%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO066-2 : 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 09:53:28 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 16 unt; 3 def)
% Number of atoms : 60 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 22 |; 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 : 38 ( 0 sgn 38 !; 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(f21,axiom,
! [X2,X0,X1] :
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
fof(f23,axiom,
between(v,u,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_between_v_and_w) ).
fof(f24,negated_conjecture,
~ colinear(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_uvw_colinear) ).
fof(f28,plain,
~ between(w,u,v),
inference(resolution,[],[f21,f24]) ).
fof(f29,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f31,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f29]) ).
fof(f56,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(f61,plain,
! [X2,X0,X1] :
( ~ between(X2,X0,X1)
| inner_pasch(X2,X0,X1,X1,X0) = X0 ),
inference(resolution,[],[f56,f31]) ).
fof(f71,plain,
u = inner_pasch(v,u,w,w,u),
inference(resolution,[],[f61,f23]) ).
fof(f85,plain,
( between(w,u,v)
| ~ between(u,w,w)
| ~ between(v,u,w) ),
inference(superposition,[],[f9,f71]) ).
fof(f88,definition,
( spl0_1
<=> between(v,u,w) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f90,plain,
( ~ between(v,u,w)
| spl0_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_2
<=> between(u,w,w) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f94,plain,
( ~ between(u,w,w)
| spl0_2 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_3
<=> between(w,u,v) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f98,plain,
( between(w,u,v)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f85,f96,f92,f88]) ).
fof(f100,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f90,f23]) ).
fof(f101,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f102,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f94,f31]) ).
fof(f103,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f104,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f98,f28]) ).
fof(f108,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f104]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f101]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f103]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f108]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f109,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO066-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 06:48:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.49 % (878483)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (878492)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=888924687:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (878489)% WARNING: option uhcvi not known.
% 0.17/0.49 % (878488)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2251174470_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (878493)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3510568831:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (878489)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3867853310:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (878490)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4015131078:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (878491)dis+10_1_sil=32000:sp=arity:random_seed=3974856829:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (878494)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3958339132:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % (878494) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-878483-878494"...
% 0.17/0.49 % (878494)...printing done.
% 0.17/0.49 % (878491) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-878483-878491"...
% 0.17/0.49 % (878494)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (878494)------------------------------
% 0.17/0.49 % (878494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (878494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (878494)CaDiCaL version: 2.1.3
% 0.17/0.49 % (878494)Termination reason: Refutation
% 0.17/0.49 % (878494)Time elapsed: 0.005 s
% 0.17/0.49 % (878494)Peak memory usage: 12 MB
% 0.17/0.49 % (878494)Instructions burned: 5 (million)
% 0.17/0.49 % (878483)Success in time 0.054 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------