%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO087+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 : n007.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 3.34s 1.38s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 12 unt; 2 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 201 ( 75 ~; 67 |; 47 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 71 !; 11 ?)
% 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(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( incident_c(X0,X1)
& ~ end_point(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
fof(f5,axiom,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X3] :
( ( incident_c(X3,X1)
& incident_c(X3,X2) )
=> ( end_point(X3,X1)
& end_point(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn) ).
fof(f10,axiom,
! [X0] :
? [X1] : inner_point(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
fof(f17,conjecture,
! [X0,X1] :
( part_of(X0,X1)
=> ~ ? [X2] : meet(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_9) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( part_of(X0,X1)
=> ~ ? [X2] : meet(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
? [X0,X1] :
( ? [X2] : meet(X2,X0,X1)
& part_of(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X3] :
( ( end_point(X3,X1)
& end_point(X3,X2) )
| ~ incident_c(X3,X1)
| ~ incident_c(X3,X2) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1,X2] :
( meet(X0,X1,X2)
<=> ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X3] :
( ( end_point(X3,X1)
& end_point(X3,X2) )
| ~ incident_c(X3,X1)
| ~ incident_c(X3,X2) ) ) ),
inference(flattening,[],[f33]) ).
fof(f41,plain,
( meet(sK2,sK0,sK1)
& part_of(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21]) ).
fof(f46,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,[],[f28]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK5(X0,X1),X0)
& incident_c(sK5(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f47]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( meet(X0,X1,X2)
| ~ incident_c(X0,X1)
| ~ incident_c(X0,X2)
| ? [X3] :
( ( ~ end_point(X3,X1)
| ~ end_point(X3,X2) )
& incident_c(X3,X1)
& incident_c(X3,X2) ) )
& ( ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X3] :
( ( end_point(X3,X1)
& end_point(X3,X2) )
| ~ incident_c(X3,X1)
| ~ incident_c(X3,X2) ) )
| ~ meet(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( meet(X0,X1,X2)
| ~ incident_c(X0,X1)
| ~ incident_c(X0,X2)
| ? [X3] :
( ( ~ end_point(X3,X1)
| ~ end_point(X3,X2) )
& incident_c(X3,X1)
& incident_c(X3,X2) ) )
& ( ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X3] :
( ( end_point(X3,X1)
& end_point(X3,X2) )
| ~ incident_c(X3,X1)
| ~ incident_c(X3,X2) ) )
| ~ meet(X0,X1,X2) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( meet(X0,X1,X2)
| ~ incident_c(X0,X1)
| ~ incident_c(X0,X2)
| ? [X3] :
( ( ~ end_point(X3,X1)
| ~ end_point(X3,X2) )
& incident_c(X3,X1)
& incident_c(X3,X2) ) )
& ( ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X4] :
( ( end_point(X4,X1)
& end_point(X4,X2) )
| ~ incident_c(X4,X1)
| ~ incident_c(X4,X2) ) )
| ~ meet(X0,X1,X2) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( meet(X0,X1,X2)
| ~ incident_c(X0,X1)
| ~ incident_c(X0,X2)
| ( ( ~ end_point(sK9(X1,X2),X1)
| ~ end_point(sK9(X1,X2),X2) )
& incident_c(sK9(X1,X2),X1)
& incident_c(sK9(X1,X2),X2) ) )
& ( ( incident_c(X0,X1)
& incident_c(X0,X2)
& ! [X4] :
( ( end_point(X4,X1)
& end_point(X4,X2) )
| ~ incident_c(X4,X1)
| ~ incident_c(X4,X2) ) )
| ~ meet(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X1,X2))],[f54]) ).
fof(f59,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(flattening,[],[f59]) ).
fof(f67,plain,
! [X0] : inner_point(sK15(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f10]) ).
fof(f68,plain,
part_of(sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
meet(sK2,sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f80,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( ~ meet(X0,X1,X2)
| ~ incident_c(X4,X1)
| ~ incident_c(X4,X2)
| end_point(X4,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f99,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f100,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f110,plain,
! [X0] : inner_point(sK15(X0),X0),
inference(cnf_transformation,[],[f67]) ).
fof(f128,plain,
! [X0] : ~ end_point(sK15(X0),X0),
inference(resolution,[],[f99,f110]) ).
fof(f129,plain,
! [X0] : incident_c(sK15(X0),X0),
inference(resolution,[],[f100,f110]) ).
fof(f135,plain,
! [X0] :
( incident_c(X0,sK1)
| ~ incident_c(X0,sK0) ),
inference(resolution,[],[f80,f68]) ).
fof(f229,plain,
! [X0] :
( end_point(X0,sK0)
| ~ incident_c(X0,sK1)
| ~ incident_c(X0,sK0) ),
inference(resolution,[],[f88,f69]) ).
fof(f401,plain,
( ~ incident_c(sK15(sK0),sK1)
| ~ incident_c(sK15(sK0),sK0) ),
inference(resolution,[],[f229,f128]) ).
fof(f403,definition,
( spl17_13
<=> incident_c(sK15(sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
fof(f404,plain,
( ~ incident_c(sK15(sK0),sK0)
| spl17_13 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f406,definition,
( spl17_14
<=> incident_c(sK15(sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl17_14])],[avatar_definition]) ).
fof(f407,plain,
( ~ incident_c(sK15(sK0),sK1)
| spl17_14 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f408,plain,
( ~ spl17_13
| ~ spl17_14 ),
inference(avatar_split_clause,[],[f401,f406,f403]) ).
fof(f409,plain,
( $false
| spl17_13 ),
inference(resolution,[],[f404,f129]) ).
fof(f411,plain,
spl17_13,
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f412,plain,
( ~ incident_c(sK15(sK0),sK0)
| spl17_14 ),
inference(resolution,[],[f407,f135]) ).
fof(f414,plain,
( ~ spl17_13
| spl17_14 ),
inference(avatar_split_clause,[],[f412,f406,f403]) ).
cnf(s19,plain,
( ~ spl17_13
| ~ spl17_14 ),
inference(sat_conversion,[],[f408]) ).
cnf(s20,plain,
spl17_13,
inference(sat_conversion,[],[f411]) ).
cnf(s21,plain,
( ~ spl17_13
| spl17_14 ),
inference(sat_conversion,[],[f414]) ).
cnf(s22,plain,
spl17_14,
inference(rat,[],[s21,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s19,s22,s20]) ).
fof(f415,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO087+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n007.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 06:52:12 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.34/1.38 % (1056319)Detected formulas, will run a generic FOF schedule.
% 3.34/1.38 % (1056328)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=731931135:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.38 % (1056328)Instruction limit reached!
% 3.34/1.38 % (1056328)------------------------------
% 3.34/1.38 % (1056328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.38 % (1056328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.38 % (1056328)CaDiCaL version: 2.1.3
% 3.34/1.38 % (1056328)Termination reason: Instruction limit
% 3.34/1.38 % (1056328)Termination phase: Saturation
% 3.34/1.38 % (1056328)Time elapsed: 0.037 s
% 3.34/1.38 % (1056328)Peak memory usage: 88 MB
% 3.34/1.38 % (1056328)Instructions burned: 121 (million)
% 3.34/1.38 % (1056330)dis-21_1_sil=8000:lcm=predicate:random_seed=1204426015: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)
% 3.34/1.38 % (1056325)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=3271930689:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.38 % (1056326)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=3266606990:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.38 % (1056327)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=763812686:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.38 % (1056324)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=857063544:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.38 % (1056329)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3951549454:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.38 % (1056327)Refutation not found, incomplete strategy
% 3.34/1.38 % (1056327)------------------------------
% 3.34/1.38 % (1056327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.38 % (1056327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.38 % (1056327)CaDiCaL version: 2.1.3
% 3.34/1.38 % (1056327)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.38 % (1056327)Time elapsed: 0.003 s
% 3.34/1.38 % (1056327)Peak memory usage: 88 MB
% 3.34/1.38 % (1056327)Instructions burned: 4 (million)
% 3.34/1.38 % (1056330)First to succeed.
% 3.34/1.38 % (1056330)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1056319"
% 3.34/1.38 % (1056329)Also succeeded, but the first one will report.
% 3.34/1.38 % (1056338)lrs+10_1_sil=8000:sp=occurrence:random_seed=1518595068:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.34/1.38 % (1056338)Also succeeded, but the first one will report.
% 3.34/1.38 % (1056327)------------------------------
% 3.34/1.38 % (1056327)------------------------------
% 3.34/1.38 % (1056330)Refutation found. Thanks to Tanya!
% 3.34/1.38 % SZS status Theorem for theBenchmark
% 3.34/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.38 % (1056330)------------------------------
% 3.34/1.38 % (1056330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.38 % (1056330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.38 % (1056330)CaDiCaL version: 2.1.3
% 3.34/1.38 % (1056330)Termination reason: Refutation
% 3.34/1.38 % (1056330)Time elapsed: 0.008 s
% 3.34/1.38 % (1056330)Peak memory usage: 89 MB
% 3.34/1.38 % (1056330)Instructions burned: 11 (million)
% 3.34/1.38 % (1056330)------------------------------
% 3.34/1.38 % (1056330)------------------------------
% 3.34/1.38 % (1056319)Success in time 0.408 s
% 3.34/1.38 % Vampire exiting
%------------------------------------------------------------------------------