%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO202+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 : n006.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 01:17:27 PM UTC 2026
% Result : Theorem 36.32s 5.08s
% Output : Proof 36.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 27
% Syntax : Number of formulae : 186 ( 126 unt; 0 def)
% Number of atoms : 302 ( 93 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 231 ( 115 ~; 79 |; 21 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 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 : 277 ( 21 sgn 138 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f14_nnf,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t34,plain,
ifeq(distinct_lines(X1,X2),true,convergent_lines(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t111,plain,
ifeq(distinct_lines(X1,X2),true,convergent_lines(X1,X2),true) = true,
inference(orient,[status(thm)],[t34]) ).
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]) ).
cnf(t13,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t249,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t252,plain,
true = ifeq(distinct_lines(parallel_through_point(X1,X2),X1),true,false,true),
inference(cp,[status(thm)],[t111,t249]) ).
cnf(t830,plain,
ifeq(distinct_lines(parallel_through_point(X1,X2),X1),true,false,true) = true,
inference(orient,[status(thm)],[t252]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t53,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t110,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t53]) ).
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]) ).
cnf(t3,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t356,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t361,plain,
true = ifeq(distinct_lines(X1,X2),true,or(false,distinct_lines(X2,X1)),true),
inference(cp,[status(thm)],[t110,t356]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t82,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t4360,plain,
true = ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t361,t82]) ).
cnf(t869,plain,
ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t4360]) ).
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t48,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_lines(X2,X3),apart_point_and_line(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t100,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_lines(X2,X3),apart_point_and_line(X1,X3)),true) = true,
inference(orient,[status(thm)],[t48]) ).
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]) ).
cnf(t12,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t308,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t312,plain,
true = ifeq(apart_point_and_line(X1,X2),true,or(distinct_lines(X2,parallel_through_point(X3,X1)),false),true),
inference(cp,[status(thm)],[t100,t308]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t81,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t4455,plain,
true = ifeq(apart_point_and_line(X1,X2),true,distinct_lines(X2,parallel_through_point(X3,X1)),true),
inference(step,[status(thm)],[t312,t81]) ).
cnf(t1273,plain,
ifeq(apart_point_and_line(X1,X2),true,distinct_lines(X2,parallel_through_point(X3,X1)),true) = true,
inference(orient,[status(thm)],[t4455]) ).
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(t79,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(t105,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)],[t79]) ).
fof(f35,conjecture,
! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,Z] :
( ~ equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0)
& convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
& distinct_points(sk0,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c46,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t5,plain,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t191,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t202,plain,
true = ifeq(true,true,ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true),true),
inference(cp,[status(thm)],[t105,t191]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t80,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t4820,plain,
true = ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true),
inference(step,[status(thm)],[t202,t80]) ).
cnf(t3378,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true) = true,
inference(orient,[status(thm)],[t4820]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi6,axiom,
ifeq(convergent_lines(X0,X1),true,or(distinct_lines(X1,X2),convergent_lines(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c48,plain,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi32,negated_conjecture,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t42,plain,
or(distinct_lines(line_connecting(sk0,sk2),X1),convergent_lines(line_connecting(sk0,sk1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi32]) ).
cnf(t154,plain,
or(distinct_lines(line_connecting(sk0,sk2),X1),convergent_lines(line_connecting(sk0,sk1),X1)) = true,
inference(orient,[status(thm)],[t42]) ).
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]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t216,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t222,plain,
true = or(distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t154,t216]) ).
cnf(t4288,plain,
true = distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t222,t81]) ).
cnf(t590,plain,
distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)) = true,
inference(orient,[status(thm)],[t4288]) ).
cnf(t3392,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),true),
inference(cp,[status(thm)],[t3378,t590]) ).
cnf(t4821,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t3392,t80]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t215,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(t45,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(t144,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(c47,plain,
distinct_points(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t6,plain,
distinct_points(sk0,sk2) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t203,plain,
distinct_points(sk0,sk2) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t209,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t144,t203]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t340,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t4320,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t209,t340]) ).
cnf(t4321,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t4320,t82]) ).
cnf(t702,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t4321]) ).
cnf(t703,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t215,t702]) ).
cnf(t4322,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t703,t80]) ).
cnf(t704,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t4322]) ).
cnf(t4822,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t4821,t704]) ).
cnf(t4823,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t4822,t82]) ).
cnf(t197,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t144,t191]) ).
cnf(t4312,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t197,t340]) ).
cnf(t4313,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t4312,t82]) ).
cnf(t666,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t4313]) ).
cnf(t667,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t215,t666]) ).
cnf(t4314,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t667,t80]) ).
cnf(t668,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t4314]) ).
cnf(t4824,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t4823,t668]) ).
cnf(t4825,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t4824,t82]) ).
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(t46,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(t143,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t198,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t143,t191]) ).
cnf(t4316,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t198,t340]) ).
cnf(t4317,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t4316,t82]) ).
cnf(t684,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t4317]) ).
cnf(t685,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t215,t684]) ).
cnf(t4318,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t685,t80]) ).
cnf(t686,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t4318]) ).
cnf(t4826,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),false),
inference(step,[status(thm)],[t4825,t686]) ).
cnf(t4827,plain,
true = apart_point_and_line(sk1,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t4826,t81]) ).
cnf(t3418,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t4827]) ).
cnf(t3422,plain,
true = ifeq(true,true,distinct_lines(line_connecting(sk0,sk2),parallel_through_point(X1,sk1)),true),
inference(cp,[status(thm)],[t1273,t3418]) ).
cnf(t4857,plain,
true = distinct_lines(line_connecting(sk0,sk2),parallel_through_point(X1,sk1)),
inference(step,[status(thm)],[t3422,t80]) ).
cnf(t3647,plain,
distinct_lines(line_connecting(sk0,sk2),parallel_through_point(X1,sk1)) = true,
inference(orient,[status(thm)],[t4857]) ).
cnf(t3648,plain,
true = ifeq(true,true,distinct_lines(parallel_through_point(X1,sk1),line_connecting(sk0,sk2)),true),
inference(cp,[status(thm)],[t869,t3647]) ).
cnf(t4864,plain,
true = distinct_lines(parallel_through_point(X1,sk1),line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t3648,t80]) ).
cnf(t3763,plain,
distinct_lines(parallel_through_point(X1,sk1),line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t4864]) ).
cnf(t3765,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t830,t3763]) ).
cnf(t4865,plain,
true = false,
inference(step,[status(thm)],[t3765,t80]) ).
cnf(t3779,plain,
false = true,
inference(orient,[status(thm)],[t4865]) ).
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(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]) ).
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(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]) ).
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(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(c49,plain,
~ equal_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0),
inference(cnf_transformation,[status(esa)],[f35_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,t3779]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:27:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.32/5.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.32/5.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------