%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO184+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 09:51:51 AM UTC 2026
% Result : Theorem 2.82s 1.38s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 19 unt; 4 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 50 ~; 47 |; 19 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
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(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
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,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X1,X2) )
=> equal_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X1,X2) )
=> equal_lines(X2,line_connecting(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f40,plain,
? [X0,X1,X2,X3] :
( ~ equal_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ equal_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& incident_point_and_line(X0,X2)
& incident_point_and_line(X1,X2) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
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(ennf_transformation,[],[f11]) ).
fof(f49,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,[],[f48]) ).
fof(f66,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f67,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
( ~ equal_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& incident_point_and_line(sK0,sK2)
& incident_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f41]) ).
fof(f83,plain,
incident_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f84,plain,
incident_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f86,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f87,plain,
~ equal_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f82]) ).
fof(f89,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f111,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f112,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f127,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(resolution,[],[f111,f87]) ).
fof(f128,plain,
~ apart_point_and_line(sK1,sK2),
inference(resolution,[],[f112,f83]) ).
fof(f129,plain,
~ apart_point_and_line(sK0,sK2),
inference(resolution,[],[f112,f84]) ).
fof(f130,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolution,[],[f89,f86]) ).
fof(f131,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolution,[],[f90,f86]) ).
fof(f278,plain,
! [X0,X1] :
( ~ distinct_lines(X1,X0)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f92,f86]) ).
fof(f386,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(resolution,[],[f278,f127]) ).
fof(f400,definition,
( spl4_12
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f401,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f403,definition,
( spl4_13
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
fof(f404,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f406,definition,
( spl4_14
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f407,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f409,definition,
( spl4_15
<=> apart_point_and_line(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
fof(f410,plain,
( apart_point_and_line(sK1,sK2)
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( spl4_12
| spl4_13
| spl4_14
| spl4_15 ),
inference(avatar_split_clause,[],[f386,f409,f406,f403,f400]) ).
fof(f412,plain,
( $false
| ~ spl4_15 ),
inference(resolution,[],[f410,f128]) ).
fof(f413,plain,
~ spl4_15,
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f414,plain,
( $false
| ~ spl4_13 ),
inference(resolution,[],[f404,f129]) ).
fof(f415,plain,
~ spl4_13,
inference(avatar_contradiction_clause,[],[f414]) ).
fof(f416,plain,
( $false
| ~ spl4_12 ),
inference(resolution,[],[f401,f131]) ).
fof(f422,plain,
~ spl4_12,
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f423,plain,
( $false
| ~ spl4_14 ),
inference(resolution,[],[f407,f130]) ).
fof(f426,plain,
~ spl4_14,
inference(avatar_contradiction_clause,[],[f423]) ).
cnf(s10,plain,
( spl4_12
| spl4_13
| spl4_14
| spl4_15 ),
inference(sat_conversion,[],[f411]) ).
cnf(s11,plain,
~ spl4_15,
inference(sat_conversion,[],[f413]) ).
cnf(s12,plain,
~ spl4_13,
inference(sat_conversion,[],[f415]) ).
cnf(s13,plain,
~ spl4_12,
inference(sat_conversion,[],[f422]) ).
cnf(s14,plain,
~ spl4_14,
inference(sat_conversion,[],[f426]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s10,s11,s14,s12,s13]) ).
fof(f427,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO184+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:27:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.82/1.38 % (4082158)Detected formulas, will run a generic FOF schedule.
% 2.82/1.38 % (4082169)dis-21_1_sil=8000:lcm=predicate:random_seed=2603961734: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)
% 2.82/1.38 % (4082169)First to succeed.
% 2.82/1.38 % (4082169)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4082158"
% 2.82/1.38 % (4082165)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=1230224304:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.38 % (4082166)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3503897606:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.38 % (4082167)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2492031703:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.38 % (4082164)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=4197968309:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.38 % (4082163)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=860228162:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.38 % (4082168)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=599134035:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.38 % (4082166)Also succeeded, but the first one will report.
% 2.82/1.38 % (4082167)Also succeeded, but the first one will report.
% 2.82/1.38 % (4082168)Also succeeded, but the first one will report.
% 2.82/1.38 % (4082169)Refutation found. Thanks to Tanya!
% 2.82/1.38 % SZS status Theorem for theBenchmark
% 2.82/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.38 % (4082169)------------------------------
% 2.82/1.38 % (4082169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.38 % (4082169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.38 % (4082169)CaDiCaL version: 2.1.3
% 2.82/1.38 % (4082169)Termination reason: Refutation
% 2.82/1.38 % (4082169)Time elapsed: 0.005 s
% 2.82/1.38 % (4082169)Peak memory usage: 89 MB
% 2.82/1.38 % (4082169)Instructions burned: 11 (million)
% 2.82/1.38 % (4082169)------------------------------
% 2.82/1.38 % (4082169)------------------------------
% 2.82/1.38 % (4082158)Success in time 0.321 s
% 2.82/1.38 % Vampire exiting
%------------------------------------------------------------------------------