%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:48:34 PM UTC 2026
% Result : Theorem 3.66s 1.48s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 119 ( 44 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 136 ( 65 ~; 53 |; 11 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 66 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f34,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f38,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f48,axiom,
! [X0] :
( strict_rel_str(incl_POSet(X0))
& rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(f49,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f51,axiom,
! [X0] :
( strict_rel_str(incl_POSet(X0))
& reflexive_relstr(incl_POSet(X0))
& transitive_relstr(incl_POSet(X0))
& antisymmetric_relstr(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).
fof(f52,axiom,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f53,conjecture,
! [X0] :
( the_carrier(incl_POSet(X0)) = X0
& the_InternalRel(incl_POSet(X0)) = inclusion_order(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).
fof(f54,negated_conjecture,
~ ! [X0] :
( the_carrier(incl_POSet(X0)) = X0
& the_InternalRel(incl_POSet(X0)) = inclusion_order(X0) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> relation_of2(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f57,plain,
! [X0] :
( strict_rel_str(incl_POSet(X0))
& reflexive_relstr(incl_POSet(X0))
& transitive_relstr(incl_POSet(X0)) ),
inference(pure_predicate_removal,[],[f51]) ).
fof(f61,plain,
! [X0] :
( strict_rel_str(incl_POSet(X0))
& reflexive_relstr(incl_POSet(X0)) ),
inference(pure_predicate_removal,[],[f57]) ).
fof(f63,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(pure_predicate_removal,[],[f61]) ).
fof(f68,plain,
? [X0] :
( the_carrier(incl_POSet(X0)) != X0
| inclusion_order(X0) != the_InternalRel(incl_POSet(X0)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f71,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X0 = X2
& X1 = X3 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f79,plain,
( sK0 != the_carrier(incl_POSet(sK0))
| inclusion_order(sK0) != the_InternalRel(incl_POSet(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f68]) ).
fof(f87,plain,
( sK0 != the_carrier(incl_POSet(sK0))
| inclusion_order(sK0) != the_InternalRel(incl_POSet(sK0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f89,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f63]) ).
fof(f90,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f93,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f94,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f95,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f104,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
( inclusion_order(sK0) != the_InternalRel(rel_str_of(sK0,inclusion_order(sK0)))
| sK0 != the_carrier(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(definition_unfolding,[],[f87,f95,f95]) ).
fof(f112,plain,
! [X0] : strict_rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(definition_unfolding,[],[f89,f95]) ).
fof(f114,plain,
! [X0] : rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(definition_unfolding,[],[f90,f95]) ).
fof(f118,plain,
! [X2,X0,X1] :
( rel_str_of(X1,X2) != X0
| the_InternalRel(X0) = X2
| ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(superposition,[],[f108,f94]) ).
fof(f121,plain,
! [X2,X0,X1] :
( rel_str_of(X1,X2) != X0
| the_carrier(X0) = X1
| ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(superposition,[],[f109,f94]) ).
fof(f148,plain,
! [X0,X1] :
( ~ relation_of2(the_InternalRel(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)))
| the_InternalRel(rel_str_of(X0,X1)) = X1
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1)) ),
inference(equality_resolution,[],[f118]) ).
fof(f151,plain,
! [X0,X1] :
( ~ relation_of2(the_InternalRel(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)))
| the_carrier(rel_str_of(X0,X1)) = X0
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1)) ),
inference(equality_resolution,[],[f121]) ).
fof(f211,plain,
! [X0,X1] :
( the_InternalRel(rel_str_of(X0,X1)) = X1
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1))
| ~ relation_of2_as_subset(the_InternalRel(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1))) ),
inference(resolution,[],[f148,f104]) ).
fof(f214,plain,
! [X0,X1] :
( the_InternalRel(rel_str_of(X0,X1)) = X1
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f211,f93]) ).
fof(f216,plain,
( inclusion_order(sK0) != inclusion_order(sK0)
| sK0 != the_carrier(rel_str_of(sK0,inclusion_order(sK0)))
| ~ strict_rel_str(rel_str_of(sK0,inclusion_order(sK0)))
| ~ rel_str(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(superposition,[],[f111,f214]) ).
fof(f222,plain,
( sK0 != the_carrier(rel_str_of(sK0,inclusion_order(sK0)))
| ~ strict_rel_str(rel_str_of(sK0,inclusion_order(sK0)))
| ~ rel_str(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(trivial_inequality_removal,[],[f216]) ).
fof(f223,plain,
( sK0 != the_carrier(rel_str_of(sK0,inclusion_order(sK0)))
| ~ rel_str(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(forward_subsumption_resolution,[],[f222,f112]) ).
fof(f224,plain,
sK0 != the_carrier(rel_str_of(sK0,inclusion_order(sK0))),
inference(forward_subsumption_resolution,[],[f223,f114]) ).
fof(f227,plain,
! [X0,X1] :
( the_carrier(rel_str_of(X0,X1)) = X0
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1))
| ~ relation_of2_as_subset(the_InternalRel(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1)),the_carrier(rel_str_of(X0,X1))) ),
inference(resolution,[],[f151,f104]) ).
fof(f232,plain,
! [X0,X1] :
( the_carrier(rel_str_of(X0,X1)) = X0
| ~ strict_rel_str(rel_str_of(X0,X1))
| ~ rel_str(rel_str_of(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f227,f93]) ).
fof(f234,plain,
( sK0 != sK0
| ~ strict_rel_str(rel_str_of(sK0,inclusion_order(sK0)))
| ~ rel_str(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(superposition,[],[f224,f232]) ).
fof(f244,plain,
( ~ strict_rel_str(rel_str_of(sK0,inclusion_order(sK0)))
| ~ rel_str(rel_str_of(sK0,inclusion_order(sK0))) ),
inference(trivial_inequality_removal,[],[f234]) ).
fof(f245,plain,
~ rel_str(rel_str_of(sK0,inclusion_order(sK0))),
inference(forward_subsumption_resolution,[],[f244,f112]) ).
fof(f246,plain,
$false,
inference(forward_subsumption_resolution,[],[f245,f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:55:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.48 % (3025170)Detected formulas, will run a generic FOF schedule.
% 3.66/1.48 % (3025178)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1947795161:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.48 % (3025178)Refutation not found, incomplete strategy
% 3.66/1.48 % (3025178)------------------------------
% 3.66/1.48 % (3025178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (3025178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (3025178)CaDiCaL version: 2.1.3
% 3.66/1.48 % (3025178)Termination reason: Refutation not found, incomplete strategy
% 3.66/1.48 % (3025178)Time elapsed: 0.001 s
% 3.66/1.48 % (3025178)Peak memory usage: 88 MB
% 3.66/1.48 % (3025181)dis-21_1_sil=8000:lcm=predicate:random_seed=2198283719: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)
% 3.66/1.48 % (3025177)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=3692784214:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.48 % (3025175)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=1163619462:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.48 % (3025176)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=3972530832:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.48 % (3025179)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=599338359:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.48 % (3025180)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4012145912:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.48 % (3025179)First to succeed.
% 3.66/1.48 % (3025179)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3025170"
% 3.66/1.48 % (3025180)Also succeeded, but the first one will report.
% 3.66/1.48 % (3025181)Also succeeded, but the first one will report.
% 3.66/1.48 % (3025178)------------------------------
% 3.66/1.48 % (3025178)------------------------------
% 3.66/1.48 % (3025189)lrs+10_1_sil=8000:sp=occurrence:random_seed=3714009059:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.48 % (3025189)Also succeeded, but the first one will report.
% 3.66/1.48 % (3025179)Refutation found. Thanks to Tanya!
% 3.66/1.48 % SZS status Theorem for theBenchmark
% 3.66/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.48 % (3025179)------------------------------
% 3.66/1.48 % (3025179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (3025179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (3025179)CaDiCaL version: 2.1.3
% 3.66/1.48 % (3025179)Termination reason: Refutation
% 3.66/1.48 % (3025179)Time elapsed: 0.007 s
% 3.66/1.48 % (3025179)Peak memory usage: 88 MB
% 3.66/1.48 % (3025179)Instructions burned: 8 (million)
% 3.66/1.48 % (3025179)------------------------------
% 3.66/1.48 % (3025179)------------------------------
% 3.66/1.48 % (3025170)Success in time 0.44 s
% 3.66/1.48 % Vampire exiting
%------------------------------------------------------------------------------