%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO193+1 : 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 : n019.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 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 80 ( 24 unt; 5 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 211 ( 90 ~; 90 |; 17 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 87 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,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(f16,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)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,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,[],[f16]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
convergent_lines(sK2,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f60,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2)
| ~ apart_point_and_line(X0,X3)
| ~ apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f64,plain,
apart_point_and_line(intersection_point(sK2,sK1),sK0),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f65,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f69,plain,
! [X0,X1] :
( ~ convergent_lines(X1,X0)
| distinct_lines(X0,X1) ),
inference(resolution,[],[f51,f40]) ).
fof(f71,plain,
distinct_lines(sK1,sK0),
inference(resolution,[],[f69,f54]) ).
fof(f75,plain,
! [X0] :
( ~ apart_point_and_line(X0,sK2)
| distinct_points(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f62,f65]) ).
fof(f78,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,sK2)
| distinct_points(intersection_point(sK0,sK1),X0)
| distinct_points(X0,X1) ),
inference(resolution,[],[f75,f62]) ).
fof(f79,plain,
! [X0,X1] :
( ~ convergent_lines(sK2,X1)
| distinct_points(X0,intersection_point(sK2,X1))
| distinct_points(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f78,f59]) ).
fof(f82,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK1),X0)
| distinct_points(X0,intersection_point(sK2,sK1)) ),
inference(resolution,[],[f79,f53]) ).
fof(f85,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,sK1)),
inference(resolution,[],[f82,f38]) ).
fof(f109,definition,
( spl3_1
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f111,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f117,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f111,f54]) ).
fof(f120,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f117]) ).
fof(f157,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(sK2,sK1),X0)
| ~ apart_point_and_line(X1,sK0)
| ~ apart_point_and_line(X1,X0)
| ~ distinct_points(X1,intersection_point(sK2,sK1))
| ~ distinct_lines(X0,sK0) ),
inference(resolution,[],[f61,f64]) ).
fof(f255,plain,
! [X0] :
( ~ apart_point_and_line(X0,sK0)
| ~ apart_point_and_line(X0,sK1)
| ~ distinct_points(X0,intersection_point(sK2,sK1))
| ~ distinct_lines(sK1,sK0)
| ~ convergent_lines(sK2,sK1) ),
inference(resolution,[],[f157,f60]) ).
fof(f278,definition,
( spl3_12
<=> convergent_lines(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f280,plain,
( ~ convergent_lines(sK2,sK1)
| spl3_12 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f282,definition,
( spl3_13
<=> distinct_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f284,plain,
( ~ distinct_lines(sK1,sK0)
| spl3_13 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl3_14
<=> ! [X0] :
( ~ apart_point_and_line(X0,sK0)
| ~ distinct_points(X0,intersection_point(sK2,sK1))
| ~ apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,sK1)
| ~ distinct_points(X0,intersection_point(sK2,sK1))
| ~ apart_point_and_line(X0,sK0) )
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( ~ spl3_12
| ~ spl3_13
| spl3_14 ),
inference(avatar_split_clause,[],[f255,f286,f282,f278]) ).
fof(f297,plain,
( $false
| spl3_12 ),
inference(resolution,[],[f280,f53]) ).
fof(f300,plain,
spl3_12,
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f301,plain,
( $false
| spl3_13 ),
inference(resolution,[],[f284,f71]) ).
fof(f304,plain,
spl3_13,
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f322,plain,
( ! [X0] :
( ~ apart_point_and_line(intersection_point(X0,sK1),sK0)
| ~ distinct_points(intersection_point(X0,sK1),intersection_point(sK2,sK1))
| ~ convergent_lines(X0,sK1) )
| ~ spl3_14 ),
inference(resolution,[],[f287,f60]) ).
fof(f420,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1)
| ~ spl3_14 ),
inference(resolution,[],[f322,f59]) ).
fof(f423,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ spl3_14 ),
inference(duplicate_literal_removal,[],[f420]) ).
fof(f425,definition,
( spl3_22
<=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_22])],[avatar_definition]) ).
fof(f427,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK2,sK1))
| spl3_22 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f428,plain,
( ~ spl3_1
| ~ spl3_22
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f423,f286,f425,f109]) ).
fof(f429,plain,
( $false
| spl3_22 ),
inference(resolution,[],[f427,f85]) ).
fof(f440,plain,
spl3_22,
inference(avatar_contradiction_clause,[],[f429]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f120]) ).
cnf(s12,plain,
( ~ spl3_12
| ~ spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f288]) ).
cnf(s14,plain,
spl3_12,
inference(sat_conversion,[],[f300]) ).
cnf(s15,plain,
spl3_13,
inference(sat_conversion,[],[f304]) ).
cnf(s22,plain,
( ~ spl3_1
| ~ spl3_14
| ~ spl3_22 ),
inference(sat_conversion,[],[f428]) ).
cnf(s23,plain,
spl3_22,
inference(sat_conversion,[],[f440]) ).
cnf(s25,plain,
( ~ spl3_1
| ~ spl3_14 ),
inference(rat,[],[s22,s23]) ).
cnf(s27,plain,
spl3_14,
inference(rat,[],[s12,s15,s14]) ).
cnf(s28,plain,
~ spl3_1,
inference(rat,[],[s25,s27]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s2,s28]) ).
fof(f442,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 07:31:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.46 % (2765176)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (2765186)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4029265806:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (2765181)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=295778616_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (2765187)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1730885333:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (2765183)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3488724412:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (2765184)dis+10_1_sil=32000:sp=arity:random_seed=3491398343:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (2765185)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=666418965:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 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 % (2765182)% WARNING: option uhcvi not known.
% 0.11/0.46 % TRYING [5]
% 0.11/0.46 % TRYING [6]
% 0.11/0.46 % (2765182)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3856028087:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (2765187) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2765176-2765187"...
% 0.11/0.46 % TRYING [7]
% 0.11/0.46 % (2765187)...printing done.
% 0.11/0.46 % (2765187)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 % (2765187)------------------------------
% 0.11/0.46 % (2765187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (2765187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (2765187)CaDiCaL version: 2.1.3
% 0.11/0.46 % (2765187)Termination reason: Refutation
% 0.11/0.46 % (2765187)Time elapsed: 0.012 s
% 0.11/0.46 % (2765187)Peak memory usage: 12 MB
% 0.11/0.46 % (2765187)Instructions burned: 17 (million)
% 0.11/0.46 % (2765176)Success in time 0.05 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------