%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO248+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 130 ( 29 unt; 0 def)
% Number of atoms : 401 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 447 ( 176 ~; 215 |; 35 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 284 ( 278 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',apt_def) ).
fof(f6,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag2) ).
fof(f8,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag3) ).
fof(f9,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag4) ).
fof(f10,axiom,
! [X0] : ~ unequally_directed_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(f11,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/GEO007+0.ax',oag6) ).
fof(f12,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/GEO007+0.ax',oag7) ).
fof(f13,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1) )
=> ( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag8) ).
fof(f14,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/GEO007+0.ax',oag9) ).
fof(f15,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(f17,axiom,
! [X0,X1] :
( ( point(X0)
& point(X1)
& distinct_points(X0,X1) )
=> line(line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco1) ).
fof(f18,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/GEO007+0.ax',oagco2) ).
fof(f19,axiom,
! [X0,X1] :
( ( point(X1)
& line(X0) )
=> line(parallel_through_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco3) ).
fof(f20,axiom,
! [X0] :
( line(X0)
=> line(reverse_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco4) ).
fof(f21,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/GEO007+0.ax',oagco5) ).
fof(f22,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/GEO007+0.ax',oagco6) ).
fof(f23,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco7) ).
fof(f24,axiom,
! [X0] : ~ distinct_lines(X0,reverse_line(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco8) ).
fof(f25,axiom,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(f26,axiom,
! [X0,X1] : ~ unequally_directed_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco10) ).
fof(f27,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/GEO007+0.ax',oaguc1) ).
fof(f28,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/GEO007+0.ax',oaguc2) ).
fof(f29,axiom,
! [X0,X1,X2] :
( left_apart_point(X0,X2)
=> ( distinct_points(X0,X1)
| left_apart_point(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagsub1) ).
fof(f30,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/GEO007+0.ax',oagsub2) ).
fof(f31,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/GEO007+0.ax',oagsub3) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( left_apart_point(X0,X2)
& left_apart_point(X1,parallel_through_point(X2,X0)) )
=> left_apart_point(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( left_apart_point(X0,X2)
& left_apart_point(X1,parallel_through_point(X2,X0)) )
=> left_apart_point(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) )
=> apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f42,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,[],[f12]) ).
fof(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f45,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(flattening,[],[f44]) ).
fof(f46,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,[],[f14]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f51,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f52,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,[],[f18]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f55,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f57,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,[],[f21]) ).
fof(f58,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,[],[f22]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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,[],[f27]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,[],[f28]) ).
fof(f63,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,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1,X2] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(flattening,[],[f64]) ).
fof(f66,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,[],[f30]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X1,X2)
| left_convergent_lines(X0,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
? [X0,X1,X2] :
( ~ left_apart_point(X1,X2)
& left_apart_point(X0,X2)
& left_apart_point(X1,parallel_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
? [X0,X1,X2] :
( ~ left_apart_point(X1,X2)
& left_apart_point(X0,X2)
& left_apart_point(X1,parallel_through_point(X2,X0)) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
( ~ left_apart_point(sK1,sK2)
& left_apart_point(sK0,sK2)
& left_apart_point(sK1,parallel_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f74,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| ~ left_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f75,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f76,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f77,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f78,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_lines(X2,X1)
| ~ distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f80,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X2,X1)
| ~ unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f81,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,[],[f43]) ).
fof(f82,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,[],[f43]) ).
fof(f83,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,[],[f43]) ).
fof(f84,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,[],[f43]) ).
fof(f85,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f86,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,[],[f47]) ).
fof(f87,plain,
! [X0,X1] : ~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f48]) ).
fof(f89,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f90,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f91,plain,
! [X0,X1] :
( line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f92,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,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f96,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f97,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,[],[f59]) ).
fof(f98,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,[],[f59]) ).
fof(f99,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f100,plain,
! [X0] : ~ distinct_lines(X0,reverse_line(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f101,plain,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[],[f25]) ).
fof(f102,plain,
! [X0,X1] : ~ unequally_directed_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f26]) ).
fof(f103,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,[],[f61]) ).
fof(f104,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,[],[f63]) ).
fof(f105,plain,
! [X2,X0,X1] :
( distinct_points(X0,X1)
| left_apart_point(X1,X2)
| ~ left_apart_point(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f106,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,[],[f67]) ).
fof(f107,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X1)
| left_convergent_lines(X2,X1)
| ~ left_convergent_lines(X2,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f108,plain,
left_apart_point(sK1,parallel_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
left_apart_point(sK0,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
~ left_apart_point(sK1,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f111,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| left_apart_point(X0,X1) ),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f112,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f113,plain,
! [X0] : distinct_points(X0,X0),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ distinct_points(X2,X1)
| distinct_points(X0,X2) ),
inference(consistent_polarity_flipping,[],[f76]) ).
fof(f115,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| line(X0)
| line(X1) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f116,plain,
! [X0,X1] : left_apart_point(X0,X1),
inference(consistent_polarity_flipping,[],[f88]) ).
fof(f117,plain,
! [X0,X1] : left_apart_point(X0,reverse_line(X1)),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f118,plain,
! [X0,X1] :
( ~ line(line_connecting(X0,X1))
| ~ point(X0)
| ~ point(X1)
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f119,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,[],[f92]) ).
fof(f120,plain,
! [X0,X1] :
( ~ line(parallel_through_point(X0,X1))
| ~ point(X1)
| line(X0) ),
inference(consistent_polarity_flipping,[],[f93]) ).
fof(f121,plain,
! [X0] :
( ~ line(reverse_line(X0))
| line(X0) ),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f122,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f123,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(X0,X1))
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f124,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,[],[f98]) ).
fof(f125,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,[],[f97]) ).
fof(f126,plain,
! [X0,X1] : apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f127,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,[],[f103]) ).
fof(f128,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,[],[f104]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ left_apart_point(X1,X2)
| left_apart_point(X0,X2) ),
inference(consistent_polarity_flipping,[],[f105]) ).
fof(f130,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,[],[f106]) ).
fof(f131,plain,
left_apart_point(sK1,sK2),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f132,plain,
~ left_apart_point(sK0,sK2),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f133,plain,
~ left_apart_point(sK1,parallel_through_point(sK2,sK0)),
inference(consistent_polarity_flipping,[],[f108]) ).
fof(f206,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f111,f112,f113,f114,f77,f78,f79,f80,f84,f83,f82,f81,f115,f86,f116,f117,f90,f89,f118,f119,f120,f121,f122,f123,f124,f125,f126,f100,f101,f102,f127,f128,f129,f130,f107,f131,f132,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO248+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n015.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 07:55:00 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 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
% 0.16/0.48 % (1326100)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (1326105)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3180535071_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % (1326105) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1326100-1326105"...
% 0.16/0.48 % (1326105)...printing done.
% 0.16/0.48 % (1326105)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (1326105)------------------------------
% 0.16/0.48 % (1326105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (1326105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (1326105)CaDiCaL version: 2.1.3
% 0.16/0.48 % (1326105)Termination reason: Refutation
% 0.16/0.48 % (1326105)Time elapsed: 0.003 s
% 0.16/0.48 % (1326105)Peak memory usage: 11 MB
% 0.16/0.48 % (1326105)Instructions burned: 7 (million)
% 0.16/0.48 % (1326100)Success in time 0.033 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------