%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO204+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 : n009.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 0.91s 0.90s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 11 unt; 5 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 218 ( 88 ~; 103 |; 11 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 82 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
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,X2] :
( ( distinct_points(X0,X1)
& equal_points(X1,X2) )
=> ( distinct_points(X0,X2)
& equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& equal_points(X1,X2) )
=> ( distinct_points(X0,X2)
& equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
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(f39,plain,
! [X0,X1] :
( equal_points(X0,X1)
=> ~ distinct_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f40,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f46,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] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& equal_points(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| ~ equal_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& equal_points(X1,X2) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
( ( ~ distinct_points(sK0,sK2)
| ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) )
& distinct_points(sK0,sK1)
& equal_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f81]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f90,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f93,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,[],[f51]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f119,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
equal_points(sK1,sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f122,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f123,plain,
( ~ distinct_points(sK0,sK2)
| ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f125,definition,
( spl3_1
<=> equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f127,plain,
( ~ equal_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| spl3_1 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,definition,
( spl3_2
<=> distinct_points(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f130,plain,
( distinct_points(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( ~ distinct_points(sK0,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f123,f129,f125]) ).
fof(f133,plain,
~ distinct_points(sK1,sK2),
inference(resolution,[],[f119,f121]) ).
fof(f134,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| spl3_1 ),
inference(resolution,[],[f120,f127]) ).
fof(f135,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(sK1,X0) ),
inference(resolution,[],[f86,f122]) ).
fof(f185,definition,
( spl3_3
<=> apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f187,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK2))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f189,definition,
( spl3_4
<=> ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f190,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| ~ distinct_points(X0,sK1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f193,definition,
( spl3_5
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f194,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK2))
| spl3_5 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f204,plain,
( distinct_points(sK1,sK2)
| spl3_2 ),
inference(resolution,[],[f131,f135]) ).
fof(f205,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f204,f133]) ).
fof(f206,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f205]) ).
fof(f208,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f195,f89]) ).
fof(f211,plain,
( $false
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f208,f130]) ).
fof(f212,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f217,plain,
( ! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| spl3_1 ),
inference(resolution,[],[f134,f93]) ).
fof(f230,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,line_connecting(sK0,sK2))
| ~ distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1) )
| spl3_1 ),
inference(resolution,[],[f217,f90]) ).
fof(f235,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,line_connecting(sK0,sK2))
| ~ distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f230,f122]) ).
fof(f237,plain,
( spl3_3
| spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f235,f125,f189,f185]) ).
fof(f263,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK1)
| ~ distinct_points(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f190,f89]) ).
fof(f269,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK1)
| ~ spl3_4 ),
inference(duplicate_literal_removal,[],[f263]) ).
fof(f270,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_4
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f269,f194]) ).
fof(f271,plain,
( $false
| ~ spl3_4
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f270,f122]) ).
fof(f272,plain,
( ~ spl3_4
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f275,plain,
( ! [X0] :
( distinct_points(sK1,X0)
| apart_point_and_line(X0,line_connecting(sK0,sK2)) )
| ~ spl3_3 ),
inference(resolution,[],[f187,f94]) ).
fof(f279,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK2))
| ~ spl3_3 ),
inference(resolution,[],[f275,f133]) ).
fof(f283,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f279,f90]) ).
fof(f286,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f283,f130]) ).
fof(f287,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f286]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
spl3_2,
inference(sat_conversion,[],[f206]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f212]) ).
cnf(s6,plain,
( spl3_1
| spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f237]) ).
cnf(s8,plain,
( ~ spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f287]) ).
cnf(s10,plain,
~ spl3_3,
inference(rat,[],[s9,s4]) ).
cnf(s11,plain,
~ spl3_5,
inference(rat,[],[s5,s4]) ).
cnf(s12,plain,
~ spl3_4,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
spl3_1,
inference(rat,[],[s6,s10,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s4,s13]) ).
fof(f288,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.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 07:35:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.91/0.90 % (1696857)Detected formulas, will run a generic FOF schedule.
% 0.91/0.90 % (1696867)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3132693849:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.91/0.90 % (1696867)First to succeed.
% 0.91/0.90 % (1696867)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1696857"
% 0.91/0.90 % (1696868)dis-21_1_sil=8000:lcm=predicate:random_seed=2397761850: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)
% 0.91/0.90 % (1696866)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2930236334:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.91/0.90 % (1696862)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=681274150:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.91/0.90 % (1696865)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2261272895:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.91/0.90 % (1696863)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=2937095020:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.91/0.90 % (1696864)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=3728275034:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.91/0.90 % (1696866)Also succeeded, but the first one will report.
% 0.91/0.90 % (1696865)Also succeeded, but the first one will report.
% 0.91/0.90 % (1696868)Also succeeded, but the first one will report.
% 0.91/0.90 % (1696867)Refutation found. Thanks to Tanya!
% 0.91/0.90 % SZS status Theorem for theBenchmark
% 0.91/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/1.10 % (1696867)------------------------------
% 2.44/1.10 % (1696867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/1.10 % (1696867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/1.10 % (1696867)CaDiCaL version: 2.1.3
% 2.44/1.10 % (1696867)Termination reason: Refutation
% 2.44/1.10 % (1696867)Time elapsed: 0.005 s
% 2.44/1.10 % (1696867)Peak memory usage: 89 MB
% 2.44/1.10 % (1696867)Instructions burned: 10 (million)
% 2.44/1.10 % (1696867)------------------------------
% 2.44/1.10 % (1696867)------------------------------
% 2.44/1.10 % (1696857)Success in time 0.297 s
% 2.44/1.10 % Vampire exiting
%------------------------------------------------------------------------------