%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:02:20 PM UTC 2026
% Result : Theorem 2.48s 1.10s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 10 unt; 5 def)
% Number of atoms : 199 ( 37 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 205 ( 84 ~; 81 |; 30 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 59 ( 0 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( ( less(X0,X1)
& less(X1,X2) )
=> less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive) ).
fof(f3,axiom,
! [X0,X1] :
( less(X0,X1)
| X0 = X1
| less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trichotomy) ).
fof(f4,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> ( less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
fof(f5,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& leq(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
fof(f11,axiom,
! [X0,X1,X2] :
( in_lopen(X0,X1,X2)
<=> ( less(X1,X0)
& leq(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_lopen) ).
fof(f41,axiom,
less(v400,v800),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v400_v800) ).
fof(f43,axiom,
( v0 != v200
& v0 != v400
& v0 != v600
& v0 != v800
& v200 != v400
& v200 != v600
& v200 != v800
& v400 != v600
& v400 != v800
& v600 != v800 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
fof(f44,conjecture,
~ ? [X0,X1] :
( in_lopen(X0,v0,v400)
& leq(v800,X0)
& in_lopen(X1,v0,v600)
& leq(v200,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl402) ).
fof(f45,negated_conjecture,
~ ~ ? [X0,X1] :
( in_lopen(X0,v0,v400)
& leq(v800,X0)
& in_lopen(X1,v0,v600)
& leq(v200,X1) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0,X1] :
( in_lopen(X0,v0,v400)
& leq(v800,X0)
& in_lopen(X1,v0,v600)
& leq(v200,X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( in_lopen(X0,X1,X2)
=> ( less(X1,X0)
& leq(X0,X2) ) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f53,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f54,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(flattening,[],[f55]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( less(X1,X0)
& leq(X0,X2) )
| ~ in_lopen(X0,X1,X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f75,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f76,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ leq(X0,X1) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
( in_lopen(sK0,v0,v400)
& leq(v800,sK0)
& in_lopen(sK1,v0,v600)
& leq(v200,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f46]) ).
fof(f79,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f80,plain,
! [X0,X1] :
( less(X0,X1)
| X0 = X1
| less(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f83,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f84,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f89,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
less(v400,v800),
inference(cnf_transformation,[],[f41]) ).
fof(f115,plain,
v400 != v800,
inference(cnf_transformation,[],[f43]) ).
fof(f126,plain,
leq(v800,sK0),
inference(cnf_transformation,[],[f77]) ).
fof(f127,plain,
in_lopen(sK0,v0,v400),
inference(cnf_transformation,[],[f77]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ in_lopen(X0,X2,X1)
| ~ leq(X1,X0)
| X0 = X1 ),
inference(resolution,[],[f84,f89]) ).
fof(f183,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = X1
| ~ less(X0,X1) ),
inference(resolution,[],[f84,f83]) ).
fof(f186,definition,
( spl2_10
<=> leq(sK0,v800) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f187,plain,
( leq(sK0,v800)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f188,plain,
( ~ leq(sK0,v800)
| spl2_10 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl2_11
<=> v800 = sK0 ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f192,plain,
( v800 = sK0
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f204,plain,
( ~ less(sK0,v800)
| spl2_10 ),
inference(resolution,[],[f188,f83]) ).
fof(f221,plain,
( ! [X0] :
( ~ less(sK0,X0)
| ~ less(X0,v800) )
| spl2_10 ),
inference(resolution,[],[f79,f204]) ).
fof(f247,plain,
! [X2,X0,X1] :
( ~ in_lopen(X1,X2,X0)
| ~ less(X0,X1)
| X0 = X1 ),
inference(resolution,[],[f183,f89]) ).
fof(f259,plain,
( ~ leq(v400,sK0)
| v400 = sK0 ),
inference(resolution,[],[f182,f127]) ).
fof(f261,definition,
( spl2_16
<=> v400 = sK0 ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f263,plain,
( v400 = sK0
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f265,definition,
( spl2_17
<=> leq(v400,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f267,plain,
( ~ leq(v400,sK0)
| spl2_17 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
( spl2_16
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f259,f265,f261]) ).
fof(f280,plain,
( ~ less(v400,sK0)
| spl2_17 ),
inference(resolution,[],[f267,f83]) ).
fof(f298,plain,
( v400 = sK0
| less(sK0,v400)
| spl2_17 ),
inference(resolution,[],[f280,f80]) ).
fof(f305,definition,
( spl2_20
<=> less(sK0,v400) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f307,plain,
( less(sK0,v400)
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f308,plain,
( spl2_20
| spl2_16
| spl2_17 ),
inference(avatar_split_clause,[],[f298,f265,f261,f305]) ).
fof(f364,plain,
( ~ less(v400,sK0)
| v400 = sK0 ),
inference(resolution,[],[f247,f127]) ).
fof(f380,plain,
( ~ less(v400,v800)
| spl2_10
| ~ spl2_20 ),
inference(resolution,[],[f221,f307]) ).
fof(f387,plain,
( $false
| spl2_10
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f380,f112]) ).
fof(f388,plain,
( spl2_10
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f393,plain,
( ~ less(v400,v800)
| spl2_10
| ~ spl2_16 ),
inference(superposition,[],[f204,f263]) ).
fof(f405,plain,
( $false
| spl2_10
| ~ spl2_16 ),
inference(forward_subsumption_resolution,[],[f393,f112]) ).
fof(f406,plain,
( spl2_10
| ~ spl2_16 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f422,plain,
( v800 = sK0
| ~ leq(v800,sK0)
| ~ spl2_10 ),
inference(resolution,[],[f187,f84]) ).
fof(f423,plain,
( v800 = sK0
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f422,f126]) ).
fof(f431,plain,
( spl2_11
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f423,f186,f190]) ).
fof(f445,plain,
( ~ less(v400,v800)
| v400 = sK0
| ~ spl2_11 ),
inference(forward_demodulation,[],[f364,f192]) ).
fof(f447,plain,
( v400 = sK0
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f445,f112]) ).
fof(f450,plain,
( spl2_16
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f447,f190,f261]) ).
fof(f452,plain,
( v400 = v800
| ~ spl2_11
| ~ spl2_16 ),
inference(superposition,[],[f263,f192]) ).
fof(f459,plain,
( $false
| ~ spl2_11
| ~ spl2_16 ),
inference(forward_subsumption_resolution,[],[f452,f115]) ).
fof(f460,plain,
( ~ spl2_11
| ~ spl2_16 ),
inference(avatar_contradiction_clause,[],[f459]) ).
cnf(s15,plain,
( spl2_16
| ~ spl2_17 ),
inference(sat_conversion,[],[f268]) ).
cnf(s17,plain,
( spl2_16
| spl2_17
| spl2_20 ),
inference(sat_conversion,[],[f308]) ).
cnf(s19,plain,
( spl2_10
| ~ spl2_20 ),
inference(sat_conversion,[],[f388]) ).
cnf(s21,plain,
( spl2_10
| ~ spl2_16 ),
inference(sat_conversion,[],[f406]) ).
cnf(s28,plain,
( ~ spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f431]) ).
cnf(s34,plain,
( ~ spl2_11
| spl2_16 ),
inference(sat_conversion,[],[f450]) ).
cnf(s36,plain,
( ~ spl2_11
| ~ spl2_16 ),
inference(sat_conversion,[],[f460]) ).
cnf(s42,plain,
( spl2_16
| spl2_20 ),
inference(rat,[],[s15,s17]) ).
cnf(s43,plain,
spl2_10,
inference(rat,[],[s42,s19,s21]) ).
cnf(s45,plain,
spl2_11,
inference(rat,[],[s28,s43]) ).
cnf(s46,plain,
~ spl2_16,
inference(rat,[],[s36,s45]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s34,s46,s45]) ).
fof(f461,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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 : Sun Sep 27 17:35:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 2.48/1.10 % (3636127)Detected formulas, will run a generic FOF schedule.
% 2.48/1.10 % (3636137)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2169027287:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.48/1.10 % (3636137)First to succeed.
% 2.48/1.10 % (3636137)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3636127"
% 2.48/1.10 % (3636138)dis-21_1_sil=8000:lcm=predicate:random_seed=3688653277: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)
% 2.48/1.10 % (3636135)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3115643036:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.48/1.10 % (3636132)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=127883476:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.48/1.10 % (3636136)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1453340724:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.48/1.10 % (3636134)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=1304656663:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.48/1.10 % (3636133)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=3518753180:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.48/1.10 % (3636136)Also succeeded, but the first one will report.
% 2.48/1.10 % (3636135)Refutation not found, incomplete strategy
% 2.48/1.10 % (3636135)------------------------------
% 2.48/1.10 % (3636135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.10 % (3636135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.10 % (3636135)CaDiCaL version: 2.1.3
% 2.48/1.10 % (3636135)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.10 % (3636135)Time elapsed: 0.005 s
% 2.48/1.10 % (3636135)Peak memory usage: 88 MB
% 2.48/1.10 % (3636135)Instructions burned: 6 (million)
% 2.48/1.10 % (3636138)Also succeeded, but the first one will report.
% 2.48/1.10 % (3636137)Refutation found. Thanks to Tanya!
% 2.48/1.10 % SZS status Theorem for theBenchmark
% 2.48/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.10 % (3636137)------------------------------
% 2.48/1.10 % (3636137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.10 % (3636137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.10 % (3636137)CaDiCaL version: 2.1.3
% 2.48/1.10 % (3636137)Termination reason: Refutation
% 2.48/1.10 % (3636137)Time elapsed: 0.006 s
% 2.48/1.10 % (3636137)Peak memory usage: 90 MB
% 2.48/1.10 % (3636137)Instructions burned: 11 (million)
% 2.48/1.10 % (3636137)------------------------------
% 2.48/1.10 % (3636137)------------------------------
% 2.48/1.10 % (3636127)Success in time 0.301 s
% 2.48/1.10 % Vampire exiting
%------------------------------------------------------------------------------