%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU257+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 : 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 12:52:37 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 16 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 223 ( 93 ~; 88 |; 24 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f8,axiom,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f9,axiom,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f10,axiom,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f11,axiom,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f12,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f13,conjecture,
! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f16,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f28,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
? [X0,X1] :
( ~ well_ordering(relation_restriction(X1,X0))
& well_ordering(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f30,plain,
? [X0,X1] :
( ~ well_ordering(relation_restriction(X1,X0))
& well_ordering(X1)
& relation(X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
( ~ well_ordering(relation_restriction(sK1,sK0))
& well_ordering(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f30]) ).
fof(f35,plain,
! [X0] :
( ~ well_ordering(X0)
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f36,plain,
! [X0] :
( ~ well_ordering(X0)
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0] :
( ~ well_ordering(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X0] :
( ~ well_ordering(X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f39,plain,
! [X0] :
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f40,plain,
! [X0] :
( ~ well_founded_relation(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X0,X1] :
( ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ connected(X1)
| connected(relation_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1] :
( ~ transitive(X1)
| transitive(relation_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X0,X1] :
( ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0,X1] :
( ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
relation(sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
well_ordering(sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
~ well_ordering(relation_restriction(sK1,sK0)),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
( well_founded_relation(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f35,f50]) ).
fof(f53,plain,
well_founded_relation(sK1),
inference(forward_subsumption_resolution,[],[f52,f49]) ).
fof(f54,plain,
( connected(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f36,f50]) ).
fof(f55,plain,
connected(sK1),
inference(forward_subsumption_resolution,[],[f54,f49]) ).
fof(f56,plain,
( antisymmetric(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f37,f50]) ).
fof(f57,plain,
antisymmetric(sK1),
inference(forward_subsumption_resolution,[],[f56,f49]) ).
fof(f58,plain,
( transitive(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f38,f50]) ).
fof(f59,plain,
transitive(sK1),
inference(forward_subsumption_resolution,[],[f58,f49]) ).
fof(f60,plain,
( reflexive(sK1)
| ~ relation(sK1) ),
inference(resolution,[],[f39,f50]) ).
fof(f61,plain,
reflexive(sK1),
inference(forward_subsumption_resolution,[],[f60,f49]) ).
fof(f62,plain,
! [X0] : relation(relation_restriction(sK1,X0)),
inference(resolution,[],[f42,f49]) ).
fof(f64,plain,
! [X0] :
( reflexive(relation_restriction(sK1,X0))
| ~ relation(sK1) ),
inference(resolution,[],[f44,f61]) ).
fof(f65,plain,
! [X0] : reflexive(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f64,f49]) ).
fof(f68,plain,
! [X0] :
( connected(relation_restriction(sK1,X0))
| ~ relation(sK1) ),
inference(resolution,[],[f45,f55]) ).
fof(f69,plain,
! [X0] : connected(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f68,f49]) ).
fof(f72,plain,
! [X0] :
( transitive(relation_restriction(sK1,X0))
| ~ relation(sK1) ),
inference(resolution,[],[f46,f59]) ).
fof(f73,plain,
! [X0] : transitive(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f72,f49]) ).
fof(f76,plain,
! [X0] :
( antisymmetric(relation_restriction(sK1,X0))
| ~ relation(sK1) ),
inference(resolution,[],[f47,f57]) ).
fof(f77,plain,
! [X0] : antisymmetric(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f76,f49]) ).
fof(f80,plain,
! [X0] :
( well_founded_relation(relation_restriction(sK1,X0))
| ~ relation(sK1) ),
inference(resolution,[],[f48,f53]) ).
fof(f81,plain,
! [X0] : well_founded_relation(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f80,f49]) ).
fof(f89,plain,
! [X0] :
( ~ reflexive(relation_restriction(sK1,X0))
| ~ transitive(relation_restriction(sK1,X0))
| ~ antisymmetric(relation_restriction(sK1,X0))
| ~ connected(relation_restriction(sK1,X0))
| well_ordering(relation_restriction(sK1,X0))
| ~ relation(relation_restriction(sK1,X0)) ),
inference(resolution,[],[f40,f81]) ).
fof(f90,plain,
! [X0] :
( ~ transitive(relation_restriction(sK1,X0))
| ~ antisymmetric(relation_restriction(sK1,X0))
| ~ connected(relation_restriction(sK1,X0))
| well_ordering(relation_restriction(sK1,X0))
| ~ relation(relation_restriction(sK1,X0)) ),
inference(forward_subsumption_resolution,[],[f89,f65]) ).
fof(f91,plain,
! [X0] :
( ~ antisymmetric(relation_restriction(sK1,X0))
| ~ connected(relation_restriction(sK1,X0))
| well_ordering(relation_restriction(sK1,X0))
| ~ relation(relation_restriction(sK1,X0)) ),
inference(forward_subsumption_resolution,[],[f90,f73]) ).
fof(f92,plain,
! [X0] :
( ~ connected(relation_restriction(sK1,X0))
| well_ordering(relation_restriction(sK1,X0))
| ~ relation(relation_restriction(sK1,X0)) ),
inference(forward_subsumption_resolution,[],[f91,f77]) ).
fof(f93,plain,
! [X0] :
( well_ordering(relation_restriction(sK1,X0))
| ~ relation(relation_restriction(sK1,X0)) ),
inference(forward_subsumption_resolution,[],[f92,f69]) ).
fof(f94,plain,
! [X0] : well_ordering(relation_restriction(sK1,X0)),
inference(forward_subsumption_resolution,[],[f93,f62]) ).
fof(f95,plain,
$false,
inference(resolution,[],[f94,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n006.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 04:21:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.47 % (3578038)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3578043)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2485071934_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % TRYING [6]
% 0.17/0.47 % (3578044)% WARNING: option uhcvi not known.
% 0.17/0.47 % TRYING [7]
% 0.17/0.47 % (3578046)dis+10_1_sil=32000:sp=arity:random_seed=2327975919:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % TRYING [8]
% 0.17/0.47 % (3578044)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2399884780:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3578045)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1726446997:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3578048)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1946124038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3578047)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2077613181:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3578049)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=293200263:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (3578048) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3578038-3578048"...
% 0.17/0.47 % (3578044) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3578038-3578044"...
% 0.17/0.47 % TRYING [9]
% 0.17/0.47 % (3578046) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3578038-3578046"...
% 0.17/0.47 % (3578048)...printing done.
% 0.17/0.47 % (3578044)...printing done.
% 0.17/0.47 % (3578048)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3578048)------------------------------
% 0.17/0.47 % (3578048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3578048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3578048)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3578048)Termination reason: Refutation
% 0.17/0.47 % (3578048)Time elapsed: 0.003 s
% 0.17/0.47 % (3578048)Peak memory usage: 11 MB
% 0.17/0.47 % (3578048)Instructions burned: 3 (million)
% 0.17/0.47 % (3578038)Success in time 0.046 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------