%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU261+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:48:03 PM UTC 2026
% Result : Theorem 4.53s 1.43s
% Output : Refutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 241 ( 87 ~; 81 |; 53 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 46 ( 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f51,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(f280,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( reflexive(X0)
=> reflexive(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( connected(X0)
=> connected(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( well_founded_relation(X0)
=> well_founded_relation(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f283,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( well_ordering(X0)
& relation_isomorphism(X0,X1,X2) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f284,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( well_ordering(X0)
& relation_isomorphism(X0,X1,X2) )
=> well_ordering(X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f283]) ).
fof(f324,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& well_ordering(X0)
& relation_isomorphism(X0,X1,X2)
& relation(X2)
& function(X2) )
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f284]) ).
fof(f325,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ well_ordering(X1)
& well_ordering(X0)
& relation_isomorphism(X0,X1,X2)
& relation(X2)
& function(X2) )
& relation(X1) )
& relation(X0) ),
inference(flattening,[],[f324]) ).
fof(f330,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f331,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( reflexive(X1)
| ~ reflexive(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( well_founded_relation(X1)
| ~ well_founded_relation(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f280]) ).
fof(f332,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( reflexive(X1)
| ~ reflexive(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( well_founded_relation(X1)
| ~ well_founded_relation(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f331]) ).
fof(f340,plain,
( ~ well_ordering(sK3)
& well_ordering(sK2)
& relation_isomorphism(sK2,sK3,sK4)
& relation(sK4)
& function(sK4)
& relation(sK3)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f325]) ).
fof(f344,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,[],[f330]) ).
fof(f345,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,[],[f344]) ).
fof(f352,plain,
relation(sK2),
inference(cnf_transformation,[],[f340]) ).
fof(f353,plain,
relation(sK3),
inference(cnf_transformation,[],[f340]) ).
fof(f354,plain,
function(sK4),
inference(cnf_transformation,[],[f340]) ).
fof(f355,plain,
relation(sK4),
inference(cnf_transformation,[],[f340]) ).
fof(f356,plain,
relation_isomorphism(sK2,sK3,sK4),
inference(cnf_transformation,[],[f340]) ).
fof(f357,plain,
well_ordering(sK2),
inference(cnf_transformation,[],[f340]) ).
fof(f358,plain,
~ well_ordering(sK3),
inference(cnf_transformation,[],[f340]) ).
fof(f368,plain,
! [X0] :
( ~ well_ordering(X0)
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f369,plain,
! [X0] :
( ~ well_ordering(X0)
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f370,plain,
! [X0] :
( ~ well_ordering(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f371,plain,
! [X0] :
( ~ well_ordering(X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f372,plain,
! [X0] :
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f373,plain,
! [X0] :
( ~ reflexive(X0)
| well_ordering(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f374,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ well_founded_relation(X0)
| well_founded_relation(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f375,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ antisymmetric(X0)
| antisymmetric(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f376,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ connected(X0)
| connected(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f377,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ transitive(X0)
| transitive(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f378,plain,
! [X2,X0,X1] :
( ~ relation_isomorphism(X0,X1,X2)
| ~ reflexive(X0)
| reflexive(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f395,plain,
well_founded_relation(sK2),
inference(unit_resulting_resolution,[],[f368,f352,f357]) ).
fof(f396,plain,
connected(sK2),
inference(unit_resulting_resolution,[],[f369,f352,f357]) ).
fof(f397,plain,
antisymmetric(sK2),
inference(unit_resulting_resolution,[],[f370,f352,f357]) ).
fof(f398,plain,
transitive(sK2),
inference(unit_resulting_resolution,[],[f371,f352,f357]) ).
fof(f399,plain,
reflexive(sK2),
inference(unit_resulting_resolution,[],[f372,f352,f357]) ).
fof(f481,plain,
well_founded_relation(sK3),
inference(unit_resulting_resolution,[],[f374,f352,f353,f354,f355,f395,f356]) ).
fof(f482,plain,
antisymmetric(sK3),
inference(unit_resulting_resolution,[],[f375,f352,f353,f354,f355,f397,f356]) ).
fof(f483,plain,
connected(sK3),
inference(unit_resulting_resolution,[],[f376,f352,f353,f354,f355,f396,f356]) ).
fof(f484,plain,
transitive(sK3),
inference(unit_resulting_resolution,[],[f377,f352,f353,f354,f355,f398,f356]) ).
fof(f485,plain,
~ reflexive(sK3),
inference(unit_resulting_resolution,[],[f373,f353,f481,f483,f482,f358,f484]) ).
fof(f486,plain,
reflexive(sK3),
inference(unit_resulting_resolution,[],[f378,f352,f353,f354,f355,f399,f356]) ).
fof(f487,plain,
$false,
inference(forward_subsumption_resolution,[],[f486,f485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU261+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n026.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Mon Sep 28 04:24:57 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.89/1.23 % (3455980)Detected formulas, will run a generic FOF schedule.
% 3.89/1.23 % (3455990)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2812798389:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.89/1.23 % (3455985)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=3864000158:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.89/1.23 % (3455986)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=955185759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.89/1.23 % (3455989)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4007222745:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.89/1.23 % (3455988)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1297189019:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.89/1.23 % (3455987)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=3264141162:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.89/1.23 % (3455991)dis-21_1_sil=8000:lcm=predicate:random_seed=1628109168: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)
% 3.89/1.23 % (3455990)Instruction limit reached!
% 3.89/1.23 % (3455990)------------------------------
% 3.89/1.23 % (3455990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.23 % (3455990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.23 % (3455990)CaDiCaL version: 2.1.3
% 3.89/1.23 % (3455990)Termination reason: Instruction limit
% 3.89/1.23 % (3455990)Termination phase: Saturation
% 3.89/1.23 % (3455990)Time elapsed: 0.050 s
% 3.89/1.23 % (3455990)Peak memory usage: 90 MB
% 3.89/1.23 % (3455990)Instructions burned: 139 (million)
% 3.89/1.23 % (3455988)Instruction limit reached!
% 3.89/1.23 % (3455988)------------------------------
% 3.89/1.23 % (3455988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.23 % (3455988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.23 % (3455988)CaDiCaL version: 2.1.3
% 3.89/1.23 % (3455988)Termination reason: Instruction limit
% 3.89/1.23 % (3455988)Termination phase: Saturation
% 3.89/1.23 % (3455988)Time elapsed: 0.069 s
% 3.89/1.23 % (3455988)Peak memory usage: 90 MB
% 3.89/1.23 % (3455988)Instructions burned: 111 (million)
% 3.89/1.23 % (3455991)Instruction limit reached!
% 3.89/1.23 % (3455991)------------------------------
% 3.89/1.23 % (3455991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.23 % (3455991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.23 % (3455991)CaDiCaL version: 2.1.3
% 3.89/1.23 % (3455991)Termination reason: Instruction limit
% 3.89/1.23 % (3455991)Termination phase: Saturation
% 3.89/1.23 % (3455991)Time elapsed: 0.075 s
% 3.89/1.23 % (3455991)Peak memory usage: 90 MB
% 3.89/1.23 % (3455991)Instructions burned: 129 (million)
% 3.89/1.23 % (3455989)Instruction limit reached!
% 3.89/1.23 % (3455989)------------------------------
% 3.89/1.23 % (3455989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.23 % (3455989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.23 % (3455989)CaDiCaL version: 2.1.3
% 3.89/1.23 % (3455989)Termination reason: Instruction limit
% 3.89/1.23 % (3455989)Termination phase: Saturation
% 3.89/1.23 % (3455989)Time elapsed: 0.080 s
% 3.89/1.23 % (3455989)Peak memory usage: 90 MB
% 3.89/1.23 % (3455989)Instructions burned: 120 (million)
% 3.89/1.23 % (3455999)lrs+10_1_sil=8000:sp=occurrence:random_seed=2352413914:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.89/1.23 % (3456000)lrs+10_1_sil=32000:urr=on:br=off:random_seed=105283358:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.89/1.23 % (3456000)First to succeed.
% 3.89/1.23 % (3456000)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3455980"
% 3.89/1.23 % (3456001)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3116385249:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.89/1.23 % (3456002)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1602196906:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.53/1.43 % (3456002)Also succeeded, but the first one will report.
% 4.53/1.43 % (3455999)Instruction limit reached!
% 4.53/1.43 % (3455999)------------------------------
% 4.53/1.43 % (3455999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.53/1.43 % (3455999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.53/1.43 % (3455999)CaDiCaL version: 2.1.3
% 4.53/1.43 % (3455999)Termination reason: Instruction limit
% 4.53/1.43 % (3455999)Termination phase: Saturation
% 4.53/1.43 % (3455999)Time elapsed: 0.102 s
% 4.53/1.43 % (3455999)Peak memory usage: 94 MB
% 4.53/1.43 % (3455999)Instructions burned: 286 (million)
% 4.53/1.43 % (3456007)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3514286740:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.53/1.43 % (3456007)Instruction limit reached!
% 4.53/1.43 % (3456007)------------------------------
% 4.53/1.43 % (3456007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.53/1.43 % (3456007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.53/1.43 % (3456007)CaDiCaL version: 2.1.3
% 4.53/1.43 % (3456007)Termination reason: Instruction limit
% 4.53/1.43 % (3456007)Termination phase: Saturation
% 4.53/1.43 % (3456007)Time elapsed: 0.100 s
% 4.53/1.43 % (3456007)Peak memory usage: 91 MB
% 4.53/1.43 % (3456007)Instructions burned: 300 (million)
% 4.53/1.43 % (3456001)Instruction limit reached!
% 4.53/1.43 % (3456001)------------------------------
% 4.53/1.43 % (3456001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.53/1.43 % (3456001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.53/1.43 % (3456001)CaDiCaL version: 2.1.3
% 4.53/1.43 % (3456001)Termination reason: Instruction limit
% 4.53/1.43 % (3456001)Termination phase: Saturation
% 4.53/1.43 % (3456001)Time elapsed: 0.223 s
% 4.53/1.43 % (3456001)Peak memory usage: 93 MB
% 4.53/1.43 % (3456001)Instructions burned: 326 (million)
% 4.53/1.43 % (3456000)Refutation found. Thanks to Tanya!
% 4.53/1.43 % SZS status Theorem for theBenchmark
% 4.53/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.53/1.43 % (3456000)------------------------------
% 4.53/1.43 % (3456000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.53/1.43 % (3456000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.53/1.43 % (3456000)CaDiCaL version: 2.1.3
% 4.53/1.43 % (3456000)Termination reason: Refutation
% 4.53/1.43 % (3456000)Time elapsed: 0.007 s
% 4.53/1.43 % (3456000)Peak memory usage: 89 MB
% 4.53/1.43 % (3456000)Instructions burned: 10 (million)
% 4.53/1.43 % (3456000)------------------------------
% 4.53/1.43 % (3456000)------------------------------
% 4.53/1.43 % (3455980)Success in time 0.585 s
% 4.53/1.43 % Vampire exiting
%------------------------------------------------------------------------------