%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO204+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 : n020.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 14.51s 2.39s
% Output : Proof 14.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 25
% Syntax : Number of formulae : 187 ( 133 unt; 0 def)
% Number of atoms : 293 ( 102 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 218 ( 112 ~; 73 |; 19 &)
% ( 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 : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 223 ( 6 sgn 123 !; 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/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t43,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(t94,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)],[t43]) ).
cnf(t16,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t163,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t16]) ).
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(t34,plain,
or(not(equal_points(X1,X2)),not(distinct_points(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(t136,plain,
or(not(equal_points(X1,X2)),not(distinct_points(X1,X2))) = true,
inference(orient,[status(thm)],[t34]) ).
fof(f35,conjecture,
! [X,Y,Z] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [X,Y,Z] :
( ( ~ equal_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& equal_points(Y,Z)
& distinct_points(X,Y) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( ~ equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
| ~ distinct_points(sk0,sk2) )
& equal_points(sk1,sk2)
& distinct_points(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f35_nnf]) ).
cnf(c47,plain,
equal_points(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t6,plain,
equal_points(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t160,plain,
equal_points(sk1,sk2) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t161,plain,
true = or(not(true),not(distinct_points(sk1,sk2))),
inference(cp,[status(thm)],[t136,t160]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t284,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t1146,plain,
true = or(false,not(distinct_points(sk1,sk2))),
inference(step,[status(thm)],[t161,t284]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t77,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1147,plain,
true = not(distinct_points(sk1,sk2)),
inference(step,[status(thm)],[t1146,t77]) ).
cnf(t472,plain,
not(distinct_points(sk1,sk2)) = true,
inference(orient,[status(thm)],[t1147]) ).
cnf(t473,plain,
false = ifeq(true,true,distinct_points(sk1,sk2),false),
inference(cp,[status(thm)],[t163,t472]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t75,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t1148,plain,
false = distinct_points(sk1,sk2),
inference(step,[status(thm)],[t473,t75]) ).
cnf(t474,plain,
distinct_points(sk1,sk2) = false,
inference(orient,[status(thm)],[t1148]) ).
cnf(t479,plain,
true = ifeq(apart_point_and_line(sk1,X1),true,or(false,apart_point_and_line(sk2,X1)),true),
inference(cp,[status(thm)],[t94,t474]) ).
cnf(t1283,plain,
true = ifeq(apart_point_and_line(sk1,X1),true,apart_point_and_line(sk2,X1),true),
inference(step,[status(thm)],[t479,t77]) ).
cnf(t997,plain,
ifeq(apart_point_and_line(sk1,X1),true,apart_point_and_line(sk2,X1),true) = true,
inference(orient,[status(thm)],[t1283]) ).
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(t74,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(t100,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)],[t74]) ).
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(t148,plain,
distinct_points(sk0,sk1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t159,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)],[t100,t148]) ).
cnf(t1267,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)],[t159,t75]) ).
cnf(t956,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)],[t1267]) ).
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(t142,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(c48,plain,
( ~ equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))
| ~ distinct_points(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t54,plain,
or(not(distinct_points(sk0,sk2)),not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)))) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t134,plain,
or(not(distinct_points(sk0,sk2)),not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)))) = true,
inference(orient,[status(thm)],[t54]) ).
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(t140,plain,
or(distinct_points(sk0,X1),distinct_points(sk1,X1)) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t475,plain,
true = or(distinct_points(sk0,sk2),false),
inference(cp,[status(thm)],[t140,t474]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t76,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1149,plain,
true = distinct_points(sk0,sk2),
inference(step,[status(thm)],[t475,t76]) ).
cnf(t484,plain,
distinct_points(sk0,sk2) = true,
inference(orient,[status(thm)],[t1149]) ).
cnf(t1150,plain,
or(not(true),not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)))) = true,
inference(step,[status(thm)],[t134,t484]) ).
cnf(t1151,plain,
or(false,not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)))) = true,
inference(step,[status(thm)],[t1150,t284]) ).
cnf(t1152,plain,
not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))) = true,
inference(step,[status(thm)],[t1151,t77]) ).
cnf(t494,plain,
not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))) = true,
inference(rw,[status(thm)],[t1152]) ).
cnf(t617,plain,
not(equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t494]) ).
cnf(t618,plain,
false = ifeq(true,true,equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t163,t617]) ).
cnf(t1195,plain,
false = equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t618,t75]) ).
cnf(t619,plain,
equal_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t1195]) ).
cnf(t620,plain,
true = or(false,distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2))),
inference(cp,[status(thm)],[t142,t619]) ).
cnf(t1196,plain,
true = distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t620,t77]) ).
cnf(t622,plain,
distinct_lines(line_connecting(sk0,sk1),line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t1196]) ).
cnf(t962,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)],[t956,t622]) ).
cnf(t1268,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)],[t962,t75]) ).
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(t40,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(t133,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X1,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t154,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t133,t148]) ).
cnf(t1201,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t154,t284]) ).
cnf(t1202,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1201,t77]) ).
cnf(t659,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1202]) ).
cnf(t660,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t163,t659]) ).
cnf(t1203,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t660,t75]) ).
cnf(t661,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1203]) ).
cnf(t1269,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)],[t1268,t661]) ).
cnf(t1270,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)],[t1269,t77]) ).
cnf(t488,plain,
true = or(not(true),not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t133,t484]) ).
cnf(t1158,plain,
true = or(false,not(apart_point_and_line(sk0,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t488,t284]) ).
cnf(t1159,plain,
true = not(apart_point_and_line(sk0,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t1158,t77]) ).
cnf(t499,plain,
not(apart_point_and_line(sk0,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t1159]) ).
cnf(t500,plain,
false = ifeq(true,true,apart_point_and_line(sk0,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t163,t499]) ).
cnf(t1160,plain,
false = apart_point_and_line(sk0,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t500,t75]) ).
cnf(t501,plain,
apart_point_and_line(sk0,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t1160]) ).
cnf(t1271,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)],[t1270,t501]) ).
cnf(t1272,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)],[t1271,t77]) ).
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(t41,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(t132,plain,
or(not(distinct_points(X1,X2)),not(apart_point_and_line(X2,line_connecting(X1,X2)))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t155,plain,
true = or(not(true),not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(cp,[status(thm)],[t132,t148]) ).
cnf(t1205,plain,
true = or(false,not(apart_point_and_line(sk1,line_connecting(sk0,sk1)))),
inference(step,[status(thm)],[t155,t284]) ).
cnf(t1206,plain,
true = not(apart_point_and_line(sk1,line_connecting(sk0,sk1))),
inference(step,[status(thm)],[t1205,t77]) ).
cnf(t677,plain,
not(apart_point_and_line(sk1,line_connecting(sk0,sk1))) = true,
inference(orient,[status(thm)],[t1206]) ).
cnf(t678,plain,
false = ifeq(true,true,apart_point_and_line(sk1,line_connecting(sk0,sk1)),false),
inference(cp,[status(thm)],[t163,t677]) ).
cnf(t1207,plain,
false = apart_point_and_line(sk1,line_connecting(sk0,sk1)),
inference(step,[status(thm)],[t678,t75]) ).
cnf(t679,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk1)) = false,
inference(orient,[status(thm)],[t1207]) ).
cnf(t1273,plain,
true = or(false,apart_point_and_line(sk1,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t1272,t679]) ).
cnf(t1274,plain,
true = apart_point_and_line(sk1,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t1273,t77]) ).
cnf(t984,plain,
apart_point_and_line(sk1,line_connecting(sk0,sk2)) = true,
inference(orient,[status(thm)],[t1274]) ).
cnf(t1000,plain,
true = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk0,sk2)),true),
inference(cp,[status(thm)],[t997,t984]) ).
cnf(t1284,plain,
true = apart_point_and_line(sk2,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t1000,t75]) ).
cnf(t489,plain,
true = or(not(true),not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(cp,[status(thm)],[t132,t484]) ).
cnf(t1162,plain,
true = or(false,not(apart_point_and_line(sk2,line_connecting(sk0,sk2)))),
inference(step,[status(thm)],[t489,t284]) ).
cnf(t1163,plain,
true = not(apart_point_and_line(sk2,line_connecting(sk0,sk2))),
inference(step,[status(thm)],[t1162,t77]) ).
cnf(t517,plain,
not(apart_point_and_line(sk2,line_connecting(sk0,sk2))) = true,
inference(orient,[status(thm)],[t1163]) ).
cnf(t518,plain,
false = ifeq(true,true,apart_point_and_line(sk2,line_connecting(sk0,sk2)),false),
inference(cp,[status(thm)],[t163,t517]) ).
cnf(t1164,plain,
false = apart_point_and_line(sk2,line_connecting(sk0,sk2)),
inference(step,[status(thm)],[t518,t75]) ).
cnf(t519,plain,
apart_point_and_line(sk2,line_connecting(sk0,sk2)) = false,
inference(orient,[status(thm)],[t1164]) ).
cnf(t1285,plain,
true = false,
inference(step,[status(thm)],[t1284,t519]) ).
cnf(t1007,plain,
false = true,
inference(orient,[status(thm)],[t1285]) ).
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]) ).
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]) ).
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,c48]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1007]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 11:28:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.51/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.51/2.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------