%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO201+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 : 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 09:51:58 AM UTC 2026
% Result : Theorem 2.56s 1.33s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 52 ~; 61 |; 5 &)
% ( 0 <=>; 7 =>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 75 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
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',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(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] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1] :
( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,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(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(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
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(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,[],[f9]) ).
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(f31,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f32,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f33,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f31]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,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,[],[f28]) ).
fof(f50,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f36,f35]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f37,f35]) ).
fof(f58,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,[],[f43,f50]) ).
fof(f65,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,[],[f58,f53]) ).
fof(f70,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,[],[f65]) ).
fof(f72,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,[],[f70,f38]) ).
fof(f97,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ convergent_lines(sK1,sK0) ),
inference(resolution,[],[f72,f33]) ).
fof(f107,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ convergent_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f97,f50]) ).
fof(f115,plain,
( ~ convergent_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f107,f53]) ).
fof(f119,plain,
~ convergent_lines(sK1,sK0),
inference(forward_subsumption_resolution,[],[f115,f32]) ).
fof(f121,plain,
! [X0] :
( convergent_lines(X0,sK0)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f119,f39]) ).
fof(f132,plain,
~ convergent_lines(sK0,sK1),
inference(resolution,[],[f121,f40]) ).
fof(f134,plain,
$false,
inference(forward_subsumption_resolution,[],[f132,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:34:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.56/1.33 % (3177179)Detected formulas, will run a generic FOF schedule.
% 2.56/1.33 % (3177188)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1133835655:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.33 % (3177188)First to succeed.
% 2.56/1.33 % (3177188)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3177179"
% 2.56/1.33 % (3177189)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3433155923:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.33 % (3177190)dis-21_1_sil=8000:lcm=predicate:random_seed=3890547100: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)
% 2.56/1.33 % (3177187)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3842551580:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.33 % (3177185)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=36863247:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.33 % (3177184)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=1913519698:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.33 % (3177186)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=2058480711:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.33 % (3177187)Refutation not found, incomplete strategy
% 2.56/1.33 % (3177187)------------------------------
% 2.56/1.33 % (3177187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (3177187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (3177187)CaDiCaL version: 2.1.3
% 2.56/1.33 % (3177187)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.33 % (3177187)Time elapsed: 0.001 s
% 2.56/1.33 % (3177187)Peak memory usage: 87 MB
% 2.56/1.33 % (3177189)Also succeeded, but the first one will report.
% 2.56/1.33 % (3177190)Also succeeded, but the first one will report.
% 2.56/1.33 % (3177188)Refutation found. Thanks to Tanya!
% 2.56/1.33 % SZS status Theorem for theBenchmark
% 2.56/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.33 % (3177188)------------------------------
% 2.56/1.33 % (3177188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (3177188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (3177188)CaDiCaL version: 2.1.3
% 2.56/1.33 % (3177188)Termination reason: Refutation
% 2.56/1.33 % (3177188)Time elapsed: 0.002 s
% 2.56/1.33 % (3177188)Peak memory usage: 88 MB
% 2.56/1.33 % (3177188)Instructions burned: 4 (million)
% 2.56/1.33 % (3177188)------------------------------
% 2.56/1.33 % (3177188)------------------------------
% 2.56/1.33 % (3177179)Success in time 0.29 s
% 2.56/1.33 % Vampire exiting
%------------------------------------------------------------------------------