%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO205+2 : 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 : n006.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 09:51:59 AM UTC 2026
% Result : Theorem 2.78s 1.25s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 78 ~; 89 |; 13 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 106 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
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',apart6) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
fof(f9,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(f11,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(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f30,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,[],[f9]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
( ( ~ convergent_lines(sK0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) )
& convergent_lines(sK0,sK1)
& ~ distinct_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f33,plain,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f34,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f35,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
~ convergent_lines(sK1,sK2),
inference(resolution,[],[f42,f33]) ).
fof(f51,plain,
! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK1) ),
inference(resolution,[],[f40,f33]) ).
fof(f54,plain,
~ distinct_lines(sK2,sK1),
inference(resolution,[],[f51,f41]) ).
fof(f56,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f43,f48]) ).
fof(f58,plain,
~ convergent_lines(sK2,sK1),
inference(resolution,[],[f54,f42]) ).
fof(f59,plain,
! [X0] :
( convergent_lines(X0,sK1)
| ~ convergent_lines(X0,sK2) ),
inference(resolution,[],[f58,f43]) ).
fof(f64,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f38,f37]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X2)
| distinct_lines(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f64,f45]) ).
fof(f69,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f39,f37]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(intersection_point(X2,X1),X3)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X3)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X3,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f47,f64]) ).
fof(f81,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X2,X1)
| ~ convergent_lines(X2,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f72,f69]) ).
fof(f86,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ distinct_lines(X2,X1)
| ~ convergent_lines(X2,X1) ),
inference(duplicate_literal_removal,[],[f81]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,intersection_point(X2,X1))
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ convergent_lines(X2,X1) ),
inference(forward_subsumption_resolution,[],[f86,f42]) ).
fof(f113,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ convergent_lines(sK0,sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(resolution,[],[f88,f35]) ).
fof(f123,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(duplicate_literal_removal,[],[f113]) ).
fof(f127,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ convergent_lines(sK0,sK2)
| distinct_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f123,f68]) ).
fof(f128,plain,
( ~ convergent_lines(sK0,sK2)
| distinct_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f127,f69]) ).
fof(f132,plain,
( ~ convergent_lines(sK0,sK2)
| distinct_lines(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f128,f59]) ).
fof(f136,plain,
~ convergent_lines(sK0,sK2),
inference(forward_subsumption_resolution,[],[f132,f54]) ).
fof(f137,plain,
~ convergent_lines(sK0,sK1),
inference(resolution,[],[f136,f56]) ).
fof(f139,plain,
$false,
inference(forward_subsumption_resolution,[],[f137,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.36 % Computer : n006.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Sun Sep 27 07:35:56 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.40 Running first-order theorem proving
% 0.07/0.40 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
% 2.78/1.25 % (2658406)Detected formulas, will run a generic FOF schedule.
% 2.78/1.25 % (2658411)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=3013212280:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.25 % (2658417)dis-21_1_sil=8000:lcm=predicate:random_seed=1886643176: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)
% 2.78/1.25 % (2658416)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2747501274:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.25 % (2658415)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3016498497:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.25 % (2658414)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1375914275:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.25 % (2658412)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=1469712340:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.25 % (2658413)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=2471737801:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.25 % (2658415)First to succeed.
% 2.78/1.25 % (2658415)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2658406"
% 2.78/1.25 % (2658417)Also succeeded, but the first one will report.
% 2.78/1.25 % (2658416)Also succeeded, but the first one will report.
% 2.78/1.25 % (2658414)Instruction limit reached!
% 2.78/1.25 % (2658414)------------------------------
% 2.78/1.25 % (2658414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.25 % (2658414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.25 % (2658414)CaDiCaL version: 2.1.3
% 2.78/1.25 % (2658414)Termination reason: Instruction limit
% 2.78/1.25 % (2658414)Termination phase: Saturation
% 2.78/1.25 % (2658414)Time elapsed: 0.061 s
% 2.78/1.25 % (2658414)Peak memory usage: 88 MB
% 2.78/1.25 % (2658414)Instructions burned: 111 (million)
% 2.78/1.25 % (2658425)lrs+10_1_sil=8000:sp=occurrence:random_seed=58438786:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.78/1.25 % (2658425)Also succeeded, but the first one will report.
% 2.78/1.25 % (2658415)Refutation found. Thanks to Tanya!
% 2.78/1.25 % SZS status Theorem for theBenchmark
% 2.78/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.45 % (2658415)------------------------------
% 3.44/1.45 % (2658415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (2658415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (2658415)CaDiCaL version: 2.1.3
% 3.44/1.45 % (2658415)Termination reason: Refutation
% 3.44/1.45 % (2658415)Time elapsed: 0.004 s
% 3.44/1.45 % (2658415)Peak memory usage: 88 MB
% 3.44/1.45 % (2658415)Instructions burned: 4 (million)
% 3.44/1.45 % (2658415)------------------------------
% 3.44/1.45 % (2658415)------------------------------
% 3.44/1.45 % (2658406)Success in time 0.411 s
% 3.44/1.45 % Vampire exiting
%------------------------------------------------------------------------------