%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO197+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 : n011.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 01:17:25 PM UTC 2026
% Result : Theorem 0.15s 20.96s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 158 ( 118 unt; 0 def)
% Number of atoms : 242 ( 101 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 152 ( 68 ~; 58 |; 15 &)
% ( 0 <=>; 11 =>; 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 : 188 ( 2 sgn 87 !; 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(t42,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(t97,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)],[t42]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( apart_point_and_line(intersection_point(Z,Y),X)
& ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( apart_point_and_line(intersection_point(sk2,sk1),sk0)
& ~ apart_point_and_line(intersection_point(sk0,sk1),sk2)
& convergent_lines(sk0,sk2)
& convergent_lines(sk2,sk1)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c17,plain,
~ apart_point_and_line(intersection_point(sk0,sk1),sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t12,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk2) = false,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t125,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk2) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t130,plain,
true = ifeq(distinct_points(intersection_point(sk0,sk1),X1),true,ifeq(distinct_lines(sk2,X2),true,or(false,or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(X1,sk2),apart_point_and_line(X1,X2)))),true),true),
inference(cp,[status(thm)],[t97,t125]) ).
cnf(t10,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t44,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t1267,plain,
true = ifeq(distinct_points(intersection_point(sk0,sk1),X1),true,ifeq(distinct_lines(sk2,X2),true,or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(X1,sk2),apart_point_and_line(X1,X2))),true),true),
inference(step,[status(thm)],[t130,t44]) ).
cnf(t914,plain,
ifeq(distinct_points(intersection_point(sk0,sk1),X1),true,ifeq(distinct_lines(sk2,X2),true,or(apart_point_and_line(intersection_point(sk0,sk1),X2),or(apart_point_and_line(X1,sk2),apart_point_and_line(X1,X2))),true),true) = true,
inference(orient,[status(thm)],[t1267]) ).
cnf(t15,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t124,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t15]) ).
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(t29,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(t56,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(c15,plain,
convergent_lines(sk2,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t5,plain,
convergent_lines(sk2,sk1) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t66,plain,
convergent_lines(sk2,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t67,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk2,sk1),sk1))),
inference(cp,[status(thm)],[t56,t66]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t152,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1136,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk2,sk1),sk1))),
inference(step,[status(thm)],[t67,t152]) ).
cnf(t1137,plain,
true = not(apart_point_and_line(intersection_point(sk2,sk1),sk1)),
inference(step,[status(thm)],[t1136,t44]) ).
cnf(t409,plain,
not(apart_point_and_line(intersection_point(sk2,sk1),sk1)) = true,
inference(orient,[status(thm)],[t1137]) ).
cnf(t410,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk2,sk1),sk1),false),
inference(cp,[status(thm)],[t124,t409]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t45,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t1138,plain,
false = apart_point_and_line(intersection_point(sk2,sk1),sk1),
inference(step,[status(thm)],[t410,t45]) ).
cnf(t411,plain,
apart_point_and_line(intersection_point(sk2,sk1),sk1) = false,
inference(orient,[status(thm)],[t1138]) ).
cnf(t943,plain,
true = ifeq(distinct_points(intersection_point(sk0,sk1),intersection_point(sk2,sk1)),true,ifeq(distinct_lines(sk2,sk1),true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),true),true),
inference(cp,[status(thm)],[t914,t411]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/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(t37,plain,
ifeq(distinct_points(X1,X2),true,or(distinct_points(X1,X3),distinct_points(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t94,plain,
ifeq(distinct_points(X1,X2),true,or(distinct_points(X1,X3),distinct_points(X2,X3)),true) = true,
inference(orient,[status(thm)],[t37]) ).
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]) ).
cnf(t7,plain,
distinct_points(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t135,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t137,plain,
true = ifeq(distinct_points(X1,X2),true,or(false,distinct_points(X2,X1)),true),
inference(cp,[status(thm)],[t94,t135]) ).
cnf(t1146,plain,
true = ifeq(distinct_points(X1,X2),true,distinct_points(X2,X1),true),
inference(step,[status(thm)],[t137,t44]) ).
cnf(t435,plain,
ifeq(distinct_points(X1,X2),true,distinct_points(X2,X1),true) = true,
inference(orient,[status(thm)],[t1146]) ).
fof(f11,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi4,axiom,
ifeq(apart_point_and_line(X0,X1),true,or(distinct_points(X0,X2),apart_point_and_line(X2,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(c18,plain,
apart_point_and_line(intersection_point(sk2,sk1),sk0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi10,negated_conjecture,
apart_point_and_line(intersection_point(sk2,sk1),sk0) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t27,plain,
or(distinct_points(intersection_point(sk2,sk1),X1),apart_point_and_line(X1,sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi10]) ).
cnf(t51,plain,
or(distinct_points(intersection_point(sk2,sk1),X1),apart_point_and_line(X1,sk0)) = true,
inference(orient,[status(thm)],[t27]) ).
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(t28,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(t57,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t28]) ).
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(t63,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t65,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t57,t63]) ).
cnf(t1131,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t65,t152]) ).
cnf(t1132,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t1131,t44]) ).
cnf(t378,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t1132]) ).
cnf(t379,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t124,t378]) ).
cnf(t1134,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t379,t45]) ).
cnf(t389,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t1134]) ).
cnf(t390,plain,
true = or(distinct_points(intersection_point(sk2,sk1),intersection_point(sk0,sk1)),false),
inference(cp,[status(thm)],[t51,t389]) ).
cnf(t8,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t43,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t1135,plain,
true = distinct_points(intersection_point(sk2,sk1),intersection_point(sk0,sk1)),
inference(step,[status(thm)],[t390,t43]) ).
cnf(t399,plain,
distinct_points(intersection_point(sk2,sk1),intersection_point(sk0,sk1)) = true,
inference(orient,[status(thm)],[t1135]) ).
cnf(t437,plain,
true = ifeq(true,true,distinct_points(intersection_point(sk0,sk1),intersection_point(sk2,sk1)),true),
inference(cp,[status(thm)],[t435,t399]) ).
cnf(t1148,plain,
true = distinct_points(intersection_point(sk0,sk1),intersection_point(sk2,sk1)),
inference(step,[status(thm)],[t437,t45]) ).
cnf(t454,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk2,sk1)) = true,
inference(orient,[status(thm)],[t1148]) ).
cnf(t1268,plain,
true = ifeq(true,true,ifeq(distinct_lines(sk2,sk1),true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),true),true),
inference(step,[status(thm)],[t943,t454]) ).
cnf(t1269,plain,
true = ifeq(distinct_lines(sk2,sk1),true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),true),
inference(step,[status(thm)],[t1268,t45]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/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(t36,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(t99,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t36]) ).
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(hi8,negated_conjecture,
convergent_lines(sk2,sk1) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t23,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk2,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8]) ).
cnf(t55,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk2,X1)) = true,
inference(orient,[status(thm)],[t23]) ).
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(t109,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t111,plain,
true = or(distinct_lines(sk1,sk2),false),
inference(cp,[status(thm)],[t55,t109]) ).
cnf(t1067,plain,
true = distinct_lines(sk1,sk2),
inference(step,[status(thm)],[t111,t43]) ).
cnf(t164,plain,
distinct_lines(sk1,sk2) = true,
inference(orient,[status(thm)],[t1067]) ).
cnf(t165,plain,
true = ifeq(true,true,or(distinct_lines(sk1,X1),distinct_lines(sk2,X1)),true),
inference(cp,[status(thm)],[t99,t164]) ).
cnf(t1101,plain,
true = or(distinct_lines(sk1,X1),distinct_lines(sk2,X1)),
inference(step,[status(thm)],[t165,t45]) ).
cnf(t301,plain,
or(distinct_lines(sk1,X1),distinct_lines(sk2,X1)) = true,
inference(orient,[status(thm)],[t1101]) ).
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]) ).
cnf(t6,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t144,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t302,plain,
true = or(false,distinct_lines(sk2,sk1)),
inference(cp,[status(thm)],[t301,t144]) ).
cnf(t1102,plain,
true = distinct_lines(sk2,sk1),
inference(step,[status(thm)],[t302,t44]) ).
cnf(t303,plain,
distinct_lines(sk2,sk1) = true,
inference(orient,[status(thm)],[t1102]) ).
cnf(t1270,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),true),
inference(step,[status(thm)],[t1269,t303]) ).
cnf(t1271,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),
inference(step,[status(thm)],[t1270,t45]) ).
cnf(t64,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(cp,[status(thm)],[t56,t63]) ).
cnf(t1129,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(step,[status(thm)],[t64,t152]) ).
cnf(t1130,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk1)),
inference(step,[status(thm)],[t1129,t44]) ).
cnf(t376,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk1)) = true,
inference(orient,[status(thm)],[t1130]) ).
cnf(t377,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk1),false),
inference(cp,[status(thm)],[t124,t376]) ).
cnf(t1133,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(step,[status(thm)],[t377,t45]) ).
cnf(t380,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk1) = false,
inference(orient,[status(thm)],[t1133]) ).
cnf(t1272,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false)),
inference(step,[status(thm)],[t1271,t380]) ).
cnf(t1273,plain,
true = or(apart_point_and_line(intersection_point(sk2,sk1),sk2),false),
inference(step,[status(thm)],[t1272,t44]) ).
cnf(t1274,plain,
true = apart_point_and_line(intersection_point(sk2,sk1),sk2),
inference(step,[status(thm)],[t1273,t43]) ).
cnf(t68,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk2,sk1),sk2))),
inference(cp,[status(thm)],[t57,t66]) ).
cnf(t1139,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk2,sk1),sk2))),
inference(step,[status(thm)],[t68,t152]) ).
cnf(t1140,plain,
true = not(apart_point_and_line(intersection_point(sk2,sk1),sk2)),
inference(step,[status(thm)],[t1139,t44]) ).
cnf(t420,plain,
not(apart_point_and_line(intersection_point(sk2,sk1),sk2)) = true,
inference(orient,[status(thm)],[t1140]) ).
cnf(t421,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk2,sk1),sk2),false),
inference(cp,[status(thm)],[t124,t420]) ).
cnf(t1141,plain,
false = apart_point_and_line(intersection_point(sk2,sk1),sk2),
inference(step,[status(thm)],[t421,t45]) ).
cnf(t422,plain,
apart_point_and_line(intersection_point(sk2,sk1),sk2) = false,
inference(orient,[status(thm)],[t1141]) ).
cnf(t1275,plain,
true = false,
inference(step,[status(thm)],[t1274,t422]) ).
cnf(t952,plain,
false = true,
inference(orient,[status(thm)],[t1275]) ).
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]) ).
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,c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t952]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO197+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/20.23 % CPULimit : 300
% 0.03/20.23 % WCLimit : 300
% 0.03/20.23 % DateTime : Wed Sep 23 11:25:26 UTC 2026
% 0.03/20.23 % CPUTime :
% 0.03/20.23 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/20.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/20.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------