%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO202+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 : n013.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 3.96s 1.45s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 57 ~; 59 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 81 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f11,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(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
=> equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
=> equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0)
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ),
inference(flattening,[],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f47,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,[],[f11]) ).
fof(f48,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,[],[f47]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f57,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f62,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
( ~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0)
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
fof(f68,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f67]) ).
fof(f69,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f67]) ).
fof(f70,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f67]) ).
fof(f71,plain,
~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f74,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f76,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,[],[f48]) ).
fof(f80,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f81,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f83,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f87,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f91,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(resolution,[],[f84,f71]) ).
fof(f99,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f87,f83]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X0,line_connecting(X1,X2))
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X3,line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f76,f74]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(intersection_point(line_connecting(X0,X2),X3),X1)
| apart_point_and_line(X0,X1)
| ~ distinct_points(intersection_point(line_connecting(X0,X2),X3),X0)
| ~ distinct_lines(X1,line_connecting(X0,X2))
| ~ distinct_points(X0,X2)
| ~ convergent_lines(line_connecting(X0,X2),X3) ),
inference(resolution,[],[f113,f81]) ).
fof(f604,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ distinct_points(intersection_point(line_connecting(X0,X2),X1),X0)
| ~ distinct_lines(X1,line_connecting(X0,X2))
| ~ distinct_points(X0,X2)
| ~ convergent_lines(line_connecting(X0,X2),X1)
| ~ convergent_lines(line_connecting(X0,X2),X1) ),
inference(resolution,[],[f149,f80]) ).
fof(f619,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ distinct_points(intersection_point(line_connecting(X0,X2),X1),X0)
| ~ distinct_lines(X1,line_connecting(X0,X2))
| ~ distinct_points(X0,X2)
| ~ convergent_lines(line_connecting(X0,X2),X1) ),
inference(duplicate_literal_removal,[],[f604]) ).
fof(f621,plain,
! [X2,X0,X1] :
( ~ distinct_points(intersection_point(line_connecting(X0,X2),X1),X0)
| apart_point_and_line(X0,X1)
| ~ distinct_points(X0,X2)
| ~ convergent_lines(line_connecting(X0,X2),X1) ),
inference(forward_subsumption_resolution,[],[f619,f99]) ).
fof(f1465,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK1)
| ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolution,[],[f621,f91]) ).
fof(f1536,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(forward_subsumption_resolution,[],[f1465,f70]) ).
fof(f1541,plain,
apart_point_and_line(sK0,line_connecting(sK0,sK2)),
inference(forward_subsumption_resolution,[],[f1536,f68]) ).
fof(f1548,plain,
~ distinct_points(sK0,sK2),
inference(resolution,[],[f1541,f74]) ).
fof(f1549,plain,
$false,
inference(forward_subsumption_resolution,[],[f1548,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:34:51 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.96/1.35 % (4086012)Detected formulas, will run a generic FOF schedule.
% 2.96/1.35 % (4086018)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=2001200726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.96/1.35 % (4086021)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=382775863:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.96/1.35 % (4086019)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=770608997:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.96/1.35 % (4086023)dis-21_1_sil=8000:lcm=predicate:random_seed=2484055280: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)
% 2.96/1.35 % (4086020)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1079832687:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.96/1.35 % (4086017)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=551813830:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.96/1.35 % (4086022)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2648902236:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.96/1.35 % (4086021)First to succeed.
% 2.96/1.35 % (4086021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4086012"
% 2.96/1.35 % (4086020)Instruction limit reached!
% 2.96/1.35 % (4086020)------------------------------
% 2.96/1.35 % (4086020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.35 % (4086020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.35 % (4086020)CaDiCaL version: 2.1.3
% 2.96/1.35 % (4086020)Termination reason: Instruction limit
% 2.96/1.35 % (4086020)Termination phase: Saturation
% 2.96/1.35 % (4086020)Time elapsed: 0.054 s
% 2.96/1.35 % (4086020)Peak memory usage: 88 MB
% 2.96/1.35 % (4086020)Instructions burned: 109 (million)
% 2.96/1.35 % (4086023)Instruction limit reached!
% 2.96/1.35 % (4086023)------------------------------
% 2.96/1.35 % (4086023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.35 % (4086023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.35 % (4086023)CaDiCaL version: 2.1.3
% 2.96/1.35 % (4086023)Termination reason: Instruction limit
% 2.96/1.35 % (4086023)Termination phase: Saturation
% 2.96/1.35 % (4086023)Time elapsed: 0.072 s
% 2.96/1.35 % (4086023)Peak memory usage: 89 MB
% 2.96/1.35 % (4086023)Instructions burned: 129 (million)
% 2.96/1.35 % (4086022)Instruction limit reached!
% 2.96/1.35 % (4086022)------------------------------
% 2.96/1.35 % (4086022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.35 % (4086022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.35 % (4086022)CaDiCaL version: 2.1.3
% 2.96/1.35 % (4086022)Termination reason: Instruction limit
% 2.96/1.35 % (4086022)Termination phase: Saturation
% 2.96/1.35 % (4086022)Time elapsed: 0.087 s
% 2.96/1.35 % (4086022)Peak memory usage: 88 MB
% 2.96/1.35 % (4086022)Instructions burned: 140 (million)
% 2.96/1.35 % (4086031)lrs+10_1_sil=8000:sp=occurrence:random_seed=1855180502:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.96/1.35 % (4086032)lrs+10_1_sil=32000:urr=on:br=off:random_seed=712856725:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.96/1.35 % (4086032)Refutation not found, incomplete strategy
% 2.96/1.35 % (4086032)------------------------------
% 2.96/1.35 % (4086032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.35 % (4086032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.35 % (4086032)CaDiCaL version: 2.1.3
% 2.96/1.35 % (4086032)Termination reason: Refutation not found, incomplete strategy
% 2.96/1.35 % (4086032)Time elapsed: 0.002 s
% 2.96/1.35 % (4086032)Peak memory usage: 88 MB
% 2.96/1.35 % (4086032)Instructions burned: 2 (million)
% 2.96/1.35 % (4086033)lrs+1011_1_sil=32000:sp=occurrence:random_seed=410205548:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.96/1.35 % (4086033)Also succeeded, but the first one will report.
% 2.96/1.35 % (4086031)Also succeeded, but the first one will report.
% 2.96/1.35 % (4086021)Refutation found. Thanks to Tanya!
% 3.96/1.45 % SZS status Theorem for theBenchmark
% 3.96/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/1.45 % (4086021)------------------------------
% 3.96/1.45 % (4086021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.45 % (4086021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.45 % (4086021)CaDiCaL version: 2.1.3
% 3.96/1.45 % (4086021)Termination reason: Refutation
% 3.96/1.45 % (4086021)Time elapsed: 0.048 s
% 3.96/1.45 % (4086021)Peak memory usage: 88 MB
% 3.96/1.45 % (4086021)Instructions burned: 87 (million)
% 3.96/1.45 % (4086021)------------------------------
% 3.96/1.45 % (4086021)------------------------------
% 3.96/1.45 % (4086012)Success in time 0.486 s
% 3.96/1.45 % Vampire exiting
%------------------------------------------------------------------------------