%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:17:21 PM UTC 2026
% Result : Theorem 20.88s 3.16s
% Output : Proof 20.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of formulae : 204 ( 136 unt; 0 def)
% Number of atoms : 336 ( 105 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 250 ( 118 ~; 90 |; 25 &)
% ( 5 <=>; 12 =>; 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 : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 346 ( 31 sgn 155 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/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(t37,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)],[t37]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/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(t15,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t241,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t15]) ).
cnf(t244,plain,
true = ifeq(distinct_lines(parallel_through_point(X1,X2),X1),true,false,true),
inference(cp,[status(thm)],[t111,t241]) ).
cnf(t928,plain,
ifeq(distinct_lines(parallel_through_point(X1,X2),X1),true,false,true) = true,
inference(orient,[status(thm)],[t244]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/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(t54,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)],[t54]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/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(t4,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t347,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t352,plain,
true = ifeq(distinct_lines(X1,X2),true,or(false,distinct_lines(X2,X1)),true),
inference(cp,[status(thm)],[t110,t347]) ).
cnf(t11,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t82,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t4161,plain,
true = ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t352,t82]) ).
cnf(t969,plain,
ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t4161]) ).
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/sandbox2/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(t49,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)],[t49]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/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(t14,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t300,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t304,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,t300]) ).
cnf(t9,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t81,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t4262,plain,
true = ifeq(apart_point_and_line(X1,X2),true,distinct_lines(X2,parallel_through_point(X3,X1)),true),
inference(step,[status(thm)],[t304,t81]) ).
cnf(t1418,plain,
ifeq(apart_point_and_line(X1,X2),true,distinct_lines(X2,parallel_through_point(X3,X1)),true) = true,
inference(orient,[status(thm)],[t4262]) ).
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/sandbox2/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,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,U,V] :
( ~ equal_points(X,intersection_point(U,V))
& incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_points(sk0,intersection_point(sk2,sk3))
& incident_point_and_line(sk0,sk3)
& incident_point_and_line(sk0,sk2)
& convergent_lines(sk2,sk3)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f35_nnf]) ).
cnf(c46,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t6,plain,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t189,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t200,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,t189]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t80,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t4431,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)],[t200,t80]) ).
cnf(t2185,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)],[t4431]) ).
cnf(t19,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t207,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t19]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/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(t48,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)],[t48]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi0,axiom,
ifeq(distinct_points(X0,X1),true,or(distinct_points(X0,X2),distinct_points(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi30,negated_conjecture,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t27,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi30]) ).
cnf(t150,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(orient,[status(thm)],[t27]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/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]) ).
cnf(t5,plain,
distinct_points(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t334,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t336,plain,
true = or(false,distinct_points(sk1,sk0)),
inference(cp,[status(thm)],[t150,t334]) ).
cnf(t4006,plain,
true = distinct_points(sk1,sk0),
inference(step,[status(thm)],[t336,t82]) ).
cnf(t433,plain,
distinct_points(sk1,sk0) = true,
inference(orient,[status(thm)],[t4006]) ).
cnf(t441,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t143,t433]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t332,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t4044,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t441,t332]) ).
cnf(t4045,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t4044,t82]) ).
cnf(t633,plain,
not(apart_point_and_line(sk0,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t4045]) ).
cnf(t634,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t207,t633]) ).
cnf(t4046,plain,
false = apart_point_and_line(sk0,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t634,t80]) ).
cnf(t635,plain,
apart_point_and_line(sk0,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t4046]) ).
cnf(t2199,plain,
true = ifeq(distinct_lines(line_connecting(sk1,sk0),X1),true,or(false,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,X1)))),true),
inference(cp,[status(thm)],[t2185,t635]) ).
cnf(t4594,plain,
true = ifeq(distinct_lines(line_connecting(sk1,sk0),X1),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,X1))),true),
inference(step,[status(thm)],[t2199,t82]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/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(t47,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)],[t47]) ).
cnf(t440,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t144,t433]) ).
cnf(t4040,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t440,t332]) ).
cnf(t4041,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t4040,t82]) ).
cnf(t615,plain,
not(apart_point_and_line(sk1,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t4041]) ).
cnf(t616,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t207,t615]) ).
cnf(t4042,plain,
false = apart_point_and_line(sk1,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t616,t80]) ).
cnf(t617,plain,
apart_point_and_line(sk1,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t4042]) ).
cnf(t4595,plain,
true = ifeq(distinct_lines(line_connecting(sk1,sk0),X1),true,or(apart_point_and_line(sk0,X1),or(false,apart_point_and_line(sk1,X1))),true),
inference(step,[status(thm)],[t4594,t617]) ).
cnf(t4596,plain,
true = ifeq(distinct_lines(line_connecting(sk1,sk0),X1),true,or(apart_point_and_line(sk0,X1),apart_point_and_line(sk1,X1)),true),
inference(step,[status(thm)],[t4595,t82]) ).
cnf(t2945,plain,
ifeq(distinct_lines(line_connecting(sk1,sk0),X1),true,or(apart_point_and_line(sk0,X1),apart_point_and_line(sk1,X1)),true) = true,
inference(orient,[status(thm)],[t4596]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/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(t52,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t95,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(orient,[status(thm)],[t52]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/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(t208,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t218,plain,
true = ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X1),false),true),
inference(cp,[status(thm)],[t95,t208]) ).
cnf(t4139,plain,
true = ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t218,t81]) ).
cnf(t903,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t4139]) ).
fof(f18,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f18_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t23,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t132,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/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]) ).
cnf(t18,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t273,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t18]) ).
cnf(t277,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t132,t273]) ).
cnf(t4025,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t277,t81]) ).
cnf(t532,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t4025]) ).
cnf(t905,plain,
true = ifeq(true,true,distinct_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t903,t532]) ).
cnf(t4141,plain,
true = distinct_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t905,t80]) ).
cnf(t914,plain,
distinct_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t4141]) ).
cnf(t2946,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,orthogonal_through_point(line_connecting(sk1,sk0),X1)),apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),X1))),true),
inference(cp,[status(thm)],[t2945,t914]) ).
cnf(t4632,plain,
true = or(apart_point_and_line(sk0,orthogonal_through_point(line_connecting(sk1,sk0),X1)),apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),X1))),
inference(step,[status(thm)],[t2946,t80]) ).
cnf(t3094,plain,
or(apart_point_and_line(sk0,orthogonal_through_point(line_connecting(sk1,sk0),X1)),apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),X1))) = true,
inference(orient,[status(thm)],[t4632]) ).
fof(f21,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/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]) ).
cnf(t13,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t316,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t3095,plain,
true = or(false,apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),sk0))),
inference(cp,[status(thm)],[t3094,t316]) ).
cnf(t4633,plain,
true = apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),sk0)),
inference(step,[status(thm)],[t3095,t82]) ).
cnf(t3097,plain,
apart_point_and_line(sk1,orthogonal_through_point(line_connecting(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t4633]) ).
cnf(t3100,plain,
true = ifeq(true,true,distinct_lines(orthogonal_through_point(line_connecting(sk1,sk0),sk0),parallel_through_point(X1,sk1)),true),
inference(cp,[status(thm)],[t1418,t3097]) ).
cnf(t4676,plain,
true = distinct_lines(orthogonal_through_point(line_connecting(sk1,sk0),sk0),parallel_through_point(X1,sk1)),
inference(step,[status(thm)],[t3100,t80]) ).
cnf(t3365,plain,
distinct_lines(orthogonal_through_point(line_connecting(sk1,sk0),sk0),parallel_through_point(X1,sk1)) = true,
inference(orient,[status(thm)],[t4676]) ).
cnf(t3366,plain,
true = ifeq(true,true,distinct_lines(parallel_through_point(X1,sk1),orthogonal_through_point(line_connecting(sk1,sk0),sk0)),true),
inference(cp,[status(thm)],[t969,t3365]) ).
cnf(t4688,plain,
true = distinct_lines(parallel_through_point(X1,sk1),orthogonal_through_point(line_connecting(sk1,sk0),sk0)),
inference(step,[status(thm)],[t3366,t80]) ).
cnf(t3523,plain,
distinct_lines(parallel_through_point(X1,sk1),orthogonal_through_point(line_connecting(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t4688]) ).
cnf(t3525,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t928,t3523]) ).
cnf(t4689,plain,
true = false,
inference(step,[status(thm)],[t3525,t80]) ).
cnf(t3533,plain,
false = true,
inference(orient,[status(thm)],[t4689]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(c50,plain,
~ equal_points(sk0,intersection_point(sk2,sk3)),
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,c50]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3533]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Wed Sep 23 11:16:29 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.88/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.88/3.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------