%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO194+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 : n016.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 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 19 unt; 6 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 198 ( 70 ~; 93 |; 19 &)
% ( 6 <=>; 10 =>; 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 : 93 ( 0 sgn 87 !; 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(f10,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/GEO008+0.ax',ceq1) ).
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(X0,X2),X1) ) ),
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(X0,X2),X1) ) ),
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(f27,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f27]) ).
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(X0,X2),X1)
& 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(X0,X2),X1)
& 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(sK0,sK2),sK1)
& 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(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
convergent_lines(sK0,sK2),
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(sK0,sK2),sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f48,f51]) ).
fof(f63,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK1),X0)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f46,f52]) ).
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(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(f92,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK2)
| distinct_points(X0,X1)
| distinct_points(intersection_point(sK0,sK1),X1) ),
inference(resolution,[],[f63,f38]) ).
fof(f248,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(X1,sK2)
| distinct_points(X1,X0) ),
inference(resolution,[],[f84,f92]) ).
fof(f264,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
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(f270,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f276,definition,
( spl3_7
<=> ! [X0,X1] :
( apart_point_and_line(X0,sK0)
| apart_point_and_line(X1,sK2)
| distinct_points(X1,X0)
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f277,plain,
( ! [X0,X1] :
( apart_point_and_line(X1,sK2)
| apart_point_and_line(X0,sK1)
| distinct_points(X1,X0)
| apart_point_and_line(X0,sK0) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f278,plain,
( spl3_4
| spl3_5
| spl3_7 ),
inference(avatar_split_clause,[],[f248,f276,f268,f264]) ).
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(f774,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| distinct_points(X0,intersection_point(sK0,sK2))
| apart_point_and_line(intersection_point(sK0,sK2),sK0) )
| ~ spl3_7 ),
inference(resolution,[],[f277,f53]) ).
fof(f791,definition,
( spl3_14
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f793,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f795,definition,
( spl3_15
<=> ! [X0] :
( apart_point_and_line(X0,sK2)
| distinct_points(X0,intersection_point(sK0,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl3_15])],[avatar_definition]) ).
fof(f796,plain,
( ! [X0] :
( distinct_points(X0,intersection_point(sK0,sK2))
| apart_point_and_line(X0,sK2) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f797,plain,
( spl3_14
| spl3_15
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f774,f276,f795,f791]) ).
fof(f825,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_15 ),
inference(resolution,[],[f796,f35]) ).
fof(f833,definition,
( spl3_17
<=> apart_point_and_line(intersection_point(sK0,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f835,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f841,plain,
( spl3_17
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f825,f795,f833]) ).
fof(f846,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_14 ),
inference(resolution,[],[f793,f79]) ).
fof(f851,plain,
( $false
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f846,f49]) ).
fof(f852,plain,
~ spl3_14,
inference(avatar_contradiction_clause,[],[f851]) ).
fof(f861,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_17 ),
inference(resolution,[],[f835,f76]) ).
fof(f867,plain,
( $false
| ~ spl3_17 ),
inference(forward_subsumption_resolution,[],[f861,f49]) ).
fof(f868,plain,
~ spl3_17,
inference(avatar_contradiction_clause,[],[f867]) ).
cnf(s4,plain,
( spl3_4
| spl3_5
| spl3_7 ),
inference(sat_conversion,[],[f278]) ).
cnf(s8,plain,
~ spl3_4,
inference(sat_conversion,[],[f294]) ).
cnf(s11,plain,
~ spl3_5,
inference(sat_conversion,[],[f336]) ).
cnf(s22,plain,
( ~ spl3_7
| spl3_14
| spl3_15 ),
inference(sat_conversion,[],[f797]) ).
cnf(s28,plain,
( ~ spl3_15
| spl3_17 ),
inference(sat_conversion,[],[f841]) ).
cnf(s30,plain,
~ spl3_14,
inference(sat_conversion,[],[f852]) ).
cnf(s34,plain,
~ spl3_17,
inference(sat_conversion,[],[f868]) ).
cnf(s36,plain,
~ spl3_15,
inference(rat,[],[s28,s34]) ).
cnf(s38,plain,
~ spl3_7,
inference(rat,[],[s22,s36,s30]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s4,s38,s11,s8]) ).
fof(f869,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO194+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n016.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 07:36:16 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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 % (2296135)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2296144)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4136681586:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2296141)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2296141)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2973036906:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2296142)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2393971531:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2296143)dis+10_1_sil=32000:sp=arity:random_seed=2325775888:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2296140)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1751863076_2999 on theBenchmark for (2999ds/0Mi)
% 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 % TRYING [6]
% 0.16/0.47 % TRYING [7]
% 0.16/0.47 % (2296143) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2296135-2296143"...
% 0.16/0.47 % (2296146)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2157382171:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (2296145)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1250280784:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2296143)...printing done.
% 0.16/0.47 % (2296143)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
% 0.16/0.48 % (2296143)------------------------------
% 0.16/0.48 % (2296143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2296143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2296143)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2296143)Termination reason: Refutation
% 0.16/0.48 % (2296143)Time elapsed: 0.019 s
% 0.16/0.48 % (2296143)Peak memory usage: 12 MB
% 0.16/0.48 % (2296143)Instructions burned: 28 (million)
% 0.16/0.48 % (2296135)Success in time 0.057 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------