%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:47:55 PM UTC 2026
% Result : Theorem 3.63s 1.48s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 7 unt; 2 def)
% Number of atoms : 194 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 216 ( 81 ~; 87 |; 34 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f33,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X0,X1)
& X0 != X1
& ~ in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f35,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f58,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
? [X0] :
( ~ ordinal(X0)
& ! [X1] :
( ( ordinal(X1)
& subset(X1,X0) )
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f75,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X1,X2] :
( ~ in(X1,X0)
| ~ in(X2,X0)
| in(X1,X2)
| X1 = X2
| in(X2,X1) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( in(X1,X0)
& in(X2,X0)
& ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( in(sK1(X0),X0)
& in(sK2(X0),X0)
& ~ in(sK1(X0),sK2(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK2(X0),sK1(X0)) ) )
& ( ! [X3,X4] :
( ~ in(X3,X0)
| ~ in(X4,X0)
| in(X3,X4)
| X3 = X4
| in(X4,X3) )
| ~ epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f79]) ).
fof(f96,plain,
( ~ ordinal(sK16)
& ! [X1] :
( ( ordinal(X1)
& subset(X1,sK16) )
| ~ in(X1,sK16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f68]) ).
fof(f105,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f110,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f111,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f114,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f164,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f166,plain,
! [X1] :
( subset(X1,sK16)
| ~ in(X1,sK16) ),
inference(cnf_transformation,[],[f96]) ).
fof(f167,plain,
! [X1] :
( ~ in(X1,sK16)
| ordinal(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f168,plain,
~ ordinal(sK16),
inference(cnf_transformation,[],[f96]) ).
fof(f178,plain,
( ~ epsilon_transitive(sK16)
| ~ epsilon_connected(sK16) ),
inference(resolution,[],[f105,f168]) ).
fof(f180,definition,
( spl17_1
<=> epsilon_connected(sK16) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f182,plain,
( ~ epsilon_connected(sK16)
| spl17_1 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f184,definition,
( spl17_2
<=> epsilon_transitive(sK16) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f186,plain,
( ~ epsilon_transitive(sK16)
| spl17_2 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(avatar_split_clause,[],[f178,f184,f180]) ).
fof(f190,plain,
( in(sK2(sK16),sK16)
| spl17_1 ),
inference(resolution,[],[f116,f182]) ).
fof(f191,plain,
( ordinal(sK2(sK16))
| spl17_1 ),
inference(resolution,[],[f190,f167]) ).
fof(f194,plain,
( in(sK1(sK16),sK16)
| spl17_1 ),
inference(resolution,[],[f117,f182]) ).
fof(f195,plain,
( ordinal(sK1(sK16))
| spl17_1 ),
inference(resolution,[],[f194,f167]) ).
fof(f208,plain,
! [X0] :
( sK1(X0) = sK2(X0)
| in(sK1(X0),sK2(X0))
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f164,f113]) ).
fof(f211,plain,
! [X0] :
( in(sK1(X0),sK2(X0))
| ~ ordinal(sK1(X0))
| ~ ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f208,f114]) ).
fof(f214,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(sK2(X0))
| ~ ordinal(sK1(X0)) ),
inference(forward_subsumption_resolution,[],[f211,f115]) ).
fof(f249,plain,
( ~ ordinal(sK2(sK16))
| ~ ordinal(sK1(sK16))
| spl17_1 ),
inference(resolution,[],[f214,f182]) ).
fof(f250,plain,
( ~ ordinal(sK1(sK16))
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f249,f191]) ).
fof(f251,plain,
( $false
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f250,f195]) ).
fof(f252,plain,
spl17_1,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f253,plain,
( ~ subset(sK0(sK16),sK16)
| spl17_2 ),
inference(resolution,[],[f186,f111]) ).
fof(f254,plain,
( in(sK0(sK16),sK16)
| spl17_2 ),
inference(resolution,[],[f186,f110]) ).
fof(f257,plain,
( ~ in(sK0(sK16),sK16)
| spl17_2 ),
inference(resolution,[],[f253,f166]) ).
fof(f270,plain,
( $false
| spl17_2 ),
inference(forward_subsumption_resolution,[],[f257,f254]) ).
fof(f271,plain,
spl17_2,
inference(avatar_contradiction_clause,[],[f270]) ).
cnf(s1,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(sat_conversion,[],[f187]) ).
cnf(s2,plain,
spl17_1,
inference(sat_conversion,[],[f252]) ).
cnf(s3,plain,
spl17_2,
inference(sat_conversion,[],[f271]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f272,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n006.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:13:40 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.48 % (3573506)Detected formulas, will run a generic FOF schedule.
% 3.63/1.48 % (3573513)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3374976139:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.48 % (3573512)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1339174097:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.48 % (3573516)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=766362457:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.48 % (3573515)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1176669025:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.48 % (3573511)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=820373070:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.48 % (3573517)dis-21_1_sil=8000:lcm=predicate:random_seed=3584680142:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.63/1.48 % (3573514)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1145773503:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.48 % (3573514)Refutation not found, incomplete strategy
% 3.63/1.48 % (3573514)------------------------------
% 3.63/1.48 % (3573514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (3573514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (3573514)CaDiCaL version: 2.1.3
% 3.63/1.48 % (3573514)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (3573514)Time elapsed: 0.001 s
% 3.63/1.48 % (3573514)Peak memory usage: 86 MB
% 3.63/1.48 % (3573515)Refutation not found, incomplete strategy
% 3.63/1.48 % (3573515)------------------------------
% 3.63/1.48 % (3573515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (3573515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (3573515)CaDiCaL version: 2.1.3
% 3.63/1.48 % (3573515)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (3573515)Time elapsed: 0.002 s
% 3.63/1.48 % (3573515)Peak memory usage: 87 MB
% 3.63/1.48 % (3573515)Instructions burned: 1 (million)
% 3.63/1.48 % (3573516)First to succeed.
% 3.63/1.48 % (3573516)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3573506"
% 3.63/1.48 % (3573517)Also succeeded, but the first one will report.
% 3.63/1.48 % (3573514)------------------------------
% 3.63/1.48 % (3573514)------------------------------
% 3.63/1.48 % (3573515)------------------------------
% 3.63/1.48 % (3573515)------------------------------
% 3.63/1.48 % (3573516)Refutation found. Thanks to Tanya!
% 3.63/1.48 % SZS status Theorem for theBenchmark
% 3.63/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.48 % (3573516)------------------------------
% 3.63/1.48 % (3573516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (3573516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (3573516)CaDiCaL version: 2.1.3
% 3.63/1.48 % (3573516)Termination reason: Refutation
% 3.63/1.48 % (3573516)Time elapsed: 0.006 s
% 3.63/1.48 % (3573516)Peak memory usage: 89 MB
% 3.63/1.48 % (3573516)Instructions burned: 7 (million)
% 3.63/1.48 % (3573516)------------------------------
% 3.63/1.48 % (3573516)------------------------------
% 3.63/1.48 % (3573506)Success in time 0.435 s
% 3.63/1.48 % Vampire exiting
%------------------------------------------------------------------------------