%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV233^5 : 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 : n026.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 08:38:05 AM UTC 2026
% Result : Theorem 0.22s 0.37s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 237 ( 54 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 194 ( 43 ~; 38 |; 20 &; 73 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 21 !; 6 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cE: $i > $o ).
thf(func_def_1,type,
cD: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f1,conjecture,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM46_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
=> ( ! [X2: $i] :
( ( X0 @ X2 )
=> ( cE @ X2 ) )
& ! [X3: $i] :
( ( X0 @ X3 )
=> ( cD @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) ) )
=> ( ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( cE @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( cD @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ? [X3: $i] :
( ( ( cD @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
| ? [X2: $i] :
( ( ( cE @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ? [X2: $i] :
( ( ( cD @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( cE @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( sK0 @ X1 )
!= $true ) )
& ( ( ( $true
!= ( cD @ sK1 ) )
& ( ( sK0 @ sK1 )
= $true ) )
| ( ( ( cE @ sK2 )
!= $true )
& ( ( sK0 @ sK2 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1),skolemize(X3,sK2)],[f6]) ).
thf(f8,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( ( sK0 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( ( cE @ sK2 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $true
!= ( cD @ sK1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( $true
!= ( cD @ sK1 ) )
| ( ( cE @ sK2 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
!= $true )
| ( ( cE @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
!= $true )
| ( ( cD @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,definition,
( spl3_1
<=> ( ( cE @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f18,plain,
( ( ( cE @ sK2 )
!= $true )
| spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,definition,
( spl3_2
<=> ( ( sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f20,f17]) ).
thf(f24,definition,
( spl3_3
<=> ( $true
= ( cD @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
!= ( cD @ sK1 ) )
| spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f26,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f11,f24,f17]) ).
thf(f28,definition,
( spl3_4
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f29,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f30,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f8,f20,f28]) ).
thf(f31,plain,
( ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f10,f28,f24]) ).
thf(f34,plain,
( ( $true
= ( cD @ sK1 ) )
| ( $true != $true )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f13,f21]) ).
thf(f35,plain,
( ( $true
= ( cD @ sK1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
( $false
| ~ spl3_2
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f35,f25]) ).
thf(f37,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f36]) ).
thf(f39,plain,
( ( ( cE @ sK2 )
= $true )
| ( $true != $true )
| ~ spl3_4 ),
inference(constrained_superposition,[],[f12,f29]) ).
thf(f41,plain,
( ( ( cE @ sK2 )
= $true )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f42,plain,
( $false
| spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f41,f18]) ).
thf(f43,plain,
( spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f42]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
( ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
( spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s7,plain,
spl3_4,
inference(rat,[],[s5,s3,s4]) ).
cnf(s8,plain,
spl3_1,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl3_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl3_2,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s9,s10]) ).
thf(f44,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV233^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.27 % Computer : n026.cluster.edu
% 0.22/0.27 % Model : x86_64 x86_64
% 0.22/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.27 % Memory : 8046.5625MB
% 0.22/0.27 % OS : Linux 6.8.0-71-generic
% 0.22/0.27 % CPULimit : 300
% 0.22/0.28 % WCLimit : 300
% 0.22/0.28 % DateTime : Tue Sep 29 15:26:12 UTC 2026
% 0.22/0.28 % CPUTime :
% 0.22/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.31 Running higher-order theorem proving
% 0.22/0.33 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
% 0.22/0.37 % (730116)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.37 % (730126)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1773699257:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.37 % (730126) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-730116-730126"...
% 0.22/0.37 % (730126)...printing done.
% 0.22/0.37 % (730126)Refutation found. Thanks to Tanya!
% 0.22/0.37 % SZS status Theorem for theBenchmark
% 0.22/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.37 % (730126)------------------------------
% 0.22/0.37 % (730126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (730126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (730126)CaDiCaL version: 2.1.3
% 0.22/0.37 % (730126)Termination reason: Refutation
% 0.22/0.37 % (730126)Time elapsed: 0.003 s
% 0.22/0.37 % (730126)Peak memory usage: 13 MB
% 0.22/0.37 % (730126)Instructions burned: 2 (million)
% 0.22/0.37 % (730116)Success in time 0.026 s
% 0.22/0.37 % Vampire exiting
%------------------------------------------------------------------------------