%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO203+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 : n020.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 01:17:28 PM UTC 2026
% Result : Theorem 19.89s 7.93s
% Output : Proof 19.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 150 ( 105 unt; 0 def)
% Number of atoms : 239 ( 72 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 192 ( 103 ~; 56 |; 21 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 183 ( 6 sgn 105 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t81,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t107,plain,
ifeq(distinct_points(X1,X2),true,ifeq(distinct_lines(X3,X4),true,or(apart_point_and_line(X1,X3),or(apart_point_and_line(X1,X4),or(apart_point_and_line(X2,X3),apart_point_and_line(X2,X4)))),true),true) = true,
inference(orient,[status(thm)],[t81]) ).
fof(f35,conjecture,
! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,Z] :
( ~ equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0)
& distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))
& convergent_lines(sk0,sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c48,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t17,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t228,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t239,plain,
true = ifeq(true,true,ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(sk0,sk1),X1),or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(intersection_point(sk0,sk2),X1),apart_point_and_line(intersection_point(sk0,sk2),X2)))),true),true),
inference(cp,[status(thm)],[t107,t228]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t82,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t3965,plain,
true = ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(sk0,sk1),X1),or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(intersection_point(sk0,sk2),X1),apart_point_and_line(intersection_point(sk0,sk2),X2)))),true),
inference(step,[status(thm)],[t239,t82]) ).
cnf(t2956,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(sk0,sk1),X1),or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(intersection_point(sk0,sk2),X1),apart_point_and_line(intersection_point(sk0,sk2),X2)))),true) = true,
inference(orient,[status(thm)],[t3965]) ).
fof(f31,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f31_nnf,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c39,plain,
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t27,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t164,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(c49,plain,
~ equal_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t34,plain,
equal_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0) = false,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t397,plain,
equal_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0) = false,
inference(orient,[status(thm)],[t34]) ).
cnf(t398,plain,
true = or(false,distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0)),
inference(cp,[status(thm)],[t164,t397]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t84,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t3526,plain,
true = distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0),
inference(step,[status(thm)],[t398,t84]) ).
cnf(t1036,plain,
distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0) = true,
inference(orient,[status(thm)],[t3526]) ).
cnf(t2963,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),true),
inference(cp,[status(thm)],[t2956,t1036]) ).
cnf(t3966,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t2963,t82]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t240,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t16]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t48,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t152,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t234,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(cp,[status(thm)],[t152,t228]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t369,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t3828,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(step,[status(thm)],[t234,t369]) ).
cnf(t3829,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))),
inference(step,[status(thm)],[t3828,t84]) ).
cnf(t2342,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(orient,[status(thm)],[t3829]) ).
cnf(t2343,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),false),
inference(cp,[status(thm)],[t240,t2342]) ).
cnf(t3830,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t2343,t82]) ).
cnf(t2344,plain,
apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = false,
inference(orient,[status(thm)],[t3830]) ).
cnf(t3967,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t3966,t2344]) ).
cnf(t3968,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t3967,t84]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t46,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t150,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(c46,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t3,plain,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t169,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t179,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t150,t169]) ).
cnf(t3481,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t179,t369]) ).
cnf(t3482,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t3481,t84]) ).
cnf(t874,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t3482]) ).
cnf(t875,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t240,t874]) ).
cnf(t3483,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t875,t82]) ).
cnf(t876,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t3483]) ).
cnf(t3969,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t3968,t876]) ).
cnf(t3970,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t3969,t84]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t49,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t151,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t235,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(cp,[status(thm)],[t151,t228]) ).
cnf(t3857,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(step,[status(thm)],[t235,t369]) ).
cnf(t3858,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))),
inference(step,[status(thm)],[t3857,t84]) ).
cnf(t2462,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))) = true,
inference(orient,[status(thm)],[t3858]) ).
cnf(t2463,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),false),
inference(cp,[status(thm)],[t240,t2462]) ).
cnf(t3859,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t2463,t82]) ).
cnf(t2464,plain,
apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = false,
inference(orient,[status(thm)],[t3859]) ).
cnf(t3971,plain,
true = or(false,apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t3970,t2464]) ).
cnf(t3972,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),sk0),
inference(step,[status(thm)],[t3971,t84]) ).
cnf(c47,plain,
convergent_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t4,plain,
convergent_lines(sk0,sk2) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t198,plain,
convergent_lines(sk0,sk2) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t208,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(cp,[status(thm)],[t150,t198]) ).
cnf(t3489,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t208,t369]) ).
cnf(t3490,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t3489,t84]) ).
cnf(t910,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk0)) = true,
inference(orient,[status(thm)],[t3490]) ).
cnf(t911,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk0),false),
inference(cp,[status(thm)],[t240,t910]) ).
cnf(t3491,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk0),
inference(step,[status(thm)],[t911,t82]) ).
cnf(t912,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk0) = false,
inference(orient,[status(thm)],[t3491]) ).
cnf(t3973,plain,
true = false,
inference(step,[status(thm)],[t3972,t912]) ).
cnf(t2998,plain,
false = true,
inference(orient,[status(thm)],[t3973]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f15_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f16_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f20_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f21_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c24,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f30_nnf,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c36,plain,
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(c38,plain,
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f32,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f32_nnf,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c40,plain,
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f33,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
fof(f33_nnf,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c42,plain,
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f34,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f34_nnf,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c44,plain,
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c15,c16,c23,c24,c36,c38,c40,c42,c44,c49]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2998]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n020.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Wed Sep 23 11:28:39 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.89/7.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.89/7.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------