%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO193+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:53:55 AM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 16 unt; 3 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 66 ~; 85 |; 19 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 75 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(f9,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/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X2,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X2,X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X2,X1),X0)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X2,X1),X0)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,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,[],[f26]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
convergent_lines(sK2,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f48,f51]) ).
fof(f76,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ convergent_lines(X1,X2)
| distinct_points(intersection_point(X1,X2),X3)
| distinct_points(X0,X3) ),
inference(resolution,[],[f44,f38]) ).
fof(f84,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f45,f55]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_points(intersection_point(sK2,X0),X1)
| ~ convergent_lines(sK2,X0)
| distinct_points(intersection_point(sK0,sK1),X1) ),
inference(resolution,[],[f80,f52]) ).
fof(f224,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,X0))
| ~ convergent_lines(sK2,X0) ),
inference(resolution,[],[f114,f35]) ).
fof(f253,definition,
( spl3_1
<=> ! [X1] :
( apart_point_and_line(intersection_point(sK2,X1),sK1)
| ~ convergent_lines(sK2,X1)
| apart_point_and_line(intersection_point(sK2,X1),sK0) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f254,plain,
( ! [X1] :
( apart_point_and_line(intersection_point(sK2,X1),sK1)
| ~ convergent_lines(sK2,X1)
| apart_point_and_line(intersection_point(sK2,X1),sK0) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f264,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f265,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK0)
| spl3_4 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f266,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f268,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f269,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f270,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f288,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f266,f79]) ).
fof(f293,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f288,f51]) ).
fof(f294,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f293]) ).
fof(f330,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f270,f76]) ).
fof(f335,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f330,f51]) ).
fof(f336,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f563,plain,
! [X0] :
( ~ convergent_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK2,X0),sK0)
| apart_point_and_line(intersection_point(sK2,X0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(resolution,[],[f224,f84]) ).
fof(f566,plain,
( ! [X0] :
( ~ convergent_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK2,X0),sK0)
| apart_point_and_line(intersection_point(sK2,X0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0) )
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f563,f269]) ).
fof(f567,plain,
( ! [X0] :
( ~ convergent_lines(sK2,X0)
| apart_point_and_line(intersection_point(sK2,X0),sK0)
| apart_point_and_line(intersection_point(sK2,X0),sK1) )
| spl3_4
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f566,f265]) ).
fof(f568,plain,
( spl3_1
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f567,f268,f264,f253]) ).
fof(f875,plain,
( ~ convergent_lines(sK2,sK1)
| apart_point_and_line(intersection_point(sK2,sK1),sK0)
| ~ convergent_lines(sK2,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f254,f76]) ).
fof(f880,plain,
( ~ convergent_lines(sK2,sK1)
| apart_point_and_line(intersection_point(sK2,sK1),sK0)
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f875]) ).
fof(f881,plain,
( apart_point_and_line(intersection_point(sK2,sK1),sK0)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f880,f50]) ).
fof(f882,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f881,f53]) ).
fof(f883,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f882]) ).
cnf(s8,plain,
~ spl3_4,
inference(sat_conversion,[],[f294]) ).
cnf(s11,plain,
~ spl3_5,
inference(sat_conversion,[],[f336]) ).
cnf(s20,plain,
( spl3_1
| spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f568]) ).
cnf(s27,plain,
~ spl3_1,
inference(sat_conversion,[],[f883]) ).
cnf(s28,plain,
( spl3_4
| spl3_5 ),
inference(rat,[],[s20,s27]) ).
cnf(s31,plain,
spl3_4,
inference(rat,[],[s28,s11]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s8,s31]) ).
fof(f884,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO193+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n014.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 07:31:02 UTC 2026
% 0.13/0.39 % 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
% 0.13/0.43 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
% 0.18/0.49 % (472766)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (472775)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3122381906:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (472772)% WARNING: option uhcvi not known.
% 0.18/0.49 % (472771)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2517898175_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (472772)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2360173309:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (472773)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3403733104:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (472774)dis+10_1_sil=32000:sp=arity:random_seed=2026152583:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (472776)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=18196138:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (472777)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1262669702:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % TRYING [2]
% 0.18/0.49 % TRYING [3]
% 0.18/0.49 % TRYING [4]
% 0.18/0.49 % TRYING [5]
% 0.18/0.49 % TRYING [6]
% 0.18/0.49 % TRYING [7]
% 0.18/0.49 % (472774) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-472766-472774"...
% 0.18/0.49 % (472772) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-472766-472772"...
% 0.18/0.49 % (472774)...printing done.
% 0.18/0.49 % (472772)...printing done.
% 0.18/0.49 % (472774)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (472774)------------------------------
% 0.18/0.49 % (472774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (472774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (472774)CaDiCaL version: 2.1.3
% 0.18/0.49 % (472774)Termination reason: Refutation
% 0.18/0.49 % (472774)Time elapsed: 0.019 s
% 0.18/0.49 % (472774)Peak memory usage: 12 MB
% 0.18/0.49 % (472774)Instructions burned: 30 (million)
% 0.18/0.49 % (472766)Success in time 0.058 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------