%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 : Tue Sep 29 12:51:47 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 13 unt; 3 def)
% Number of atoms : 252 ( 15 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 292 ( 115 ~; 138 |; 20 &)
% ( 11 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f12,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f27,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f29,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f31,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f58,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f65]) ).
fof(f77,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f87,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f118,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) = X0
| identity_relation(X0) != X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f120,plain,
( ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12))
| ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f121,plain,
( in(apply(sK12,sK11),sK10)
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f122,plain,
( in(sK11,relation_dom(sK12))
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f123,plain,
function(sK12),
inference(cnf_transformation,[],[f66]) ).
fof(f124,plain,
relation(sK12),
inference(cnf_transformation,[],[f66]) ).
fof(f130,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f118]) ).
fof(f136,plain,
! [X0] : ~ relation(identity_relation(X0)),
inference(consistent_polarity_flipping,[],[f77]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ in(apply(X2,X0),relation_dom(X1))
| relation(X1)
| ~ function(X2)
| relation(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| relation(X1)
| ~ function(X2)
| relation(X2)
| in(X0,relation_dom(X2))
| ~ function(X1) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| relation(X1)
| ~ function(X2)
| relation(X2)
| in(apply(X2,X0),relation_dom(X1))
| ~ function(X1) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f155,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f159,plain,
~ relation(sK12),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f161,definition,
( spl13_1
<=> in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f162,plain,
( in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| spl13_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl13_2
<=> in(sK11,relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f166,plain,
( in(sK11,relation_dom(sK12))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl13_3
<=> in(apply(sK12,sK11),sK10) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f170,plain,
( in(apply(sK12,sK11),sK10)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f120,f169,f165,f161]) ).
fof(f173,plain,
( spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f121,f169,f161]) ).
fof(f174,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f122,f165,f161]) ).
fof(f216,plain,
! [X0] :
( relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f155,f87]) ).
fof(f217,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f216,f136]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ in(apply(X1,X2),X0)
| relation(identity_relation(X0))
| ~ function(X1)
| relation(X1)
| ~ function(identity_relation(X0))
| ~ in(X2,relation_dom(X1))
| in(X2,relation_dom(relation_composition(X1,identity_relation(X0)))) ),
inference(superposition,[],[f152,f217]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ in(apply(X1,X2),X0)
| ~ function(X1)
| relation(X1)
| ~ function(identity_relation(X0))
| ~ in(X2,relation_dom(X1))
| in(X2,relation_dom(relation_composition(X1,identity_relation(X0)))) ),
inference(forward_subsumption_resolution,[],[f246,f136]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ in(apply(X1,X2),X0)
| ~ function(X1)
| relation(X1)
| ~ in(X2,relation_dom(X1))
| in(X2,relation_dom(relation_composition(X1,identity_relation(X0)))) ),
inference(forward_subsumption_resolution,[],[f247,f87]) ).
fof(f421,plain,
( ~ function(sK12)
| relation(sK12)
| ~ in(sK11,relation_dom(sK12))
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ spl13_3 ),
inference(resolution,[],[f249,f170]) ).
fof(f426,plain,
( relation(sK12)
| ~ in(sK11,relation_dom(sK12))
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f421,f123]) ).
fof(f429,plain,
( ~ in(sK11,relation_dom(sK12))
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f426,f159]) ).
fof(f432,plain,
( in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f429,f166]) ).
fof(f435,plain,
( $false
| spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f432,f163]) ).
fof(f436,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f438,plain,
( relation(identity_relation(sK10))
| ~ function(sK12)
| relation(sK12)
| in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(resolution,[],[f162,f154]) ).
fof(f439,plain,
( relation(identity_relation(sK10))
| ~ function(sK12)
| relation(sK12)
| in(sK11,relation_dom(sK12))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(resolution,[],[f162,f153]) ).
fof(f445,plain,
( ~ function(sK12)
| relation(sK12)
| in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f438,f136]) ).
fof(f459,plain,
( relation(sK12)
| in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f445,f123]) ).
fof(f460,plain,
( in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f459,f159]) ).
fof(f461,plain,
( in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f460,f87]) ).
fof(f462,plain,
( in(apply(sK12,sK11),sK10)
| ~ spl13_1 ),
inference(forward_demodulation,[],[f461,f217]) ).
fof(f465,plain,
( spl13_3
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f462,f161,f169]) ).
fof(f466,plain,
( ~ function(sK12)
| relation(sK12)
| in(sK11,relation_dom(sK12))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f439,f136]) ).
fof(f467,plain,
( relation(sK12)
| in(sK11,relation_dom(sK12))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f466,f123]) ).
fof(f468,plain,
( in(sK11,relation_dom(sK12))
| ~ function(identity_relation(sK10))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f467,f159]) ).
fof(f469,plain,
( in(sK11,relation_dom(sK12))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f468,f87]) ).
fof(f470,plain,
( spl13_2
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f469,f161,f165]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f172]) ).
cnf(s2,plain,
( spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f173]) ).
cnf(s3,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s6,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(sat_conversion,[],[f436]) ).
cnf(s9,plain,
( ~ spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f465]) ).
cnf(s10,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f470]) ).
cnf(s12,plain,
spl13_1,
inference(rat,[],[s6,s2,s3]) ).
cnf(s13,plain,
spl13_2,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
spl13_3,
inference(rat,[],[s9,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s14,s12]) ).
fof(f471,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n020.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 03:22:34 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (3995017)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3995034)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3707901299_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (3995035)% WARNING: option uhcvi not known.
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (3995037)dis+10_1_sil=32000:sp=arity:random_seed=3498440053:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3995036)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1313146479:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3995035)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1929200919:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (3995040)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1293815002:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3995038)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1742839706:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3995041)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2868195851:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [6]
% 0.16/0.48 % (3995035) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3995017-3995035"...
% 0.16/0.48 % (3995037) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3995017-3995037"...
% 0.16/0.48 % (3995035)...printing done.
% 0.16/0.48 % (3995037)...printing done.
% 0.16/0.48 % (3995035)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3995035)------------------------------
% 0.16/0.48 % (3995035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3995035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3995035)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3995035)Termination reason: Refutation
% 0.16/0.48 % (3995035)Time elapsed: 0.013 s
% 0.16/0.48 % (3995035)Peak memory usage: 12 MB
% 0.16/0.48 % (3995035)Instructions burned: 16 (million)
% 0.16/0.48 % (3995017)Success in time 0.057 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------