%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:17:27 PM UTC 2026
% Result : Theorem 19.52s 2.98s
% Output : Proof 19.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 123 ( 95 unt; 0 def)
% Number of atoms : 179 ( 78 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 : 126 ( 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/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t37,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(t58,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)],[t37]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( distinct_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0)
& convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
& distinct_points(sk0,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c17,plain,
distinct_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t19,plain,
distinct_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t89,plain,
distinct_points(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),sk0) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t97,plain,
true = ifeq(true,true,ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X1),or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X2),or(apart_point_and_line(sk0,X1),apart_point_and_line(sk0,X2)))),true),true),
inference(cp,[status(thm)],[t58,t89]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t1925,plain,
true = ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X1),or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X2),or(apart_point_and_line(sk0,X1),apart_point_and_line(sk0,X2)))),true),
inference(step,[status(thm)],[t97,t40]) ).
cnf(t1395,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X1),or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),X2),or(apart_point_and_line(sk0,X1),apart_point_and_line(sk0,X2)))),true) = true,
inference(orient,[status(thm)],[t1925]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi6,axiom,
ifeq(convergent_lines(X0,X1),true,or(distinct_lines(X1,X2),convergent_lines(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c16,plain,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi9,negated_conjecture,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t21,plain,
or(distinct_lines(line_connecting(sk0,sk2),X1),convergent_lines(line_connecting(sk0,sk1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi9]) ).
cnf(t51,plain,
or(distinct_lines(line_connecting(sk0,sk2),X1),convergent_lines(line_connecting(sk0,sk1),X1)) = true,
inference(orient,[status(thm)],[t21]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t120,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t127,plain,
true = or(distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t51,t120]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t38,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1588,plain,
true = distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t127,t38]) ).
cnf(t224,plain,
distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)) = true,
inference(orient,[status(thm)],[t1588]) ).
cnf(t1437,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)),or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1))))),true),
inference(cp,[status(thm)],[t1395,t224]) ).
cnf(t1926,plain,
true = or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)),or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t1437,t40]) ).
cnf(t12,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t107,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/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t23,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(t49,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t13,plain,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t98,plain,
convergent_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t105,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t49,t98]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t131,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1891,plain,
true = or(false,not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t105,t131]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t39,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1892,plain,
true = not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t1891,t39]) ).
cnf(t1227,plain,
not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t1892]) ).
cnf(t1228,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t107,t1227]) ).
cnf(t1893,plain,
false = apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t1228,t40]) ).
cnf(t1229,plain,
apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t1893]) ).
cnf(t1927,plain,
true = or(false,or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t1926,t1229]) ).
cnf(t1928,plain,
true = or(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t1927,t39]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t22,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(t50,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t104,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t50,t98]) ).
cnf(t1869,plain,
true = or(false,not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t104,t131]) ).
cnf(t1870,plain,
true = not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1869,t39]) ).
cnf(t1094,plain,
not(apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1870]) ).
cnf(t1095,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t107,t1094]) ).
cnf(t1871,plain,
false = apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t1095,t40]) ).
cnf(t1096,plain,
apart_point_and_line(intersection_point(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1871]) ).
cnf(t1929,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t1928,t1096]) ).
cnf(t1930,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1929,t39]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t24,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(t48,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(c15,plain,
distinct_points(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t6,plain,
distinct_points(sk0,sk2) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t80,plain,
distinct_points(sk0,sk2) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t86,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t48,t80]) ).
cnf(t1607,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t86,t131]) ).
cnf(t1608,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t1607,t39]) ).
cnf(t265,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t1608]) ).
cnf(t266,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t107,t265]) ).
cnf(t1609,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t266,t40]) ).
cnf(t267,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t1609]) ).
cnf(t1931,plain,
true = or(false,apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1930,t267]) ).
cnf(t1932,plain,
true = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t1931,t39]) ).
cnf(c14,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t5,plain,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t71,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t77,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t48,t71]) ).
cnf(t1599,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t77,t131]) ).
cnf(t1600,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1599,t39]) ).
cnf(t241,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1600]) ).
cnf(t242,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t107,t241]) ).
cnf(t1601,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t242,t40]) ).
cnf(t243,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1601]) ).
cnf(t1933,plain,
true = false,
inference(step,[status(thm)],[t1932,t243]) ).
cnf(t1461,plain,
false = true,
inference(orient,[status(thm)],[t1933]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(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,t1461]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.37 % Computer : n006.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Sep 23 11:26:56 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.52/2.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.52/2.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------