%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 2.54s 1.27s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 16 unt; 4 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 144 ( 57 ~; 62 |; 14 &)
% ( 4 <=>; 7 =>; 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 : 68 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',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/sandbox2/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(f37,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)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,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(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f51,f40]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| ~ distinct_points(X2,X3)
| apart_point_and_line(X2,X1) ),
inference(resolution,[],[f60,f48]) ).
fof(f70,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK2)) ),
inference(resolution,[],[f62,f52]) ).
fof(f76,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2)) ),
inference(resolution,[],[f70,f55]) ).
fof(f80,definition,
( spl3_1
<=> apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f82,plain,
( apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl3_2
<=> apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f86,plain,
( apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl3_3
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f90,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl3_4
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f94,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f76,f92,f88,f84,f80]) ).
fof(f117,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_3 ),
inference(resolution,[],[f90,f44]) ).
fof(f120,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f117,f54]) ).
fof(f121,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f124,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_4 ),
inference(resolution,[],[f94,f44]) ).
fof(f127,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f124,f53]) ).
fof(f128,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f127]) ).
fof(f141,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_2 ),
inference(resolution,[],[f86,f46]) ).
fof(f144,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f141,f52]) ).
fof(f145,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f144]) ).
fof(f149,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(resolution,[],[f82,f47]) ).
fof(f152,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f149,f52]) ).
fof(f153,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f152]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f128]) ).
cnf(s7,plain,
~ spl3_2,
inference(sat_conversion,[],[f145]) ).
cnf(s8,plain,
~ spl3_1,
inference(sat_conversion,[],[f153]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s5,s4,s7,s8]) ).
fof(f154,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:37:26 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/1.27 % (2497906)Detected formulas, will run a generic FOF schedule.
% 2.54/1.27 % (2497911)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=957036537:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.27 % (2497917)dis-21_1_sil=8000:lcm=predicate:random_seed=2464061946: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)
% 2.54/1.27 % (2497913)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=529012075:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.27 % (2497912)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=25583687:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.27 % (2497914)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=86064595:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.27 % (2497916)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1339196090:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.27 % (2497914)Refutation not found, incomplete strategy
% 2.54/1.27 % (2497914)------------------------------
% 2.54/1.27 % (2497914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.27 % (2497914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.27 % (2497914)CaDiCaL version: 2.1.3
% 2.54/1.27 % (2497914)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.27 % (2497914)Time elapsed: 0.001 s
% 2.54/1.27 % (2497914)Peak memory usage: 87 MB
% 2.54/1.27 % (2497916)First to succeed.
% 2.54/1.27 % (2497916)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2497906"
% 2.54/1.27 % (2497915)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2385838385:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.27 % (2497915)Instruction limit reached!
% 2.54/1.27 % (2497915)------------------------------
% 2.54/1.27 % (2497915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.27 % (2497915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.27 % (2497915)CaDiCaL version: 2.1.3
% 2.54/1.27 % (2497915)Termination reason: Instruction limit
% 2.54/1.27 % (2497915)Termination phase: Saturation
% 2.54/1.27 % (2497915)Time elapsed: 0.044 s
% 2.54/1.27 % (2497915)Peak memory usage: 87 MB
% 2.54/1.27 % (2497915)Instructions burned: 120 (million)
% 2.54/1.27 % (2497917)Instruction limit reached!
% 2.54/1.27 % (2497917)------------------------------
% 2.54/1.27 % (2497917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.27 % (2497917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.27 % (2497917)CaDiCaL version: 2.1.3
% 2.54/1.27 % (2497917)Termination reason: Instruction limit
% 2.54/1.27 % (2497917)Termination phase: Saturation
% 2.54/1.27 % (2497917)Time elapsed: 0.074 s
% 2.54/1.27 % (2497917)Peak memory usage: 89 MB
% 2.54/1.27 % (2497917)Instructions burned: 131 (million)
% 2.54/1.27 % (2497925)lrs+10_1_sil=8000:sp=occurrence:random_seed=3020104150:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.54/1.27 % (2497926)lrs+10_1_sil=32000:urr=on:br=off:random_seed=973206091:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.54/1.27 % (2497926)Also succeeded, but the first one will report.
% 2.54/1.27 % (2497914)------------------------------
% 2.54/1.27 % (2497914)------------------------------
% 2.54/1.27 % (2497916)Refutation found. Thanks to Tanya!
% 2.54/1.27 % SZS status Theorem for theBenchmark
% 2.54/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.47 % (2497916)------------------------------
% 3.44/1.47 % (2497916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.47 % (2497916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.47 % (2497916)CaDiCaL version: 2.1.3
% 3.44/1.47 % (2497916)Termination reason: Refutation
% 3.44/1.47 % (2497916)Time elapsed: 0.005 s
% 3.44/1.47 % (2497916)Peak memory usage: 89 MB
% 3.44/1.47 % (2497916)Instructions burned: 5 (million)
% 3.44/1.47 % (2497916)------------------------------
% 3.44/1.47 % (2497916)------------------------------
% 3.44/1.47 % (2497906)Success in time 0.402 s
% 3.44/1.47 % Vampire exiting
%------------------------------------------------------------------------------