%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO200+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 3.63s 1.49s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 12 unt; 3 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 58 ~; 66 |; 3 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
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(f36,conjecture,
! [X0,X1] :
( distinct_points(X0,X1)
=> equal_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( distinct_points(X0,X1)
=> equal_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f40,plain,
? [X0,X1] :
( ~ equal_lines(line_connecting(X0,X1),line_connecting(X1,X0))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f50,plain,
( ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
fof(f51,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
fof(f52,plain,
~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f58,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f59,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f60,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f51,f57]) ).
fof(f61,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(resolution,[],[f52,f59]) ).
fof(f64,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK1,sK0))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK1,sK0))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) ),
inference(resolution,[],[f61,f56]) ).
fof(f69,plain,
! [X0] :
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK1,sK0))
| ~ distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(sK1,sK0) ),
inference(resolution,[],[f64,f54]) ).
fof(f74,definition,
( spl2_1
<=> distinct_points(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f75,plain,
( distinct_points(sK1,sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( ~ distinct_points(sK1,sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl2_2
<=> ! [X0] :
( apart_point_and_line(X0,line_connecting(sK1,sK0))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f79,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK1,sK0))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl2_3
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f83,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f69,f81,f78,f74]) ).
fof(f94,plain,
( distinct_points(sK0,sK0)
| spl2_1 ),
inference(resolution,[],[f76,f60]) ).
fof(f95,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f94,f58]) ).
fof(f96,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f95]) ).
fof(f98,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl2_3 ),
inference(resolution,[],[f83,f53]) ).
fof(f100,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f98,f51]) ).
fof(f101,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f113,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1)
| ~ distinct_points(sK1,sK0)
| ~ spl2_2 ),
inference(resolution,[],[f79,f53]) ).
fof(f116,plain,
( ~ distinct_points(sK0,sK1)
| ~ distinct_points(sK1,sK0)
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f113,f54]) ).
fof(f117,plain,
( ~ distinct_points(sK1,sK0)
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f116,f51]) ).
fof(f118,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f117,f75]) ).
fof(f119,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f118]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
~ spl2_3,
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f119]) ).
cnf(s6,plain,
~ spl2_2,
inference(rat,[],[s5,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s6,s3]) ).
fof(f120,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:34:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 3.63/1.49 % (4085164)Detected formulas, will run a generic FOF schedule.
% 3.63/1.49 % (4085171)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=567500520:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.49 % (4085173)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1179878460:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.49 % (4085170)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=1617365799:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.49 % (4085172)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3957436656:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.49 % (4085169)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=3948529866:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.49 % (4085175)dis-21_1_sil=8000:lcm=predicate:random_seed=849979406: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)
% 3.63/1.49 % (4085172)First to succeed.
% 3.63/1.49 % (4085173)Also succeeded, but the first one will report.
% 3.63/1.49 % (4085174)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=957500424:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.49 % (4085172)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4085164"
% 3.63/1.49 % (4085174)Also succeeded, but the first one will report.
% 3.63/1.49 % (4085175)Instruction limit reached!
% 3.63/1.49 % (4085175)------------------------------
% 3.63/1.49 % (4085175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.49 % (4085175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.49 % (4085175)CaDiCaL version: 2.1.3
% 3.63/1.49 % (4085175)Termination reason: Instruction limit
% 3.63/1.49 % (4085175)Termination phase: Saturation
% 3.63/1.49 % (4085175)Time elapsed: 0.086 s
% 3.63/1.49 % (4085175)Peak memory usage: 89 MB
% 3.63/1.49 % (4085175)Instructions burned: 130 (million)
% 3.63/1.49 % (4085183)lrs+10_1_sil=8000:sp=occurrence:random_seed=432331534:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.49 % (4085172)Refutation found. Thanks to Tanya!
% 3.63/1.49 % SZS status Theorem for theBenchmark
% 3.63/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.49 % (4085172)------------------------------
% 3.63/1.49 % (4085172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.49 % (4085172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.49 % (4085172)CaDiCaL version: 2.1.3
% 3.63/1.49 % (4085172)Termination reason: Refutation
% 3.63/1.49 % (4085172)Time elapsed: 0.004 s
% 3.63/1.49 % (4085172)Peak memory usage: 89 MB
% 3.63/1.49 % (4085172)Instructions burned: 3 (million)
% 3.63/1.49 % (4085172)------------------------------
% 3.63/1.49 % (4085172)------------------------------
% 3.63/1.49 % (4085164)Success in time 0.434 s
% 3.63/1.49 % Vampire exiting
%------------------------------------------------------------------------------