%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU234+3 : 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 : n002.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 12:52:32 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 8 unt; 3 def)
% Number of atoms : 167 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 61 ~; 75 |; 11 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 51 ( 0 sgn 50 !; 1 ?)
% 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(f31,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(f33,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( ordinal(X1)
& subset(X1,X0) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f57,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(flattening,[],[f57]) ).
fof(f60,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f61,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(f63,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| X0 = X1
| in(X1,X0)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f63]) ).
fof(f67,plain,
? [X0] :
( ~ ordinal(X0)
& ! [X1] :
( ( ordinal(X1)
& subset(X1,X0) )
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f79,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f84,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f85,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f87,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f89,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f140,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f142,plain,
! [X1] :
( ~ in(X1,sK17)
| subset(X1,sK17) ),
inference(cnf_transformation,[],[f67]) ).
fof(f143,plain,
! [X1] :
( ~ in(X1,sK17)
| ordinal(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f144,plain,
~ ordinal(sK17),
inference(cnf_transformation,[],[f67]) ).
fof(f157,plain,
! [X0] :
( ~ ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(consistent_polarity_flipping,[],[f79]) ).
fof(f161,plain,
! [X0] :
( subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f162,plain,
! [X0] :
( ~ in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f164,plain,
! [X0] :
( ~ in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f165,plain,
! [X0] :
( ~ in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f166,plain,
! [X0] :
( in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f167,plain,
! [X0] :
( in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f189,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X1)
| ~ in(X1,X0)
| X0 = X1
| ordinal(X0) ),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f191,plain,
ordinal(sK17),
inference(consistent_polarity_flipping,[],[f144]) ).
fof(f192,plain,
! [X1] :
( in(X1,sK17)
| ~ ordinal(X1) ),
inference(consistent_polarity_flipping,[],[f143]) ).
fof(f193,plain,
! [X1] :
( ~ subset(X1,sK17)
| in(X1,sK17) ),
inference(consistent_polarity_flipping,[],[f142]) ).
fof(f210,plain,
( ~ epsilon_transitive(sK17)
| ~ epsilon_connected(sK17) ),
inference(resolution,[],[f157,f191]) ).
fof(f212,definition,
( spl18_1
<=> epsilon_connected(sK17) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f214,plain,
( ~ epsilon_connected(sK17)
| spl18_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f216,definition,
( spl18_2
<=> epsilon_transitive(sK17) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f219,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f210,f216,f212]) ).
fof(f220,plain,
( epsilon_transitive(sK17)
| in(sK0(sK17),sK17) ),
inference(resolution,[],[f161,f193]) ).
fof(f222,definition,
( spl18_3
<=> in(sK0(sK17),sK17) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f224,plain,
( in(sK0(sK17),sK17)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,plain,
( spl18_3
| spl18_2 ),
inference(avatar_split_clause,[],[f220,f216,f222]) ).
fof(f237,plain,
( epsilon_connected(sK17)
| ~ ordinal(sK1(sK17)) ),
inference(resolution,[],[f164,f192]) ).
fof(f241,plain,
( ~ ordinal(sK1(sK17))
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f237,f214]) ).
fof(f242,plain,
( epsilon_connected(sK17)
| ~ ordinal(sK2(sK17)) ),
inference(resolution,[],[f165,f192]) ).
fof(f246,plain,
( ~ ordinal(sK2(sK17))
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f242,f214]) ).
fof(f276,plain,
! [X0] :
( ordinal(sK1(X0))
| ~ in(sK1(X0),sK2(X0))
| sK1(X0) = sK2(X0)
| ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(resolution,[],[f189,f167]) ).
fof(f277,plain,
! [X0] :
( ordinal(sK1(X0))
| sK1(X0) = sK2(X0)
| ordinal(sK2(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f276,f166]) ).
fof(f280,plain,
! [X0] :
( ordinal(sK2(X0))
| ordinal(sK1(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[],[f277,f88]) ).
fof(f288,plain,
( epsilon_transitive(sK17)
| ~ spl18_3 ),
inference(resolution,[],[f224,f162]) ).
fof(f290,plain,
( spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f288,f222,f216]) ).
fof(f339,plain,
( ordinal(sK1(sK17))
| epsilon_connected(sK17)
| spl18_1 ),
inference(resolution,[],[f280,f246]) ).
fof(f342,plain,
( epsilon_connected(sK17)
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f339,f241]) ).
fof(f343,plain,
( $false
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f342,f214]) ).
fof(f344,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f343]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f219]) ).
cnf(s2,plain,
( spl18_2
| spl18_3 ),
inference(sat_conversion,[],[f225]) ).
cnf(s4,plain,
( spl18_2
| ~ spl18_3 ),
inference(sat_conversion,[],[f290]) ).
cnf(s5,plain,
spl18_1,
inference(sat_conversion,[],[f344]) ).
cnf(s6,plain,
~ spl18_2,
inference(rat,[],[s1,s5]) ).
cnf(s7,plain,
~ spl18_3,
inference(rat,[],[s4,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f345,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:16:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.46 % (4138147)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (4138156)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=314494283:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (4138153)% WARNING: option uhcvi not known.
% 0.16/0.46 % (4138152)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2981780539_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (4138153)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=647371847:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (4138154)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3833131326:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (4138155)dis+10_1_sil=32000:sp=arity:random_seed=215409172:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (4138158)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=680923592:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (4138157)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2499367564:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % (4138153) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4138147-4138153"...
% 0.16/0.46 % (4138155) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4138147-4138155"...
% 0.16/0.46 % TRYING [5]
% 0.16/0.46 % (4138153)...printing done.
% 0.16/0.46 % (4138155)...printing done.
% 0.16/0.46 % (4138153)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (4138153)------------------------------
% 0.16/0.46 % (4138153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (4138153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (4138153)CaDiCaL version: 2.1.3
% 0.16/0.46 % (4138153)Termination reason: Refutation
% 0.16/0.46 % (4138153)Time elapsed: 0.007 s
% 0.16/0.46 % (4138153)Peak memory usage: 12 MB
% 0.16/0.46 % (4138153)Instructions burned: 8 (million)
% 0.16/0.46 % (4138147)Success in time 0.042 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------