%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU382+1 : 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 : 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 12:48:38 PM UTC 2026
% Result : Theorem 3.69s 1.51s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 78 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 21 |; 14 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 53 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f27,axiom,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f31,axiom,
! [X0] :
( reflexive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& transitive(inclusion_order(X0))
& v1_partfun1(inclusion_order(X0),X0,X0)
& relation_of2_as_subset(inclusion_order(X0),X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(f33,axiom,
! [X0] :
( strict_rel_str(incl_POSet(X0))
& rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(f60,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/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f78,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f84,conjecture,
! [X0] : the_carrier(boole_POSet(X0)) = powerset(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
fof(f85,negated_conjecture,
~ ! [X0] : the_carrier(boole_POSet(X0)) = powerset(X0),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f86,axiom,
! [X0] : boole_POSet(X0) = incl_POSet(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
fof(f93,plain,
! [X0] :
( reflexive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& transitive(inclusion_order(X0))
& relation_of2_as_subset(inclusion_order(X0),X0,X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f94,plain,
! [X0] :
( reflexive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& relation_of2_as_subset(inclusion_order(X0),X0,X0) ),
inference(pure_predicate_removal,[],[f93]) ).
fof(f95,plain,
! [X0] :
( reflexive(inclusion_order(X0))
& relation_of2_as_subset(inclusion_order(X0),X0,X0) ),
inference(pure_predicate_removal,[],[f94]) ).
fof(f96,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(pure_predicate_removal,[],[f95]) ).
fof(f99,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f99]) ).
fof(f161,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,[],[f60]) ).
fof(f173,plain,
? [X0] : powerset(X0) != the_carrier(boole_POSet(X0)),
inference(ennf_transformation,[],[f85]) ).
fof(f214,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f215,plain,
powerset(sK26) != the_carrier(boole_POSet(sK26)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X0,sK26)],[f173]) ).
fof(f216,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f323,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f326,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f327,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f328,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f161]) ).
fof(f494,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
fof(f501,plain,
powerset(sK26) != the_carrier(boole_POSet(sK26)),
inference(cnf_transformation,[],[f215]) ).
fof(f502,plain,
! [X0] : boole_POSet(X0) = incl_POSet(powerset(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f542,plain,
! [X0] : relation_of2(inclusion_order(X0),X0,X0),
inference(resolution,[],[f494,f326]) ).
fof(f637,plain,
! [X2,X0,X1] :
( rel_str_of(X0,inclusion_order(X0)) != rel_str_of(X1,X2)
| X0 = X1 ),
inference(resolution,[],[f542,f400]) ).
fof(f640,plain,
! [X2,X0,X1] :
( incl_POSet(X0) != rel_str_of(X1,X2)
| X0 = X1 ),
inference(forward_demodulation,[],[f637,f323]) ).
fof(f896,plain,
! [X0,X1] :
( incl_POSet(X1) != X0
| the_carrier(X0) = X1
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(superposition,[],[f640,f216]) ).
fof(f1067,plain,
! [X0] :
( the_carrier(incl_POSet(X0)) = X0
| ~ strict_rel_str(incl_POSet(X0))
| ~ rel_str(incl_POSet(X0)) ),
inference(equality_resolution,[],[f896]) ).
fof(f1068,plain,
! [X0] :
( the_carrier(incl_POSet(X0)) = X0
| ~ rel_str(incl_POSet(X0)) ),
inference(forward_subsumption_resolution,[],[f1067,f328]) ).
fof(f1069,plain,
! [X0] : the_carrier(incl_POSet(X0)) = X0,
inference(forward_subsumption_resolution,[],[f1068,f327]) ).
fof(f1070,plain,
! [X0] : powerset(X0) = the_carrier(boole_POSet(X0)),
inference(superposition,[],[f1069,f502]) ).
fof(f1090,plain,
powerset(sK26) != powerset(sK26),
inference(superposition,[],[f501,f1070]) ).
fof(f1101,plain,
$false,
inference(trivial_inequality_removal,[],[f1090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU382+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 05:05:01 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
% 3.69/1.51 % (2267900)Detected formulas, will run a generic FOF schedule.
% 3.69/1.51 % (2267906)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=3104232512:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.69/1.51 % (2267907)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=3986887194:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.69/1.51 % (2267905)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=1909324100:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.69/1.51 % (2267908)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2746714376:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.69/1.51 % (2267909)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3858712101:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.69/1.51 % (2267911)dis-21_1_sil=8000:lcm=predicate:random_seed=2690521545: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)
% 3.69/1.51 % (2267910)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2055488806:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.69/1.51 % (2267908)Refutation not found, incomplete strategy
% 3.69/1.51 % (2267908)------------------------------
% 3.69/1.51 % (2267908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.51 % (2267908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.51 % (2267908)CaDiCaL version: 2.1.3
% 3.69/1.51 % (2267908)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.51 % (2267908)Time elapsed: 0.001 s
% 3.69/1.51 % (2267908)Peak memory usage: 88 MB
% 3.69/1.51 % (2267908)Instructions burned: 1 (million)
% 3.69/1.51 % (2267909)Refutation not found, incomplete strategy
% 3.69/1.51 % (2267909)------------------------------
% 3.69/1.51 % (2267909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.51 % (2267909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.51 % (2267909)CaDiCaL version: 2.1.3
% 3.69/1.51 % (2267909)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.51 % (2267909)Time elapsed: 0.003 s
% 3.69/1.51 % (2267909)Peak memory usage: 88 MB
% 3.69/1.51 % (2267909)Instructions burned: 4 (million)
% 3.69/1.51 % (2267910)First to succeed.
% 3.69/1.51 % (2267910)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2267900"
% 3.69/1.51 % (2267911)Also succeeded, but the first one will report.
% 3.69/1.51 % (2267908)------------------------------
% 3.69/1.51 % (2267908)------------------------------
% 3.69/1.51 % (2267909)------------------------------
% 3.69/1.51 % (2267909)------------------------------
% 3.69/1.51 % (2267910)Refutation found. Thanks to Tanya!
% 3.69/1.51 % SZS status Theorem for theBenchmark
% 3.69/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.51 % (2267910)------------------------------
% 3.69/1.51 % (2267910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.51 % (2267910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.51 % (2267910)CaDiCaL version: 2.1.3
% 3.69/1.51 % (2267910)Termination reason: Refutation
% 3.69/1.51 % (2267910)Time elapsed: 0.020 s
% 3.69/1.51 % (2267910)Peak memory usage: 89 MB
% 3.69/1.51 % (2267910)Instructions burned: 26 (million)
% 3.69/1.51 % (2267910)------------------------------
% 3.69/1.51 % (2267910)------------------------------
% 3.69/1.51 % (2267900)Success in time 0.434 s
% 3.69/1.51 % Vampire exiting
%------------------------------------------------------------------------------