%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 09:53:36 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 27 unt; 6 def)
% Number of atoms : 176 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 68 ~; 57 |; 30 &)
% ( 13 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn 73 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( ( part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) )
=> ( part_of(X2,X3)
| part_of(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( incident_c(X0,X1)
& ~ end_point(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(f18,conjecture,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> ( incident_c(X1,X0)
& incident_c(X2,X0)
& incident_c(X3,X0)
& X1 != X2
& X2 != X3
& X1 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> ( incident_c(X1,X0)
& incident_c(X2,X0)
& incident_c(X3,X0)
& X1 != X2
& X2 != X3
& X1 != X3 ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(flattening,[],[f24]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f43,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_c(X1,X0)
| ~ incident_c(X2,X0)
| ~ incident_c(X3,X0)
| X1 = X2
| X2 = X3
| X1 = X3 )
& between_c(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ part_of(X1,X0)
| incident_c(X2,X0)
| ~ incident_c(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f60,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f61,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| inner_point(X2,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X3,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X1,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| part_of(sK13(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f42]) ).
fof(f90,plain,
( sK15 = sK17
| sK16 = sK17
| sK15 = sK16
| ~ incident_c(sK17,sK14)
| ~ incident_c(sK16,sK14)
| ~ incident_c(sK15,sK14) ),
inference(cnf_transformation,[],[f43]) ).
fof(f91,plain,
between_c(sK14,sK15,sK16,sK17),
inference(cnf_transformation,[],[f43]) ).
fof(f96,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f89]) ).
fof(f98,definition,
( spl18_1
<=> incident_c(sK15,sK14) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f100,plain,
( ~ incident_c(sK15,sK14)
| spl18_1 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f102,definition,
( spl18_2
<=> incident_c(sK16,sK14) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f106,definition,
( spl18_3
<=> incident_c(sK17,sK14) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f110,definition,
( spl18_4
<=> sK15 = sK16 ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f112,plain,
( sK15 = sK16
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,definition,
( spl18_5
<=> sK16 = sK17 ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f116,plain,
( sK16 = sK17
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl18_6
<=> sK15 = sK17 ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f120,plain,
( sK15 = sK17
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_4
| spl18_5
| spl18_6 ),
inference(avatar_split_clause,[],[f90,f118,f114,f110,f106,f102,f98]) ).
fof(f173,plain,
inner_point(sK16,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f85,f91]) ).
fof(f176,plain,
incident_c(sK16,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f173,f62]) ).
fof(f177,plain,
~ end_point(sK16,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f173,f61]) ).
fof(f178,plain,
end_point(sK17,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f86,f91]) ).
fof(f182,plain,
incident_c(sK17,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f178,f60]) ).
fof(f183,plain,
end_point(sK15,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f87,f91]) ).
fof(f187,plain,
incident_c(sK15,sK13(sK14,sK15,sK16,sK17)),
inference(resolution,[],[f183,f60]) ).
fof(f188,plain,
part_of(sK13(sK14,sK15,sK16,sK17),sK14),
inference(resolution,[],[f88,f91]) ).
fof(f190,plain,
! [X0] :
( ~ incident_c(X0,sK13(sK14,sK15,sK16,sK17))
| incident_c(X0,sK14) ),
inference(resolution,[],[f188,f44]) ).
fof(f238,plain,
incident_c(sK15,sK14),
inference(resolution,[],[f190,f187]) ).
fof(f239,plain,
incident_c(sK16,sK14),
inference(resolution,[],[f190,f176]) ).
fof(f240,plain,
incident_c(sK17,sK14),
inference(resolution,[],[f190,f182]) ).
fof(f241,plain,
spl18_3,
inference(avatar_split_clause,[],[f240,f106]) ).
fof(f242,plain,
spl18_2,
inference(avatar_split_clause,[],[f239,f102]) ).
fof(f243,plain,
( $false
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f238,f100]) ).
fof(f244,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f249,plain,
( ~ end_point(sK16,sK13(sK14,sK15,sK16,sK16))
| ~ spl18_5 ),
inference(superposition,[],[f177,f116]) ).
fof(f250,plain,
( end_point(sK16,sK13(sK14,sK15,sK16,sK16))
| ~ spl18_5 ),
inference(superposition,[],[f178,f116]) ).
fof(f260,plain,
( $false
| ~ spl18_5 ),
inference(forward_subsumption_resolution,[],[f249,f250]) ).
fof(f261,plain,
~ spl18_5,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f262,plain,
( between_c(sK14,sK15,sK16,sK15)
| ~ spl18_6 ),
inference(superposition,[],[f91,f120]) ).
fof(f279,plain,
( $false
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f262,f96]) ).
fof(f280,plain,
~ spl18_6,
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f285,plain,
( ~ end_point(sK15,sK13(sK14,sK15,sK15,sK17))
| ~ spl18_4 ),
inference(superposition,[],[f177,f112]) ).
fof(f289,plain,
( end_point(sK15,sK13(sK14,sK15,sK15,sK17))
| ~ spl18_4 ),
inference(superposition,[],[f183,f112]) ).
fof(f296,plain,
( $false
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f285,f289]) ).
fof(f297,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f296]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_4
| spl18_5
| spl18_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s3,plain,
spl18_3,
inference(sat_conversion,[],[f241]) ).
cnf(s4,plain,
spl18_2,
inference(sat_conversion,[],[f242]) ).
cnf(s5,plain,
spl18_1,
inference(sat_conversion,[],[f244]) ).
cnf(s6,plain,
~ spl18_5,
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
~ spl18_6,
inference(sat_conversion,[],[f280]) ).
cnf(s9,plain,
~ spl18_4,
inference(sat_conversion,[],[f297]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s6,s9,s3,s4,s5]) ).
fof(f298,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:03:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % (1686242)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (1686250)dis+10_1_sil=32000:sp=arity:random_seed=3892718143:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (1686248)% WARNING: option uhcvi not known.
% 0.17/0.46 % (1686247)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2430164242_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (1686249)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1505263159:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (1686248)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2678274766:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (1686251)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2651897163:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (1686253)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=653157675:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (1686252)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=956677231:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (1686251) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1686242-1686251"...
% 0.17/0.46 % (1686251)...printing done.
% 0.17/0.46 % (1686251)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1686251)------------------------------
% 0.17/0.47 % (1686251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1686251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1686251)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1686251)Termination reason: Refutation
% 0.17/0.47 % (1686251)Time elapsed: 0.009 s
% 0.17/0.47 % (1686251)Peak memory usage: 12 MB
% 0.17/0.47 % (1686251)Instructions burned: 12 (million)
% 0.17/0.47 % (1686242)Success in time 0.053 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------