%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO220+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 : 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 09:54:06 AM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 12 unt; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 255 ( 108 ~; 116 |; 16 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 198 ( 192 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
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(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',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/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(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( ( ( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) )
& ( ~ convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X2) ) )
=> ( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(f18,conjecture,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f27,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,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(f33,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,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(f35,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f37,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
? [X0,X1,X2] :
( convergent_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2] :
( convergent_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
( convergent_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK1)
& ~ unorthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f44]) ).
fof(f46,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f47,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f48,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f49,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f50,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f51,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f55,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X2,X0)
| unorthogonal_lines(X2,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X2,X0)
| convergent_lines(X2,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| convergent_lines(X2,X0)
| unorthogonal_lines(X2,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1)
| convergent_lines(X2,X0)
| convergent_lines(X2,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X2,X0)
| unorthogonal_lines(X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f67,plain,
~ unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f45]) ).
fof(f68,plain,
convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f69,plain,
! [X0] : distinct_points(X0,X0),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f70,plain,
! [X0] : distinct_lines(X0,X0),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ distinct_points(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| ~ distinct_lines(X2,X1)
| distinct_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f73,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f74,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f75,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f76,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X3,X1)
| ~ apart_point_and_line(X3,X2)
| distinct_points(X0,X3)
| distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) ),
inference(consistent_polarity_flipping,[],[f58]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X2,X0) ),
inference(consistent_polarity_flipping,[],[f59]) ).
fof(f88,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f69,f70,f48,f71,f72,f51,f73,f74,f75,f76,f77,f78,f79,f80,f60,f64,f63,f62,f61,f65,f68,f67,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO220+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:43:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.10/0.46 % (896764)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (896769)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3501306341_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.46 % TRYING [1]
% 0.10/0.46 % TRYING [2]
% 0.10/0.46 % TRYING [3]
% 0.10/0.46 % (896769) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-896764-896769"...
% 0.10/0.46 % (896769)...printing done.
% 0.10/0.46 % (896769)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (896769)------------------------------
% 0.10/0.46 % (896769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (896769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (896769)CaDiCaL version: 2.1.3
% 0.10/0.46 % (896769)Termination reason: Refutation
% 0.10/0.46 % (896769)Time elapsed: 0.002 s
% 0.10/0.46 % (896769)Peak memory usage: 11 MB
% 0.10/0.46 % (896769)Instructions burned: 6 (million)
% 0.10/0.46 % (896764)Success in time 0.031 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------