%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO195+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 : 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 2.67s 1.29s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 12 unt; 3 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 69 ~; 93 |; 17 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 90 !; 6 ?)
% 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(f12,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(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,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(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,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(X1,X0),X2) ) ),
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(f29,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
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] :
( ~ apart_point_and_line(intersection_point(X1,X0),X2)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X1,X0),X2)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK0),sK2)
& 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)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
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(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(intersection_point(sK1,sK0),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f43,f40]) ).
fof(f58,plain,
! [X0] :
( distinct_points(intersection_point(sK0,sK1),X0)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f49,f55]) ).
fof(f62,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f51,f40]) ).
fof(f68,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,[],[f62,f48]) ).
fof(f83,plain,
! [X2,X0,X1] :
( apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X0)
| ~ convergent_lines(X0,X2)
| apart_point_and_line(intersection_point(sK0,sK1),X2)
| apart_point_and_line(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f68,f58]) ).
fof(f97,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0,sK1),X1)
| apart_point_and_line(intersection_point(sK1,sK0),X1)
| ~ convergent_lines(X1,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK1,sK0),X0) ),
inference(resolution,[],[f83,f56]) ).
fof(f132,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ convergent_lines(sK0,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK1,sK0),X0)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f97,f46]) ).
fof(f139,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ convergent_lines(sK0,X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK1,sK0),X0) ),
inference(forward_subsumption_resolution,[],[f132,f54]) ).
fof(f144,definition,
( spl3_2
<=> apart_point_and_line(intersection_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f145,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK0),sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f146,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f149,definition,
( spl3_3
<=> ! [X0] :
( ~ convergent_lines(sK0,X0)
| apart_point_and_line(intersection_point(sK1,sK0),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0] :
( ~ convergent_lines(sK0,X0)
| apart_point_and_line(intersection_point(sK1,sK0),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK1,sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f154,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f139,f152,f149]) ).
fof(f156,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl3_2 ),
inference(resolution,[],[f146,f46]) ).
fof(f162,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f156,f57]) ).
fof(f165,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f162,f54]) ).
fof(f166,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f186,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_3 ),
inference(resolution,[],[f150,f54]) ).
fof(f190,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f186,f145]) ).
fof(f196,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_2
| ~ spl3_3 ),
inference(resolution,[],[f190,f47]) ).
fof(f199,plain,
( $false
| spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f196,f54]) ).
fof(f200,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f206,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl3_4 ),
inference(resolution,[],[f154,f47]) ).
fof(f214,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f206,f57]) ).
fof(f217,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f214,f54]) ).
fof(f218,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f217]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f155]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f166]) ).
cnf(s4,plain,
( spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f218]) ).
cnf(s6,plain,
~ spl3_3,
inference(rat,[],[s4,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s5,s6]) ).
fof(f219,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO195+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:37:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 2.67/1.29 % (2297899)Detected formulas, will run a generic FOF schedule.
% 2.67/1.29 % (2297956)dis-21_1_sil=8000:lcm=predicate:random_seed=241572009: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)
% 2.67/1.29 % (2297951)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=1767821490:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.29 % (2297950)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=1711075459:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.29 % (2297952)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=1878740163:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.29 % (2297954)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3968615789:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.29 % (2297955)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=945401060:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.29 % (2297954)Refutation not found, incomplete strategy
% 2.67/1.29 % (2297954)------------------------------
% 2.67/1.29 % (2297954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2297954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2297954)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2297954)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.29 % (2297954)Time elapsed: 0.001 s
% 2.67/1.29 % (2297954)Peak memory usage: 87 MB
% 2.67/1.29 % (2297956)Instruction limit reached!
% 2.67/1.29 % (2297956)------------------------------
% 2.67/1.29 % (2297956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2297956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2297956)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2297956)Termination reason: Instruction limit
% 2.67/1.29 % (2297956)Termination phase: Saturation
% 2.67/1.29 % (2297956)Time elapsed: 0.038 s
% 2.67/1.29 % (2297956)Peak memory usage: 89 MB
% 2.67/1.29 % (2297956)Instructions burned: 132 (million)
% 2.67/1.29 % (2297955)First to succeed.
% 2.67/1.29 % (2297955)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2297899"
% 2.67/1.29 % (2297953)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2136715511:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.29 % (2297953)Refutation not found, incomplete strategy
% 2.67/1.29 % (2297953)------------------------------
% 2.67/1.29 % (2297953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.29 % (2297953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.29 % (2297953)CaDiCaL version: 2.1.3
% 2.67/1.29 % (2297953)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.29 % (2297953)Time elapsed: 0.002 s
% 2.67/1.29 % (2297953)Peak memory usage: 87 MB
% 2.67/1.29 % (2297963)lrs+10_1_sil=8000:sp=occurrence:random_seed=4209227589:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.67/1.29 % (2297963)Also succeeded, but the first one will report.
% 2.67/1.29 % (2297954)------------------------------
% 2.67/1.29 % (2297954)------------------------------
% 2.67/1.29 % (2297955)Refutation found. Thanks to Tanya!
% 2.67/1.29 % SZS status Theorem for theBenchmark
% 2.67/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.49 % (2297955)------------------------------
% 3.56/1.49 % (2297955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.49 % (2297955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.49 % (2297955)CaDiCaL version: 2.1.3
% 3.56/1.49 % (2297955)Termination reason: Refutation
% 3.56/1.49 % (2297955)Time elapsed: 0.010 s
% 3.56/1.49 % (2297955)Peak memory usage: 89 MB
% 3.56/1.49 % (2297955)Instructions burned: 14 (million)
% 3.56/1.49 % (2297955)------------------------------
% 3.56/1.49 % (2297955)------------------------------
% 3.56/1.49 % (2297899)Success in time 0.429 s
% 3.56/1.49 % Vampire exiting
%------------------------------------------------------------------------------