%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET008^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:23:09 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 52 ( 15 ~; 0 |; 15 &; 22 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 28 ( 18 ^; 8 !; 2 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_78_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
& ~ ( X0 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] : $false ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( $false
& ( sK1 @ Y0 ) ) ) ),
inference(boolean_simplification,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] : $false ) ),
inference(boolean_simplification,[],[f10]) ).
thf(f12,plain,
$false,
inference(trivial_inequality_removal,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:40:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.20/0.28 % (1246121)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1246131)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1669170603:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1246131) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1246121-1246131"...
% 0.20/0.28 % (1246131)...printing done.
% 0.20/0.28 % (1246131)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1246131)------------------------------
% 0.20/0.28 % (1246131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1246131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1246131)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1246131)Termination reason: Refutation
% 0.20/0.28 % (1246131)Time elapsed: 0.001 s
% 0.20/0.28 % (1246131)Peak memory usage: 12 MB
% 0.20/0.28 % (1246121)Success in time 0.034 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------