%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO184+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 09:53:51 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 44 ~; 40 |; 19 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 38 !; 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/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/sandbox/benchmark/Axioms/GEO006+0.ax',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/Axioms/GEO006+0.ax',cu1) ).
fof(f15,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_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)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,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,[],[f28]) ).
fof(f52,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f77,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f48,f56]) ).
fof(f81,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2) ),
inference(resolution,[],[f77,f55]) ).
fof(f96,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f81,f52]) ).
fof(f98,definition,
( spl4_3
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f100,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f107,definition,
( spl4_5
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f109,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f114,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f96,f53]) ).
fof(f115,plain,
( spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f114,f98,f107]) ).
fof(f116,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_3 ),
inference(resolution,[],[f100,f45]) ).
fof(f119,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f116,f55]) ).
fof(f120,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f121,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_5 ),
inference(resolution,[],[f109,f44]) ).
fof(f124,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f121,f55]) ).
fof(f125,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f124]) ).
cnf(s5,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
~ spl4_3,
inference(sat_conversion,[],[f120]) ).
cnf(s7,plain,
~ spl4_5,
inference(sat_conversion,[],[f125]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s7,s6]) ).
fof(f126,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO184+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n007.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 07:25:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % (1071445)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (1071453)dis+10_1_sil=32000:sp=arity:random_seed=313867603:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (1071453) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1071445-1071453"...
% 0.11/0.44 % (1071453)...printing done.
% 0.11/0.44 % (1071453)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (1071453)------------------------------
% 0.11/0.44 % (1071453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (1071453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (1071453)CaDiCaL version: 2.1.3
% 0.11/0.44 % (1071453)Termination reason: Refutation
% 0.11/0.44 % (1071453)Time elapsed: 0.002 s
% 0.11/0.44 % (1071453)Peak memory usage: 12 MB
% 0.11/0.44 % (1071453)Instructions burned: 3 (million)
% 0.11/0.44 % (1071445)Success in time 0.028 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------