%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 01:17:26 PM UTC 2026
% Result : Theorem 12.60s 7.65s
% Output : Proof 12.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 155 ( 106 unt; 0 def)
% Number of atoms : 244 ( 75 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 195 ( 106 ~; 63 |; 13 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 195 ( 6 sgn 112 !; 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/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(t73,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(t99,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)],[t73]) ).
fof(f35,conjecture,
! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y] :
( ~ equal_lines(line_connecting(X,Y),line_connecting(Y,X))
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0))
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f35_nnf]) ).
cnf(c46,plain,
distinct_points(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t5,plain,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t146,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t157,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)],[t99,t146]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t74,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t1197,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)],[t157,t74]) ).
cnf(t924,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)],[t1197]) ).
fof(f31,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f31_nnf,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c39,plain,
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t23,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t140,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(c47,plain,
~ equal_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t16,plain,
equal_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)) = false,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t307,plain,
equal_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t308,plain,
true = or(false,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0))),
inference(cp,[status(thm)],[t140,t307]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t76,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t1086,plain,
true = distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t308,t76]) ).
cnf(t472,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)) = true,
inference(orient,[status(thm)],[t1086]) ).
cnf(t930,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0))))),true),
inference(cp,[status(thm)],[t924,t472]) ).
cnf(t1198,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0))))),
inference(step,[status(thm)],[t930,t74]) ).
cnf(t15,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t158,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t15]) ).
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(t41,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(t132,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t152,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t132,t146]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t279,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1103,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t152,t279]) ).
cnf(t1104,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1103,t76]) ).
cnf(t536,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1104]) ).
cnf(t537,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t158,t536]) ).
cnf(t1105,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t537,t74]) ).
cnf(t538,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1105]) ).
cnf(t1199,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0))))),
inference(step,[status(thm)],[t1198,t538]) ).
cnf(t1200,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t1199,t76]) ).
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(t42,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(t131,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t42]) ).
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(hi0,axiom,
ifeq(distinct_points(X0,X1),true,or(distinct_points(X0,X2),distinct_points(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(hi30,negated_conjecture,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t22,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi30]) ).
cnf(t138,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(orient,[status(thm)],[t22]) ).
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(t281,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t283,plain,
true = or(false,distinct_points(sk1,sk0)),
inference(cp,[status(thm)],[t138,t281]) ).
cnf(t1048,plain,
true = distinct_points(sk1,sk0),
inference(step,[status(thm)],[t283,t76]) ).
cnf(t338,plain,
distinct_points(sk1,sk0) = true,
inference(orient,[status(thm)],[t1048]) ).
cnf(t346,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t131,t338]) ).
cnf(t1069,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t346,t279]) ).
cnf(t1070,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t1069,t76]) ).
cnf(t441,plain,
not(apart_point_and_line(sk0,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t1070]) ).
cnf(t442,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t158,t441]) ).
cnf(t1071,plain,
false = apart_point_and_line(sk0,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t442,t74]) ).
cnf(t443,plain,
apart_point_and_line(sk0,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t1071]) ).
cnf(t1201,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t1200,t443]) ).
cnf(t1202,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t1201,t76]) ).
cnf(t153,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t131,t146]) ).
cnf(t1107,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t153,t279]) ).
cnf(t1108,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1107,t76]) ).
cnf(t554,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1108]) ).
cnf(t555,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t158,t554]) ).
cnf(t1109,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t555,t74]) ).
cnf(t556,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1109]) ).
cnf(t1203,plain,
true = or(false,apart_point_and_line(sk1,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t1202,t556]) ).
cnf(t1204,plain,
true = apart_point_and_line(sk1,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t1203,t76]) ).
cnf(t345,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t132,t338]) ).
cnf(t1065,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t345,t279]) ).
cnf(t1066,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t1065,t76]) ).
cnf(t423,plain,
not(apart_point_and_line(sk1,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t1066]) ).
cnf(t424,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t158,t423]) ).
cnf(t1067,plain,
false = apart_point_and_line(sk1,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t424,t74]) ).
cnf(t425,plain,
apart_point_and_line(sk1,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t1067]) ).
cnf(t1205,plain,
true = false,
inference(step,[status(thm)],[t1204,t425]) ).
cnf(t948,plain,
false = true,
inference(orient,[status(thm)],[t1205]) ).
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(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]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f15_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f16,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f16_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f20,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f20_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f21_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c24,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f30_nnf,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c36,plain,
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(c38,plain,
( ~ distinct_lines(X0,X1)
| ~ equal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f32,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f32_nnf,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y] :
( ( convergent_lines(X,Y)
| parallel_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c40,plain,
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f33,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
fof(f33_nnf,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c42,plain,
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f34,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f34_nnf,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X,Y] :
( ( unorthogonal_lines(X,Y)
| orthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c44,plain,
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c15,c16,c23,c24,c36,c38,c40,c42,c44,c47]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t948]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.99 % Computer : n019.cluster.edu
% 0.09/5.99 % Model : x86_64 x86_64
% 0.09/5.99 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.99 % Memory : 8046.5625MB
% 0.09/5.99 % OS : Linux 6.8.0-71-generic
% 0.09/5.99 % CPULimit : 300
% 0.09/5.99 % WCLimit : 300
% 0.09/5.99 % DateTime : Wed Sep 23 11:26:41 UTC 2026
% 0.09/5.99 % CPUTime :
% 0.09/5.99 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.60/7.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.60/7.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------