%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO179+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 09:53:49 AM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 11 unt; 2 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 43 ~; 47 |; 8 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ( distinct_lines(line_connecting(X0,X1),line_connecting(X2,X0))
& distinct_lines(line_connecting(X0,X1),line_connecting(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ( distinct_lines(line_connecting(X0,X1),line_connecting(X2,X0))
& distinct_lines(line_connecting(X0,X1),line_connecting(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f44,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] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,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(f51,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f76,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(line_connecting(X0,X1),line_connecting(X2,X0))
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X2,X1)) )
& distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(line_connecting(X0,X1),line_connecting(X2,X0))
| ~ distinct_lines(line_connecting(X0,X1),line_connecting(X2,X1)) )
& distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f84,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f85,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f114,plain,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f115,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f77]) ).
fof(f116,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f120,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f149,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f151,definition,
( spl3_1
<=> distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f153,plain,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0))
| spl3_1 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl3_2
<=> distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f157,plain,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK1))
| spl3_2 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f114,f155,f151]) ).
fof(f167,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,line_connecting(X1,X2))
| distinct_points(X0,X1)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f124,f119]) ).
fof(f168,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,line_connecting(X1,X2))
| distinct_points(X0,X2)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f124,f120]) ).
fof(f175,plain,
! [X2,X0,X1] :
( distinct_lines(X1,line_connecting(X0,X2))
| apart_point_and_line(X0,X1)
| ~ distinct_points(X0,X2) ),
inference(resolution,[],[f125,f119]) ).
fof(f267,plain,
( distinct_points(sK2,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f167,f149]) ).
fof(f270,plain,
distinct_points(sK2,sK0),
inference(forward_subsumption_resolution,[],[f267,f116]) ).
fof(f271,plain,
( distinct_points(sK2,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f168,f149]) ).
fof(f274,plain,
distinct_points(sK2,sK1),
inference(forward_subsumption_resolution,[],[f271,f116]) ).
fof(f279,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK2,sK0)
| spl3_1 ),
inference(resolution,[],[f175,f153]) ).
fof(f287,plain,
( ~ distinct_points(sK2,sK0)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f279,f149]) ).
fof(f308,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f287,f270]) ).
fof(f309,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f321,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK2,sK1)
| spl3_2 ),
inference(resolution,[],[f157,f175]) ).
fof(f323,plain,
( ~ distinct_points(sK2,sK1)
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f321,f149]) ).
fof(f325,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f323,f274]) ).
fof(f326,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f325]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f158]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f309]) ).
cnf(s4,plain,
spl3_2,
inference(sat_conversion,[],[f326]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f327,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO179+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 07:26:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.47 % (890430)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (890436)% WARNING: option uhcvi not known.
% 0.15/0.47 % (890436)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=190337881:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (890436) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-890430-890436"...
% 0.15/0.47 % (890436)...printing done.
% 0.15/0.47 % (890436)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (890436)------------------------------
% 0.15/0.47 % (890436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (890436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (890436)CaDiCaL version: 2.1.3
% 0.15/0.47 % (890436)Termination reason: Refutation
% 0.15/0.47 % (890436)Time elapsed: 0.004 s
% 0.15/0.47 % (890436)Peak memory usage: 12 MB
% 0.15/0.47 % (890436)Instructions burned: 8 (million)
% 0.15/0.47 % (890430)Success in time 0.036 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------