%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO214+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 : n013.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 01:17:32 PM UTC 2026
% Result : Theorem 6.17s 1.26s
% Output : Proof 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 69 unt; 0 def)
% Number of atoms : 119 ( 38 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 77 ( 43 ~; 21 |; 9 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 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 : 118 ( 6 sgn 61 !; 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(t35,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(t46,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)],[t35]) ).
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(t26,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(t49,plain,
ifeq(convergent_lines(X1,X2),true,or(convergent_lines(X1,X3),convergent_lines(X2,X3)),true) = true,
inference(orient,[status(thm)],[t26]) ).
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(t18,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t70,plain,
or(convergent_lines(X1,X2),unorthogonal_lines(X1,X2)) = true,
inference(orient,[status(thm)],[t18]) ).
fof(f20,conjecture,
! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f20_neg,negated_conjecture,
~ ! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [L,M] :
( ~ unorthogonal_lines(M,L)
& unorthogonal_lines(L,M) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( ~ unorthogonal_lines(sk1,sk0)
& unorthogonal_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c26,plain,
~ unorthogonal_lines(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t8,plain,
unorthogonal_lines(sk1,sk0) = false,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t163,plain,
unorthogonal_lines(sk1,sk0) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t164,plain,
true = or(convergent_lines(sk1,sk0),false),
inference(cp,[status(thm)],[t70,t163]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t41,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t340,plain,
true = convergent_lines(sk1,sk0),
inference(step,[status(thm)],[t164,t41]) ).
cnf(t210,plain,
convergent_lines(sk1,sk0) = true,
inference(orient,[status(thm)],[t340]) ).
cnf(t212,plain,
true = ifeq(true,true,or(convergent_lines(sk1,X1),convergent_lines(sk0,X1)),true),
inference(cp,[status(thm)],[t49,t210]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t358,plain,
true = or(convergent_lines(sk1,X1),convergent_lines(sk0,X1)),
inference(step,[status(thm)],[t212,t40]) ).
cnf(t277,plain,
or(convergent_lines(sk1,X1),convergent_lines(sk0,X1)) = true,
inference(orient,[status(thm)],[t358]) ).
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(t82,plain,
convergent_lines(X1,X1) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t278,plain,
true = or(false,convergent_lines(sk0,sk1)),
inference(cp,[status(thm)],[t277,t82]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t42,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t359,plain,
true = convergent_lines(sk0,sk1),
inference(step,[status(thm)],[t278,t42]) ).
cnf(t279,plain,
convergent_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t359]) ).
cnf(t288,plain,
true = ifeq(true,true,ifeq(unorthogonal_lines(sk0,sk1),true,or(convergent_lines(sk0,X1),unorthogonal_lines(sk1,X1)),true),true),
inference(cp,[status(thm)],[t46,t279]) ).
cnf(t376,plain,
true = ifeq(unorthogonal_lines(sk0,sk1),true,or(convergent_lines(sk0,X1),unorthogonal_lines(sk1,X1)),true),
inference(step,[status(thm)],[t288,t40]) ).
cnf(c25,plain,
unorthogonal_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t7,plain,
unorthogonal_lines(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t72,plain,
unorthogonal_lines(sk0,sk1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t377,plain,
true = ifeq(true,true,or(convergent_lines(sk0,X1),unorthogonal_lines(sk1,X1)),true),
inference(step,[status(thm)],[t376,t72]) ).
cnf(t378,plain,
true = or(convergent_lines(sk0,X1),unorthogonal_lines(sk1,X1)),
inference(step,[status(thm)],[t377,t40]) ).
cnf(t309,plain,
or(convergent_lines(sk0,X1),unorthogonal_lines(sk1,X1)) = true,
inference(orient,[status(thm)],[t378]) ).
cnf(t310,plain,
true = or(false,unorthogonal_lines(sk1,sk0)),
inference(cp,[status(thm)],[t309,t82]) ).
cnf(t379,plain,
true = unorthogonal_lines(sk1,sk0),
inference(step,[status(thm)],[t310,t42]) ).
cnf(t380,plain,
true = false,
inference(step,[status(thm)],[t379,t163]) ).
cnf(t312,plain,
false = true,
inference(orient,[status(thm)],[t380]) ).
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(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]) ).
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]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c14,c15,c22,c23,c26]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t312]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO214+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:31:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.17/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.17/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------