%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:52:07 AM UTC 2026
% Result : Theorem 3.59s 1.49s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 103 ( 49 ~; 34 |; 13 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(f19,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f28,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int1) ).
fof(f30,axiom,
! [X0,X1] :
( ( line(X0)
& point(X1) )
=> line(orthogonal_through_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',orth1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1] :
( ( point(X0)
& line(X1) )
=> ? [X2] :
( point(X2)
& incident_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( point(X0)
& line(X1) )
=> ? [X2] :
( point(X2)
& incident_point_and_line(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f71,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( ! [X2] :
( ~ point(X2)
| ~ incident_point_and_line(X2,X1) )
& point(X0)
& line(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1] :
( ! [X2] :
( ~ point(X2)
| ~ incident_point_and_line(X2,X1) )
& point(X0)
& line(X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( ! [X2] :
( ~ point(X2)
| ~ incident_point_and_line(X2,sK1) )
& point(sK0)
& line(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f79]) ).
fof(f90,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f99,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f104,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f114,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f117,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
line(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
point(sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2] :
( ~ incident_point_and_line(X2,sK1)
| ~ point(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f99,f104]) ).
fof(f125,plain,
! [X0,X1] :
( incident_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f90,f117]) ).
fof(f129,plain,
! [X0] :
( ~ point(intersection_point(X0,sK1))
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f125,f120]) ).
fof(f131,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| ~ line(X0)
| ~ line(sK1)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f129,f114]) ).
fof(f132,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| ~ line(X0)
| ~ line(sK1) ),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ~ convergent_lines(X0,sK1)
| ~ line(X0) ),
inference(forward_subsumption_resolution,[],[f132,f118]) ).
fof(f135,plain,
! [X0] : ~ line(orthogonal_through_point(sK1,X0)),
inference(resolution,[],[f133,f123]) ).
fof(f137,plain,
! [X0] :
( ~ line(sK1)
| ~ point(X0) ),
inference(resolution,[],[f135,f116]) ).
fof(f138,plain,
! [X0] : ~ point(X0),
inference(forward_subsumption_resolution,[],[f137,f118]) ).
fof(f139,plain,
$false,
inference(resolution,[],[f138,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:44:19 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.59/1.49 % (2772939)Detected formulas, will run a generic FOF schedule.
% 3.59/1.49 % (2772948)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=741255752:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.49 % (2772948)Refutation not found, incomplete strategy
% 3.59/1.49 % (2772948)------------------------------
% 3.59/1.49 % (2772948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.49 % (2772948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.49 % (2772948)CaDiCaL version: 2.1.3
% 3.59/1.49 % (2772948)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.49 % (2772948)Time elapsed: 0.0000 s
% 3.59/1.49 % (2772948)Peak memory usage: 86 MB
% 3.59/1.49 % (2772950)dis-21_1_sil=8000:lcm=predicate:random_seed=99783457: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)
% 3.59/1.49 % (2772946)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=1281579143:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.49 % (2772945)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=50902408:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.49 % (2772949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4112305218:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.49 % (2772944)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=2772991384:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.49 % (2772947)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=139329903:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.49 % (2772947)Refutation not found, incomplete strategy
% 3.59/1.49 % (2772947)------------------------------
% 3.59/1.49 % (2772947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.49 % (2772947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.49 % (2772947)CaDiCaL version: 2.1.3
% 3.59/1.49 % (2772947)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.49 % (2772947)Time elapsed: 0.001 s
% 3.59/1.49 % (2772947)Peak memory usage: 86 MB
% 3.59/1.49 % (2772949)First to succeed.
% 3.59/1.49 % (2772950)Also succeeded, but the first one will report.
% 3.59/1.49 % (2772949)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2772939"
% 3.59/1.49 % (2772948)------------------------------
% 3.59/1.49 % (2772948)------------------------------
% 3.59/1.49 % (2772947)------------------------------
% 3.59/1.49 % (2772947)------------------------------
% 3.59/1.49 % (2772949)Refutation found. Thanks to Tanya!
% 3.59/1.49 % SZS status Theorem for theBenchmark
% 3.59/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.49 % (2772949)------------------------------
% 3.59/1.49 % (2772949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.49 % (2772949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.49 % (2772949)CaDiCaL version: 2.1.3
% 3.59/1.49 % (2772949)Termination reason: Refutation
% 3.59/1.49 % (2772949)Time elapsed: 0.003 s
% 3.59/1.49 % (2772949)Peak memory usage: 88 MB
% 3.59/1.49 % (2772949)Instructions burned: 3 (million)
% 3.59/1.49 % (2772949)------------------------------
% 3.59/1.49 % (2772949)------------------------------
% 3.59/1.49 % (2772939)Success in time 0.429 s
% 3.59/1.49 % Vampire exiting
%------------------------------------------------------------------------------