%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO202+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 : n006.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 09:53:59 AM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 17 unt; 4 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 176 ( 63 ~; 81 |; 19 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 83 !; 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(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
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] :
( ( 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(f14,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)],[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(f21,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f21]) ).
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] :
( 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,[],[f14]) ).
fof(f33,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,[],[f32]) ).
fof(f34,plain,
( distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& convergent_lines(line_connecting(sK0,sK1),line_connecting(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(f42,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
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(f49,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(resolution,[],[f48,f49]) ).
fof(f54,plain,
! [X0] :
( distinct_points(sK2,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f38,f50]) ).
fof(f55,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f38,f51]) ).
fof(f58,plain,
! [X0,X1] :
( distinct_points(sK0,X0)
| distinct_points(X0,X1)
| distinct_points(sK2,X1) ),
inference(resolution,[],[f54,f38]) ).
fof(f61,plain,
! [X0,X1] :
( distinct_points(sK0,X0)
| distinct_points(X0,X1)
| distinct_points(sK1,X1) ),
inference(resolution,[],[f55,f38]) ).
fof(f66,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK2) ),
inference(resolution,[],[f58,f35]) ).
fof(f75,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK1) ),
inference(resolution,[],[f61,f35]) ).
fof(f91,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f95,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f98,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK1)) ),
inference(resolution,[],[f45,f53]) ).
fof(f201,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1)) ),
inference(resolution,[],[f98,f52]) ).
fof(f237,definition,
( spl3_3
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f239,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,definition,
( spl3_4
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f243,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f282,definition,
( spl3_12
<=> apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f284,plain,
( apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2))
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl3_13
<=> apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f288,plain,
( apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1))
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f328,plain,
( spl3_13
| spl3_12
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f201,f241,f237,f282,f286]) ).
fof(f357,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f239,f42]) ).
fof(f363,plain,
( distinct_points(sK0,sK0)
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f357,f66]) ).
fof(f364,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f363,f35]) ).
fof(f365,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f450,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f243,f42]) ).
fof(f456,plain,
( distinct_points(sK0,sK0)
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f450,f75]) ).
fof(f457,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f456,f35]) ).
fof(f458,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f459,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_12 ),
inference(resolution,[],[f284,f91]) ).
fof(f467,plain,
( $false
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f459,f49]) ).
fof(f468,plain,
~ spl3_12,
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f478,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_13 ),
inference(resolution,[],[f288,f95]) ).
fof(f486,plain,
( $false
| ~ spl3_13 ),
inference(forward_subsumption_resolution,[],[f478,f49]) ).
fof(f487,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[],[f486]) ).
cnf(s27,plain,
( spl3_3
| spl3_4
| spl3_12
| spl3_13 ),
inference(sat_conversion,[],[f328]) ).
cnf(s47,plain,
~ spl3_3,
inference(sat_conversion,[],[f365]) ).
cnf(s58,plain,
~ spl3_4,
inference(sat_conversion,[],[f458]) ).
cnf(s59,plain,
~ spl3_12,
inference(sat_conversion,[],[f468]) ).
cnf(s61,plain,
~ spl3_13,
inference(sat_conversion,[],[f487]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s27,s61,s59,s58,s47]) ).
fof(f488,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO202+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.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 07:34:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.47 % (2656755)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2656765)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3491682891:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2656761)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2656761)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3613324703:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2656760)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2258258470_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (2656763)dis+10_1_sil=32000:sp=arity:random_seed=1879109442:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2656762)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1158931904:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2656764)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2382778937:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2656766)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=993716748:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (2656763) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2656755-2656763"...
% 0.16/0.47 % TRYING [6]
% 0.16/0.47 % (2656763)...printing done.
% 0.16/0.47 % (2656763)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2656763)------------------------------
% 0.16/0.47 % (2656763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2656763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2656763)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2656763)Termination reason: Refutation
% 0.16/0.47 % (2656763)Time elapsed: 0.010 s
% 0.16/0.47 % (2656763)Peak memory usage: 12 MB
% 0.16/0.47 % (2656763)Instructions burned: 14 (million)
% 0.16/0.47 % (2656755)Success in time 0.051 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------