%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO223+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 01:17:36 PM UTC 2026
% Result : Theorem 26.16s 3.71s
% Output : Proof 26.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 26
% Syntax : Number of formulae : 169 ( 108 unt; 0 def)
% Number of atoms : 286 ( 74 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 244 ( 127 ~; 80 |; 23 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 299 ( 28 sgn 139 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [L,M,N] :
( ( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N) )
& ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ) )
=> ( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cotno1) ).
fof(f24_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)],[f24]) ).
fof(f24_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)],[f24_nnf]) ).
cnf(c29,plain,
( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t66,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X3,X1),convergent_lines(X3,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t79,plain,
ifeq(convergent_lines(X1,X2),true,ifeq(unorthogonal_lines(X1,X2),true,or(unorthogonal_lines(X3,X1),convergent_lines(X3,X2)),true),true) = true,
inference(orient,[status(thm)],[t66]) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f19_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)],[f19]) ).
fof(f19_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)],[f19_nnf]) ).
cnf(c22,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t65,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)],[c22]) ).
cnf(t82,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)],[t65]) ).
fof(f5,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/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(t42,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(t85,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t42]) ).
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]) ).
cnf(t11,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t174,plain,
convergent_lines(parallel_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t179,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,or(false,convergent_lines(X3,X1)),true),
inference(cp,[status(thm)],[t85,t174]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t74,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t1873,plain,
true = ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true),
inference(step,[status(thm)],[t179,t74]) ).
cnf(t800,plain,
ifeq(convergent_lines(parallel_through_point(X1,X2),X3),true,convergent_lines(X3,X1),true) = true,
inference(orient,[status(thm)],[t1873]) ).
fof(f14,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f14_nnf,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t29,plain,
ifeq(distinct_lines(X1,X2),true,convergent_lines(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t103,plain,
ifeq(distinct_lines(X1,X2),true,convergent_lines(X1,X2),true) = true,
inference(orient,[status(thm)],[t29]) ).
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(t20,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t136,plain,
or(equal_lines(X1,X2),distinct_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t20]) ).
fof(f35,conjecture,
! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f35_neg,negated_conjecture,
~ ! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A,L] : ~ equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
~ equal_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f35_nnf]) ).
cnf(c46,plain,
~ equal_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(t25,plain,
equal_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = false,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t290,plain,
equal_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = false,
inference(orient,[status(thm)],[t25]) ).
cnf(t291,plain,
true = or(false,distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0))),
inference(cp,[status(thm)],[t136,t290]) ).
cnf(t1809,plain,
true = distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t291,t74]) ).
cnf(t501,plain,
distinct_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t1809]) ).
cnf(t503,plain,
true = ifeq(true,true,convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),true),
inference(cp,[status(thm)],[t103,t501]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t72,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t1843,plain,
true = convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)),
inference(step,[status(thm)],[t503,t72]) ).
cnf(t658,plain,
convergent_lines(parallel_through_point(sk1,sk0),orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0)) = true,
inference(orient,[status(thm)],[t1843]) ).
cnf(t801,plain,
true = ifeq(true,true,convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true),
inference(cp,[status(thm)],[t800,t658]) ).
cnf(t1874,plain,
true = convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),
inference(step,[status(thm)],[t801,t72]) ).
cnf(t804,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1) = true,
inference(orient,[status(thm)],[t1874]) ).
cnf(t819,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1),unorthogonal_lines(sk1,X1)),true),true),
inference(cp,[status(thm)],[t82,t804]) ).
cnf(t1990,plain,
true = ifeq(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),sk1),true,or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1),unorthogonal_lines(sk1,X1)),true),
inference(step,[status(thm)],[t819,t72]) ).
fof(f25,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',couo1) ).
fof(f25_nnf,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c31,plain,
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t44,plain,
ifeq(convergent_lines(X1,X2),true,or(unorthogonal_lines(X3,X1),unorthogonal_lines(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t86,plain,
ifeq(convergent_lines(X1,X2),true,or(unorthogonal_lines(X3,X1),unorthogonal_lines(X3,X2)),true) = true,
inference(orient,[status(thm)],[t44]) ).
fof(f18,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f18_nnf,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t18,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t124,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t18]) ).
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]) ).
cnf(t13,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t206,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t208,plain,
true = or(convergent_lines(orthogonal_through_point(X1,X2),X1),false),
inference(cp,[status(thm)],[t124,t206]) ).
cnf(t5,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t73,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t1764,plain,
true = convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(step,[status(thm)],[t208,t73]) ).
cnf(t353,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1764]) ).
cnf(t362,plain,
true = ifeq(true,true,or(unorthogonal_lines(X1,orthogonal_through_point(X2,X3)),unorthogonal_lines(X1,X2)),true),
inference(cp,[status(thm)],[t86,t353]) ).
cnf(t1828,plain,
true = or(unorthogonal_lines(X1,orthogonal_through_point(X2,X3)),unorthogonal_lines(X1,X2)),
inference(step,[status(thm)],[t362,t72]) ).
cnf(t595,plain,
or(unorthogonal_lines(X1,orthogonal_through_point(X2,X3)),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t1828]) ).
cnf(t596,plain,
true = or(false,unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1)),
inference(cp,[status(thm)],[t595,t206]) ).
cnf(t1829,plain,
true = unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1),
inference(step,[status(thm)],[t596,t74]) ).
cnf(t598,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X1,X2),X3),X1) = true,
inference(orient,[status(thm)],[t1829]) ).
cnf(t1991,plain,
true = ifeq(true,true,or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1),unorthogonal_lines(sk1,X1)),true),
inference(step,[status(thm)],[t1990,t598]) ).
cnf(t1992,plain,
true = or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1),unorthogonal_lines(sk1,X1)),
inference(step,[status(thm)],[t1991,t72]) ).
cnf(t1388,plain,
or(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sk1,sk0),sk0),X1),unorthogonal_lines(sk1,X1)) = true,
inference(orient,[status(thm)],[t1992]) ).
cnf(t1389,plain,
true = or(false,unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0))),
inference(cp,[status(thm)],[t1388,t206]) ).
cnf(t1993,plain,
true = unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)),
inference(step,[status(thm)],[t1389,t74]) ).
cnf(t1390,plain,
unorthogonal_lines(sk1,orthogonal_through_point(sk1,sk0)) = true,
inference(orient,[status(thm)],[t1993]) ).
cnf(t1401,plain,
true = ifeq(convergent_lines(sk1,orthogonal_through_point(sk1,sk0)),true,ifeq(true,true,or(unorthogonal_lines(X1,sk1),convergent_lines(X1,orthogonal_through_point(sk1,sk0))),true),true),
inference(cp,[status(thm)],[t79,t1390]) ).
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]) ).
cnf(t2,plain,
convergent_lines(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t143,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t147,plain,
true = ifeq(convergent_lines(X1,X2),true,or(false,convergent_lines(X2,X1)),true),
inference(cp,[status(thm)],[t85,t143]) ).
cnf(t1784,plain,
true = ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true),
inference(step,[status(thm)],[t147,t74]) ).
cnf(t415,plain,
ifeq(convergent_lines(X1,X2),true,convergent_lines(X2,X1),true) = true,
inference(orient,[status(thm)],[t1784]) ).
cnf(t416,plain,
true = ifeq(true,true,convergent_lines(X1,orthogonal_through_point(X1,X2)),true),
inference(cp,[status(thm)],[t415,t353]) ).
cnf(t1785,plain,
true = convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(step,[status(thm)],[t416,t72]) ).
cnf(t419,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)) = true,
inference(orient,[status(thm)],[t1785]) ).
cnf(t2038,plain,
true = ifeq(true,true,ifeq(true,true,or(unorthogonal_lines(X1,sk1),convergent_lines(X1,orthogonal_through_point(sk1,sk0))),true),true),
inference(step,[status(thm)],[t1401,t419]) ).
cnf(t2039,plain,
true = ifeq(true,true,or(unorthogonal_lines(X1,sk1),convergent_lines(X1,orthogonal_through_point(sk1,sk0))),true),
inference(step,[status(thm)],[t2038,t72]) ).
cnf(t2040,plain,
true = or(unorthogonal_lines(X1,sk1),convergent_lines(X1,orthogonal_through_point(sk1,sk0))),
inference(step,[status(thm)],[t2039,t72]) ).
cnf(t1607,plain,
or(unorthogonal_lines(X1,sk1),convergent_lines(X1,orthogonal_through_point(sk1,sk0))) = true,
inference(orient,[status(thm)],[t2040]) ).
cnf(t1609,plain,
true = or(unorthogonal_lines(orthogonal_through_point(sk1,sk0),sk1),false),
inference(cp,[status(thm)],[t1607,t143]) ).
cnf(t2041,plain,
true = unorthogonal_lines(orthogonal_through_point(sk1,sk0),sk1),
inference(step,[status(thm)],[t1609,t73]) ).
cnf(t2042,plain,
true = false,
inference(step,[status(thm)],[t2041,t206]) ).
cnf(t1611,plain,
false = true,
inference(orient,[status(thm)],[t2042]) ).
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(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]) ).
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]) ).
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(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(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]) ).
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(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,c46]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1611]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 11:34:33 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.16/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.16/3.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------