%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU189+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 : n002.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 12:47:39 PM UTC 2026
% Result : Theorem 3.60s 1.48s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 9 unt; 0 def)
% Number of atoms : 97 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 48 ~; 39 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 1 <~>)
% 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 : 18 ( 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f10,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f21,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f22,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f23,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f27,plain,
? [X0] :
( ( relation_dom(X0) = empty_set
<~> relation_rng(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f30,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f33]) ).
fof(f36,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f37,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f36]) ).
fof(f39,plain,
? [X0] :
( ( relation_rng(X0) != empty_set
| relation_dom(X0) != empty_set )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(nnf_transformation,[],[f27]) ).
fof(f40,plain,
? [X0] :
( ( relation_rng(X0) != empty_set
| relation_dom(X0) != empty_set )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
( ( empty_set != relation_rng(sK0)
| empty_set != relation_dom(sK0) )
& ( empty_set = relation_rng(sK0)
| empty_set = relation_dom(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f40]) ).
fof(f46,plain,
relation(sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f47,plain,
( empty_set = relation_rng(sK0)
| empty_set = relation_dom(sK0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f48,plain,
( empty_set != relation_rng(sK0)
| empty_set != relation_dom(sK0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f51,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f53,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f73,plain,
! [X0] :
( relation_dom(X0) = X0
| ~ empty(X0) ),
inference(superposition,[],[f52,f53]) ).
fof(f74,plain,
! [X0] :
( relation_rng(X0) = X0
| ~ empty(X0) ),
inference(superposition,[],[f51,f53]) ).
fof(f88,plain,
( empty_set != sK0
| empty_set != relation_dom(sK0)
| ~ empty(sK0) ),
inference(superposition,[],[f48,f74]) ).
fof(f94,plain,
( empty_set != relation_dom(sK0)
| ~ empty(sK0) ),
inference(forward_subsumption_resolution,[],[f88,f53]) ).
fof(f99,plain,
( empty_set != sK0
| ~ empty(sK0)
| ~ empty(sK0) ),
inference(superposition,[],[f94,f73]) ).
fof(f100,plain,
( empty_set != sK0
| ~ empty(sK0) ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f101,plain,
~ empty(sK0),
inference(forward_subsumption_resolution,[],[f100,f53]) ).
fof(f103,plain,
( ~ empty(empty_set)
| empty(sK0)
| ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(superposition,[],[f60,f47]) ).
fof(f107,plain,
( empty(sK0)
| ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(forward_subsumption_resolution,[],[f103,f61]) ).
fof(f108,plain,
( ~ relation(sK0)
| empty_set = relation_dom(sK0) ),
inference(forward_subsumption_resolution,[],[f107,f101]) ).
fof(f109,plain,
empty_set = relation_dom(sK0),
inference(forward_subsumption_resolution,[],[f108,f46]) ).
fof(f112,plain,
( ~ empty(empty_set)
| empty(sK0)
| ~ relation(sK0) ),
inference(superposition,[],[f57,f109]) ).
fof(f117,plain,
( empty(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f112,f61]) ).
fof(f118,plain,
~ relation(sK0),
inference(forward_subsumption_resolution,[],[f117,f101]) ).
fof(f119,plain,
$false,
inference(forward_subsumption_resolution,[],[f118,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:00:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.60/1.48 % (4134441)Detected formulas, will run a generic FOF schedule.
% 3.60/1.48 % (4134447)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=1699417605:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.48 % (4134446)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=2986879045:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.48 % (4134452)dis-21_1_sil=8000:lcm=predicate:random_seed=4276185693: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)
% 3.60/1.48 % (4134448)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=2997792839:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.48 % (4134449)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3008319205:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.48 % (4134450)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1224781343:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.48 % (4134451)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3265839547:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.48 % (4134450)First to succeed.
% 3.60/1.48 % (4134449)Also succeeded, but the first one will report.
% 3.60/1.48 % (4134451)Also succeeded, but the first one will report.
% 3.60/1.48 % (4134450)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4134441"
% 3.60/1.48 % (4134452)Instruction limit reached!
% 3.60/1.48 % (4134452)------------------------------
% 3.60/1.48 % (4134452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (4134452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (4134452)CaDiCaL version: 2.1.3
% 3.60/1.48 % (4134452)Termination reason: Instruction limit
% 3.60/1.48 % (4134452)Termination phase: Saturation
% 3.60/1.48 % (4134452)Time elapsed: 0.062 s
% 3.60/1.48 % (4134452)Peak memory usage: 89 MB
% 3.60/1.48 % (4134452)Instructions burned: 129 (million)
% 3.60/1.48 % (4134460)lrs+10_1_sil=8000:sp=occurrence:random_seed=2248186051:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.60/1.48 % (4134460)Also succeeded, but the first one will report.
% 3.60/1.48 % (4134450)Refutation found. Thanks to Tanya!
% 3.60/1.48 % SZS status Theorem for theBenchmark
% 3.60/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.48 % (4134450)------------------------------
% 3.60/1.48 % (4134450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.48 % (4134450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.48 % (4134450)CaDiCaL version: 2.1.3
% 3.60/1.48 % (4134450)Termination reason: Refutation
% 3.60/1.48 % (4134450)Time elapsed: 0.003 s
% 3.60/1.48 % (4134450)Peak memory usage: 88 MB
% 3.60/1.48 % (4134450)Instructions burned: 3 (million)
% 3.60/1.48 % (4134450)------------------------------
% 3.60/1.48 % (4134450)------------------------------
% 3.60/1.48 % (4134441)Success in time 0.43 s
% 3.60/1.48 % Vampire exiting
%------------------------------------------------------------------------------