%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO064-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:53:27 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 17 unt; 3 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
fof(f19,axiom,
! [X2,X0,X1] :
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
fof(f23,axiom,
between(w,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_w_and_u) ).
fof(f24,negated_conjecture,
~ colinear(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_uvw_colinear) ).
fof(f27,plain,
! [X2,X0,X1] :
( equidistant(X0,X1,X2,X2)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : ~ equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f33,plain,
~ between(u,v,w),
inference(resolution,[],[f19,f24]) ).
fof(f37,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f28,f27]) ).
fof(f39,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f37]) ).
fof(f247,plain,
! [X2,X3,X0,X1] :
( ~ between(X3,X0,X2)
| ~ between(X0,X1,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 ),
inference(resolution,[],[f8,f7]) ).
fof(f833,plain,
! [X2,X0,X1] :
( ~ between(X2,X0,X1)
| inner_pasch(X2,X0,X1,X1,X0) = X0 ),
inference(resolution,[],[f247,f39]) ).
fof(f850,plain,
v = inner_pasch(w,v,u,u,v),
inference(resolution,[],[f833,f23]) ).
fof(f856,plain,
( between(u,v,w)
| ~ between(v,u,u)
| ~ between(w,v,u) ),
inference(superposition,[],[f9,f850]) ).
fof(f859,definition,
( spl0_1
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f861,plain,
( ~ between(w,v,u)
| spl0_1 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f863,definition,
( spl0_2
<=> between(v,u,u) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f865,plain,
( ~ between(v,u,u)
| spl0_2 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f867,definition,
( spl0_3
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f869,plain,
( between(u,v,w)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f870,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f856,f867,f863,f859]) ).
fof(f871,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f861,f23]) ).
fof(f872,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f871]) ).
fof(f873,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f865,f39]) ).
fof(f874,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f873]) ).
fof(f875,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f869,f33]) ).
fof(f879,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f875]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f870]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f872]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f874]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f879]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f880,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO064-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 06:48:24 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.46 % (878058)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (878069)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1037387426:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (878064)% WARNING: option uhcvi not known.
% 0.12/0.46 % (878066)dis+10_1_sil=32000:sp=arity:random_seed=3550011266:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (878063)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=266841784_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.46 % (878065)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2891518206:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (878064)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4133155695:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.46 % (878068)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1147879669:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (878067)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=402461963:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % TRYING [1]
% 0.12/0.46 % TRYING [2]
% 0.12/0.46 % (878069) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-878058-878069"...
% 0.12/0.46 % TRYING [3]
% 0.12/0.46 % (878069)...printing done.
% 0.12/0.46 % (878069)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (878069)------------------------------
% 0.12/0.46 % (878069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (878069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (878069)CaDiCaL version: 2.1.3
% 0.12/0.46 % (878069)Termination reason: Refutation
% 0.12/0.46 % (878069)Time elapsed: 0.012 s
% 0.12/0.46 % (878069)Peak memory usage: 12 MB
% 0.12/0.46 % (878069)Instructions burned: 30 (million)
% 0.12/0.46 % (878058)Success in time 0.043 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------