%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO202+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 : n013.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 09:53:58 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 18 unt; 3 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 58 ~; 78 |; 11 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
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(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] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
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(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] :
( distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(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) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] : convergent_lines(X0,X0),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f61,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f63,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f64,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( distinct_lines(X2,X3)
| distinct_points(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) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X2)
| convergent_lines(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f69,plain,
~ distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f70,plain,
~ distinct_points(sK0,sK1),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f71,plain,
~ distinct_points(sK0,sK2),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f72,plain,
~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f78,plain,
! [X0,X1] :
( ~ distinct_lines(X1,X0)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f68,f57]) ).
fof(f83,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X1)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f65,f69]) ).
fof(f133,plain,
! [X0] :
( distinct_lines(line_connecting(sK0,sK2),X0)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolution,[],[f83,f64]) ).
fof(f138,plain,
! [X0] :
( distinct_lines(line_connecting(sK0,sK2),X0)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
inference(forward_subsumption_resolution,[],[f133,f72]) ).
fof(f143,definition,
( spl3_1
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f145,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f147,definition,
( spl3_2
<=> ! [X0] :
( distinct_lines(line_connecting(sK0,sK2),X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f148,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0)
| apart_point_and_line(sK0,X0)
| distinct_lines(line_connecting(sK0,sK2),X0) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f149,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f138,f147,f143]) ).
fof(f151,definition,
( spl3_3
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f152,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl3_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f169,plain,
( distinct_points(sK0,sK1)
| ~ spl3_3 ),
inference(resolution,[],[f153,f61]) ).
fof(f172,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f169,f70]) ).
fof(f173,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f333,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1))
| convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(resolution,[],[f148,f63]) ).
fof(f337,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f333,f78]) ).
fof(f338,plain,
( convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_2
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f337,f152]) ).
fof(f339,plain,
( $false
| ~ spl3_2
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f338,f72]) ).
fof(f340,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f430,plain,
( distinct_points(sK0,sK2)
| ~ spl3_1 ),
inference(resolution,[],[f145,f61]) ).
fof(f433,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f430,f71]) ).
fof(f434,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f433]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f149]) ).
cnf(s5,plain,
~ spl3_3,
inference(sat_conversion,[],[f173]) ).
cnf(s6,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f340]) ).
cnf(s7,plain,
~ spl3_1,
inference(sat_conversion,[],[f434]) ).
cnf(s8,plain,
~ spl3_2,
inference(rat,[],[s6,s5]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
fof(f435,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 07:34:36 UTC 2026
% 0.13/0.38 % 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
% 0.13/0.42 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
% 0.17/0.48 % (4085572)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (4085577)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1673772365_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % (4085578)% WARNING: option uhcvi not known.
% 0.17/0.48 % TRYING [6]
% 0.17/0.48 % (4085578)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2720588956:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (4085579)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1034521883:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (4085582)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2257735092:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (4085580)dis+10_1_sil=32000:sp=arity:random_seed=3512314935:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (4085581)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3343629973:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (4085583)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2022066818:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [7]
% 0.17/0.48 % TRYING [8]
% 0.17/0.48 % TRYING [9]
% 0.17/0.48 % (4085578) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4085572-4085578"...
% 0.17/0.48 % (4085582) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4085572-4085582"...
% 0.17/0.48 % (4085578)...printing done.
% 0.17/0.48 % (4085582)...printing done.
% 0.17/0.48 % (4085578)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (4085578)------------------------------
% 0.17/0.48 % (4085578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (4085578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (4085578)CaDiCaL version: 2.1.3
% 0.17/0.48 % (4085578)Termination reason: Refutation
% 0.17/0.48 % (4085578)Time elapsed: 0.020 s
% 0.17/0.48 % (4085578)Peak memory usage: 12 MB
% 0.17/0.48 % (4085578)Instructions burned: 34 (million)
% 0.17/0.48 % (4085572)Success in time 0.054 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------