%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO223+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 : n007.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 01:17:36 PM UTC 2026
% Result : Theorem 30.22s 4.37s
% Output : Proof 30.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 21
% Syntax : Number of formulae : 173 ( 132 unt; 0 def)
% Number of atoms : 258 ( 98 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 166 ( 81 ~; 69 |; 7 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 320 ( 28 sgn 115 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f18_nnf,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c19,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t41,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(convergent_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t58,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(convergent_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t41]) ).
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(t129,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t142,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(false,unorthogonal_lines(X2,X1)),true),true),
inference(cp,[status(thm)],[t58,t129]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t50,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t3239,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true),
inference(step,[status(thm)],[t142,t50]) ).
cnf(t1231,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t3239]) ).
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(t30,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t61,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t134,plain,
true = ifeq(convergent_lines(X1,X2),true,or(false,convergent_lines(X2,X1)),true),
inference(cp,[status(thm)],[t61,t129]) ).
cnf(t3056,plain,
true = ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true),
inference(step,[status(thm)],[t134,t50]) ).
cnf(t299,plain,
ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t3056]) ).
fof(f17,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f17_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t18,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t81,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t18]) ).
fof(f19,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f19_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c22,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t13,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t167,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t168,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t81,t167]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t49,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t3040,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t168,t49]) ).
cnf(t227,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t3040]) ).
cnf(t300,plain,
true = ifeq(true,true,convergent_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t299,t227]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t48,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t3057,plain,
true = convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t300,t48]) ).
cnf(t304,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t3057]) ).
cnf(t1232,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,unorthogonal_lines(orthogonal_through_point(X1,X2),X1),true),true),
inference(cp,[status(thm)],[t1231,t304]) ).
cnf(t3240,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,unorthogonal_lines(orthogonal_through_point(X1,X2),X1),true),
inference(step,[status(thm)],[t1232,t48]) ).
cnf(t3241,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true),
inference(step,[status(thm)],[t3240,t167]) ).
cnf(t1247,plain,
ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true) = true,
inference(orient,[status(thm)],[t3241]) ).
cnf(c21,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t43,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t60,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X1,X3),unorthogonal_lines(X2,X3)),true),true) = true,
inference(orient,[status(thm)],[t43]) ).
fof(f14,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f14_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t11,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t148,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t153,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,or(false,convergent_lines(X3,X1)),true),
inference(cp,[status(thm)],[t61,t148]) ).
cnf(t3105,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true),
inference(step,[status(thm)],[t153,t50]) ).
cnf(t573,plain,
ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true) = true,
inference(orient,[status(thm)],[t3105]) ).
fof(f16,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
fof(f16_nnf,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Y,Z,X] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi7,axiom,
ifeq(distinct_lines(X0,X1),true,or(apart_point_and_line(X2,X0),or(apart_point_and_line(X2,X1),convergent_lines(X0,X1))),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
fof(f22,conjecture,
! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22_neg,negated_conjecture,
~ ! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A,L] : distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f22_nnf]) ).
cnf(c25,plain,
distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi14,negated_conjecture,
distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t45,plain,
or(apart_point_and_line(X1,parallel_through_point(sk1,sk0)),or(apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi14]) ).
cnf(t79,plain,
or(apart_point_and_line(X1,parallel_through_point(sk1,sk0)),or(apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)))) = true,
inference(orient,[status(thm)],[t45]) ).
fof(f15,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f15_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t10,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t113,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t122,plain,
true = or(false,or(apart_point_and_line(sk0,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)))),
inference(cp,[status(thm)],[t79,t113]) ).
cnf(t3049,plain,
true = or(apart_point_and_line(sk0,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t122,t50]) ).
fof(f20,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
fof(f20_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c23,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t9,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t97,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t3050,plain,
true = or(false,convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t3049,t97]) ).
cnf(t3051,plain,
true = convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t3050,t50]) ).
cnf(t269,plain,
convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t3051]) ).
cnf(t574,plain,
true = ifeq(true,true,convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true),
inference(cp,[status(thm)],[t573,t269]) ).
cnf(t3106,plain,
true = convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),
inference(step,[status(thm)],[t574,t48]) ).
cnf(t577,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1) = true,
inference(orient,[status(thm)],[t3106]) ).
cnf(t1239,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true),true),
inference(cp,[status(thm)],[t1231,t577]) ).
cnf(t3416,plain,
true = ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true),
inference(step,[status(thm)],[t1239,t48]) ).
fof(f21,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
fof(f21_nnf,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [L,M,A,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c24,plain,
( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t44,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(X3,X1),or(apart_point_and_line(X3,X2),or(unorthogonal_lines(X1,X4),unorthogonal_lines(X2,X4)))),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t66,plain,
ifeq(distinct_lines(X1,X2),true,or(apart_point_and_line(X3,X1),or(apart_point_and_line(X3,X2),or(unorthogonal_lines(X1,X4),unorthogonal_lines(X2,X4)))),true) = true,
inference(orient,[status(thm)],[t44]) ).
cnf(t104,plain,
true = ifeq(distinct_lines(orthogonal_through_point(X1,X2),X3),true,or(false,or(apart_point_and_line(X2,X3),or(unorthogonal_lines(orthogonal_through_point(X1,X2),X4),unorthogonal_lines(X3,X4)))),true),
inference(cp,[status(thm)],[t66,t97]) ).
cnf(t3281,plain,
true = ifeq(distinct_lines(orthogonal_through_point(X1,X2),X3),true,or(apart_point_and_line(X2,X3),or(unorthogonal_lines(orthogonal_through_point(X1,X2),X4),unorthogonal_lines(X3,X4))),true),
inference(step,[status(thm)],[t104,t50]) ).
cnf(t1474,plain,
ifeq(distinct_lines(orthogonal_through_point(X1,X2),X3),true,or(apart_point_and_line(X2,X3),or(unorthogonal_lines(orthogonal_through_point(X1,X2),X4),unorthogonal_lines(X3,X4))),true) = true,
inference(orient,[status(thm)],[t3281]) ).
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(t31,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t62,plain,
ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X3),convergent_lines(X1,X3)),true) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t132,plain,
true = ifeq(convergent_lines(X1,X2),true,or(distinct_lines(X2,X1),false),true),
inference(cp,[status(thm)],[t62,t129]) ).
cnf(t3052,plain,
true = ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true),
inference(step,[status(thm)],[t132,t49]) ).
cnf(t286,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t3052]) ).
cnf(t305,plain,
true = ifeq(true,true,distinct_lines(orthogonal_through_point(X1,X2),X1),true),
inference(cp,[status(thm)],[t286,t304]) ).
cnf(t3058,plain,
true = distinct_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t305,t48]) ).
cnf(t320,plain,
distinct_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t3058]) ).
cnf(t1475,plain,
true = ifeq(true,true,or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3))),true),
inference(cp,[status(thm)],[t1474,t320]) ).
cnf(t3282,plain,
true = or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3))),
inference(step,[status(thm)],[t1475,t48]) ).
cnf(t1509,plain,
or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3))) = true,
inference(orient,[status(thm)],[t3282]) ).
cnf(t1510,plain,
true = or(false,or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3))),
inference(cp,[status(thm)],[t1509,t97]) ).
cnf(t3286,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3)),
inference(step,[status(thm)],[t1510,t50]) ).
cnf(t1532,plain,
or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X3),unorthogonal_lines(orthogonal_through_point(X1,X2),X3)) = true,
inference(orient,[status(thm)],[t3286]) ).
cnf(t1533,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),false),
inference(cp,[status(thm)],[t1532,t167]) ).
cnf(t3287,plain,
true = unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),
inference(step,[status(thm)],[t1533,t49]) ).
cnf(t1534,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1) = true,
inference(orient,[status(thm)],[t3287]) ).
cnf(t3417,plain,
true = ifeq(true,true,unorthogonal_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true),
inference(step,[status(thm)],[t3416,t1534]) ).
cnf(t3418,plain,
true = unorthogonal_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t3417,t48]) ).
cnf(t2815,plain,
unorthogonal_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t3418]) ).
cnf(t2816,plain,
true = ifeq(convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true,ifeq(true,true,or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)),true),true),
inference(cp,[status(thm)],[t60,t2815]) ).
cnf(t578,plain,
true = ifeq(true,true,convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true),
inference(cp,[status(thm)],[t299,t577]) ).
cnf(t3107,plain,
true = convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t578,t48]) ).
cnf(t593,plain,
convergent_lines(sk1,orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t3107]) ).
cnf(t3419,plain,
true = ifeq(true,true,ifeq(true,true,or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)),true),true),
inference(step,[status(thm)],[t2816,t593]) ).
cnf(t3420,plain,
true = ifeq(true,true,or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)),true),
inference(step,[status(thm)],[t3419,t48]) ).
cnf(t3421,plain,
true = or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)),
inference(step,[status(thm)],[t3420,t48]) ).
cnf(t2819,plain,
or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1)) = true,
inference(orient,[status(thm)],[t3421]) ).
cnf(t2820,plain,
true = or(unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),false),
inference(cp,[status(thm)],[t2819,t167]) ).
cnf(t3422,plain,
true = unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),
inference(step,[status(thm)],[t2820,t49]) ).
cnf(t2821,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t3422]) ).
cnf(t2822,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t1247,t2821]) ).
cnf(t3423,plain,
true = false,
inference(step,[status(thm)],[t2822,t48]) ).
cnf(t2830,plain,
false = true,
inference(orient,[status(thm)],[t3423]) ).
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(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,c14,c15,c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2830]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 11:31:36 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.22/4.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.22/4.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------