%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 09:53:47 AM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 8 unt; 2 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 34 ~; 33 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 44 ( 0 sgn 36 !; 8 ?)
% 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(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(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/sandbox2/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(f31,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(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
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(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK1,sK2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
~ distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,definition,
( spl4_1
<=> apart_point_and_line(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f59,plain,
( apart_point_and_line(sK1,sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl4_2
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f63,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f52,f61,f57]) ).
fof(f80,plain,
( ! [X0] :
( apart_point_and_line(sK0,X0)
| distinct_lines(sK2,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f50,f63]) ).
fof(f82,plain,
( ! [X0] :
( ~ distinct_points(sK0,X0)
| distinct_lines(sK2,line_connecting(sK0,X0)) )
| ~ spl4_2 ),
inference(resolution,[],[f80,f44]) ).
fof(f100,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_2 ),
inference(resolution,[],[f82,f54]) ).
fof(f103,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f100,f55]) ).
fof(f104,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f105,plain,
( ! [X0] :
( apart_point_and_line(sK1,X0)
| distinct_lines(sK2,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f59,f50]) ).
fof(f110,plain,
( ! [X0] :
( ~ distinct_points(X0,sK1)
| distinct_lines(sK2,line_connecting(X0,sK1)) )
| ~ spl4_1 ),
inference(resolution,[],[f105,f45]) ).
fof(f122,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_1 ),
inference(resolution,[],[f110,f54]) ).
fof(f127,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f122,f55]) ).
fof(f128,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f104]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 07:26:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.43 % (3202433)Will run a generic schedule for satisfiability detection.
% 0.09/0.43 % (3202443)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=55014779:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.43 % (3202443) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3202433-3202443"...
% 0.09/0.43 % (3202443)...printing done.
% 0.09/0.43 % (3202443)Refutation found. Thanks to Tanya!
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.43 % (3202443)------------------------------
% 0.09/0.43 % (3202443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.43 % (3202443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.43 % (3202443)CaDiCaL version: 2.1.3
% 0.09/0.43 % (3202443)Termination reason: Refutation
% 0.09/0.43 % (3202443)Time elapsed: 0.002 s
% 0.09/0.43 % (3202443)Peak memory usage: 12 MB
% 0.09/0.43 % (3202443)Instructions burned: 3 (million)
% 0.09/0.43 % (3202433)Success in time 0.027 s
% 0.09/0.43 % Vampire exiting
%------------------------------------------------------------------------------