%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO248+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 : n015.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 09:54:14 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 30
% Syntax : Number of formulae : 142 ( 22 unt; 0 def)
% Number of atoms : 440 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 483 ( 185 ~; 240 |; 34 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 322 ( 319 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( right_apart_point(X0,X1)
<=> left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a2_defns) ).
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
fof(f6,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| right_apart_point(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a6_defns) ).
fof(f11,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax1_basics) ).
fof(f12,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax2_basics) ).
fof(f13,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax3_basics) ).
fof(f14,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax4_basics) ).
fof(f15,axiom,
! [X0] : equally_directed_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(f16,axiom,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X1)
=> ( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax6_basics) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax7_basics) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
fof(f19,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax9_basics) ).
fof(f20,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax10_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(f22,axiom,
! [X0,X1] :
( ( point(X0)
& point(X1)
& distinct_points(X0,X1) )
=> line(line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax1_cons_objs) ).
fof(f23,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1)
& unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax2_cons_objs) ).
fof(f24,axiom,
! [X0,X1] :
( ( point(X1)
& line(X0) )
=> line(parallel_through_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax3_cons_objs) ).
fof(f25,axiom,
! [X0] :
( line(X0)
=> line(reverse_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax4_cons_objs) ).
fof(f26,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
& ~ apart_point_and_line(X1,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax5_cons_objs) ).
fof(f27,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
& ~ apart_point_and_line(intersection_point(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax6_cons_objs) ).
fof(f28,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax7_cons_objs) ).
fof(f29,axiom,
! [X0] : ~ distinct_lines(X0,reverse_line(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax8_cons_objs) ).
fof(f30,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax9_cons_objs) ).
fof(f31,axiom,
! [X0,X1] : equally_directed_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax10_cons_objs) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( left_apart_point(X0,X2)
| left_apart_point(X1,X2)
| left_apart_point(X0,X3)
| left_apart_point(X1,X3)
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax1_uniq_cons) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& left_apart_point(X0,X2) )
=> ( left_apart_point(X1,X2)
| left_convergent_lines(line_connecting(X0,X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax2_uniq_cons) ).
fof(f34,axiom,
! [X0,X1,X2] :
( left_apart_point(X0,X2)
=> ( distinct_points(X0,X1)
| left_apart_point(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax1_subs) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( left_apart_point(X0,X1)
& unequally_directed_lines(X1,X2) )
=> ( distinct_lines(X1,X2)
| left_apart_point(X0,reverse_line(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax2_subs) ).
fof(f36,axiom,
! [X0,X1,X2] :
( left_convergent_lines(X0,X1)
=> ( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax3_subs) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& incident_point_and_line(X1,parallel_lines(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& incident_point_and_line(X1,parallel_lines(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f40,plain,
~ ! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
=> apart_point_and_line(X1,X2) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f45,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f47,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f51,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f57,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f59,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f61,plain,
! [X0,X1] :
( ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
& ~ apart_point_and_line(X1,line_connecting(X0,X1)) )
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f62,plain,
! [X0,X1] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
& ~ apart_point_and_line(intersection_point(X0,X1),X1) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
& ~ apart_point_and_line(intersection_point(X0,X1),X1) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X0,X2)
| left_apart_point(X1,X2)
| left_apart_point(X0,X3)
| left_apart_point(X1,X3)
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X3))
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( left_apart_point(X0,X2)
| left_apart_point(X1,X2)
| left_apart_point(X0,X3)
| left_apart_point(X1,X3)
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X3))
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( left_apart_point(X1,X2)
| left_convergent_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1)
| ~ left_apart_point(X0,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0,X1,X2] :
( left_apart_point(X1,X2)
| left_convergent_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1)
| ~ left_apart_point(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1,X2] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| left_apart_point(X0,reverse_line(X2))
| ~ left_apart_point(X0,X1)
| ~ unequally_directed_lines(X1,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| left_apart_point(X0,reverse_line(X2))
| ~ left_apart_point(X0,X1)
| ~ unequally_directed_lines(X1,X2) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f74,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f76,plain,
! [X0,X1] :
( ( right_apart_point(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) )
& ( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f77,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f78,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
( ~ apart_point_and_line(sK1,sK2)
& apart_point_and_line(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f75]) ).
fof(f80,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f81,plain,
! [X0,X1] :
( right_apart_point(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f82,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f83,plain,
! [X0,X1] :
( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f84,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| ~ right_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f85,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| ~ left_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f86,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f87,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f88,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f89,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_lines(X2,X1)
| ~ distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f90,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f91,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f92,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,reverse_line(X2))
| unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f93,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,reverse_line(X2))
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f94,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f95,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f96,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f97,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f98,plain,
! [X0,X1] : ~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f52]) ).
fof(f99,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f52]) ).
fof(f100,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f53]) ).
fof(f101,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f53]) ).
fof(f102,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f103,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f104,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f105,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f106,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f107,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f108,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f109,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f110,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f111,plain,
! [X0] : ~ distinct_lines(X0,reverse_line(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f112,plain,
! [X0,X1] :
( equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f113,plain,
! [X0,X1] : equally_directed_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f31]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( left_apart_point(X0,X2)
| left_apart_point(X1,X2)
| left_apart_point(X0,X3)
| left_apart_point(X1,X3)
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X3))
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f115,plain,
! [X2,X0,X1] :
( left_apart_point(X1,X2)
| left_convergent_lines(line_connecting(X0,X1),X2)
| ~ distinct_points(X0,X1)
| ~ left_apart_point(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X2,X0,X1] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f117,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| left_apart_point(X0,reverse_line(X2))
| ~ left_apart_point(X0,X1)
| ~ unequally_directed_lines(X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f118,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
! [X0,X1] :
( ~ right_apart_point(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f122,plain,
! [X0,X1] :
( left_apart_point(X0,reverse_line(X1))
| right_apart_point(X0,X1) ),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f123,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f124,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| right_apart_point(X0,X1) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f125,plain,
! [X0,X1] :
( left_apart_point(X0,X1)
| ~ right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f126,plain,
! [X0] : distinct_points(X0,X0),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ distinct_points(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f128,plain,
! [X0] : ~ equally_directed_lines(X0,X0),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X2,X1)
| unequally_directed_lines(X0,X2) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f93]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X2))
| ~ unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f134,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f135,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f136,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f137,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ line(X0)
| ~ line(X1)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f103]) ).
fof(f138,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f139,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f140,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f141,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f142,plain,
! [X0,X1] :
( ~ equally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0)))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f143,plain,
! [X0,X1] : ~ equally_directed_lines(parallel_through_point(X1,X0),X1),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( left_apart_point(X0,X2)
| left_apart_point(X1,X2)
| left_apart_point(X0,X3)
| left_apart_point(X1,X3)
| left_apart_point(X0,reverse_line(X2))
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X3))
| left_apart_point(X1,reverse_line(X3))
| distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f145,plain,
! [X2,X0,X1] :
( left_apart_point(X1,X2)
| left_convergent_lines(line_connecting(X0,X1),X2)
| distinct_points(X0,X1)
| ~ left_apart_point(X0,X2) ),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f147,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| left_apart_point(X0,reverse_line(X2))
| ~ left_apart_point(X0,X1)
| unequally_directed_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X2,X1)
| ~ left_convergent_lines(X2,X0) ),
inference(consistent_polarity_flipping,[],[f118]) ).
fof(f216,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f121,f122,f123,f85,f124,f125,f126,f127,f88,f89,f128,f129,f130,f131,f132,f133,f134,f135,f99,f98,f101,f100,f136,f137,f104,f105,f138,f139,f140,f141,f110,f111,f142,f143,f144,f145,f146,f147,f148,f120,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO248+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 : n015.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 07:55:15 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
% 0.16/0.46 % (1326513)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (1326518)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2841147563_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % (1326518) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326513-1326518"...
% 0.16/0.46 % (1326519)% WARNING: option uhcvi not known.
% 0.16/0.46 % (1326518)...printing done.
% 0.16/0.46 % (1326518)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (1326518)------------------------------
% 0.16/0.46 % (1326518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (1326518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (1326518)CaDiCaL version: 2.1.3
% 0.16/0.46 % (1326518)Termination reason: Refutation
% 0.16/0.46 % (1326518)Time elapsed: 0.003 s
% 0.16/0.46 % (1326518)Peak memory usage: 12 MB
% 0.16/0.46 % (1326518)Instructions burned: 9 (million)
% 0.16/0.46 % (1326513)Success in time 0.027 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------