%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO205+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 : 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 01:17:28 PM UTC 2026
% Result : Theorem 3.57s 1.70s
% Output : Proof 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 104 unt; 0 def)
% Number of atoms : 202 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 130 ( 65 ~; 47 |; 9 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 143 ( 2 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(t23,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(t45,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)],[t23]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ( distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))
| ~ convergent_lines(sk0,sk2) )
& ~ distinct_lines(sk1,sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c15,plain,
~ distinct_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t5,plain,
distinct_lines(sk1,sk2) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t104,plain,
distinct_lines(sk1,sk2) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t109,plain,
true = ifeq(apart_point_and_line(X1,sk1),true,or(false,apart_point_and_line(X1,sk2)),true),
inference(cp,[status(thm)],[t45,t104]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t37,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t789,plain,
true = ifeq(apart_point_and_line(X1,sk1),true,apart_point_and_line(X1,sk2),true),
inference(step,[status(thm)],[t109,t37]) ).
cnf(t331,plain,
ifeq(apart_point_and_line(X1,sk1),true,apart_point_and_line(X1,sk2),true) = true,
inference(orient,[status(thm)],[t789]) ).
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(t34,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(t48,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)],[t34]) ).
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]) ).
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(t18,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7]) ).
cnf(t62,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t18]) ).
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(t74,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t75,plain,
true = or(distinct_lines(sk1,sk0),false),
inference(cp,[status(thm)],[t62,t74]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t36,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t719,plain,
true = distinct_lines(sk1,sk0),
inference(step,[status(thm)],[t75,t36]) ).
cnf(t113,plain,
distinct_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t719]) ).
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)],[t48,t113]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t857,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,t35]) ).
cnf(t582,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)],[t857]) ).
cnf(c16,plain,
( distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2))
| ~ convergent_lines(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t27,plain,
ifeq(convergent_lines(sk0,sk2),true,distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t43,plain,
ifeq(convergent_lines(sk0,sk2),true,distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t105,plain,
true = or(false,convergent_lines(sk0,sk2)),
inference(cp,[status(thm)],[t62,t104]) ).
cnf(t721,plain,
true = convergent_lines(sk0,sk2),
inference(step,[status(thm)],[t105,t37]) ).
cnf(t130,plain,
convergent_lines(sk0,sk2) = true,
inference(orient,[status(thm)],[t721]) ).
cnf(t722,plain,
ifeq(true,true,distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)),true) = true,
inference(step,[status(thm)],[t43,t130]) ).
cnf(t723,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(step,[status(thm)],[t722,t35]) ).
cnf(t140,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(rw,[status(thm)],[t723]) ).
cnf(t257,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk0,sk2)) = true,
inference(orient,[status(thm)],[t140]) ).
cnf(t583,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(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),true),
inference(cp,[status(thm)],[t582,t257]) ).
cnf(t858,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(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t583,t35]) ).
cnf(t12,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t73,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t12]) ).
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(t58,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(t64,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t70,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(cp,[status(thm)],[t58,t64]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t94,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t775,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(step,[status(thm)],[t70,t94]) ).
cnf(t776,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk1)),
inference(step,[status(thm)],[t775,t37]) ).
cnf(t291,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk1)) = true,
inference(orient,[status(thm)],[t776]) ).
cnf(t292,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk1),false),
inference(cp,[status(thm)],[t73,t291]) ).
cnf(t777,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(step,[status(thm)],[t292,t35]) ).
cnf(t293,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk1) = false,
inference(orient,[status(thm)],[t777]) ).
cnf(t859,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)))),
inference(step,[status(thm)],[t858,t293]) ).
cnf(t860,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t859,t37]) ).
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(t59,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t69,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t59,t64]) ).
cnf(t772,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t69,t94]) ).
cnf(t773,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t772,t37]) ).
cnf(t280,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t773]) ).
cnf(t281,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t73,t280]) ).
cnf(t774,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t281,t35]) ).
cnf(t282,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t774]) ).
cnf(t861,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t860,t282]) ).
cnf(t862,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),sk1),apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t861,t37]) ).
cnf(t137,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(cp,[status(thm)],[t59,t130]) ).
cnf(t730,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk0))),
inference(step,[status(thm)],[t137,t94]) ).
cnf(t731,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk0)),
inference(step,[status(thm)],[t730,t37]) ).
cnf(t165,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk0)) = true,
inference(orient,[status(thm)],[t731]) ).
cnf(t166,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk0),false),
inference(cp,[status(thm)],[t73,t165]) ).
cnf(t732,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk0),
inference(step,[status(thm)],[t166,t35]) ).
cnf(t167,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk0) = false,
inference(orient,[status(thm)],[t732]) ).
cnf(t863,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk2),sk1),false),
inference(step,[status(thm)],[t862,t167]) ).
cnf(t864,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),sk1),
inference(step,[status(thm)],[t863,t36]) ).
cnf(t597,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk1) = true,
inference(orient,[status(thm)],[t864]) ).
cnf(t598,plain,
true = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk2),true),
inference(cp,[status(thm)],[t331,t597]) ).
cnf(t867,plain,
true = apart_point_and_line(intersection_point(sk0,sk2),sk2),
inference(step,[status(thm)],[t598,t35]) ).
cnf(t138,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk2),sk2))),
inference(cp,[status(thm)],[t58,t130]) ).
cnf(t733,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk2),sk2))),
inference(step,[status(thm)],[t138,t94]) ).
cnf(t734,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk2),sk2)),
inference(step,[status(thm)],[t733,t37]) ).
cnf(t176,plain,
not(apart_point_and_line(intersection_point(sk0,sk2),sk2)) = true,
inference(orient,[status(thm)],[t734]) ).
cnf(t177,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk2),sk2),false),
inference(cp,[status(thm)],[t73,t176]) ).
cnf(t735,plain,
false = apart_point_and_line(intersection_point(sk0,sk2),sk2),
inference(step,[status(thm)],[t177,t35]) ).
cnf(t178,plain,
apart_point_and_line(intersection_point(sk0,sk2),sk2) = false,
inference(orient,[status(thm)],[t735]) ).
cnf(t868,plain,
true = false,
inference(step,[status(thm)],[t867,t178]) ).
cnf(t606,plain,
false = true,
inference(orient,[status(thm)],[t868]) ).
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,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t606]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:23:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.57/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.57/1.70 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------