%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT106+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 : n001.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 12:02:23 PM UTC 2026
% Result : Unsatisfiable 3.70s 1.57s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 16 unt; 3 def)
% Number of atoms : 90 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 36 ~; 29 |; 7 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& leq(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_antisym) ).
fof(f6,axiom,
! [X0,X1] :
( less(X0,X1)
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_implies_leq) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_trans) ).
fof(f11,axiom,
! [X0,X1,X2] :
( in_lopen(X0,X1,X2)
<=> ( less(X1,X0)
& leq(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_lopen) ).
fof(f32,axiom,
less(v600,v800),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ord_v600_v800) ).
fof(f33,axiom,
( v0 != v600
& v0 != v800
& v600 != v800 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct) ).
fof(f35,axiom,
in_lopen(w,v0,v600),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wit_in_lopen) ).
fof(f36,axiom,
leq(v800,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wit_leq) ).
fof(f37,plain,
! [X0,X1,X2] :
( in_lopen(X0,X1,X2)
=> ( less(X1,X0)
& leq(X0,X2) ) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f46,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( less(X1,X0)
& leq(X0,X2) )
| ~ in_lopen(X0,X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f62,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f63,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f62]) ).
fof(f67,plain,
less(v600,v800),
inference(cnf_transformation,[],[f32]) ).
fof(f68,plain,
v600 != v800,
inference(cnf_transformation,[],[f33]) ).
fof(f71,plain,
in_lopen(w,v0,v600),
inference(cnf_transformation,[],[f35]) ).
fof(f72,plain,
leq(v800,w),
inference(cnf_transformation,[],[f36]) ).
fof(f75,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ in_lopen(X0,X1,X2)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f109,plain,
~ sQ0_eqProxy(v600,v800),
inference(equality_proxy_replacement,[],[f68,f106]) ).
fof(f122,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(equality_proxy_replacement,[],[f92,f106]) ).
fof(f172,plain,
leq(w,v600),
inference(resolution,[],[f93,f71]) ).
fof(f202,definition,
( spl1_10
<=> leq(v800,v600) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f203,plain,
( ~ leq(v800,v600)
| spl1_10 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f279,plain,
( ! [X0] :
( ~ leq(v800,X0)
| ~ leq(X0,v600) )
| spl1_10 ),
inference(resolution,[],[f203,f95]) ).
fof(f328,plain,
( ~ leq(v800,w)
| spl1_10 ),
inference(resolution,[],[f279,f172]) ).
fof(f329,plain,
( $false
| spl1_10 ),
inference(resolution,[],[f328,f72]) ).
fof(f332,plain,
spl1_10,
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f463,plain,
( ~ leq(v600,v800)
| ~ leq(v800,v600) ),
inference(resolution,[],[f122,f109]) ).
fof(f468,definition,
( spl1_32
<=> leq(v600,v800) ),
introduced(definition,[new_symbols(definition,[spl1_32])],[avatar_definition]) ).
fof(f469,plain,
( ~ leq(v600,v800)
| spl1_32 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,plain,
( ~ spl1_10
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f463,f468,f202]) ).
fof(f473,plain,
( ~ less(v600,v800)
| spl1_32 ),
inference(resolution,[],[f469,f75]) ).
fof(f474,plain,
( $false
| spl1_32 ),
inference(resolution,[],[f473,f67]) ).
fof(f476,plain,
spl1_32,
inference(avatar_contradiction_clause,[],[f474]) ).
cnf(s20,plain,
spl1_10,
inference(sat_conversion,[],[f332]) ).
cnf(s37,plain,
( ~ spl1_10
| ~ spl1_32 ),
inference(sat_conversion,[],[f471]) ).
cnf(s38,plain,
spl1_32,
inference(sat_conversion,[],[f476]) ).
cnf(s39,plain,
~ spl1_10,
inference(rat,[],[s37,s38]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s20,s39]) ).
fof(f477,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT106+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 % Computer : n001.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8046.5625MB
% 0.13/0.44 % OS : Linux 6.8.0-71-generic
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Sun Sep 27 17:44:46 UTC 2026
% 0.13/0.44 % CPUTime :
% 0.13/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 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
% 3.70/1.57 % (3829993)Detected formulas, will run a generic FOF schedule.
% 3.70/1.57 % (3829998)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=3774424015:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.70/1.57 % (3829999)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=3785923980:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.70/1.57 % (3830003)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1602639259:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.70/1.57 % (3830004)dis-21_1_sil=8000:lcm=predicate:random_seed=687837281: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)
% 3.70/1.57 % (3830000)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=2434250248:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.70/1.57 % (3830001)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=31452161:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.70/1.57 % (3830002)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=620097324:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.70/1.57 % (3830002)Refutation not found, incomplete strategy
% 3.70/1.57 % (3830002)------------------------------
% 3.70/1.57 % (3830002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.57 % (3830002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.57 % (3830002)CaDiCaL version: 2.1.3
% 3.70/1.57 % (3830001)Refutation not found, incomplete strategy
% 3.70/1.57 % (3830001)------------------------------
% 3.70/1.57 % (3830001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.57 % (3830002)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.57 % (3830002)Time elapsed: 0.0000 s
% 3.70/1.57 % (3830002)Peak memory usage: 86 MB
% 3.70/1.57 % (3830001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.57 % (3830001)CaDiCaL version: 2.1.3
% 3.70/1.57 % (3830001)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.57 % (3830001)Time elapsed: 0.0000 s
% 3.70/1.57 % (3830001)Peak memory usage: 86 MB
% 3.70/1.57 % (3830004)First to succeed.
% 3.70/1.57 % (3830004)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3829993"
% 3.70/1.57 % (3830003)Also succeeded, but the first one will report.
% 3.70/1.57 % (3830001)------------------------------
% 3.70/1.57 % (3830001)------------------------------
% 3.70/1.57 % (3830002)------------------------------
% 3.70/1.57 % (3830002)------------------------------
% 3.70/1.57 % (3830004)Refutation found. Thanks to Tanya!
% 3.70/1.57 % SZS status Unsatisfiable for theBenchmark
% 3.70/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.57 % (3830004)------------------------------
% 3.70/1.57 % (3830004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.57 % (3830004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.57 % (3830004)CaDiCaL version: 2.1.3
% 3.70/1.57 % (3830004)Termination reason: Refutation
% 3.70/1.57 % (3830004)Time elapsed: 0.006 s
% 3.70/1.57 % (3830004)Peak memory usage: 89 MB
% 3.70/1.57 % (3830004)Instructions burned: 7 (million)
% 3.70/1.57 % (3830004)------------------------------
% 3.70/1.57 % (3830004)------------------------------
% 3.70/1.57 % (3829993)Success in time 0.438 s
% 3.70/1.57 % Vampire exiting
%------------------------------------------------------------------------------