%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT080+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 2.56s 1.31s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 10 unt; 6 def)
% Number of atoms : 211 ( 59 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 236 ( 93 ~; 62 |; 71 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 53 ( 0 sgn 41 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( less(X0,X1)
| X0 = X1
| less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trichotomy) ).
fof(f4,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> ( less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_def) ).
fof(f5,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& leq(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_antisym) ).
fof(f10,axiom,
! [X0,X1,X2] :
( in_closed(X0,X1,X2)
<=> ( leq(X1,X0)
& leq(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_closed) ).
fof(f72,axiom,
less(v600,v800),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v600_v800) ).
fof(f73,axiom,
( v0 != v8
& v0 != v32
& v0 != v100
& v0 != v150
& v0 != v300
& v0 != v500
& v0 != v600
& v0 != v800
& v8 != v32
& v8 != v100
& v8 != v150
& v8 != v300
& v8 != v500
& v8 != v600
& v8 != v800
& v32 != v100
& v32 != v150
& v32 != v300
& v32 != v500
& v32 != v600
& v32 != v800
& v100 != v150
& v100 != v300
& v100 != v500
& v100 != v600
& v100 != v800
& v150 != v300
& v150 != v500
& v150 != v600
& v150 != v800
& v300 != v500
& v300 != v600
& v300 != v800
& v500 != v600
& v500 != v800
& v600 != v800 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
fof(f74,conjecture,
~ ? [X0,X1,X2,X3] :
( in_closed(X0,v600,v600)
& in_closed(X0,v800,v800)
& less(v100,X1)
& in_open(X1,v0,v500)
& leq(v8,X2)
& in_lopen(X2,v0,v32)
& in_lopen(X3,v0,v300)
& leq(v150,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',odrl365) ).
fof(f75,negated_conjecture,
~ ~ ? [X0,X1,X2,X3] :
( in_closed(X0,v600,v600)
& in_closed(X0,v800,v800)
& less(v100,X1)
& in_open(X1,v0,v500)
& leq(v8,X2)
& in_lopen(X2,v0,v32)
& in_lopen(X3,v0,v300)
& leq(v150,X3) ),
inference(negated_conjecture,[status(cth)],[f74]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( in_closed(X0,v600,v600)
& in_closed(X0,v800,v800)
& less(v100,X1)
& in_open(X1,v0,v500)
& leq(v8,X2)
& in_lopen(X2,v0,v32)
& in_lopen(X3,v0,v300)
& leq(v150,X3) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( in_closed(X0,X1,X2)
=> ( leq(X1,X0)
& leq(X0,X2) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(flattening,[],[f91]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( leq(X1,X0)
& leq(X0,X2) )
| ~ in_closed(X0,X1,X2) ),
inference(ennf_transformation,[],[f77]) ).
fof(f113,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f114,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ leq(X0,X1) ) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
( in_closed(sK0,v600,v600)
& in_closed(sK0,v800,v800)
& less(v100,sK1)
& in_open(sK1,v0,v500)
& leq(v8,sK2)
& in_lopen(sK2,v0,v32)
& in_lopen(sK3,v0,v300)
& leq(v150,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f76]) ).
fof(f118,plain,
! [X0,X1] :
( less(X0,X1)
| X0 = X1
| less(X1,X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f121,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f122,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f127,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f128,plain,
! [X2,X0,X1] :
( leq(X1,X0)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f181,plain,
less(v600,v800),
inference(cnf_transformation,[],[f72]) ).
fof(f182,plain,
v600 != v800,
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
in_closed(sK0,v800,v800),
inference(cnf_transformation,[],[f115]) ).
fof(f225,plain,
in_closed(sK0,v600,v600),
inference(cnf_transformation,[],[f115]) ).
fof(f344,plain,
! [X2,X0,X1] :
( ~ in_closed(X1,X0,X2)
| ~ leq(X1,X0)
| X0 = X1 ),
inference(resolution,[],[f122,f128]) ).
fof(f345,plain,
! [X2,X0,X1] :
( ~ in_closed(X0,X2,X1)
| ~ leq(X1,X0)
| X0 = X1 ),
inference(resolution,[],[f122,f127]) ).
fof(f460,plain,
( ~ leq(sK0,v800)
| v800 = sK0 ),
inference(resolution,[],[f344,f224]) ).
fof(f461,plain,
( ~ leq(sK0,v600)
| v600 = sK0 ),
inference(resolution,[],[f344,f225]) ).
fof(f463,definition,
( spl4_22
<=> v600 = sK0 ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
fof(f465,plain,
( v600 = sK0
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f467,definition,
( spl4_23
<=> leq(sK0,v600) ),
introduced(definition,[new_symbols(definition,[spl4_23])],[avatar_definition]) ).
fof(f469,plain,
( ~ leq(sK0,v600)
| spl4_23 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f470,plain,
( spl4_22
| ~ spl4_23 ),
inference(avatar_split_clause,[],[f461,f467,f463]) ).
fof(f472,definition,
( spl4_24
<=> v800 = sK0 ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
fof(f474,plain,
( v800 = sK0
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f476,definition,
( spl4_25
<=> leq(sK0,v800) ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
fof(f478,plain,
( ~ leq(sK0,v800)
| spl4_25 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f479,plain,
( spl4_24
| ~ spl4_25 ),
inference(avatar_split_clause,[],[f460,f476,f472]) ).
fof(f486,plain,
( ~ leq(v600,sK0)
| v600 = sK0 ),
inference(resolution,[],[f345,f225]) ).
fof(f488,definition,
( spl4_26
<=> leq(v600,sK0) ),
introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition]) ).
fof(f490,plain,
( ~ leq(v600,sK0)
| spl4_26 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f491,plain,
( spl4_22
| ~ spl4_26 ),
inference(avatar_split_clause,[],[f486,f488,f463]) ).
fof(f501,plain,
( ~ less(sK0,v600)
| spl4_23 ),
inference(resolution,[],[f469,f121]) ).
fof(f509,plain,
( ~ less(sK0,v800)
| spl4_25 ),
inference(resolution,[],[f478,f121]) ).
fof(f542,plain,
( ~ less(v600,sK0)
| spl4_26 ),
inference(resolution,[],[f490,f121]) ).
fof(f585,plain,
( v600 = sK0
| less(v600,sK0)
| spl4_23 ),
inference(resolution,[],[f501,f118]) ).
fof(f593,definition,
( spl4_31
<=> less(v600,sK0) ),
introduced(definition,[new_symbols(definition,[spl4_31])],[avatar_definition]) ).
fof(f596,plain,
( spl4_31
| spl4_22
| spl4_23 ),
inference(avatar_split_clause,[],[f585,f467,f463,f593]) ).
fof(f623,plain,
( ~ spl4_31
| spl4_26 ),
inference(avatar_split_clause,[],[f542,f488,f593]) ).
fof(f632,plain,
( ~ less(v600,v800)
| ~ spl4_22
| spl4_25 ),
inference(superposition,[],[f509,f465]) ).
fof(f633,plain,
( $false
| ~ spl4_22
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f632,f181]) ).
fof(f634,plain,
( ~ spl4_22
| spl4_25 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f640,plain,
( v600 = v800
| ~ spl4_22
| ~ spl4_24 ),
inference(forward_demodulation,[],[f474,f465]) ).
fof(f644,plain,
( $false
| ~ spl4_22
| ~ spl4_24 ),
inference(forward_subsumption_resolution,[],[f640,f182]) ).
fof(f645,plain,
( ~ spl4_22
| ~ spl4_24 ),
inference(avatar_contradiction_clause,[],[f644]) ).
cnf(s18,plain,
( spl4_22
| ~ spl4_23 ),
inference(sat_conversion,[],[f470]) ).
cnf(s19,plain,
( spl4_24
| ~ spl4_25 ),
inference(sat_conversion,[],[f479]) ).
cnf(s20,plain,
( spl4_22
| ~ spl4_26 ),
inference(sat_conversion,[],[f491]) ).
cnf(s27,plain,
( spl4_22
| spl4_23
| spl4_31 ),
inference(sat_conversion,[],[f596]) ).
cnf(s32,plain,
( spl4_26
| ~ spl4_31 ),
inference(sat_conversion,[],[f623]) ).
cnf(s33,plain,
( ~ spl4_22
| spl4_25 ),
inference(sat_conversion,[],[f634]) ).
cnf(s36,plain,
( ~ spl4_22
| ~ spl4_24 ),
inference(sat_conversion,[],[f645]) ).
cnf(s42,plain,
spl4_22,
inference(rat,[],[s27,s32,s18,s20]) ).
cnf(s43,plain,
~ spl4_24,
inference(rat,[],[s36,s42]) ).
cnf(s46,plain,
spl4_25,
inference(rat,[],[s33,s42]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s19,s46,s43]) ).
fof(f646,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT080+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 17:35:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.56/1.31 % (1484791)Detected formulas, will run a generic FOF schedule.
% 2.56/1.31 % (1484801)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3118868581:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.31 % (1484801)First to succeed.
% 2.56/1.31 % (1484801)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1484791"
% 2.56/1.31 % (1484802)dis-21_1_sil=8000:lcm=predicate:random_seed=3915415969: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)
% 2.56/1.31 % (1484800)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2591605249:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.31 % (1484799)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=93771521:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.31 % (1484797)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=2574004066:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.31 % (1484796)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=2613901875:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.31 % (1484798)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=2259553154:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.31 % (1484800)Also succeeded, but the first one will report.
% 2.56/1.31 % (1484799)Also succeeded, but the first one will report.
% 2.56/1.31 % (1484802)Also succeeded, but the first one will report.
% 2.56/1.31 % (1484801)Refutation found. Thanks to Tanya!
% 2.56/1.31 % SZS status Theorem for theBenchmark
% 2.56/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.31 % (1484801)------------------------------
% 2.56/1.31 % (1484801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (1484801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (1484801)CaDiCaL version: 2.1.3
% 2.56/1.31 % (1484801)Termination reason: Refutation
% 2.56/1.31 % (1484801)Time elapsed: 0.006 s
% 2.56/1.31 % (1484801)Peak memory usage: 90 MB
% 2.56/1.31 % (1484801)Instructions burned: 14 (million)
% 2.56/1.31 % (1484801)------------------------------
% 2.56/1.31 % (1484801)------------------------------
% 2.56/1.31 % (1484791)Success in time 0.274 s
% 2.56/1.31 % Vampire exiting
%------------------------------------------------------------------------------