%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV457^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:38:40 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 86 ( 5 ~; 0 |; 0 &; 81 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 21 ( 0 ^; 18 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
sK1: sK0 > $o ).
thf(func_def_3,type,
sK2: sK0 ).
thf(f1,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INSERT_INSERT_') ).
thf(f2,conjecture,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INSERT_AC_1') ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/INSERT' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/INSERT' @ X0 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/INSERT' @ X0 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
? [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/INSERT' @ X0 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
!= ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f7,plain,
( ( 'const/sets/INSERT' @ sK0 @ sK2 @ sK1 )
!= ( 'const/sets/INSERT' @ sK0 @ sK2 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/INSERT' @ X0 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( 'const/sets/INSERT' @ sK0 @ sK2 @ sK1 )
!= ( 'const/sets/INSERT' @ sK0 @ sK2 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
$false,
inference(forward_subsumption_resolution,[],[f9,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV457^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:49:50 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.28 % (1211819)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1211835)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2549561921:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (1211835) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1211819-1211835"...
% 0.22/0.28 % (1211835)...printing done.
% 0.22/0.28 % (1211835)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1211835)------------------------------
% 0.22/0.28 % (1211835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1211835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1211835)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1211835)Termination reason: Refutation
% 0.22/0.28 % (1211835)Time elapsed: 0.001 s
% 0.22/0.28 % (1211835)Peak memory usage: 12 MB
% 0.22/0.28 % (1211835)Instructions burned: 1 (million)
% 0.22/0.28 % (1211819)Success in time 0.033 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------