%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 34.66s 4.82s
% Output : Proof 34.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 167 ( 114 unt; 0 def)
% Number of atoms : 264 ( 83 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 206 ( 109 ~; 70 |; 13 &)
% ( 5 <=>; 9 =>; 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 : 214 ( 6 sgn 121 !; 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/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f10_nnf,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t75,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(t106,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)],[t75]) ).
fof(f13,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi6,axiom,
ifeq(convergent_lines(X0,X1),true,or(distinct_lines(X1,X2),convergent_lines(X0,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f35,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y] :
( ~ equal_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ~ equal_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0))
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f35_nnf]) ).
cnf(c46,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi30,negated_conjecture,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t23,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi30]) ).
cnf(t146,plain,
or(distinct_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t184,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t186,plain,
true = or(distinct_lines(sk1,sk0),false),
inference(cp,[status(thm)],[t146,t184]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t77,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t12740,plain,
true = distinct_lines(sk1,sk0),
inference(step,[status(thm)],[t186,t77]) ).
cnf(t341,plain,
distinct_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t12740]) ).
cnf(t352,plain,
true = ifeq(distinct_points(X1,X2),true,ifeq(true,true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),true),
inference(cp,[status(thm)],[t106,t341]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t76,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t14464,plain,
true = ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true),
inference(step,[status(thm)],[t352,t76]) ).
cnf(t11975,plain,
ifeq(distinct_points(X1,X2),true,or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,sk0),or(apart_point_and_line(X2,sk1),apart_point_and_line(X2,sk0)))),true) = true,
inference(orient,[status(thm)],[t14464]) ).
fof(f30,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox2/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(c37,plain,
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t25,plain,
or(equal_points(X1,X2),distinct_points(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t148,plain,
or(equal_points(X1,X2),distinct_points(X1,X2)) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(c47,plain,
~ equal_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t16,plain,
equal_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)) = false,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t335,plain,
equal_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t336,plain,
true = or(false,distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0))),
inference(cp,[status(thm)],[t148,t335]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t78,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t12792,plain,
true = distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)),
inference(step,[status(thm)],[t336,t78]) ).
cnf(t581,plain,
distinct_points(intersection_point(sk0,sk1),intersection_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t12792]) ).
cnf(t11977,plain,
true = ifeq(true,true,or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),true),
inference(cp,[status(thm)],[t11975,t581]) ).
cnf(t14465,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk1),or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),
inference(step,[status(thm)],[t11977,t76]) ).
cnf(t15,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t183,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/sandbox2/benchmark/theBenchmark.p',ci4) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t42,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(t137,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t3,plain,
convergent_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t153,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t164,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(cp,[status(thm)],[t137,t153]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t308,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t12822,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk1))),
inference(step,[status(thm)],[t164,t308]) ).
cnf(t12823,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk1)),
inference(step,[status(thm)],[t12822,t78]) ).
cnf(t657,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk1)) = true,
inference(orient,[status(thm)],[t12823]) ).
cnf(t658,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk1),false),
inference(cp,[status(thm)],[t183,t657]) ).
cnf(t12824,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(step,[status(thm)],[t658,t76]) ).
cnf(t659,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk1) = false,
inference(orient,[status(thm)],[t12824]) ).
cnf(t14466,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)))),
inference(step,[status(thm)],[t14465,t659]) ).
cnf(t14467,plain,
true = or(apart_point_and_line(intersection_point(sk0,sk1),sk0),or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t14466,t78]) ).
fof(f8,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
fof(f8_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t41,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(t138,plain,
or(not(convergent_lines(X1,X2)),not(apart_point_and_line(intersection_point(X1,X2),X1))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t163,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(cp,[status(thm)],[t138,t153]) ).
cnf(t12818,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk0,sk1),sk0))),
inference(step,[status(thm)],[t163,t308]) ).
cnf(t12819,plain,
true = not(apart_point_and_line(intersection_point(sk0,sk1),sk0)),
inference(step,[status(thm)],[t12818,t78]) ).
cnf(t639,plain,
not(apart_point_and_line(intersection_point(sk0,sk1),sk0)) = true,
inference(orient,[status(thm)],[t12819]) ).
cnf(t640,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk0,sk1),sk0),false),
inference(cp,[status(thm)],[t183,t639]) ).
cnf(t12820,plain,
false = apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(step,[status(thm)],[t640,t76]) ).
cnf(t641,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk0) = false,
inference(orient,[status(thm)],[t12820]) ).
cnf(t14468,plain,
true = or(false,or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t14467,t641]) ).
cnf(t14469,plain,
true = or(apart_point_and_line(intersection_point(sk1,sk0),sk1),apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t14468,t78]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f5_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi2,axiom,
ifeq(convergent_lines(X0,X1),true,or(convergent_lines(X0,X2),convergent_lines(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t22,plain,
or(convergent_lines(sk0,X1),convergent_lines(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi30]) ).
cnf(t131,plain,
or(convergent_lines(sk0,X1),convergent_lines(sk1,X1)) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t187,plain,
true = or(false,convergent_lines(sk1,sk0)),
inference(cp,[status(thm)],[t131,t184]) ).
cnf(t12741,plain,
true = convergent_lines(sk1,sk0),
inference(step,[status(thm)],[t187,t78]) ).
cnf(t353,plain,
convergent_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t12741]) ).
cnf(t365,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk1,sk0),sk1))),
inference(cp,[status(thm)],[t138,t353]) ).
cnf(t12765,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk1,sk0),sk1))),
inference(step,[status(thm)],[t365,t308]) ).
cnf(t12766,plain,
true = not(apart_point_and_line(intersection_point(sk1,sk0),sk1)),
inference(step,[status(thm)],[t12765,t78]) ).
cnf(t526,plain,
not(apart_point_and_line(intersection_point(sk1,sk0),sk1)) = true,
inference(orient,[status(thm)],[t12766]) ).
cnf(t527,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk1,sk0),sk1),false),
inference(cp,[status(thm)],[t183,t526]) ).
cnf(t12767,plain,
false = apart_point_and_line(intersection_point(sk1,sk0),sk1),
inference(step,[status(thm)],[t527,t76]) ).
cnf(t528,plain,
apart_point_and_line(intersection_point(sk1,sk0),sk1) = false,
inference(orient,[status(thm)],[t12767]) ).
cnf(t14470,plain,
true = or(false,apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t14469,t528]) ).
cnf(t14471,plain,
true = apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(step,[status(thm)],[t14470,t78]) ).
cnf(t366,plain,
true = or(not(true),not(apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(cp,[status(thm)],[t137,t353]) ).
cnf(t12769,plain,
true = or(false,not(apart_point_and_line(intersection_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t366,t308]) ).
cnf(t12770,plain,
true = not(apart_point_and_line(intersection_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t12769,t78]) ).
cnf(t544,plain,
not(apart_point_and_line(intersection_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t12770]) ).
cnf(t545,plain,
false = ifeq(true,true,apart_point_and_line(intersection_point(sk1,sk0),sk0),false),
inference(cp,[status(thm)],[t183,t544]) ).
cnf(t12773,plain,
false = apart_point_and_line(intersection_point(sk1,sk0),sk0),
inference(step,[status(thm)],[t545,t76]) ).
cnf(t547,plain,
apart_point_and_line(intersection_point(sk1,sk0),sk0) = false,
inference(orient,[status(thm)],[t12773]) ).
cnf(t14472,plain,
true = false,
inference(step,[status(thm)],[t14471,t547]) ).
cnf(t12059,plain,
false = true,
inference(orient,[status(thm)],[t14472]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f6,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f15,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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]) ).
cnf(c36,plain,
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f31,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/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(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/sandbox2/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/sandbox2/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/sandbox2/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,t12059]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Wed Sep 23 11:27:06 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 34.66/4.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.66/4.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------