%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 9.27s 6.77s
% Output : Proof 9.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 119 ( 91 unt; 0 def)
% Number of atoms : 175 ( 74 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 110 ( 54 ~; 37 |; 11 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 124 ( 2 sgn 60 !; 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/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(t38,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(t71,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)],[t38]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( distinct_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)],[f14_neg]) ).
fof(f14_sk,plain,
( distinct_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])],[f14_nnf]) ).
cnf(c16,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t13,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t93,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t101,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)],[t71,t93]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t783,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)],[t101,t42]) ).
cnf(t534,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)],[t783]) ).
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(hi1,axiom,
ifeq(distinct_lines(X0,X1),true,or(distinct_lines(X0,X2),distinct_lines(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c17,plain,
distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi10,negated_conjecture,
distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),sk0) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t33,plain,
or(distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),X1),distinct_lines(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi10]) ).
cnf(t51,plain,
or(distinct_lines(line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),X1),distinct_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t33]) ).
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(t5,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t133,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t139,plain,
true = or(false,distinct_lines(sk0,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))),
inference(cp,[status(thm)],[t51,t133]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t41,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t721,plain,
true = distinct_lines(sk0,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t139,t41]) ).
cnf(t335,plain,
distinct_lines(sk0,line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = true,
inference(orient,[status(thm)],[t721]) ).
cnf(t536,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),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,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))))),true),
inference(cp,[status(thm)],[t534,t335]) ).
cnf(t784,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),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,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))))),
inference(step,[status(thm)],[t536,t42]) ).
cnf(t12,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t109,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t12]) ).
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]) ).
cnf(t23,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(t53,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(c14,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t3,plain,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t77,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t83,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t53,t77]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t142,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t693,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t83,t142]) ).
cnf(t694,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t693,t41]) ).
cnf(t275,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t694]) ).
cnf(t276,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t109,t275]) ).
cnf(t695,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t276,t42]) ).
cnf(t277,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t695]) ).
cnf(t785,plain,
true = or(false,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,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))))),
inference(step,[status(thm)],[t784,t277]) ).
cnf(t786,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,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(step,[status(thm)],[t785,t41]) ).
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(t25,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(t55,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t99,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)],[t55,t93]) ).
cnf(t757,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)],[t99,t142]) ).
cnf(t758,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)],[t757,t41]) ).
cnf(t448,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)],[t758]) ).
cnf(t449,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)],[t109,t448]) ).
cnf(t759,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t449,t42]) ).
cnf(t450,plain,
apart_point_and_line(intersection_point(sk0,sk1),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = false,
inference(orient,[status(thm)],[t759]) ).
cnf(t787,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))))),
inference(step,[status(thm)],[t786,t450]) ).
cnf(t788,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),sk0),apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))),
inference(step,[status(thm)],[t787,t41]) ).
cnf(c15,plain,
convergent_lines(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t4,plain,
convergent_lines(sk0,sk2) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t85,plain,
convergent_lines(sk0,sk2) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t91,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(cp,[status(thm)],[t53,t85]) ).
cnf(t703,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t91,t142]) ).
cnf(t704,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t703,t41]) ).
cnf(t300,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk0)) = true,
inference(orient,[status(thm)],[t704]) ).
cnf(t301,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk0),false),
inference(cp,[status(thm)],[t109,t300]) ).
cnf(t705,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk0),
inference(step,[status(thm)],[t301,t42]) ).
cnf(t302,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk0) = false,
inference(orient,[status(thm)],[t705]) ).
cnf(t789,plain,
true = or(false,apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2)))),
inference(step,[status(thm)],[t788,t302]) ).
cnf(t790,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t789,t41]) ).
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(t26,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(t54,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t100,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)],[t54,t93]) ).
cnf(t761,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)],[t100,t142]) ).
cnf(t762,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)],[t761,t41]) ).
cnf(t463,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)],[t762]) ).
cnf(t464,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)],[t109,t463]) ).
cnf(t763,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))),
inference(step,[status(thm)],[t464,t42]) ).
cnf(t465,plain,
apart_point_and_line(intersection_point(sk0,sk2),line_connecting(intersection_point(sk0,sk1),intersection_point(sk0,sk2))) = false,
inference(orient,[status(thm)],[t763]) ).
cnf(t791,plain,
true = false,
inference(step,[status(thm)],[t790,t465]) ).
cnf(t554,plain,
false = true,
inference(orient,[status(thm)],[t791]) ).
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]) ).
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]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t554]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 11:30:29 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.27/6.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.27/6.77 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------