%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO181+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 01:17:18 PM UTC 2026
% Result : Theorem 7.77s 1.54s
% Output : Proof 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 18
% Syntax : Number of formulae : 152 ( 112 unt; 0 def)
% Number of atoms : 228 ( 96 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 140 ( 64 ~; 58 |; 5 &)
% ( 0 <=>; 13 =>; 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 : 186 ( 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(t35,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(t44,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)],[t35]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Y,line_connecting(X,Z)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Y,line_connecting(X,Z)) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(Y,line_connecting(X,Z))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ~ apart_point_and_line(sk1,line_connecting(sk0,sk2))
& apart_point_and_line(sk2,line_connecting(sk0,sk1))
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
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(t73,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t81,plain,
true = ifeq(true,true,ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true),true),
inference(cp,[status(thm)],[t44,t73]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t551,plain,
true = ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true),
inference(step,[status(thm)],[t81,t36]) ).
cnf(t402,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(sk0,X1),or(apart_point_and_line(sk0,X2),or(apart_point_and_line(sk1,X1),apart_point_and_line(sk1,X2)))),true) = true,
inference(orient,[status(thm)],[t551]) ).
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(t29,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(t52,plain,
ifeq(distinct_lines(X1,X2),true,or(distinct_lines(X1,X3),distinct_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t29]) ).
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(t3,plain,
distinct_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t115,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t117,plain,
true = ifeq(distinct_lines(X1,X2),true,or(false,distinct_lines(X2,X1)),true),
inference(cp,[status(thm)],[t52,t115]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t38,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t543,plain,
true = ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t117,t38]) ).
cnf(t358,plain,
ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t543]) ).
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/sandbox/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(hi5,axiom,
ifeq(apart_point_and_line(X0,X1),true,or(distinct_lines(X1,X2),apart_point_and_line(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(c15,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi8,negated_conjecture,
apart_point_and_line(sk2,line_connecting(sk0,sk1)) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t19,plain,
or(distinct_lines(line_connecting(sk0,sk1),X1),apart_point_and_line(sk2,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi8]) ).
cnf(t72,plain,
or(distinct_lines(line_connecting(sk0,sk1),X1),apart_point_and_line(sk2,X1)) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t13,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t83,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t13]) ).
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(t24,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(t68,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t24]) ).
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(t30,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(t45,plain,
ifeq(distinct_points(X1,X2),true,or(distinct_points(X1,X3),distinct_points(X2,X3)),true) = true,
inference(orient,[status(thm)],[t30]) ).
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(t20,plain,
or(distinct_points(sk2,X1),apart_point_and_line(X1,line_connecting(sk0,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi8]) ).
cnf(t67,plain,
or(distinct_points(sk2,X1),apart_point_and_line(X1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t20]) ).
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(t23,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(t69,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(t78,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t69,t73]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t104,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t492,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t78,t104]) ).
cnf(t493,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t492,t38]) ).
cnf(t168,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t493]) ).
cnf(t169,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t83,t168]) ).
cnf(t494,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t169,t36]) ).
cnf(t170,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t494]) ).
cnf(t173,plain,
true = or(distinct_points(sk2,sk0),false),
inference(cp,[status(thm)],[t67,t170]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t37,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t495,plain,
true = distinct_points(sk2,sk0),
inference(step,[status(thm)],[t173,t37]) ).
cnf(t180,plain,
distinct_points(sk2,sk0) = true,
inference(orient,[status(thm)],[t495]) ).
cnf(t182,plain,
true = ifeq(true,true,or(distinct_points(sk2,X1),distinct_points(sk0,X1)),true),
inference(cp,[status(thm)],[t45,t180]) ).
cnf(t503,plain,
true = or(distinct_points(sk2,X1),distinct_points(sk0,X1)),
inference(step,[status(thm)],[t182,t36]) ).
cnf(t214,plain,
or(distinct_points(sk2,X1),distinct_points(sk0,X1)) = true,
inference(orient,[status(thm)],[t503]) ).
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(t4,plain,
distinct_points(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t94,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t215,plain,
true = or(false,distinct_points(sk0,sk2)),
inference(cp,[status(thm)],[t214,t94]) ).
cnf(t504,plain,
true = distinct_points(sk0,sk2),
inference(step,[status(thm)],[t215,t38]) ).
cnf(t216,plain,
distinct_points(sk0,sk2) = true,
inference(orient,[status(thm)],[t504]) ).
cnf(t220,plain,
true = or(not(true),not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t68,t216]) ).
cnf(t508,plain,
true = or(false,not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t220,t104]) ).
cnf(t509,plain,
true = not(apart_point_and_line(sk2,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t508,t38]) ).
cnf(t234,plain,
not(apart_point_and_line(sk2,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t509]) ).
cnf(t235,plain,
false = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t83,t234]) ).
cnf(t510,plain,
false = apart_point_and_line(sk2,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t235,t36]) ).
cnf(t236,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t510]) ).
cnf(t239,plain,
true = or(distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t72,t236]) ).
cnf(t515,plain,
true = distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t239,t37]) ).
cnf(t255,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t515]) ).
cnf(t362,plain,
true = ifeq(true,true,distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),true),
inference(cp,[status(thm)],[t358,t255]) ).
cnf(t547,plain,
true = distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t362,t36]) ).
cnf(t391,plain,
distinct_lines(line_connecting(sk0,sk2),line_connecting(sk0,sk1)) = true,
inference(orient,[status(thm)],[t547]) ).
cnf(t404,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),true),
inference(cp,[status(thm)],[t402,t391]) ).
cnf(t552,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t404,t36]) ).
cnf(t219,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t69,t216]) ).
cnf(t505,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t219,t104]) ).
cnf(t506,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t505,t38]) ).
cnf(t223,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t506]) ).
cnf(t224,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t83,t223]) ).
cnf(t507,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t224,t36]) ).
cnf(t225,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t507]) ).
cnf(t553,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t552,t225]) ).
cnf(t554,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t553,t38]) ).
cnf(t555,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t554,t170]) ).
cnf(t556,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk2)),apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t555,t38]) ).
cnf(c16,plain,
~ apart_point_and_line(sk1,line_connecting(sk0,sk2)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk2)) = false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t84,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t557,plain,
true = or(false,apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t556,t84]) ).
cnf(t558,plain,
true = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t557,t38]) ).
cnf(t79,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t68,t73]) ).
cnf(t516,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t79,t104]) ).
cnf(t517,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t516,t38]) ).
cnf(t261,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t517]) ).
cnf(t262,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t83,t261]) ).
cnf(t518,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t262,t36]) ).
cnf(t263,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t518]) ).
cnf(t559,plain,
true = false,
inference(step,[status(thm)],[t558,t263]) ).
cnf(t430,plain,
false = true,
inference(orient,[status(thm)],[t559]) ).
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]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t430]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:18:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.77/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------