%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO264+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 : n009.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 0.14s 5.93s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 30 unt; 0 def)
% Number of atoms : 113 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 133 ( 78 ~; 24 |; 23 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 90 ( 11 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,conjecture,
! [A,B,C,D] :
( left_apart_point(C,line_connecting(A,B))
=> ( ( right_apart_point(D,line_connecting(C,A))
& right_apart_point(D,line_connecting(B,C)) )
=> left_apart_point(D,line_connecting(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [A,B,C,D] :
( left_apart_point(C,line_connecting(A,B))
=> ( ( right_apart_point(D,line_connecting(C,A))
& right_apart_point(D,line_connecting(B,C)) )
=> left_apart_point(D,line_connecting(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [A,B,C,D] :
( ~ left_apart_point(D,line_connecting(A,B))
& right_apart_point(D,line_connecting(C,A))
& right_apart_point(D,line_connecting(B,C))
& left_apart_point(C,line_connecting(A,B)) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( ~ left_apart_point(sk3,line_connecting(sk0,sk1))
& right_apart_point(sk3,line_connecting(sk2,sk0))
& right_apart_point(sk3,line_connecting(sk1,sk2))
& left_apart_point(sk2,line_connecting(sk0,sk1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f36_nnf]) ).
cnf(c69,plain,
~ left_apart_point(sk3,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi71,negated_conjecture,
ifeq(left_apart_point(sk3,line_connecting(sk0,sk1)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(c66,plain,
left_apart_point(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi54,negated_conjecture,
left_apart_point(sk2,line_connecting(sk0,sk1)) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
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(hi3,axiom,
left_apart_point(X0,X1) = false,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi71,hi54,hi3]) ).
cnf(t167,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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]) ).
cnf(c46,plain,
~ left_apart_point(X0,reverse_line(X1)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
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(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(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,c69]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t167]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO264+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n009.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 11:45:19 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------