%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO037-2 : 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 09:53:21 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 17 unt; 3 def)
% Number of atoms : 63 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 22 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
fof(f19,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
fof(f21,definition,
( spl0_1
<=> between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl0_2
<=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f27,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl0_3
<=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f19,f29,f25,f21]) ).
fof(f141,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f142,plain,
( equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_3 ),
inference(superposition,[],[f5,f31]) ).
fof(f144,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f141]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X1,X0) ),
inference(resolution,[],[f2,f1]) ).
fof(f190,plain,
! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(resolution,[],[f155,f5]) ).
fof(f192,plain,
( equidistant(lower_dimension_point_1,lower_dimension_point_2,v,v)
| ~ spl0_3 ),
inference(resolution,[],[f155,f142]) ).
fof(f193,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_3 ),
inference(resolution,[],[f192,f3]) ).
fof(f198,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_3 ),
inference(superposition,[],[f12,f193]) ).
fof(f203,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f198,f144]) ).
fof(f204,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f203]) ).
fof(f227,plain,
! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2),
inference(resolution,[],[f190,f155]) ).
fof(f231,plain,
! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0)),
inference(resolution,[],[f227,f155]) ).
fof(f235,plain,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,extension(X5,X4,X1,X0))
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[],[f231,f2]) ).
fof(f879,plain,
( ~ equidistant(lower_dimension_point_2,lower_dimension_point_1,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| spl0_2 ),
inference(resolution,[],[f235,f27]) ).
fof(f882,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f879,f231]) ).
fof(f883,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f882]) ).
fof(f884,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f23,f4]) ).
fof(f885,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f884]) ).
cnf(s24,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s216,plain,
~ spl0_3,
inference(sat_conversion,[],[f204]) ).
cnf(s515,plain,
spl0_2,
inference(sat_conversion,[],[f883]) ).
cnf(s524,plain,
spl0_1,
inference(sat_conversion,[],[f885]) ).
cnf(s535,plain,
$false,
inference(rat,[],[s24,s216,s515,s524]) ).
fof(f886,plain,
$false,
inference(avatar_sat_refutation,[],[s535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 06:41:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.43 % (3050975)Will run a generic schedule for satisfiability detection.
% 0.09/0.43 % (3050982)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1935478970:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.43 % (3050981)% WARNING: option uhcvi not known.
% 0.09/0.43 % (3050980)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1480214064_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.43 % (3050981)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2906097691:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.43 % (3050983)dis+10_1_sil=32000:sp=arity:random_seed=860962063:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.43 % (3050984)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3474450553:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.43 % (3050985)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=180027459:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.43 % (3050986)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2162632542:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.43 % TRYING [1]
% 0.09/0.43 % TRYING [2]
% 0.09/0.43 % (3050982) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3050975-3050982"...
% 0.09/0.43 % (3050982)...printing done.
% 0.09/0.43 % TRYING [3]
% 0.09/0.43 % (3050982)Refutation found. Thanks to Tanya!
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.43 % (3050982)------------------------------
% 0.09/0.43 % (3050982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.43 % (3050982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.43 % (3050982)CaDiCaL version: 2.1.3
% 0.09/0.43 % (3050982)Termination reason: Refutation
% 0.09/0.43 % (3050982)Time elapsed: 0.010 s
% 0.09/0.43 % (3050982)Peak memory usage: 12 MB
% 0.09/0.43 % (3050982)Instructions burned: 23 (million)
% 0.09/0.43 % (3050975)Success in time 0.034 s
% 0.09/0.43 % Vampire exiting
%------------------------------------------------------------------------------