%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO201+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 8.42s 12.03s
% Output : Proof 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 125 ( 93 unt; 0 def)
% Number of atoms : 181 ( 78 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 113 ( 57 ~; 44 |; 3 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 136 ( 2 sgn 67 !; 2 ?)
% 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(t33,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(t46,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)],[t33]) ).
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(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]) ).
fof(f14,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y] :
( distinct_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0))
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f14_nnf]) ).
cnf(c14,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi7,negated_conjecture,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t17,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7]) ).
cnf(t61,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t17]) ).
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(t82,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t83,plain,
true = or(distinct_lines(sk1,sk0),false),
inference(cp,[status(thm)],[t61,t82]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t35,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t416,plain,
true = distinct_lines(sk1,sk0),
inference(step,[status(thm)],[t83,t35]) ).
cnf(t113,plain,
distinct_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t416]) ).
cnf(t119,plain,
true = ifeq(distinct_points(X1,X2),true,ifeq(true,true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),true),
inference(cp,[status(thm)],[t46,t113]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t494,plain,
true = ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),
inference(step,[status(thm)],[t119,t34]) ).
cnf(t337,plain,
ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true) = true,
inference(orient,[status(thm)],[t494]) ).
cnf(c15,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t12,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t71,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t339,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),true),
inference(cp,[status(thm)],[t337,t71]) ).
cnf(t495,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),
inference(step,[status(thm)],[t339,t34]) ).
cnf(t11,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t81,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t11]) ).
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(t20,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t57,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t3,plain,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t63,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t69,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(cp,[status(thm)],[t57,t63]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t103,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t444,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(step,[status(thm)],[t69,t103]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t36,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t445,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk1)),
inference(step,[status(thm)],[t444,t36]) ).
cnf(t199,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk1)) = true,
inference(orient,[status(thm)],[t445]) ).
cnf(t200,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk1),false),
inference(cp,[status(thm)],[t81,t199]) ).
cnf(t446,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(step,[status(thm)],[t200,t34]) ).
cnf(t201,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk1) = false,
inference(orient,[status(thm)],[t446]) ).
cnf(t496,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),
inference(step,[status(thm)],[t495,t201]) ).
cnf(t497,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t496,t36]) ).
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(t19,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(t58,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t68,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t58,t63]) ).
cnf(t441,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t68,t103]) ).
cnf(t442,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t441,t36]) ).
cnf(t188,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t442]) ).
cnf(t189,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t81,t188]) ).
cnf(t443,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t189,t34]) ).
cnf(t190,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t443]) ).
cnf(t498,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t497,t190]) ).
cnf(t499,plain,
true = or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t498,t36]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi2,axiom,
ifeq(convergent_lines(X0,X1),true,or(convergent_lines(X0,X2),convergent_lines(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t16,plain,
or(convergent_lines(sk0,X1),convergent_lines(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(t53,plain,
or(convergent_lines(sk0,X1),convergent_lines(sk1,X1)) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t84,plain,
true = or(false,convergent_lines(sk1,sk0)),
inference(cp,[status(thm)],[t53,t82]) ).
cnf(t417,plain,
true = convergent_lines(sk1,sk0),
inference(step,[status(thm)],[t84,t36]) ).
cnf(t120,plain,
convergent_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t417]) ).
cnf(t127,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk1,sk0),sk1))),
inference(cp,[status(thm)],[t58,t120]) ).
cnf(t418,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk1,sk0),sk1))),
inference(step,[status(thm)],[t127,t103]) ).
cnf(t419,plain,
true = not(apart_point_and_line(intersection_point(sk1,sk0),sk1)),
inference(step,[status(thm)],[t418,t36]) ).
cnf(t132,plain,
not(apart_point_and_line(intersection_point(sk1,sk0),sk1)) = true,
inference(orient,[status(thm)],[t419]) ).
cnf(t133,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk1,sk0),sk1),false),
inference(cp,[status(thm)],[t81,t132]) ).
cnf(t420,plain,
false = apart_point_and_line(intersection_point(sk1,sk0),sk1),
inference(step,[status(thm)],[t133,t34]) ).
cnf(t134,plain,
apart_point_and_line(intersection_point(sk1,sk0),sk1) = false,
inference(orient,[status(thm)],[t420]) ).
cnf(t500,plain,
true = or(false,apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t499,t134]) ).
cnf(t501,plain,
true = apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(step,[status(thm)],[t500,t36]) ).
cnf(t128,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(cp,[status(thm)],[t57,t120]) ).
cnf(t421,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t128,t103]) ).
cnf(t422,plain,
true = not(apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t421,t36]) ).
cnf(t143,plain,
not(apart_point_and_line(intersection_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t422]) ).
cnf(t144,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk1,sk0),sk0),false),
inference(cp,[status(thm)],[t81,t143]) ).
cnf(t423,plain,
false = apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(step,[status(thm)],[t144,t34]) ).
cnf(t145,plain,
apart_point_and_line(intersection_point(sk1,sk0),sk0) = false,
inference(orient,[status(thm)],[t423]) ).
cnf(t502,plain,
true = false,
inference(step,[status(thm)],[t501,t145]) ).
cnf(t349,plain,
false = true,
inference(orient,[status(thm)],[t502]) ).
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(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]) ).
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]) ).
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(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,t349]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n026.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Wed Sep 23 11:29:49 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.42/12.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/12.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------