%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO216+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 09:54:04 AM UTC 2026
% Result : Theorem 0.15s 0.49s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 145 ( 25 unt; 0 def)
% Number of atoms : 428 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 477 ( 194 ~; 239 |; 21 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 351 ( 350 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/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(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f18,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f19,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f20,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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f22,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f25,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/sandbox/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(f27,axiom,
! [X0,X1] :
( ( point(X0)
& point(X1)
& distinct_points(X0,X1) )
=> line(line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',con1) ).
fof(f28,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1)
& convergent_lines(X0,X1) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',int1) ).
fof(f29,axiom,
! [X0,X1] :
( ( line(X0)
& point(X1) )
=> line(parallel_through_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',par1) ).
fof(f30,axiom,
! [X0,X1] :
( ( line(X0)
& point(X1) )
=> line(orthogonal_through_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',orth1) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(f36,conjecture,
! [X0] : ~ orthogonal_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0] : ~ orthogonal_lines(X0,X0),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
=> ~ unorthogonal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f39,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f49,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(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(flattening,[],[f49]) ).
fof(f51,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(f52,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f51]) ).
fof(f53,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(f54,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f58,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f65,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,[],[f25]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f70,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0] : orthogonal_lines(X0,X0),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
orthogonal_lines(sK0,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f78]) ).
fof(f80,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f81,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f83,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_lines(X2,X1)
| ~ distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f90,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,[],[f50]) ).
fof(f91,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f92,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f93,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X2,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f97,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f98,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f99,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f100,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f101,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f102,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f103,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f104,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| convergent_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f115,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ line(X0)
| ~ point(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f116,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
orthogonal_lines(sK0,sK0),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
! [X0] : distinct_points(X0,X0),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ distinct_points(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f120,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f121,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f122,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f123,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f124,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,[],[f90]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f126,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f127,plain,
! [X0,X1] : apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f129,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f130,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X2)
| unorthogonal_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f131,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| ~ unorthogonal_lines(X2,X1)
| ~ convergent_lines(X0,X2)
| unorthogonal_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X2)
| unorthogonal_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f100]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X2,X1)
| ~ convergent_lines(X0,X2)
| unorthogonal_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f134,plain,
! [X0,X1] : unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f135,plain,
! [X0,X1] : apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(consistent_polarity_flipping,[],[f104]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| ~ unorthogonal_lines(X1,X3)
| ~ unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f105]) ).
fof(f137,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1)
| convergent_lines(X2,X0)
| convergent_lines(X2,X1) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1)
| convergent_lines(X2,X0)
| ~ unorthogonal_lines(X2,X1) ),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X2,X0)
| convergent_lines(X2,X1) ),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X2,X0)
| ~ unorthogonal_lines(X2,X1) ),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X2,X0)
| ~ unorthogonal_lines(X2,X1) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f143,plain,
! [X0,X1] :
( ~ line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f144,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| line(X0)
| line(X1)
| ~ convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f145,plain,
! [X0,X1] :
( ~ line(parallel_through_point(X0,X1))
| line(X0)
| ~ point(X1) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f146,plain,
! [X0,X1] :
( ~ line(orthogonal_through_point(X0,X1))
| line(X0)
| ~ point(X1) ),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f147,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f148,plain,
~ orthogonal_lines(sK0,sK0),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f164,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f118,f81,f82,f119,f84,f85,f120,f121,f122,f123,f124,f125,f126,f93,f94,f95,f127,f128,f129,f130,f131,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f142,f143,f144,f145,f146,f147,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO216+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 % Computer : n026.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 07:44:12 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.45 Running first-order model finding
% 0.12/0.45 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
% 0.15/0.49 % (2502313)Will run a generic schedule for satisfiability detection.
% 0.15/0.49 % (2502318)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=275898931_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.49 % TRYING [1]
% 0.15/0.49 % (2502318) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2502313-2502318"...
% 0.15/0.49 % (2502319)% WARNING: option uhcvi not known.
% 0.15/0.49 % (2502318)...printing done.
% 0.15/0.49 % (2502318)Refutation found. Thanks to Tanya!
% 0.15/0.49 % SZS status Theorem for theBenchmark
% 0.15/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (2502318)------------------------------
% 0.15/0.49 % (2502318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (2502318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (2502318)CaDiCaL version: 2.1.3
% 0.15/0.49 % (2502318)Termination reason: Refutation
% 0.15/0.49 % (2502318)Time elapsed: 0.002 s
% 0.15/0.49 % (2502318)Peak memory usage: 11 MB
% 0.15/0.49 % (2502318)Instructions burned: 6 (million)
% 0.15/0.49 % (2502313)Success in time 0.033 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------