%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO223+2 : 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 26.05s 3.79s
% Output : Proof 26.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 148 ( 123 unt; 0 def)
% Number of atoms : 213 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 118 ( 53 ~; 53 |; 7 &)
% ( 0 <=>; 5 =>; 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 280 ( 28 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,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(f16_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)],[f16]) ).
fof(f16_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)],[f16_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)],[f16_sk]) ).
cnf(t34,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(t51,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)],[t34]) ).
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(t0,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t120,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t132,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)],[t51,t120]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t43,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t1300,plain,
true = ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true),
inference(step,[status(thm)],[t132,t43]) ).
cnf(t654,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,unorthogonal_lines(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t1300]) ).
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',apart6) ).
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(t24,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(t54,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t124,plain,
true = ifeq(convergent_lines(X1,X2),true,or(false,convergent_lines(X2,X1)),true),
inference(cp,[status(thm)],[t54,t120]) ).
cnf(t1188,plain,
true = ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true),
inference(step,[status(thm)],[t124,t43]) ).
cnf(t257,plain,
ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t1188]) ).
fof(f15,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f15_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c17,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t15,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t74,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f17,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f17_nnf,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [L,A] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c22,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t11,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t156,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t157,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t74,t156]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t42,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t1176,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t157,t42]) ).
cnf(t217,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1176]) ).
cnf(t258,plain,
true = ifeq(true,true,convergent_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t257,t217]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t1190,plain,
true = convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t258,t41]) ).
cnf(t270,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t1190]) ).
cnf(t655,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)],[t654,t270]) ).
cnf(t1301,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)],[t655,t41]) ).
cnf(t1302,plain,
true = ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true),
inference(step,[status(thm)],[t1301,t156]) ).
cnf(t670,plain,
ifeq(unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),true,false,true) = true,
inference(orient,[status(thm)],[t1302]) ).
cnf(c21,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t36,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(t53,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)],[t36]) ).
cnf(t159,plain,
true = ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,or(false,unorthogonal_lines(X3,X1)),true),true),
inference(cp,[status(thm)],[t53,t156]) ).
cnf(t1386,plain,
true = ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,unorthogonal_lines(X3,X1),true),true),
inference(step,[status(thm)],[t159,t43]) ).
cnf(t983,plain,
ifeq(convergent_lines(orthogonal_through_point(X1,X2),X3),true,ifeq(unorthogonal_lines(orthogonal_through_point(X1,X2),X3),true,unorthogonal_lines(X3,X1),true),true) = true,
inference(orient,[status(thm)],[t1386]) ).
fof(f12,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f12_nnf,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Y,X] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c14,plain,
~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t9,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t138,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t142,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,or(false,convergent_lines(X3,X1)),true),
inference(cp,[status(thm)],[t54,t138]) ).
cnf(t1216,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true),
inference(step,[status(thm)],[t142,t43]) ).
cnf(t371,plain,
ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true) = true,
inference(orient,[status(thm)],[t1216]) ).
fof(f14,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(f14_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)],[f14]) ).
fof(f14_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)],[f14_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)],[f14_sk]) ).
cnf(hi11,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(f20,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(f20_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)],[f20]) ).
fof(f20_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)],[f20_neg]) ).
fof(f20_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])],[f20_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)],[f20_sk]) ).
cnf(hi18,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(t38,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)],[hi11,hi18]) ).
cnf(t72,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)],[t38]) ).
fof(f13,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f13_nnf,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t8,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t102,plain,
apart_point_and_line(X1,parallel_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t113,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)],[t72,t102]) ).
cnf(t1185,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)],[t113,t43]) ).
fof(f18,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
fof(f18_nnf,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c23,plain,
~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t7,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t84,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t1186,plain,
true = or(false,convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0))),
inference(step,[status(thm)],[t1185,t84]) ).
cnf(t1187,plain,
true = convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t1186,t43]) ).
cnf(t243,plain,
convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t1187]) ).
cnf(t372,plain,
true = ifeq(true,true,convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true),
inference(cp,[status(thm)],[t371,t243]) ).
cnf(t1217,plain,
true = convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),
inference(step,[status(thm)],[t372,t41]) ).
cnf(t375,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1) = true,
inference(orient,[status(thm)],[t1217]) ).
cnf(t984,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(sk1,sk0)),true),true),
inference(cp,[status(thm)],[t983,t375]) ).
cnf(t1387,plain,
true = ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true),
inference(step,[status(thm)],[t984,t41]) ).
cnf(t999,plain,
ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true) = true,
inference(orient,[status(thm)],[t1387]) ).
fof(f19,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(f19_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)],[f19]) ).
fof(f19_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)],[f19_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)],[f19_sk]) ).
cnf(t37,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(t59,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)],[t37]) ).
fof(f11,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f11_nnf,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t19,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t55,plain,
ifeq(convergent_lines(X1,X2),true,distinct_lines(X1,X2),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t218,plain,
true = ifeq(true,true,distinct_lines(orthogonal_through_point(X1,X2),X1),true),
inference(cp,[status(thm)],[t55,t217]) ).
cnf(t1180,plain,
true = distinct_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t218,t41]) ).
cnf(t234,plain,
distinct_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1180]) ).
cnf(t239,plain,
true = ifeq(true,true,or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))),true),
inference(cp,[status(thm)],[t59,t234]) ).
cnf(t1396,plain,
true = or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))),
inference(step,[status(thm)],[t239,t41]) ).
cnf(t1052,plain,
or(apart_point_and_line(X1,orthogonal_through_point(X2,X3)),or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X3),X4),unorthogonal_lines(X2,X4)))) = true,
inference(orient,[status(thm)],[t1396]) ).
cnf(t1053,plain,
true = or(false,or(apart_point_and_line(X1,X2),or(unorthogonal_lines(orthogonal_through_point(X2,X1),X3),unorthogonal_lines(X2,X3)))),
inference(cp,[status(thm)],[t1052,t84]) ).
cnf(t1397,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)],[t1053,t43]) ).
cnf(t1057,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)],[t1397]) ).
cnf(t1058,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)],[t1057,t84]) ).
cnf(t1398,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)],[t1058,t43]) ).
cnf(t1061,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)],[t1398]) ).
cnf(t1062,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),false),
inference(cp,[status(thm)],[t1061,t156]) ).
cnf(t1399,plain,
true = unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1),
inference(step,[status(thm)],[t1062,t42]) ).
cnf(t1063,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X2),X1) = true,
inference(orient,[status(thm)],[t1399]) ).
cnf(t1400,plain,
ifeq(true,true,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),true) = true,
inference(step,[status(thm)],[t999,t1063]) ).
cnf(t1401,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(step,[status(thm)],[t1400,t41]) ).
cnf(t1072,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(rw,[status(thm)],[t1401]) ).
cnf(t1074,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t1072]) ).
cnf(t1075,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t670,t1074]) ).
cnf(t1404,plain,
true = false,
inference(step,[status(thm)],[t1075,t41]) ).
cnf(t1084,plain,
false = true,
inference(orient,[status(thm)],[t1404]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c14,c15,c22,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1084]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 11:31:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.05/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.05/3.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------