TSTP Solution File: SEU261+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU261+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:30:28 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 320 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 377 ( 134 ~; 118 |; 100 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 69 ( 54 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,plain,
$false,
inference(subsumption_resolution,[],[f90,f85]) ).
fof(f85,plain,
reflexive(sK4),
inference(subsumption_resolution,[],[f80,f64]) ).
fof(f64,plain,
reflexive(sK3),
inference(resolution,[],[f59,f36]) ).
fof(f36,plain,
! [X0] :
( ~ sP0(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( sP0(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ sP0(X0) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0] :
( ( sP0(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] :
( sP0(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f59,plain,
sP0(sK3),
inference(subsumption_resolution,[],[f55,f31]) ).
fof(f31,plain,
well_ordering(sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ~ well_ordering(sK4)
& relation_isomorphism(sK3,sK4,sK5)
& well_ordering(sK3)
& function(sK5)
& relation(sK5)
& relation(sK4)
& relation(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f7,f18,f17,f16]) ).
fof(f16,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& relation_isomorphism(X0,X1,X2)
& well_ordering(X0)
& function(X2)
& relation(X2) )
& relation(X1) )
& relation(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& relation_isomorphism(sK3,X1,X2)
& well_ordering(sK3)
& function(X2)
& relation(X2) )
& relation(X1) )
& relation(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& relation_isomorphism(sK3,X1,X2)
& well_ordering(sK3)
& function(X2)
& relation(X2) )
& relation(X1) )
=> ( ? [X2] :
( ~ well_ordering(sK4)
& relation_isomorphism(sK3,sK4,X2)
& well_ordering(sK3)
& function(X2)
& relation(X2) )
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
( ? [X2] :
( ~ well_ordering(sK4)
& relation_isomorphism(sK3,sK4,X2)
& well_ordering(sK3)
& function(X2)
& relation(X2) )
=> ( ~ well_ordering(sK4)
& relation_isomorphism(sK3,sK4,sK5)
& well_ordering(sK3)
& function(sK5)
& relation(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f7,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& relation_isomorphism(X0,X1,X2)
& well_ordering(X0)
& function(X2)
& relation(X2) )
& relation(X1) )
& relation(X0) ),
inference(flattening,[],[f6]) ).
fof(f6,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& relation_isomorphism(X0,X1,X2)
& well_ordering(X0)
& function(X2)
& relation(X2) )
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_isomorphism(X0,X1,X2)
& well_ordering(X0) )
=> well_ordering(X1) ) ) ) ),
inference(negated_conjecture,[],[f4]) ).
fof(f4,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_isomorphism(X0,X1,X2)
& well_ordering(X0) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f55,plain,
( ~ well_ordering(sK3)
| sP0(sK3) ),
inference(resolution,[],[f34,f51]) ).
fof(f51,plain,
sP1(sK3),
inference(resolution,[],[f42,f27]) ).
fof(f27,plain,
relation(sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f8,f12,f11]) ).
fof(f12,plain,
! [X0] :
( ( well_ordering(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f34,plain,
! [X0] :
( ~ sP1(X0)
| ~ well_ordering(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ well_ordering(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f12]) ).
fof(f80,plain,
( ~ reflexive(sK3)
| reflexive(sK4) ),
inference(resolution,[],[f75,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ reflexive(X1)
| reflexive(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ( well_founded_relation(X0)
| ~ well_founded_relation(X1) )
& ( antisymmetric(X0)
| ~ antisymmetric(X1) )
& ( connected(X0)
| ~ connected(X1) )
& ( transitive(X0)
| ~ transitive(X1) )
& ( reflexive(X0)
| ~ reflexive(X1) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f75,plain,
sP2(sK4,sK3),
inference(subsumption_resolution,[],[f74,f27]) ).
fof(f74,plain,
( sP2(sK4,sK3)
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f73,f28]) ).
fof(f28,plain,
relation(sK4),
inference(cnf_transformation,[],[f19]) ).
fof(f73,plain,
( sP2(sK4,sK3)
| ~ relation(sK4)
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f72,f29]) ).
fof(f29,plain,
relation(sK5),
inference(cnf_transformation,[],[f19]) ).
fof(f72,plain,
( sP2(sK4,sK3)
| ~ relation(sK5)
| ~ relation(sK4)
| ~ relation(sK3) ),
inference(subsumption_resolution,[],[f71,f30]) ).
fof(f30,plain,
function(sK5),
inference(cnf_transformation,[],[f19]) ).
fof(f71,plain,
( sP2(sK4,sK3)
| ~ function(sK5)
| ~ relation(sK5)
| ~ relation(sK4)
| ~ relation(sK3) ),
inference(resolution,[],[f48,f32]) ).
fof(f32,plain,
relation_isomorphism(sK3,sK4,sK5),
inference(cnf_transformation,[],[f19]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| sP2(X1,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP2(X1,X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f10,f14]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( well_founded_relation(X0)
=> well_founded_relation(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( connected(X0)
=> connected(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( reflexive(X0)
=> reflexive(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f90,plain,
~ reflexive(sK4),
inference(subsumption_resolution,[],[f89,f84]) ).
fof(f84,plain,
transitive(sK4),
inference(subsumption_resolution,[],[f79,f63]) ).
fof(f63,plain,
transitive(sK3),
inference(resolution,[],[f59,f37]) ).
fof(f37,plain,
! [X0] :
( ~ sP0(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f79,plain,
( ~ transitive(sK3)
| transitive(sK4) ),
inference(resolution,[],[f75,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ transitive(X1)
| transitive(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f89,plain,
( ~ transitive(sK4)
| ~ reflexive(sK4) ),
inference(subsumption_resolution,[],[f88,f82]) ).
fof(f82,plain,
antisymmetric(sK4),
inference(subsumption_resolution,[],[f77,f62]) ).
fof(f62,plain,
antisymmetric(sK3),
inference(resolution,[],[f59,f38]) ).
fof(f38,plain,
! [X0] :
( ~ sP0(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f77,plain,
( ~ antisymmetric(sK3)
| antisymmetric(sK4) ),
inference(resolution,[],[f75,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ antisymmetric(X1)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f88,plain,
( ~ antisymmetric(sK4)
| ~ transitive(sK4)
| ~ reflexive(sK4) ),
inference(subsumption_resolution,[],[f87,f83]) ).
fof(f83,plain,
connected(sK4),
inference(subsumption_resolution,[],[f78,f61]) ).
fof(f61,plain,
connected(sK3),
inference(resolution,[],[f59,f39]) ).
fof(f39,plain,
! [X0] :
( ~ sP0(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f78,plain,
( ~ connected(sK3)
| connected(sK4) ),
inference(resolution,[],[f75,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ connected(X1)
| connected(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f87,plain,
( ~ connected(sK4)
| ~ antisymmetric(sK4)
| ~ transitive(sK4)
| ~ reflexive(sK4) ),
inference(subsumption_resolution,[],[f86,f69]) ).
fof(f69,plain,
~ sP0(sK4),
inference(subsumption_resolution,[],[f66,f33]) ).
fof(f33,plain,
~ well_ordering(sK4),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
( ~ sP0(sK4)
| well_ordering(sK4) ),
inference(resolution,[],[f35,f52]) ).
fof(f52,plain,
sP1(sK4),
inference(resolution,[],[f42,f28]) ).
fof(f35,plain,
! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f86,plain,
( sP0(sK4)
| ~ connected(sK4)
| ~ antisymmetric(sK4)
| ~ transitive(sK4)
| ~ reflexive(sK4) ),
inference(resolution,[],[f81,f41]) ).
fof(f41,plain,
! [X0] :
( ~ well_founded_relation(X0)
| sP0(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f81,plain,
well_founded_relation(sK4),
inference(subsumption_resolution,[],[f76,f60]) ).
fof(f60,plain,
well_founded_relation(sK3),
inference(resolution,[],[f59,f40]) ).
fof(f40,plain,
! [X0] :
( ~ sP0(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f76,plain,
( ~ well_founded_relation(sK3)
| well_founded_relation(sK4) ),
inference(resolution,[],[f75,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ well_founded_relation(X1)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU261+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 11:17:25 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (8972)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (8975)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (8976)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (8980)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 % (8979)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 % (8977)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38 % (8981)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 % (8978)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38 Detected minimum model sizes of [1]
% 0.14/0.38 Detected maximum model sizes of [4]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 Detected minimum model sizes of [1]
% 0.14/0.38 Detected maximum model sizes of [4]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 Detected minimum model sizes of [1]
% 0.14/0.38 Detected maximum model sizes of [4]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 Detected minimum model sizes of [1]
% 0.14/0.38 Detected maximum model sizes of [4]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (8979)First to succeed.
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (8975)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (8980)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (8977)Also succeeded, but the first one will report.
% 0.14/0.38 % (8976)Also succeeded, but the first one will report.
% 0.14/0.38 % (8978)Also succeeded, but the first one will report.
% 0.14/0.38 % (8979)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8972"
% 0.14/0.38 TRYING [4]
% 0.14/0.39 % (8979)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (8979)------------------------------
% 0.14/0.39 % (8979)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (8979)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (8979)Memory used [KB]: 743
% 0.14/0.39 % (8979)Time elapsed: 0.005 s
% 0.14/0.39 % (8979)Instructions burned: 5 (million)
% 0.14/0.39 % (8972)Success in time 0.018 s
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