%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 09:54:00 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 16 unt; 6 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 83 ~; 88 |; 11 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 64 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
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(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
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] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ( ~ convergent_lines(sK0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) )
& convergent_lines(sK0,sK1)
& ~ distinct_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
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] :
( ~ 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,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
( ~ convergent_lines(sK0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,definition,
( spl3_1
<=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f58,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl3_2
<=> convergent_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f61,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f54,f60,f56]) ).
fof(f72,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f51,f53]) ).
fof(f76,plain,
( distinct_lines(sK1,sK2)
| spl3_2 ),
inference(resolution,[],[f72,f62]) ).
fof(f77,plain,
distinct_lines(sK1,sK0),
inference(resolution,[],[f72,f40]) ).
fof(f80,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f76,f52]) ).
fof(f81,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f89,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f48,f77]) ).
fof(f516,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_1 ),
inference(resolution,[],[f89,f58]) ).
fof(f526,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f528,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f530,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f532,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f539,definition,
( spl3_7
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f541,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f543,definition,
( spl3_8
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f545,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f555,plain,
( spl3_7
| spl3_8
| spl3_4
| spl3_5
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f516,f56,f530,f526,f543,f539]) ).
fof(f556,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_4 ),
inference(resolution,[],[f528,f46]) ).
fof(f559,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f556,f61]) ).
fof(f560,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f617,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(sK0,sK2),X0)
| distinct_lines(sK1,X0) )
| ~ spl3_5 ),
inference(resolution,[],[f532,f50]) ).
fof(f634,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_7 ),
inference(resolution,[],[f541,f47]) ).
fof(f637,plain,
( $false
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f634,f53]) ).
fof(f638,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f639,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_8 ),
inference(resolution,[],[f545,f46]) ).
fof(f642,plain,
( $false
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f639,f53]) ).
fof(f643,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f642]) ).
fof(f663,plain,
( distinct_lines(sK1,sK2)
| ~ convergent_lines(sK0,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f617,f47]) ).
fof(f672,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f663,f52]) ).
fof(f673,plain,
( $false
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f672,f61]) ).
fof(f674,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f673]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f81]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_4
| spl3_5
| spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f555]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f560]) ).
cnf(s18,plain,
~ spl3_7,
inference(sat_conversion,[],[f638]) ).
cnf(s19,plain,
~ spl3_8,
inference(sat_conversion,[],[f643]) ).
cnf(s22,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f674]) ).
cnf(s25,plain,
( ~ spl3_1
| spl3_4
| spl3_5 ),
inference(rat,[],[s8,s19,s18]) ).
cnf(s27,plain,
~ spl3_5,
inference(rat,[],[s22,s2]) ).
cnf(s29,plain,
~ spl3_4,
inference(rat,[],[s9,s2]) ).
cnf(s30,plain,
~ spl3_1,
inference(rat,[],[s25,s27,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s1,s2,s30]) ).
fof(f675,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n005.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 07:35:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.44 % (3655118)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (3655128)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3164398639:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (3655124)% WARNING: option uhcvi not known.
% 0.11/0.44 % (3655123)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4269486615_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % (3655125)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=15393402:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (3655129)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4054795178:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (3655126)dis+10_1_sil=32000:sp=arity:random_seed=1853729728:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (3655127)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2865515359:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (3655124)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1499183840:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % TRYING [1]
% 0.11/0.44 % TRYING [2]
% 0.11/0.44 % TRYING [3]
% 0.11/0.44 % (3655128) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3655118-3655128"...
% 0.11/0.44 % TRYING [4]
% 0.11/0.44 % (3655128)...printing done.
% 0.11/0.44 % TRYING [5]
% 0.11/0.44 % (3655128)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (3655128)------------------------------
% 0.11/0.44 % (3655128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (3655128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (3655128)CaDiCaL version: 2.1.3
% 0.11/0.44 % (3655128)Termination reason: Refutation
% 0.11/0.44 % (3655128)Time elapsed: 0.010 s
% 0.11/0.44 % (3655128)Peak memory usage: 12 MB
% 0.11/0.44 % (3655128)Instructions burned: 29 (million)
% 0.11/0.44 % (3655118)Success in time 0.035 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------