%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO084+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:51:29 AM UTC 2026
% Result : Theorem 2.54s 1.25s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 13 unt; 2 def)
% Number of atoms : 153 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 171 ( 62 ~; 61 |; 39 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 59 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X1)
| incident_c(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( part_of(X0,X2)
& part_of(X1,X2)
& meet(X3,X0,X1) )
=> part_of(sum(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_6_2) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( part_of(X0,X2)
& part_of(X1,X2)
& meet(X3,X0,X1) )
=> part_of(sum(X0,X1),X2) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& part_of(X0,X2)
& part_of(X1,X2)
& meet(X3,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& part_of(X0,X2)
& part_of(X1,X2)
& meet(X3,X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f42,plain,
( ~ part_of(sum(sK0,sK1),sK2)
& part_of(sK0,sK2)
& part_of(sK1,sK2)
& meet(sK3,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f22]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( X0 = sum(X1,X2)
| ? [X3] :
( ( ( ~ incident_c(X3,X1)
& ~ incident_c(X3,X2) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X1)
| incident_c(X3,X2)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X1)
& ~ incident_c(X3,X2) ) )
& ( incident_c(X3,X1)
| incident_c(X3,X2)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( X0 = sum(X1,X2)
| ? [X3] :
( ( ( ~ incident_c(X3,X1)
& ~ incident_c(X3,X2) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X1)
| incident_c(X3,X2)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X1)
& ~ incident_c(X3,X2) ) )
& ( incident_c(X3,X1)
| incident_c(X3,X2)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( X0 = sum(X1,X2)
| ? [X3] :
( ( ( ~ incident_c(X3,X1)
& ~ incident_c(X3,X2) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X1)
| incident_c(X3,X2)
| incident_c(X3,X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X1)
& ~ incident_c(X4,X2) ) )
& ( incident_c(X4,X1)
| incident_c(X4,X2)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( X0 = sum(X1,X2)
| ( ( ( ~ incident_c(sK7(X0,X1,X2),X1)
& ~ incident_c(sK7(X0,X1,X2),X2) )
| ~ incident_c(sK7(X0,X1,X2),X0) )
& ( incident_c(sK7(X0,X1,X2),X1)
| incident_c(sK7(X0,X1,X2),X2)
| incident_c(sK7(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X1)
& ~ incident_c(X4,X2) ) )
& ( incident_c(X4,X1)
| incident_c(X4,X2)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f48]) ).
fof(f54,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK10(X0,X1),X0)
& incident_c(sK10(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f55]) ).
fof(f70,plain,
part_of(sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f71,plain,
part_of(sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f72,plain,
~ part_of(sum(sK0,sK1),sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f77,plain,
! [X2,X0,X1,X4] :
( incident_c(X4,X1)
| incident_c(X4,X2)
| ~ incident_c(X4,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f93,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] :
( part_of(X1,X0)
| incident_c(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f117,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,sum(X1,X2))
| incident_c(X4,X2)
| incident_c(X4,X1) ),
inference(equality_resolution,[],[f77]) ).
fof(f135,plain,
incident_c(sK10(sK2,sum(sK0,sK1)),sum(sK0,sK1)),
inference(resolution,[],[f94,f72]) ).
fof(f136,plain,
~ incident_c(sK10(sK2,sum(sK0,sK1)),sK2),
inference(resolution,[],[f95,f72]) ).
fof(f140,plain,
! [X0] :
( incident_c(X0,sK2)
| ~ incident_c(X0,sK1) ),
inference(resolution,[],[f93,f70]) ).
fof(f141,plain,
! [X0] :
( incident_c(X0,sK2)
| ~ incident_c(X0,sK0) ),
inference(resolution,[],[f93,f71]) ).
fof(f144,plain,
~ incident_c(sK10(sK2,sum(sK0,sK1)),sK1),
inference(resolution,[],[f140,f136]) ).
fof(f147,plain,
~ incident_c(sK10(sK2,sum(sK0,sK1)),sK0),
inference(resolution,[],[f141,f136]) ).
fof(f164,plain,
( incident_c(sK10(sK2,sum(sK0,sK1)),sK1)
| incident_c(sK10(sK2,sum(sK0,sK1)),sK0) ),
inference(resolution,[],[f117,f135]) ).
fof(f167,definition,
( spl18_1
<=> incident_c(sK10(sK2,sum(sK0,sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f168,plain,
( incident_c(sK10(sK2,sum(sK0,sK1)),sK0)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,definition,
( spl18_2
<=> incident_c(sK10(sK2,sum(sK0,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f171,plain,
( incident_c(sK10(sK2,sum(sK0,sK1)),sK1)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f164,f170,f167]) ).
fof(f173,plain,
( $false
| ~ spl18_2 ),
inference(resolution,[],[f171,f144]) ).
fof(f174,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
( $false
| ~ spl18_1 ),
inference(resolution,[],[f168,f147]) ).
fof(f176,plain,
~ spl18_1,
inference(avatar_contradiction_clause,[],[f175]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s2,plain,
~ spl18_2,
inference(sat_conversion,[],[f174]) ).
cnf(s3,plain,
~ spl18_1,
inference(sat_conversion,[],[f176]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f177,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO084+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 06:53:17 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.54/1.25 % (459542)Detected formulas, will run a generic FOF schedule.
% 2.54/1.25 % (459553)dis-21_1_sil=8000:lcm=predicate:random_seed=1040917767: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)
% 2.54/1.25 % (459553)First to succeed.
% 2.54/1.25 % (459553)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-459542"
% 2.54/1.25 % (459550)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4031056419:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.25 % (459551)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1085363155:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.25 % (459548)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=945436390:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.25 % (459547)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=1096465989:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.25 % (459549)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=3019276698:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.25 % (459550)Refutation not found, incomplete strategy
% 2.54/1.25 % (459550)------------------------------
% 2.54/1.25 % (459550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.25 % (459550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.25 % (459550)CaDiCaL version: 2.1.3
% 2.54/1.25 % (459550)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.25 % (459550)Time elapsed: 0.010 s
% 2.54/1.25 % (459550)Peak memory usage: 88 MB
% 2.54/1.25 % (459550)Instructions burned: 12 (million)
% 2.54/1.25 % (459552)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1665369757:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.25 % (459552)Also succeeded, but the first one will report.
% 2.54/1.25 % (459551)Instruction limit reached!
% 2.54/1.25 % (459551)------------------------------
% 2.54/1.25 % (459551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.25 % (459551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.25 % (459551)CaDiCaL version: 2.1.3
% 2.54/1.25 % (459551)Termination reason: Instruction limit
% 2.54/1.25 % (459551)Termination phase: Saturation
% 2.54/1.25 % (459551)Time elapsed: 0.076 s
% 2.54/1.25 % (459551)Peak memory usage: 88 MB
% 2.54/1.25 % (459551)Instructions burned: 120 (million)
% 2.54/1.25 % (459553)Refutation found. Thanks to Tanya!
% 2.54/1.25 % SZS status Theorem for theBenchmark
% 2.54/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.25 % (459553)------------------------------
% 2.54/1.25 % (459553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.25 % (459553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.25 % (459553)CaDiCaL version: 2.1.3
% 2.54/1.25 % (459553)Termination reason: Refutation
% 2.54/1.25 % (459553)Time elapsed: 0.003 s
% 2.54/1.25 % (459553)Peak memory usage: 89 MB
% 2.54/1.25 % (459553)Instructions burned: 4 (million)
% 2.54/1.25 % (459553)------------------------------
% 2.54/1.25 % (459553)------------------------------
% 2.54/1.25 % (459542)Success in time 0.29 s
% 2.54/1.25 % Vampire exiting
%------------------------------------------------------------------------------