%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO182+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 : n009.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 01:17:19 PM UTC 2026
% Result : Theorem 8.59s 6.65s
% Output : Proof 8.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 141 ( 105 unt; 0 def)
% Number of atoms : 209 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 129 ( 61 ~; 51 |; 5 &)
% ( 0 <=>; 12 =>; 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 : 165 ( 2 sgn 78 !; 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(Z,line_connecting(Y,X)) ) ),
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(Z,line_connecting(Y,X)) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(Y,X))
& 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(sk2,line_connecting(sk1,sk0))
& 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(t697,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(t497,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)],[t697]) ).
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(t116,plain,
distinct_lines(X1,X1) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t118,plain,
true = ifeq(distinct_lines(X1,X2),true,or(false,distinct_lines(X2,X1)),true),
inference(cp,[status(thm)],[t52,t116]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t38,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t643,plain,
true = ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t118,t38]) ).
cnf(t367,plain,
ifeq(distinct_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t643]) ).
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(c16,plain,
~ apart_point_and_line(sk2,line_connecting(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t11,plain,
apart_point_and_line(sk2,line_connecting(sk1,sk0)) = false,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t84,plain,
apart_point_and_line(sk2,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t87,plain,
true = or(distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t72,t84]) ).
cnf(t6,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t37,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t585,plain,
true = distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t87,t37]) ).
cnf(t163,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk1,sk0)) = true,
inference(orient,[status(thm)],[t585]) ).
cnf(t369,plain,
true = ifeq(true,true,distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)),true),
inference(cp,[status(thm)],[t367,t163]) ).
cnf(t645,plain,
true = distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t369,t36]) ).
cnf(t386,plain,
distinct_lines(line_connecting(sk1,sk0),line_connecting(sk0,sk1)) = true,
inference(orient,[status(thm)],[t645]) ).
cnf(t501,plain,
true = ifeq(true,true,or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),true),
inference(cp,[status(thm)],[t497,t386]) ).
cnf(t698,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk1,sk0)),or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t501,t36]) ).
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(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(t65,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(orient,[status(thm)],[t17]) ).
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(t95,plain,
distinct_points(X1,X1) = false,
inference(orient,[status(thm)],[t4]) ).
cnf(t96,plain,
true = or(false,distinct_points(sk1,sk0)),
inference(cp,[status(thm)],[t65,t95]) ).
cnf(t575,plain,
true = distinct_points(sk1,sk0),
inference(step,[status(thm)],[t96,t38]) ).
cnf(t124,plain,
distinct_points(sk1,sk0) = true,
inference(orient,[status(thm)],[t575]) ).
cnf(t131,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t68,t124]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t105,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t579,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t131,t105]) ).
cnf(t580,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t579,t38]) ).
cnf(t147,plain,
not(apart_point_and_line(sk0,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t580]) ).
cnf(t148,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t83,t147]) ).
cnf(t581,plain,
false = apart_point_and_line(sk0,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t148,t36]) ).
cnf(t149,plain,
apart_point_and_line(sk0,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t581]) ).
cnf(t699,plain,
true = or(false,or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1))))),
inference(step,[status(thm)],[t698,t149]) ).
cnf(t700,plain,
true = or(apart_point_and_line(sk0,line_connecting(sk0,sk1)),or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t699,t38]) ).
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(t592,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t78,t105]) ).
cnf(t593,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t592,t38]) ).
cnf(t176,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t593]) ).
cnf(t177,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t83,t176]) ).
cnf(t594,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t177,t36]) ).
cnf(t178,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t594]) ).
cnf(t701,plain,
true = or(false,or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t700,t178]) ).
cnf(t702,plain,
true = or(apart_point_and_line(sk1,line_connecting(sk1,sk0)),apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t701,t38]) ).
cnf(t130,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(cp,[status(thm)],[t69,t124]) ).
cnf(t576,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk1,sk0)))),
inference(step,[status(thm)],[t130,t105]) ).
cnf(t577,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk1,sk0))),
inference(step,[status(thm)],[t576,t38]) ).
cnf(t136,plain,
not(apart_point_and_line(sk1,line_connecting(sk1,sk0))) = true,
inference(orient,[status(thm)],[t577]) ).
cnf(t137,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk1,sk0)),false),
inference(cp,[status(thm)],[t83,t136]) ).
cnf(t578,plain,
false = apart_point_and_line(sk1,line_connecting(sk1,sk0)),
inference(step,[status(thm)],[t137,t36]) ).
cnf(t138,plain,
apart_point_and_line(sk1,line_connecting(sk1,sk0)) = false,
inference(orient,[status(thm)],[t578]) ).
cnf(t703,plain,
true = or(false,apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t702,t138]) ).
cnf(t704,plain,
true = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t703,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(t616,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t79,t105]) ).
cnf(t617,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t616,t38]) ).
cnf(t269,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t617]) ).
cnf(t270,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t83,t269]) ).
cnf(t618,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t270,t36]) ).
cnf(t271,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t618]) ).
cnf(t705,plain,
true = false,
inference(step,[status(thm)],[t704,t271]) ).
cnf(t525,plain,
false = true,
inference(orient,[status(thm)],[t705]) ).
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,t525]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO182+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 11:19:34 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.59/6.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.59/6.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------