%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET585^5 : 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 : n003.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 08:23:18 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 60 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 74 ( 14 ~; 4 |; 16 &; 35 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 16 !; 12 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a ).
thf(func_def_6,type,
sK3: a > $o ).
thf(f1,conjecture,
! [X3: a,X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( ( X0 @ X3 )
| ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_38_pme) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( ( X0 @ X3 )
| ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ( X3 @ X0 )
& ( X2 @ X0 ) )
=> ( ( X3 @ X0 )
| ( X1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X3: a > $o,X0: a,X2: a > $o] :
( ( ( $true
= ( X2 @ X0 ) )
& ( $true
= ( X3 @ X0 ) ) )
=> ( ( $true
= ( X1 @ X0 ) )
| ( $true
= ( X3 @ X0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X3: a > $o,X0: a,X2: a > $o] :
( ( $true
!= ( X1 @ X0 ) )
& ( $true
!= ( X3 @ X0 ) )
& ( $true
= ( X2 @ X0 ) )
& ( $true
= ( X3 @ X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X2: a > $o,X1: a > $o,X0: a,X3: a > $o] :
( ( $true
!= ( X1 @ X0 ) )
& ( $true
= ( X3 @ X0 ) )
& ( $true
= ( X2 @ X0 ) )
& ( $true
!= ( X3 @ X0 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a,X3: a > $o] :
( ( ( X1 @ X2 )
!= $true )
& ( $true
= ( X3 @ X2 ) )
& ( ( X0 @ X2 )
= $true )
& ( $true
!= ( X3 @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( sK1 @ sK2 ) )
& ( $true
= ( sK3 @ sK2 ) )
& ( ( sK0 @ sK2 )
= $true )
& ( $true
!= ( sK3 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
( $true
!= ( sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( sK3 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,definition,
( spl4_2
<=> ( $true
= ( sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f23,plain,
spl4_2,
inference(avatar_split_clause,[],[f11,f20]) ).
thf(f29,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f9,f20]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f23]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f29]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
thf(f30,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET585^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:39:58 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.21/0.27 % (2508765)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2508773)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=727131649: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)
% 0.21/0.27 % (2508773) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2508765-2508773"...
% 0.21/0.27 % (2508773)...printing done.
% 0.21/0.27 % (2508773)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (2508773)------------------------------
% 0.21/0.27 % (2508773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2508773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2508773)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2508773)Termination reason: Refutation
% 0.21/0.27 % (2508773)Time elapsed: 0.001 s
% 0.21/0.27 % (2508773)Peak memory usage: 12 MB
% 0.21/0.27 % (2508773)Instructions burned: 1 (million)
% 0.21/0.27 % (2508765)Success in time 0.028 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------