%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO198+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 : n018.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 09:51:57 AM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 24 ~; 22 |; 19 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 59 !; 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(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
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,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& incident_point_and_line(intersection_point(X0,X1),X2) )
=> incident_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& incident_point_and_line(intersection_point(X0,X1),X2) )
=> incident_point_and_line(intersection_point(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f42,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2] :
( ~ incident_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& incident_point_and_line(intersection_point(X0,X1),X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2] :
( ~ incident_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& incident_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) )
& ( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f79,plain,
( ~ incident_point_and_line(intersection_point(sK0,sK2),sK1)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2)
& incident_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f77]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f85,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
~ incident_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f124,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(resolution,[],[f117,f122]) ).
fof(f126,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f85,f82]) ).
fof(f129,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f126,f95]) ).
fof(f167,plain,
! [X0] :
( distinct_lines(sK1,X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0) ),
inference(resolution,[],[f92,f124]) ).
fof(f169,plain,
! [X0] :
( convergent_lines(sK1,X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0) ),
inference(resolution,[],[f167,f94]) ).
fof(f171,plain,
! [X0] : apart_point_and_line(intersection_point(sK0,sK2),parallel_through_point(sK1,X0)),
inference(resolution,[],[f169,f129]) ).
fof(f178,plain,
$false,
inference(resolution,[],[f171,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 07:35:53 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.43 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
% 0.17/1.50 % (1992772)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (1992781)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=620603501:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (1992781)Refutation not found, incomplete strategy
% 0.17/1.50 % (1992781)------------------------------
% 0.17/1.50 % (1992781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1992781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1992781)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1992781)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (1992781)Time elapsed: 0.001 s
% 0.17/1.50 % (1992781)Peak memory usage: 88 MB
% 0.17/1.50 % (1992777)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=828487671:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (1992779)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=3264341999:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (1992778)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=670901606:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (1992782)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4051241732:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (1992780)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3672704361:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (1992783)dis-21_1_sil=8000:lcm=predicate:random_seed=4165067149: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)
% 0.17/1.50 % (1992782)First to succeed.
% 0.17/1.50 % (1992782)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1992772"
% 0.17/1.50 % (1992780)Instruction limit reached!
% 0.17/1.50 % (1992780)------------------------------
% 0.17/1.50 % (1992780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1992780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1992780)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1992780)Termination reason: Instruction limit
% 0.17/1.50 % (1992780)Termination phase: Saturation
% 0.17/1.50 % (1992780)Time elapsed: 0.055 s
% 0.17/1.50 % (1992780)Peak memory usage: 88 MB
% 0.17/1.50 % (1992780)Instructions burned: 111 (million)
% 0.17/1.50 % (1992783)Instruction limit reached!
% 0.17/1.50 % (1992783)------------------------------
% 0.17/1.50 % (1992783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1992783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1992783)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1992783)Termination reason: Instruction limit
% 0.17/1.50 % (1992783)Termination phase: Saturation
% 0.17/1.50 % (1992783)Time elapsed: 0.077 s
% 0.17/1.50 % (1992783)Peak memory usage: 88 MB
% 0.17/1.50 % (1992783)Instructions burned: 129 (million)
% 0.17/1.50 % (1992781)------------------------------
% 0.17/1.50 % (1992781)------------------------------
% 0.17/1.50 % (1992791)lrs+10_1_sil=8000:sp=occurrence:random_seed=3152062142:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.50 % (1992793)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2520002290:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 0.17/1.50 % (1992792)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1892083880:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.17/1.50 % (1992792)Refutation not found, incomplete strategy
% 0.17/1.50 % (1992792)------------------------------
% 0.17/1.50 % (1992792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1992792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1992792)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1992792)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (1992792)Time elapsed: 0.002 s
% 0.17/1.50 % (1992792)Peak memory usage: 88 MB
% 0.17/1.50 % (1992792)Instructions burned: 2 (million)
% 0.17/1.50 % (1992782)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (1992782)------------------------------
% 0.17/1.50 % (1992782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1992782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1992782)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1992782)Termination reason: Refutation
% 0.17/1.50 % (1992782)Time elapsed: 0.004 s
% 0.17/1.50 % (1992782)Peak memory usage: 88 MB
% 0.17/1.50 % (1992782)Instructions burned: 5 (million)
% 0.17/1.50 % (1992782)------------------------------
% 0.17/1.50 % (1992782)------------------------------
% 0.17/1.50 % (1992772)Success in time 0.434 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------