%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET200^5 : 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 : 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 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 164 ( 58 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 190 ( 37 ~; 35 |; 20 &; 80 @)
% ( 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 : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 38 !; 15 ?; 53 :)
% 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 > $o ).
thf(func_def_6,type,
sK3: a > $o ).
thf(func_def_7,type,
sK4: a ).
thf(f1,conjecture,
! [X1: a > $o,X3: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) )
=> ! [X4: a] :
( ( ( X2 @ X4 )
| ( X0 @ X4 ) )
=> ( ( X1 @ X4 )
| ( X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_34_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X3: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) )
=> ! [X4: a] :
( ( ( X2 @ X4 )
| ( X0 @ X4 ) )
=> ( ( X1 @ X4 )
| ( X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) )
& ! [X5: a] :
( ( X2 @ X5 )
=> ( X0 @ X5 ) ) )
=> ! [X6: a] :
( ( ( X3 @ X6 )
| ( X2 @ X6 ) )
=> ( ( X0 @ X6 )
| ( X1 @ X6 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X3: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a] :
( ( ( X3 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( X2 @ X5 )
= $true )
=> ( $true
= ( X0 @ X5 ) ) ) )
=> ! [X6: a] :
( ( ( ( X2 @ X6 )
= $true )
| ( ( X3 @ X6 )
= $true ) )
=> ( ( ( X0 @ X6 )
= $true )
| ( ( X1 @ X6 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X3: a > $o,X1: a > $o,X0: a > $o] :
( ? [X6: a] :
( ( ( X0 @ X6 )
!= $true )
& ( ( X1 @ X6 )
!= $true )
& ( ( ( X2 @ X6 )
= $true )
| ( ( X3 @ X6 )
= $true ) ) )
& ! [X4: a] :
( ( ( X3 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o,X3: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( ( X3 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) )
& ? [X6: a] :
( ( ( X0 @ X6 )
!= $true )
& ( ( X1 @ X6 )
!= $true )
& ( ( ( X2 @ X6 )
= $true )
| ( ( X3 @ X6 )
= $true ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X0 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X3 @ X5 )
!= $true ) )
& ? [X6: a] :
( ( ( X1 @ X6 )
!= $true )
& ( ( X0 @ X6 )
!= $true )
& ( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X6 )
= $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( ( sK0 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( sK1 @ X5 )
= $true )
| ( $true
!= ( sK3 @ X5 ) ) )
& ( ( sK1 @ sK4 )
!= $true )
& ( $true
!= ( sK0 @ sK4 ) )
& ( ( ( sK3 @ sK4 )
= $true )
| ( ( sK2 @ sK4 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4)],[f7]) ).
thf(f9,plain,
( ( ( sK3 @ sK4 )
= $true )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( sK0 @ sK4 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( sK1 @ sK4 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X5: a] :
( ( $true
!= ( sK3 @ X5 ) )
| ( ( sK1 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( ( sK0 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,definition,
( spl5_1
<=> ( ( sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f19,plain,
( ( ( sK3 @ sK4 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f21,definition,
( spl5_2
<=> ( ( sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f23,plain,
( ( ( sK2 @ sK4 )
= $true )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f9,f21,f17]) ).
thf(f25,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true != $true )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f13,f23]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f26,f10]) ).
thf(f28,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f27]) ).
thf(f29,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $true != $true )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f12,f19]) ).
thf(f30,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f30,f11]) ).
thf(f32,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET200^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:37:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.07/0.25 % (3996717)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.25 % (3996729)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=239905436:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.25 % (3996729) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3996717-3996729"...
% 0.07/0.25 % (3996729)...printing done.
% 0.07/0.25 % (3996729)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (3996729)------------------------------
% 0.07/0.26 % (3996729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3996729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3996729)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3996729)Termination reason: Refutation
% 0.07/0.26 % (3996729)Time elapsed: 0.001 s
% 0.07/0.26 % (3996729)Peak memory usage: 13 MB
% 0.07/0.26 % (3996729)Instructions burned: 2 (million)
% 0.07/0.26 % (3996717)Success in time 0.017 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------