%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV445^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:38:38 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 62 ( 8 ~; 2 |; 0 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 6 ^; 23 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK1: sK0 ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [X1: X0] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNIV_') ).
thf(f2,axiom,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [Y0: X0] : $true ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
? [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
!= $true ),
inference(ennf_transformation,[],[f6]) ).
thf(f9,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( X2 @ X1 )
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [Y0: X0] : $true ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( ( 'const/sets/IN' @ sK0 @ sK1
@ ^ [Y0: sK0] : $true )
!= $true ),
inference(definition_unfolding,[],[f11,f13]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $true )
| ( ( X2 @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f12]) ).
thf(f26,plain,
( ( $true != $true )
| ( $false
= ( ^ [Y0: sK0] : $true
@ sK1 ) ) ),
inference(constrained_superposition,[],[f16,f18]) ).
thf(f33,plain,
( $false
= ( ^ [Y0: sK0] : $true
@ sK1 ) ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f34,plain,
$false = $true,
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
$false,
inference(trivial_inequality_removal,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV445^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:47:01 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.29 % (2836593)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2836603)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2436052802:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (2836603) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2836593-2836603"...
% 0.23/0.29 % (2836603)...printing done.
% 0.23/0.29 % (2836603)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (2836603)------------------------------
% 0.23/0.29 % (2836603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2836603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2836603)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2836603)Termination reason: Refutation
% 0.23/0.29 % (2836603)Time elapsed: 0.001 s
% 0.23/0.29 % (2836603)Peak memory usage: 12 MB
% 0.23/0.29 % (2836603)Instructions burned: 1 (million)
% 0.23/0.29 % (2836593)Success in time 0.036 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------