%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO286^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:47:21 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 49 ( 7 ~; 0 |; 8 &; 26 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 17 ( 1 ^; 9 !; 7 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTEST1) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ( X0 @ y )
= $true )
=> ( ? [X1: $i] :
( ( cR @ X1 )
= $true )
=> ( ( cQ @ y )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cQ @ y )
!= $true )
& ? [X1: $i] :
( ( cR @ X1 )
= $true )
& ! [X0: $i > $o] :
( ( X0 @ y )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X1: $i] :
( ( cR @ X1 )
= $true )
& ( ( cQ @ y )
!= $true )
& ! [X0: $i > $o] :
( ( X0 @ y )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i] :
( $true
= ( cR @ X0 ) )
& ( ( cQ @ y )
!= $true )
& ! [X1: $i > $o] :
( $true
= ( X1 @ y ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
= ( cR @ sK0 ) )
& ( ( cQ @ y )
!= $true )
& ! [X1: $i > $o] :
( $true
= ( X1 @ y ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X1: $i > $o] :
( $true
= ( X1 @ y ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( ^ [Y0: $i] : $false
@ y )
= $true ),
inference(primitive_instantiation,[],[f9]) ).
thf(f17,plain,
$false = $true,
inference(beta-eta_normalization,[],[f15]) ).
thf(f18,plain,
$false,
inference(trivial_inequality_removal,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO286^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:43:00 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.27 % (2908144)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2908161)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3209174776:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (2908161) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2908144-2908161"...
% 0.20/0.27 % (2908161)...printing done.
% 0.20/0.27 % (2908161)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2908161)------------------------------
% 0.20/0.27 % (2908161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2908161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2908161)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2908161)Termination reason: Refutation
% 0.20/0.27 % (2908161)Time elapsed: 0.001 s
% 0.20/0.27 % (2908161)Peak memory usage: 12 MB
% 0.20/0.27 % (2908161)Instructions burned: 1 (million)
% 0.20/0.27 % (2908144)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------