%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 01:17:47 PM UTC 2026
% Result : Theorem 8.84s 11.68s
% Output : Proof 8.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 39 unt; 0 def)
% Number of atoms : 173 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 190 ( 97 ~; 47 |; 37 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 132 ( 11 sgn 81 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_defns) ).
fof(f6_nnf,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [L,M] :
( ( ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M)
| convergent_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c14,plain,
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi14,axiom,
ifeq(convergent_lines(X0,X1),true,unequally_directed_opposite_lines(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
fof(f36,conjecture,
! [L,M,N,A,B,C] :
( ( convergent_lines(M,N)
& convergent_lines(L,N)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),intersection_point(M,parallel_through_point(N,B)),intersection_point(M,parallel_through_point(N,C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M,N,A,B,C] :
( ( convergent_lines(M,N)
& convergent_lines(L,N)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),intersection_point(M,parallel_through_point(N,B)),intersection_point(M,parallel_through_point(N,C))) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M,N,A,B,C] :
( ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),intersection_point(M,parallel_through_point(N,B)),intersection_point(M,parallel_through_point(N,C)))
& convergent_lines(M,N)
& convergent_lines(L,N)
& convergent_lines(L,M)
& between_on_line(L,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ between_on_line(sk1,intersection_point(sk1,parallel_through_point(sk2,sk3)),intersection_point(sk1,parallel_through_point(sk2,sk4)),intersection_point(sk1,parallel_through_point(sk2,sk5)))
& convergent_lines(sk1,sk2)
& convergent_lines(sk0,sk2)
& convergent_lines(sk0,sk1)
& between_on_line(sk0,sk3,sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5])],[f36_nnf]) ).
cnf(c67,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi55,negated_conjecture,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h0,plain,
unequally_directed_opposite_lines(sk0,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi55]) ).
fof(f0,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(unequally_directed_opposite_lines(X0,X1),true,unequally_directed_lines(X0,reverse_line(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h6,plain,
unequally_directed_lines(sk0,reverse_line(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(c13,plain,
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi13,axiom,
ifeq(convergent_lines(X0,X1),true,unequally_directed_lines(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h1,plain,
unequally_directed_lines(sk0,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi55]) ).
fof(f18,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
fof(f18_nnf,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c44,plain,
( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,axiom,
ifeq(unequally_directed_lines(X0,X1),true,ifeq(unequally_directed_lines(X0,reverse_line(X1)),true,or(left_convergent_lines(X0,X1),left_convergent_lines(X0,reverse_line(X1))),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
fof(f20,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
fof(f20_nnf,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c47,plain,
~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi6,axiom,
left_convergent_lines(X0,X1) = false,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t13,plain,
or(false,false) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1,h6,hi6]) ).
cnf(t12,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t122,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t367,plain,
false = true,
inference(step,[status(thm)],[t13,t122]) ).
cnf(t351,plain,
false = true,
inference(orient,[status(thm)],[t367]) ).
fof(f3,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
fof(f3_nnf,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( ( unequally_directed_lines(X,Y)
| equally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f4,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
fof(f4_nnf,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| equally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c8,plain,
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f10,axiom,
! [A] : ~ distinct_points(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
fof(f10_nnf,plain,
! [A] : ~ distinct_points(A,A),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : ~ distinct_points(A,A),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c33,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f12,axiom,
! [L] : ~ distinct_lines(L,L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_basics) ).
fof(f12_nnf,plain,
! [L] : ~ distinct_lines(L,L),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [L] : ~ distinct_lines(L,L),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c35,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f19,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
fof(f19_nnf,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c45,plain,
~ left_apart_point(X0,X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c46,plain,
~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(c48,plain,
~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f25,axiom,
! [A,B] :
( distinct_points(A,B)
=> ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_cons_objs) ).
fof(f25_nnf,plain,
! [A,B] :
( ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) )
| ~ distinct_points(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) )
| ~ distinct_points(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c53,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(c54,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f26,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_cons_objs) ).
fof(f26_nnf,plain,
! [L,M] :
( ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [L,M] :
( ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c55,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(c56,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f27,axiom,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_cons_objs) ).
fof(f27_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c57,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f28,axiom,
! [L] : ~ distinct_lines(L,reverse_line(L)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_cons_objs) ).
fof(f28_nnf,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c58,plain,
~ distinct_lines(X0,reverse_line(X0)),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(c70,plain,
~ between_on_line(sk1,intersection_point(sk1,parallel_through_point(sk2,sk3)),intersection_point(sk1,parallel_through_point(sk2,sk4)),intersection_point(sk1,parallel_through_point(sk2,sk5))),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c8,c33,c35,c45,c46,c47,c48,c53,c54,c55,c56,c57,c58,c70]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t351]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n017.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Wed Sep 23 11:40:56 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.84/11.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.84/11.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------