%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET201^5 : 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 : n009.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 08:23:16 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 168 ( 57 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 176 ( 30 ~; 21 |; 28 &; 79 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cV: a > $o ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( cV @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 ) )
=> ( ( cV @ X3 )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_41_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( cV @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X0 @ X3 )
& ( X2 @ X3 ) )
=> ( ( cV @ X3 )
& ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( cV @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X5: a] :
( ( ( X0 @ X5 )
& ( X1 @ X5 ) )
=> ( ( cV @ X5 )
& ( X2 @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( cV @ X3 )
= $true ) ) )
=> ! [X5: a] :
( ( ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X0 @ X5 ) ) )
=> ( ( $true
= ( X2 @ X5 ) )
& ( ( cV @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( ( $true
!= ( X2 @ X5 ) )
| ( ( cV @ X5 )
!= $true ) )
& ( $true
= ( X1 @ X5 ) )
& ( $true
= ( X0 @ X5 ) ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( $true
= ( X0 @ X5 ) )
& ( ( $true
!= ( X2 @ X5 ) )
| ( ( cV @ X5 )
!= $true ) )
& ( $true
= ( X1 @ X5 ) ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( ( X2 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
!= $true ) )
& ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
= ( X1 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X2 @ X5 ) )
| ( ( cV @ X5 )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
= ( sK0 @ sK3 ) )
& ( ( ( sK1 @ sK3 )
!= $true )
| ( $true
!= ( cV @ sK3 ) ) )
& ( $true
= ( sK2 @ sK3 ) )
& ! [X4: a] :
( ( ( sK0 @ X4 )
!= $true )
| ( ( sK1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( ( cV @ X5 )
= $true ) ) ),
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,
! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( ( cV @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X4: a] :
( ( ( sK0 @ X4 )
!= $true )
| ( ( sK1 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( ( sK1 @ sK3 )
!= $true )
| ( $true
!= ( cV @ sK3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,definition,
( spl4_1
<=> ( $true
= ( cV @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f21,definition,
( spl4_2
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f23,plain,
( ( ( sK1 @ sK3 )
!= $true )
| spl4_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f12,f21,f17]) ).
thf(f25,plain,
( ( $true
= ( cV @ sK3 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f11]) ).
thf(f26,plain,
( $true
= ( cV @ sK3 ) ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f29,plain,
spl4_1,
inference(avatar_split_clause,[],[f26,f17]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f10,f13]) ).
thf(f31,plain,
( ( sK1 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( $false
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f31,f23]) ).
thf(f33,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
spl4_2,
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET201^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n009.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 13:37:45 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.20 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
% 0.08/0.26 % (3996459)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (3996465)lrs+10_16_si=on:nwc=1.5:random_seed=3470085102:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.26 % (3996465) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3996459-3996465"...
% 0.08/0.26 % (3996465)...printing done.
% 0.08/0.26 % (3996465)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3996465)------------------------------
% 0.08/0.26 % (3996465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3996465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3996465)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3996465)Termination reason: Refutation
% 0.08/0.26 % (3996465)Time elapsed: 0.002 s
% 0.08/0.26 % (3996465)Peak memory usage: 13 MB
% 0.08/0.26 % (3996465)Instructions burned: 2 (million)
% 0.08/0.26 % (3996459)Success in time 0.041 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------