%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:51:51 AM UTC 2026
% Result : Theorem 2.57s 1.24s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 43 ~; 26 |; 15 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) )
=> ( incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) )
=> ( incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ) ),
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(f39,plain,
! [X0,X1] :
( equal_points(X0,X1)
=> ~ distinct_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X0,X2)
| ~ incident_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f42,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X0,X2)
| ~ incident_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) ),
inference(flattening,[],[f41]) ).
fof(f43,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(f44,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f50,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f54,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f64,plain,
( ( ~ incident_point_and_line(sK0,sK2)
| ~ incident_point_and_line(sK0,sK3) )
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& equal_points(sK0,intersection_point(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f42]) ).
fof(f65,plain,
equal_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f64]) ).
fof(f66,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
( ~ incident_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f69,plain,
! [X2,X0,X1] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f74,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f78,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f85,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(resolution,[],[f77,f65]) ).
fof(f86,plain,
( apart_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(resolution,[],[f78,f68]) ).
fof(f88,plain,
! [X2,X0,X1] :
( distinct_points(X0,intersection_point(X1,X2))
| ~ apart_point_and_line(X0,X2)
| ~ convergent_lines(X1,X2) ),
inference(resolution,[],[f69,f73]) ).
fof(f89,plain,
! [X2,X0,X1] :
( distinct_points(X0,intersection_point(X1,X2))
| ~ apart_point_and_line(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(resolution,[],[f69,f74]) ).
fof(f132,plain,
( ~ apart_point_and_line(sK0,sK3)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f88,f85]) ).
fof(f134,plain,
~ apart_point_and_line(sK0,sK3),
inference(forward_subsumption_resolution,[],[f132,f66]) ).
fof(f137,plain,
~ incident_point_and_line(sK0,sK2),
inference(resolution,[],[f134,f86]) ).
fof(f141,plain,
apart_point_and_line(sK0,sK2),
inference(resolution,[],[f137,f78]) ).
fof(f145,plain,
( ~ apart_point_and_line(sK0,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(resolution,[],[f89,f85]) ).
fof(f147,plain,
~ apart_point_and_line(sK0,sK2),
inference(forward_subsumption_resolution,[],[f145,f66]) ).
fof(f156,plain,
$false,
inference(forward_subsumption_resolution,[],[f141,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 07:28:07 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 2.57/1.24 % (3169459)Detected formulas, will run a generic FOF schedule.
% 2.57/1.24 % (3169468)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=976489728:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.24 % (3169468)First to succeed.
% 2.57/1.24 % (3169468)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3169459"
% 2.57/1.24 % (3169464)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=1040772078:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.24 % (3169467)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2543721118:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.24 % (3169469)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=103478705:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.24 % (3169470)dis-21_1_sil=8000:lcm=predicate:random_seed=3647754640: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)
% 2.57/1.24 % (3169466)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=3925913757:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.24 % (3169465)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=3188813440:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.24 % (3169470)Also succeeded, but the first one will report.
% 2.57/1.24 % (3169467)Also succeeded, but the first one will report.
% 2.57/1.24 % (3169469)Also succeeded, but the first one will report.
% 2.57/1.24 % (3169468)Refutation found. Thanks to Tanya!
% 2.57/1.24 % SZS status Theorem for theBenchmark
% 2.57/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.24 % (3169468)------------------------------
% 2.57/1.24 % (3169468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.24 % (3169468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.24 % (3169468)CaDiCaL version: 2.1.3
% 2.57/1.24 % (3169468)Termination reason: Refutation
% 2.57/1.24 % (3169468)Time elapsed: 0.002 s
% 2.57/1.24 % (3169468)Peak memory usage: 88 MB
% 2.57/1.24 % (3169468)Instructions burned: 3 (million)
% 2.57/1.24 % (3169468)------------------------------
% 2.57/1.24 % (3169468)------------------------------
% 2.57/1.24 % (3169459)Success in time 0.3 s
% 2.57/1.24 % Vampire exiting
%------------------------------------------------------------------------------