%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO173+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:53:47 AM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 38 ~; 42 |; 17 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f48]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK1,sK2)
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& distinct_lines(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f85,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f115,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f228,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f89,f115]) ).
fof(f240,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2) ),
inference(resolution,[],[f228,f117]) ).
fof(f243,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f240,f118]) ).
fof(f245,definition,
( spl4_5
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f247,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f252,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f243,f119]) ).
fof(f254,definition,
( spl4_7
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f256,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f252,f245,f254]) ).
fof(f258,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_5 ),
inference(resolution,[],[f247,f86]) ).
fof(f261,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f258,f117]) ).
fof(f262,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f263,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_7 ),
inference(resolution,[],[f256,f85]) ).
fof(f266,plain,
( $false
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f263,f117]) ).
fof(f267,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f266]) ).
cnf(s5,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f257]) ).
cnf(s6,plain,
~ spl4_5,
inference(sat_conversion,[],[f262]) ).
cnf(s7,plain,
~ spl4_7,
inference(sat_conversion,[],[f267]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s7,s6]) ).
fof(f268,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO173+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:25:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (165096)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (165106)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1305670016:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (165102)% WARNING: option uhcvi not known.
% 0.11/0.46 % (165101)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3164543256_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (165102)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1456455515:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (165103)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=645389278:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (165104)dis+10_1_sil=32000:sp=arity:random_seed=1062060619:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (165105)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1088715885:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (165107)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3948112434:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % (165104) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-165096-165104"...
% 0.11/0.46 % (165104)...printing done.
% 0.11/0.46 % TRYING [5]
% 0.11/0.46 % (165102) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-165096-165102"...
% 0.11/0.46 % (165104)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (165104)------------------------------
% 0.11/0.46 % (165104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (165104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (165104)CaDiCaL version: 2.1.3
% 0.11/0.46 % (165104)Termination reason: Refutation
% 0.11/0.46 % (165104)Time elapsed: 0.005 s
% 0.11/0.46 % (165104)Peak memory usage: 12 MB
% 0.11/0.46 % (165104)Instructions burned: 6 (million)
% 0.11/0.46 % (165096)Success in time 0.04 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------