%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:17:28 PM UTC 2026
% Result : Theorem 8.08s 11.57s
% Output : Proof 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 99 unt; 0 def)
% Number of atoms : 197 ( 84 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 130 ( 65 ~; 47 |; 9 &)
% ( 0 <=>; 9 =>; 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 : 141 ( 2 sgn 69 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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(t23,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_points(X1,X3),apart_point_and_line(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t44,plain,
ifeq(apart_point_and_line(X1,X2),true,or(distinct_points(X1,X3),apart_point_and_line(X3,X2)),true) = true,
inference(orient,[status(thm)],[t23]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( ( distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& ~ distinct_points(Y,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ( distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
| ~ distinct_points(sk0,sk2) )
& ~ distinct_points(sk1,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c15,plain,
~ distinct_points(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t6,plain,
distinct_points(sk1,sk2) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t82,plain,
distinct_points(sk1,sk2) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t87,plain,
true = ifeq(apart_point_and_line(sk1,X1),true,or(false,apart_point_and_line(sk2,X1)),true),
inference(cp,[status(thm)],[t44,t82]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t36,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t419,plain,
true = ifeq(apart_point_and_line(sk1,X1),true,apart_point_and_line(sk2,X1),true),
inference(step,[status(thm)],[t87,t36]) ).
cnf(t264,plain,
ifeq(apart_point_and_line(sk1,X1),true,apart_point_and_line(sk2,X1),true) = true,
inference(orient,[status(thm)],[t419]) ).
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(t33,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(t39,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)],[t33]) ).
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(t61,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t69,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)],[t39,t61]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t435,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)],[t69,t34]) ).
cnf(t304,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)],[t435]) ).
cnf(c16,plain,
( distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
| ~ distinct_points(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t28,plain,
ifeq(distinct_points(sk0,sk2),true,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t42,plain,
ifeq(distinct_points(sk0,sk2),true,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),true) = true,
inference(orient,[status(thm)],[t28]) ).
fof(f3,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/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(hi7,negated_conjecture,
distinct_points(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t17,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi7]) ).
cnf(t55,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t83,plain,
true = or(distinct_points(sk0,sk2),false),
inference(cp,[status(thm)],[t55,t82]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t35,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t373,plain,
true = distinct_points(sk0,sk2),
inference(step,[status(thm)],[t83,t35]) ).
cnf(t121,plain,
distinct_points(sk0,sk2) = true,
inference(orient,[status(thm)],[t373]) ).
cnf(t374,plain,
ifeq(true,true,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),true) = true,
inference(step,[status(thm)],[t42,t121]) ).
cnf(t375,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(step,[status(thm)],[t374,t34]) ).
cnf(t131,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(rw,[status(thm)],[t375]) ).
cnf(t222,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t131]) ).
cnf(t306,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2))))),true),
inference(cp,[status(thm)],[t304,t222]) ).
cnf(t436,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2))))),
inference(step,[status(thm)],[t306,t34]) ).
cnf(t12,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t71,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t12]) ).
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]) ).
cnf(t20,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(t58,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t66,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t58,t61]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t92,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t408,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t66,t92]) ).
cnf(t409,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t408,t36]) ).
cnf(t233,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t409]) ).
cnf(t234,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t71,t233]) ).
cnf(t410,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t234,t34]) ).
cnf(t235,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t410]) ).
cnf(t437,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2))))),
inference(step,[status(thm)],[t436,t235]) ).
cnf(t438,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk2)),or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t437,t36]) ).
cnf(t127,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t58,t121]) ).
cnf(t382,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t127,t92]) ).
cnf(t383,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t382,t36]) ).
cnf(t156,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t383]) ).
cnf(t157,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t71,t156]) ).
cnf(t384,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t157,t34]) ).
cnf(t158,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t384]) ).
cnf(t439,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t438,t158]) ).
cnf(t440,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk0,sk1)),apart_point_and_line(sk1,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t439,t36]) ).
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]) ).
cnf(t21,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(t57,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t67,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t57,t61]) ).
cnf(t411,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t67,t92]) ).
cnf(t412,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t411,t36]) ).
cnf(t244,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t412]) ).
cnf(t245,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t71,t244]) ).
cnf(t413,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t245,t34]) ).
cnf(t246,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t413]) ).
cnf(t441,plain,
true = or(false,apart_point_and_line(sk1,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t440,t246]) ).
cnf(t442,plain,
true = apart_point_and_line(sk1,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t441,t36]) ).
cnf(t320,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t442]) ).
cnf(t321,plain,
true = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk0,sk2)),true),
inference(cp,[status(thm)],[t264,t320]) ).
cnf(t445,plain,
true = apart_point_and_line(sk2,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t321,t34]) ).
cnf(t128,plain,
true = or(not(true),not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t57,t121]) ).
cnf(t385,plain,
true = or(false,not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t128,t92]) ).
cnf(t386,plain,
true = not(apart_point_and_line(sk2,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t385,t36]) ).
cnf(t167,plain,
not(apart_point_and_line(sk2,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t386]) ).
cnf(t168,plain,
false = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t71,t167]) ).
cnf(t387,plain,
false = apart_point_and_line(sk2,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t168,t34]) ).
cnf(t169,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t387]) ).
cnf(t446,plain,
true = false,
inference(step,[status(thm)],[t445,t169]) ).
cnf(t326,plain,
false = true,
inference(orient,[status(thm)],[t446]) ).
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(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]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t326]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n008.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Wed Sep 23 11:28:51 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.08/11.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.08/11.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------