%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO227+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 : n018.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 01:17:37 PM UTC 2026
% Result : Theorem 3.43s 1.07s
% Output : Proof 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 100 ( 64 unt; 0 def)
% Number of atoms : 159 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 141 ( 82 ~; 33 |; 21 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 124 ( 11 sgn 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
cnf(t37,plain,
or(not(equally_directed_opposite_lines(X1,X2)),not(unequally_directed_opposite_lines(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t160,plain,
or(not(equally_directed_opposite_lines(X1,X2)),not(unequally_directed_opposite_lines(X1,X2))) = true,
inference(orient,[status(thm)],[t37]) ).
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(c1,plain,
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t45,plain,
ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,unequally_directed_opposite_lines(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t101,plain,
ifeq(unequally_directed_lines(X1,reverse_line(X2)),true,unequally_directed_opposite_lines(X1,X2),true) = true,
inference(orient,[status(thm)],[t45]) ).
fof(f17,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
fof(f17_nnf,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c43,plain,
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t30,plain,
or(unequally_directed_lines(X1,X2),unequally_directed_lines(X1,reverse_line(X2))) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t153,plain,
or(unequally_directed_lines(X1,X2),unequally_directed_lines(X1,reverse_line(X2))) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t19,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t180,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t19]) ).
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]) ).
cnf(t36,plain,
or(not(equally_directed_lines(X1,X2)),not(unequally_directed_lines(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t159,plain,
or(not(equally_directed_lines(X1,X2)),not(unequally_directed_lines(X1,X2))) = true,
inference(orient,[status(thm)],[t36]) ).
fof(f36,conjecture,
! [L,M] :
~ ( equally_directed_opposite_lines(L,M)
& equally_directed_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f36_neg,negated_conjecture,
~ ! [L,M] :
~ ( equally_directed_opposite_lines(L,M)
& equally_directed_lines(L,M) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f36_nnf,plain,
? [L,M] :
( equally_directed_opposite_lines(L,M)
& equally_directed_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f36_neg]) ).
fof(f36_sk,plain,
( equally_directed_opposite_lines(sk0,sk1)
& equally_directed_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f36_nnf]) ).
cnf(c66,plain,
equally_directed_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(t5,plain,
equally_directed_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t174,plain,
equally_directed_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t175,plain,
true = or(not(true),not(unequally_directed_lines(sk0,sk1))),
inference(cp,[status(thm)],[t159,t174]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t196,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t509,plain,
true = or(false,not(unequally_directed_lines(sk0,sk1))),
inference(step,[status(thm)],[t175,t196]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t92,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t510,plain,
true = not(unequally_directed_lines(sk0,sk1)),
inference(step,[status(thm)],[t509,t92]) ).
cnf(t345,plain,
not(unequally_directed_lines(sk0,sk1)) = true,
inference(orient,[status(thm)],[t510]) ).
cnf(t346,plain,
false = ifeq(true,true,unequally_directed_lines(sk0,sk1),false),
inference(cp,[status(thm)],[t180,t345]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t90,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t511,plain,
false = unequally_directed_lines(sk0,sk1),
inference(step,[status(thm)],[t346,t90]) ).
cnf(t347,plain,
unequally_directed_lines(sk0,sk1) = false,
inference(orient,[status(thm)],[t511]) ).
cnf(t350,plain,
true = or(false,unequally_directed_lines(sk0,reverse_line(sk1))),
inference(cp,[status(thm)],[t153,t347]) ).
cnf(t512,plain,
true = unequally_directed_lines(sk0,reverse_line(sk1)),
inference(step,[status(thm)],[t350,t92]) ).
cnf(t364,plain,
unequally_directed_lines(sk0,reverse_line(sk1)) = true,
inference(orient,[status(thm)],[t512]) ).
cnf(t370,plain,
true = ifeq(true,true,unequally_directed_opposite_lines(sk0,sk1),true),
inference(cp,[status(thm)],[t101,t364]) ).
cnf(t513,plain,
true = unequally_directed_opposite_lines(sk0,sk1),
inference(step,[status(thm)],[t370,t90]) ).
cnf(t394,plain,
unequally_directed_opposite_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t513]) ).
cnf(t397,plain,
true = or(not(equally_directed_opposite_lines(sk0,sk1)),not(true)),
inference(cp,[status(thm)],[t160,t394]) ).
cnf(c67,plain,
equally_directed_opposite_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(t6,plain,
equally_directed_opposite_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t177,plain,
equally_directed_opposite_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t514,plain,
true = or(not(true),not(true)),
inference(step,[status(thm)],[t397,t177]) ).
cnf(t515,plain,
true = or(false,not(true)),
inference(step,[status(thm)],[t514,t196]) ).
cnf(t516,plain,
true = not(true),
inference(step,[status(thm)],[t515,t92]) ).
cnf(t517,plain,
true = false,
inference(step,[status(thm)],[t516,t196]) ).
cnf(t399,plain,
false = true,
inference(orient,[status(thm)],[t517]) ).
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]) ).
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]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t399]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO227+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:37:05 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.43/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------