadjoin @ sK0 @ sK3 ) )
& ( sK1 = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f5]) ).
thf(f7,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( setadjoin @ sK1 @ sK2 )
!= ( setadjoin @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
sK2 = sK3,
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( setadjoin @ sK0 @ sK3 )
!= ( setadjoin @ sK0 @ sK3 ) ),
inference(definition_unfolding,[],[f8,f7,f9]) ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU552^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n009.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:49:45 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.20/0.26 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
% 0.20/0.30 % (4024205)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (4024210)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=31778104:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (4024210) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4024205-4024210"...
% 0.20/0.30 % (4024210)...printing done.
% 0.20/0.30 % (4024210)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (4024210)------------------------------
% 0.20/0.30 % (4024210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (4024210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (4024210)CaDiCaL version: 2.1.3
% 0.20/0.30 % (4024210)Termination reason: Refutation
% 0.20/0.30 % (4024210)Time elapsed: 0.0000 s
% 0.20/0.30 % (4024210)Peak memory usage: 11 MB
% 0.20/0.30 % (4024205)Success in time 0.028 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------