%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 09:51:55 AM UTC 2026
% Result : Theorem 2.36s 1.06s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 21 unt; 5 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 181 ( 66 ~; 82 |; 19 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 82 ( 0 sgn 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
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/theBenchmark.p',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/theBenchmark.p',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/theBenchmark.p',ceq1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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] :
( ~ 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(f16,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,[],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f24,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(f25,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f24]) ).
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(ennf_transformation,[],[f9]) ).
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(flattening,[],[f26]) ).
fof(f32,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)],[f16]) ).
fof(f33,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f35,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f36,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
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,[],[f27]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f56,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(resolution,[],[f38,f47]) ).
fof(f57,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(resolution,[],[f39,f47]) ).
fof(f58,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK2),
inference(resolution,[],[f56,f33]) ).
fof(f59,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolution,[],[f56,f35]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X3)
| ~ convergent_lines(X3,X1) ),
inference(resolution,[],[f45,f40]) ).
fof(f65,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK0),
inference(resolution,[],[f57,f33]) ).
fof(f66,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolution,[],[f57,f35]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X4)
| ~ apart_point_and_line(X3,X4) ),
inference(resolution,[],[f64,f44]) ).
fof(f95,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| ~ apart_point_and_line(X1,X2) ),
inference(resolution,[],[f70,f35]) ).
fof(f137,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f138,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f235,definition,
( spl3_21
<=> ! [X0] :
( ~ apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition]) ).
fof(f236,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f250,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f95,f58]) ).
fof(f267,definition,
( spl3_23
<=> apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_23])],[avatar_definition]) ).
fof(f268,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f269,plain,
( spl3_23
| spl3_5
| spl3_21 ),
inference(avatar_split_clause,[],[f250,f235,f137,f267]) ).
fof(f301,definition,
( spl3_25
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_25])],[avatar_definition]) ).
fof(f302,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f304,definition,
( spl3_26
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_26])],[avatar_definition]) ).
fof(f305,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f307,plain,
( $false
| ~ spl3_25 ),
inference(resolution,[],[f302,f59]) ).
fof(f308,plain,
~ spl3_25,
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f309,plain,
( $false
| ~ spl3_5 ),
inference(resolution,[],[f138,f65]) ).
fof(f310,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
( $false
| ~ spl3_23 ),
inference(resolution,[],[f268,f37]) ).
fof(f312,plain,
~ spl3_23,
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f313,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_21 ),
inference(resolution,[],[f236,f36]) ).
fof(f325,plain,
( spl3_25
| spl3_26
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f313,f235,f304,f301]) ).
fof(f326,plain,
( $false
| ~ spl3_26 ),
inference(resolution,[],[f305,f66]) ).
fof(f327,plain,
~ spl3_26,
inference(avatar_contradiction_clause,[],[f326]) ).
cnf(s17,plain,
( spl3_5
| spl3_21
| spl3_23 ),
inference(sat_conversion,[],[f269]) ).
cnf(s21,plain,
~ spl3_25,
inference(sat_conversion,[],[f308]) ).
cnf(s22,plain,
~ spl3_5,
inference(sat_conversion,[],[f310]) ).
cnf(s23,plain,
~ spl3_23,
inference(sat_conversion,[],[f312]) ).
cnf(s24,plain,
( ~ spl3_21
| spl3_25
| spl3_26 ),
inference(sat_conversion,[],[f325]) ).
cnf(s25,plain,
~ spl3_26,
inference(sat_conversion,[],[f327]) ).
cnf(s26,plain,
( ~ spl3_21
| spl3_25 ),
inference(rat,[],[s24,s25]) ).
cnf(s27,plain,
~ spl3_21,
inference(rat,[],[s26,s21]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s17,s23,s27,s22]) ).
fof(f328,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 07:36:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.36/1.06 % (2297016)Detected formulas, will run a generic FOF schedule.
% 2.36/1.06 % (2297068)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2945712649:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.36/1.06 % (2297070)dis-21_1_sil=8000:lcm=predicate:random_seed=3828842146:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.36/1.06 % (2297064)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1519517396:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.36/1.06 % (2297069)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1412043244:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.36/1.06 % (2297066)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2735003332:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.36/1.06 % (2297067)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=595915711:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.36/1.06 % (2297065)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=28793765:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.36/1.06 % (2297067)Refutation not found, incomplete strategy
% 2.36/1.06 % (2297067)------------------------------
% 2.36/1.06 % (2297067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.36/1.06 % (2297067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.06 % (2297067)CaDiCaL version: 2.1.3
% 2.36/1.06 % (2297067)Termination reason: Refutation not found, incomplete strategy
% 2.36/1.06 % (2297067)Time elapsed: 0.001 s
% 2.36/1.06 % (2297067)Peak memory usage: 87 MB
% 2.36/1.06 % (2297070)First to succeed.
% 2.36/1.06 % (2297070)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2297016"
% 2.36/1.06 % (2297069)Also succeeded, but the first one will report.
% 2.36/1.06 % (2297068)Also succeeded, but the first one will report.
% 2.36/1.06 % (2297067)------------------------------
% 2.36/1.06 % (2297067)------------------------------
% 2.36/1.06 % (2297070)Refutation found. Thanks to Tanya!
% 2.36/1.06 % SZS status Theorem for theBenchmark
% 2.36/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.16 % (2297070)------------------------------
% 0.16/1.16 % (2297070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.16 % (2297070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.16 % (2297070)CaDiCaL version: 2.1.3
% 0.16/1.16 % (2297070)Termination reason: Refutation
% 0.16/1.16 % (2297070)Time elapsed: 0.007 s
% 0.16/1.16 % (2297070)Peak memory usage: 89 MB
% 0.16/1.16 % (2297070)Instructions burned: 10 (million)
% 0.16/1.16 % (2297070)------------------------------
% 0.16/1.16 % (2297070)------------------------------
% 0.16/1.16 % (2297016)Success in time 0.427 s
% 0.16/1.16 % Vampire exiting
%------------------------------------------------------------------------------