%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU188+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 : n019.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 12:47:38 PM UTC 2026
% Result : Theorem 3.40s 1.36s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 77 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 34 ~; 30 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f20,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f21,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f31,conjecture,
! [X0] :
( relation(X0)
=> ( ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f36,plain,
? [X0] :
( empty_set != X0
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f37,plain,
? [X0] :
( empty_set != X0
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f40]) ).
fof(f45,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f46,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f53,plain,
( empty_set != sK0
& ( empty_set = relation_dom(sK0)
| empty_set = relation_rng(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f37]) ).
fof(f65,plain,
relation(sK0),
inference(cnf_transformation,[],[f53]) ).
fof(f66,plain,
( empty_set = relation_rng(sK0)
| empty_set = relation_dom(sK0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f67,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f53]) ).
fof(f71,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f107,plain,
! [X0] :
( sK0 != X0
| ~ empty(X0) ),
inference(superposition,[],[f67,f88]) ).
fof(f108,plain,
~ empty(sK0),
inference(equality_resolution,[],[f107]) ).
fof(f112,plain,
( ~ empty(empty_set)
| empty(sK0)
| ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(superposition,[],[f83,f66]) ).
fof(f113,plain,
( empty(sK0)
| ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(forward_subsumption_resolution,[],[f112,f91]) ).
fof(f114,plain,
( ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(forward_subsumption_resolution,[],[f113,f108]) ).
fof(f115,plain,
empty_set = relation_dom(sK0),
inference(forward_subsumption_resolution,[],[f114,f65]) ).
fof(f116,plain,
( ~ empty(empty_set)
| empty(sK0)
| ~ relation(sK0) ),
inference(superposition,[],[f71,f115]) ).
fof(f119,plain,
( empty(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f116,f91]) ).
fof(f120,plain,
~ relation(sK0),
inference(forward_subsumption_resolution,[],[f119,f108]) ).
fof(f121,plain,
$false,
inference(forward_subsumption_resolution,[],[f120,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:57:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.40/1.36 % (3645381)Detected formulas, will run a generic FOF schedule.
% 3.40/1.36 % (3645388)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=1851812477:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.36 % (3645386)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=3994916276:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.36 % (3645389)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=427256548:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.36 % (3645390)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1379820755:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.36 % (3645392)dis-21_1_sil=8000:lcm=predicate:random_seed=55812036: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)
% 3.40/1.36 % (3645387)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=421060842:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.36 % (3645391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2184117044:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.36 % (3645390)First to succeed.
% 3.40/1.36 % (3645389)Also succeeded, but the first one will report.
% 3.40/1.36 % (3645390)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3645381"
% 3.40/1.36 % (3645391)Also succeeded, but the first one will report.
% 3.40/1.36 % (3645392)Refutation not found, incomplete strategy
% 3.40/1.36 % (3645392)------------------------------
% 3.40/1.36 % (3645392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.36 % (3645392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.36 % (3645392)CaDiCaL version: 2.1.3
% 3.40/1.36 % (3645392)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.36 % (3645392)Time elapsed: 0.020 s
% 3.40/1.36 % (3645392)Peak memory usage: 89 MB
% 3.40/1.36 % (3645392)Instructions burned: 30 (million)
% 3.40/1.36 % (3645390)Refutation found. Thanks to Tanya!
% 3.40/1.36 % SZS status Theorem for theBenchmark
% 3.40/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.36 % (3645390)------------------------------
% 3.40/1.36 % (3645390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.36 % (3645390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.36 % (3645390)CaDiCaL version: 2.1.3
% 3.40/1.36 % (3645390)Termination reason: Refutation
% 3.40/1.36 % (3645390)Time elapsed: 0.003 s
% 3.40/1.36 % (3645390)Peak memory usage: 88 MB
% 3.40/1.36 % (3645390)Instructions burned: 2 (million)
% 3.40/1.36 % (3645390)------------------------------
% 3.40/1.36 % (3645390)------------------------------
% 3.40/1.36 % (3645381)Success in time 0.414 s
% 3.40/1.36 % Vampire exiting
%------------------------------------------------------------------------------