%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET618^5 : 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 : 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 08:23:23 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% 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 : 30 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 75 ( 23 ~; 7 |; 15 &; 30 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 23 ( 18 ^; 4 !; 1 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) )
| ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) ) ) )
= ( ^ [X2: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_93_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) )
| ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) ) ) )
= ( ^ [X2: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) )
| ( ( X0 @ X1 )
& ~ ( X0 @ X1 ) ) ) )
= ( ^ [X2: a] : $false ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK0 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(boolean_simplification,[],[f7]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] : $false ) ),
inference(boolean_simplification,[],[f9]) ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET618^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n020.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:40:35 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.09/0.26 % (1064784)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (1064799)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=778216455: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)
% 0.09/0.26 % (1064799) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1064784-1064799"...
% 0.09/0.26 % (1064799)...printing done.
% 0.09/0.26 % (1064799)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (1064799)------------------------------
% 0.09/0.26 % (1064799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (1064799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (1064799)CaDiCaL version: 2.1.3
% 0.09/0.26 % (1064799)Termination reason: Refutation
% 0.09/0.26 % (1064799)Time elapsed: 0.001 s
% 0.09/0.26 % (1064799)Peak memory usage: 12 MB
% 0.09/0.26 % (1064799)Instructions burned: 1 (million)
% 0.09/0.26 % (1064784)Success in time 0.029 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------