%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:52:33 PM UTC 2026
% Result : Theorem 0.12s 0.47s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 10 unt; 4 def)
% Number of atoms : 163 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 172 ( 75 ~; 78 |; 1 &)
% ( 10 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 43 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,plain,
? [X0] :
( ( reflexive(X0)
<~> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,X2),X0)
| ~ is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f62,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f64,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f66,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X0] :
( ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
( in(sK3,relation_field(sK2))
| ~ reflexive(sK2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f75,plain,
( ~ in(ordered_pair(sK3,sK3),sK2)
| ~ reflexive(sK2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f76,plain,
! [X1] :
( ~ in(X1,relation_field(sK2))
| in(ordered_pair(X1,X1),sK2)
| reflexive(sK2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
relation(sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f93,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK0(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f63,f64]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ is_reflexive_in(X0,X1)
| ~ in(X2,X1)
| in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f61,f64]) ).
fof(f96,plain,
! [X1] :
( ~ in(X1,relation_field(sK2))
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),sK2)
| reflexive(sK2) ),
inference(definition_unfolding,[],[f76,f64]) ).
fof(f97,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK3),singleton(sK3)),sK2)
| ~ reflexive(sK2) ),
inference(definition_unfolding,[],[f75,f64]) ).
fof(f99,definition,
( spl9_1
<=> reflexive(sK2) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f100,plain,
( reflexive(sK2)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( ~ reflexive(sK2)
| spl9_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f103,definition,
( spl9_2
<=> in(sK3,relation_field(sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f105,plain,
( in(sK3,relation_field(sK2))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f74,f103,f99]) ).
fof(f108,definition,
( spl9_3
<=> in(unordered_pair(unordered_pair(sK3,sK3),singleton(sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f110,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK3),singleton(sK3)),sK2)
| spl9_3 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f97,f108,f99]) ).
fof(f113,definition,
( spl9_4
<=> ! [X1] :
( ~ in(X1,relation_field(sK2))
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),sK2) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f114,plain,
( ! [X1] :
( ~ in(X1,relation_field(sK2))
| in(unordered_pair(unordered_pair(X1,X1),singleton(X1)),sK2) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f96,f113,f99]) ).
fof(f116,plain,
( ! [X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),sK2)
| ~ in(X1,relation_field(sK2)) )
| ~ spl9_4 ),
inference(forward_demodulation,[],[f114,f59]) ).
fof(f170,plain,
( ~ is_reflexive_in(sK2,relation_field(sK2))
| ~ relation(sK2)
| spl9_1 ),
inference(resolution,[],[f66,f101]) ).
fof(f171,plain,
( ~ is_reflexive_in(sK2,relation_field(sK2))
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f170,f77]) ).
fof(f180,plain,
( in(sK0(sK2,relation_field(sK2)),relation_field(sK2))
| ~ relation(sK2)
| spl9_1 ),
inference(resolution,[],[f62,f171]) ).
fof(f181,plain,
( in(sK0(sK2,relation_field(sK2)),relation_field(sK2))
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f180,f77]) ).
fof(f194,plain,
( ~ in(unordered_pair(unordered_pair(sK0(sK2,relation_field(sK2)),sK0(sK2,relation_field(sK2))),singleton(sK0(sK2,relation_field(sK2)))),sK2)
| ~ relation(sK2)
| spl9_1 ),
inference(resolution,[],[f93,f171]) ).
fof(f198,plain,
( ~ in(unordered_pair(unordered_pair(sK0(sK2,relation_field(sK2)),sK0(sK2,relation_field(sK2))),singleton(sK0(sK2,relation_field(sK2)))),sK2)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f194,f77]) ).
fof(f200,plain,
( ~ in(unordered_pair(singleton(sK0(sK2,relation_field(sK2))),unordered_pair(sK0(sK2,relation_field(sK2)),sK0(sK2,relation_field(sK2)))),sK2)
| spl9_1 ),
inference(forward_demodulation,[],[f198,f59]) ).
fof(f219,plain,
( ~ in(sK0(sK2,relation_field(sK2)),relation_field(sK2))
| spl9_1
| ~ spl9_4 ),
inference(resolution,[],[f200,f116]) ).
fof(f220,plain,
( $false
| spl9_1
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f219,f181]) ).
fof(f221,plain,
( spl9_1
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f222,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK3)),sK2)
| spl9_3 ),
inference(forward_demodulation,[],[f110,f59]) ).
fof(f237,plain,
( is_reflexive_in(sK2,relation_field(sK2))
| ~ relation(sK2)
| ~ spl9_1 ),
inference(resolution,[],[f100,f67]) ).
fof(f238,plain,
( is_reflexive_in(sK2,relation_field(sK2))
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f237,f77]) ).
fof(f240,plain,
( ! [X0] :
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),sK2)
| ~ relation(sK2) )
| ~ spl9_1 ),
inference(resolution,[],[f238,f94]) ).
fof(f241,plain,
( ! [X0] :
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),sK2) )
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f240,f77]) ).
fof(f242,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK2)
| ~ in(X0,relation_field(sK2)) )
| ~ spl9_1 ),
inference(forward_demodulation,[],[f241,f59]) ).
fof(f246,plain,
( ~ in(sK3,relation_field(sK2))
| ~ spl9_1
| spl9_3 ),
inference(resolution,[],[f242,f222]) ).
fof(f250,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f246,f105]) ).
fof(f251,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f250]) ).
cnf(s1,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f106]) ).
cnf(s2,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(sat_conversion,[],[f111]) ).
cnf(s3,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f115]) ).
cnf(s7,plain,
( spl9_1
| ~ spl9_4 ),
inference(sat_conversion,[],[f221]) ).
cnf(s11,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f251]) ).
cnf(s12,plain,
spl9_1,
inference(rat,[],[s3,s7]) ).
cnf(s13,plain,
~ spl9_3,
inference(rat,[],[s2,s12]) ).
cnf(s14,plain,
spl9_2,
inference(rat,[],[s1,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s11,s12,s13,s14]) ).
fof(f252,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:19:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.47 % (2252742)Will run a generic schedule for satisfiability detection.
% 0.12/0.47 % (2252747)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=974298090_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.47 % TRYING [1]
% 0.12/0.47 % TRYING [2]
% 0.12/0.47 % TRYING [3]
% 0.12/0.47 % (2252753)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=303287289:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.47 % (2252749)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1018618151:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.47 % (2252750)dis+10_1_sil=32000:sp=arity:random_seed=2124728948:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.47 % (2252751)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2596886945:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.47 % (2252752)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1662005656:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.47 % (2252748)% WARNING: option uhcvi not known.
% 0.12/0.47 % (2252748)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1435540016:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.47 % (2252751) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2252742-2252751"...
% 0.12/0.47 % (2252752) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2252742-2252752"...
% 0.12/0.47 % (2252750) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2252742-2252750"...
% 0.12/0.47 % TRYING [4]
% 0.12/0.47 % (2252751)...printing done.
% 0.12/0.47 % (2252752)...printing done.
% 0.12/0.47 % (2252751)Refutation found. Thanks to Tanya!
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.48 % (2252751)------------------------------
% 0.12/0.48 % (2252751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.48 % (2252751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.48 % (2252751)CaDiCaL version: 2.1.3
% 0.12/0.48 % (2252751)Termination reason: Refutation
% 0.12/0.48 % (2252751)Time elapsed: 0.006 s
% 0.12/0.48 % (2252751)Peak memory usage: 12 MB
% 0.12/0.48 % (2252751)Instructions burned: 7 (million)
% 0.12/0.48 % (2252742)Success in time 0.043 s
% 0.12/0.48 % Vampire exiting
%------------------------------------------------------------------------------