%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU189+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 : n016.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 3.64s 1.48s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 98 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 48 ~; 39 |; 11 &)
% ( 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(f64,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f66,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f67,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f153,axiom,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f157,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f158,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f157]) ).
fof(f161,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f244,plain,
? [X0] :
( ( relation_dom(X0) = empty_set
<~> relation_rng(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f158]) ).
fof(f251,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f161]) ).
fof(f271,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f272,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f271]) ).
fof(f274,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f275,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f274]) ).
fof(f327,plain,
? [X0] :
( ( empty_set != relation_rng(X0)
| empty_set != relation_dom(X0) )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(nnf_transformation,[],[f244]) ).
fof(f328,plain,
? [X0] :
( ( empty_set != relation_rng(X0)
| empty_set != relation_dom(X0) )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f327]) ).
fof(f329,plain,
( ( empty_set != relation_rng(sK6)
| empty_set != relation_dom(sK6) )
& ( empty_set = relation_rng(sK6)
| empty_set = relation_dom(sK6) )
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f328]) ).
fof(f483,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f153]) ).
fof(f484,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f153]) ).
fof(f489,plain,
relation(sK6),
inference(cnf_transformation,[],[f329]) ).
fof(f490,plain,
( empty_set = relation_rng(sK6)
| empty_set = relation_dom(sK6) ),
inference(cnf_transformation,[],[f329]) ).
fof(f491,plain,
( empty_set != relation_rng(sK6)
| empty_set != relation_dom(sK6) ),
inference(cnf_transformation,[],[f329]) ).
fof(f504,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f506,plain,
empty(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f608,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f611,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f797,plain,
! [X0] :
( relation_rng(X0) = X0
| ~ empty(X0) ),
inference(superposition,[],[f483,f504]) ).
fof(f798,plain,
! [X0] :
( relation_dom(X0) = X0
| ~ empty(X0) ),
inference(superposition,[],[f484,f504]) ).
fof(f867,plain,
( empty_set != sK6
| empty_set != relation_dom(sK6)
| ~ empty(sK6) ),
inference(superposition,[],[f491,f797]) ).
fof(f873,plain,
( empty_set != relation_dom(sK6)
| ~ empty(sK6) ),
inference(forward_subsumption_resolution,[],[f867,f504]) ).
fof(f876,plain,
( empty_set != sK6
| ~ empty(sK6)
| ~ empty(sK6) ),
inference(superposition,[],[f873,f798]) ).
fof(f877,plain,
( empty_set != sK6
| ~ empty(sK6) ),
inference(duplicate_literal_removal,[],[f876]) ).
fof(f880,plain,
~ empty(sK6),
inference(forward_subsumption_resolution,[],[f877,f504]) ).
fof(f944,plain,
( ~ empty(empty_set)
| empty(sK6)
| ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(superposition,[],[f611,f490]) ).
fof(f948,plain,
( empty(sK6)
| ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(forward_subsumption_resolution,[],[f944,f506]) ).
fof(f949,plain,
( ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(forward_subsumption_resolution,[],[f948,f880]) ).
fof(f950,plain,
empty_set = relation_dom(sK6),
inference(forward_subsumption_resolution,[],[f949,f489]) ).
fof(f953,plain,
( ~ empty(empty_set)
| empty(sK6)
| ~ relation(sK6) ),
inference(superposition,[],[f608,f950]) ).
fof(f958,plain,
( empty(sK6)
| ~ relation(sK6) ),
inference(forward_subsumption_resolution,[],[f953,f506]) ).
fof(f959,plain,
~ relation(sK6),
inference(forward_subsumption_resolution,[],[f958,f880]) ).
fof(f960,plain,
$false,
inference(forward_subsumption_resolution,[],[f959,f489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:02:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.64/1.48 % (3244486)Detected formulas, will run a generic FOF schedule.
% 3.64/1.48 % (3244492)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=2593883913:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.48 % (3244494)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1375950930:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.48 % (3244493)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=2356732373:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.48 % (3244495)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1300798934:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.48 % (3244491)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=2620935384:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.48 % (3244497)dis-21_1_sil=8000:lcm=predicate:random_seed=837013623: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)
% 3.64/1.48 % (3244495)First to succeed.
% 3.64/1.48 % (3244495)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3244486"
% 3.64/1.48 % (3244494)Also succeeded, but the first one will report.
% 3.64/1.48 % (3244496)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=197058257:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/1.48 % (3244496)Also succeeded, but the first one will report.
% 3.64/1.48 % (3244497)Instruction limit reached!
% 3.64/1.48 % (3244497)------------------------------
% 3.64/1.48 % (3244497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.48 % (3244497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.48 % (3244497)CaDiCaL version: 2.1.3
% 3.64/1.48 % (3244497)Termination reason: Instruction limit
% 3.64/1.48 % (3244497)Termination phase: Saturation
% 3.64/1.48 % (3244497)Time elapsed: 0.078 s
% 3.64/1.48 % (3244497)Peak memory usage: 90 MB
% 3.64/1.48 % (3244497)Instructions burned: 130 (million)
% 3.64/1.48 % (3244495)Refutation found. Thanks to Tanya!
% 3.64/1.48 % SZS status Theorem for theBenchmark
% 3.64/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.48 % (3244495)------------------------------
% 3.64/1.48 % (3244495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.48 % (3244495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.48 % (3244495)CaDiCaL version: 2.1.3
% 3.64/1.48 % (3244495)Termination reason: Refutation
% 3.64/1.48 % (3244495)Time elapsed: 0.012 s
% 3.64/1.48 % (3244495)Peak memory usage: 88 MB
% 3.64/1.48 % (3244495)Instructions burned: 16 (million)
% 3.64/1.48 % (3244495)------------------------------
% 3.64/1.48 % (3244495)------------------------------
% 3.64/1.48 % (3244486)Success in time 0.439 s
% 3.64/1.48 % Vampire exiting
%------------------------------------------------------------------------------