%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO201+1 : 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 : n003.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 09:51:58 AM UTC 2026
% Result : Theorem 3.74s 1.45s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 14 unt; 4 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 144 ( 60 ~; 70 |; 3 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 68 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f15,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
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] :
( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f35]) ).
fof(f39,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,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] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f42,f39]) ).
fof(f57,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f50,f39]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X2,X3)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X1) ),
inference(resolution,[],[f57,f47]) ).
fof(f67,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK1,sK0),X1)
| apart_point_and_line(intersection_point(sK1,sK0),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X1) ),
inference(resolution,[],[f59,f52]) ).
fof(f70,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK1,sK0),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(resolution,[],[f67,f51]) ).
fof(f75,definition,
( spl2_1
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f77,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl2_2
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f81,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl2_3
<=> apart_point_and_line(intersection_point(sK1,sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f85,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl2_4
<=> apart_point_and_line(intersection_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f89,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,plain,
( spl2_1
| spl2_2
| spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f70,f87,f83,f79,f75]) ).
fof(f94,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_2 ),
inference(resolution,[],[f81,f45]) ).
fof(f97,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f94,f51]) ).
fof(f98,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f101,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_3 ),
inference(resolution,[],[f85,f46]) ).
fof(f105,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_3 ),
inference(resolution,[],[f101,f55]) ).
fof(f107,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f105,f51]) ).
fof(f108,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f109,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_4 ),
inference(resolution,[],[f89,f45]) ).
fof(f116,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_4 ),
inference(resolution,[],[f109,f55]) ).
fof(f118,plain,
( $false
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f116,f51]) ).
fof(f119,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f120,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f77,f46]) ).
fof(f123,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f120,f51]) ).
fof(f124,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f123]) ).
cnf(s1,plain,
( spl2_1
| spl2_2
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f98]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f108]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f119]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s3,s2,s5]) ).
fof(f125,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 07:36:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.74/1.45 % (169265)Detected formulas, will run a generic FOF schedule.
% 3.74/1.45 % (169334)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=1922405203:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.74/1.45 % (169333)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=2425458124:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.74/1.45 % (169336)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=2969998530:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.74/1.45 % (169340)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=22411740:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.74/1.45 % (169340)First to succeed.
% 3.74/1.45 % (169340)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-169265"
% 3.74/1.45 % (169342)dis-21_1_sil=8000:lcm=predicate:random_seed=3150551523: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)
% 3.74/1.45 % (169337)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=531564804:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.74/1.45 % (169337)Refutation not found, incomplete strategy
% 3.74/1.45 % (169337)------------------------------
% 3.74/1.45 % (169337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.45 % (169337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.45 % (169337)CaDiCaL version: 2.1.3
% 3.74/1.45 % (169337)Termination reason: Refutation not found, incomplete strategy
% 3.74/1.45 % (169337)Time elapsed: 0.001 s
% 3.74/1.45 % (169337)Peak memory usage: 87 MB
% 3.74/1.45 % (169338)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=683570102:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.74/1.45 % (169338)Refutation not found, incomplete strategy
% 3.74/1.45 % (169338)------------------------------
% 3.74/1.45 % (169338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.45 % (169338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.45 % (169338)CaDiCaL version: 2.1.3
% 3.74/1.45 % (169338)Termination reason: Refutation not found, incomplete strategy
% 3.74/1.45 % (169338)Time elapsed: 0.001 s
% 3.74/1.45 % (169338)Peak memory usage: 88 MB
% 3.74/1.45 % (169342)Instruction limit reached!
% 3.74/1.45 % (169342)------------------------------
% 3.74/1.45 % (169342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.45 % (169342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.45 % (169342)CaDiCaL version: 2.1.3
% 3.74/1.45 % (169342)Termination reason: Instruction limit
% 3.74/1.45 % (169342)Termination phase: Saturation
% 3.74/1.45 % (169342)Time elapsed: 0.073 s
% 3.74/1.45 % (169342)Peak memory usage: 89 MB
% 3.74/1.45 % (169342)Instructions burned: 129 (million)
% 3.74/1.45 % (169359)lrs+10_1_sil=8000:sp=occurrence:random_seed=2202111375:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.74/1.45 % (169337)------------------------------
% 3.74/1.45 % (169337)------------------------------
% 3.74/1.45 % (169359)Also succeeded, but the first one will report.
% 3.74/1.45 % (169338)------------------------------
% 3.74/1.45 % (169338)------------------------------
% 3.74/1.45 % (169334)Also succeeded, but the first one will report.
% 3.74/1.45 % (169340)Refutation found. Thanks to Tanya!
% 3.74/1.45 % SZS status Theorem for theBenchmark
% 3.74/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 4.73/1.64 % (169340)------------------------------
% 4.73/1.64 % (169340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.73/1.64 % (169340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.73/1.64 % (169340)CaDiCaL version: 2.1.3
% 4.73/1.64 % (169340)Termination reason: Refutation
% 4.73/1.64 % (169340)Time elapsed: 0.005 s
% 4.73/1.64 % (169340)Peak memory usage: 89 MB
% 4.73/1.64 % (169340)Instructions burned: 5 (million)
% 4.73/1.64 % (169340)------------------------------
% 4.73/1.64 % (169340)------------------------------
% 4.73/1.64 % (169265)Success in time 0.587 s
% 4.73/1.64 % Vampire exiting
%------------------------------------------------------------------------------