%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 09:53:26 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 21 unt; 4 def)
% Number of atoms : 101 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 46 ~; 40 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X1,X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
fof(f29,axiom,
! [X2,X0,X1] : X0 = extension(X1,X0,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
fof(f30,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(reorient_equations,[],[f29]) ).
fof(f47,axiom,
! [X0,X1] :
( extension(X0,X1,X0,X1) = extension(X0,X1,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
fof(f48,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_congruence) ).
fof(f54,plain,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(definition_unfolding,[],[f48,f19,f19]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,X1,X4,X5)
| equidistant(X0,X1,X2,X3)
| ~ equidistant(X2,X3,X4,X5) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : ~ equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( equidistant(X0,X1,X2,X3)
| ~ equidistant(X2,X3,X0,X1) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( equidistant(X0,X1,X2,X3)
| ~ equidistant(X1,X0,X2,X3) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X3,X2) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f79,plain,
equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f90,plain,
! [X2,X3,X0,X1] : ~ equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[],[f66,f60]) ).
fof(f95,plain,
! [X2,X3,X0,X1] : ~ equidistant(X0,X1,X2,extension(X3,X2,X1,X0)),
inference(resolution,[],[f67,f90]) ).
fof(f113,plain,
! [X2,X3,X0,X1] : ~ equidistant(X0,X1,extension(X2,X3,X1,X0),X3),
inference(resolution,[],[f95,f68]) ).
fof(f177,plain,
( equidistant(v,u,v,extension(extension(u,v,u,v),v,v,extension(u,v,u,v)))
| v = extension(u,v,u,v) ),
inference(superposition,[],[f79,f47]) ).
fof(f199,definition,
( spl0_1
<=> v = extension(u,v,u,v) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f200,plain,
( v != extension(u,v,u,v)
| spl0_1 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( v = extension(u,v,u,v)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f203,definition,
( spl0_2
<=> equidistant(v,u,v,extension(extension(u,v,u,v),v,v,extension(u,v,u,v))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f205,plain,
( equidistant(v,u,v,extension(extension(u,v,u,v),v,v,extension(u,v,u,v)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f177,f203,f199]) ).
fof(f208,definition,
( spl0_3
<=> v = u ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f210,plain,
( v = u
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f217,plain,
( v != extension(v,v,v,v)
| spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f200,f210]) ).
fof(f219,plain,
( v != v
| spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f217,f30]) ).
fof(f220,plain,
( $false
| spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f219]) ).
fof(f221,plain,
( spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f224,plain,
( equidistant(v,u,v,extension(v,v,v,v))
| ~ spl0_1 ),
inference(superposition,[],[f79,f201]) ).
fof(f233,plain,
( ~ equidistant(v,u,v,v)
| ~ spl0_1 ),
inference(superposition,[],[f113,f201]) ).
fof(f252,plain,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| ~ equidistant(X4,X5,X2,X3) ),
inference(resolution,[],[f58,f60]) ).
fof(f287,plain,
( equidistant(v,u,v,v)
| ~ spl0_1 ),
inference(superposition,[],[f224,f30]) ).
fof(f288,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f287,f233]) ).
fof(f290,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f292,plain,
( equidistant(v,u,v,extension(extension(u,v,v,u),v,v,extension(u,v,v,u)))
| v = u
| ~ spl0_2 ),
inference(superposition,[],[f205,f47]) ).
fof(f294,definition,
( spl0_5
<=> equidistant(v,u,v,extension(extension(u,v,v,u),v,v,extension(u,v,v,u))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f296,plain,
( equidistant(v,u,v,extension(extension(u,v,v,u),v,v,extension(u,v,v,u)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,plain,
( spl0_3
| spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f292,f203,f294,f208]) ).
fof(f377,plain,
! [X2,X3,X0,X1,X4,X5] : ~ equidistant(X0,extension(X1,X0,X2,extension(X3,X2,X4,X5)),X4,X5),
inference(resolution,[],[f252,f90]) ).
fof(f388,plain,
! [X2,X3,X0,X1,X4,X5] : ~ equidistant(X0,X1,X2,extension(X3,X2,X4,extension(X5,X4,X0,X1))),
inference(resolution,[],[f377,f66]) ).
fof(f487,plain,
( $false
| ~ spl0_5 ),
inference(resolution,[],[f388,f296]) ).
fof(f505,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f487]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f206]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f221]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f290]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f297]) ).
cnf(s6,plain,
~ spl0_5,
inference(sat_conversion,[],[f505]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_3 ),
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
~ spl0_3,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
~ spl0_2,
inference(rat,[],[s7,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9,s4]) ).
fof(f506,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n020.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 06:47:34 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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 % (3053312)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (3053323)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3627206396:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (3053318)% WARNING: option uhcvi not known.
% 0.17/0.46 % (3053323) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3053312-3053323"...
% 0.17/0.46 % (3053322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3679960616:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (3053317)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=963095656_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (3053318)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=167385534:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (3053319)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=351331750:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (3053320)dis+10_1_sil=32000:sp=arity:random_seed=3811508652:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (3053321)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=631504220:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (3053323)...printing done.
% 0.17/0.46 % (3053323)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (3053323)------------------------------
% 0.17/0.46 % (3053323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (3053323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (3053323)CaDiCaL version: 2.1.3
% 0.17/0.46 % (3053323)Termination reason: Refutation
% 0.17/0.46 % (3053323)Time elapsed: 0.006 s
% 0.17/0.46 % (3053323)Peak memory usage: 12 MB
% 0.17/0.46 % (3053323)Instructions burned: 15 (million)
% 0.17/0.46 % (3053312)Success in time 0.039 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------