%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:17:31 PM UTC 2026
% Result : Theorem 5.24s 1.09s
% Output : Proof 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 57 unt; 0 def)
% Number of atoms : 89 ( 25 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 70 ( 46 ~; 15 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 92 ( 8 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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(hi17,axiom,
ifeq(distinct_lines(X0,X1),true,or(apart_point_and_line(X2,X0),or(apart_point_and_line(X2,X1),or(unorthogonal_lines(X0,X3),unorthogonal_lines(X1,X3)))),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
fof(f20,conjecture,
! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f20_neg,negated_conjecture,
~ ! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [A,L,M] :
( distinct_lines(L,orthogonal_through_point(M,A))
& ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( distinct_lines(sk1,orthogonal_through_point(sk2,sk0))
& ~ unorthogonal_lines(sk1,sk2)
& ~ apart_point_and_line(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f20_nnf]) ).
cnf(c27,plain,
distinct_lines(sk1,orthogonal_through_point(sk2,sk0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi18,negated_conjecture,
distinct_lines(sk1,orthogonal_through_point(sk2,sk0)) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t42,plain,
or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk0)),or(unorthogonal_lines(sk1,X2),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi18]) ).
cnf(t76,plain,
or(apart_point_and_line(X1,sk1),or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk0)),or(unorthogonal_lines(sk1,X2),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X2)))) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(c25,plain,
~ apart_point_and_line(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t0,plain,
apart_point_and_line(sk0,sk1) = false,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t124,plain,
apart_point_and_line(sk0,sk1) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t136,plain,
true = or(false,or(apart_point_and_line(sk0,orthogonal_through_point(sk2,sk0)),or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1)))),
inference(cp,[status(thm)],[t76,t124]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t47,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t432,plain,
true = or(apart_point_and_line(sk0,orthogonal_through_point(sk2,sk0)),or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1))),
inference(step,[status(thm)],[t136,t47]) ).
fof(f18,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('/export/starexec/sandbox/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(t9,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t90,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t433,plain,
true = or(false,or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1))),
inference(step,[status(thm)],[t432,t90]) ).
cnf(t434,plain,
true = or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1)),
inference(step,[status(thm)],[t433,t47]) ).
cnf(t364,plain,
or(unorthogonal_lines(sk1,X1),unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1)) = true,
inference(orient,[status(thm)],[t434]) ).
cnf(c26,plain,
~ unorthogonal_lines(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t8,plain,
unorthogonal_lines(sk1,sk2) = false,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t178,plain,
unorthogonal_lines(sk1,sk2) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t365,plain,
true = or(false,unorthogonal_lines(orthogonal_through_point(sk2,sk0),sk2)),
inference(cp,[status(thm)],[t364,t178]) ).
cnf(t435,plain,
true = unorthogonal_lines(orthogonal_through_point(sk2,sk0),sk2),
inference(step,[status(thm)],[t365,t47]) ).
fof(f17,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/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(t14,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t192,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t436,plain,
true = false,
inference(step,[status(thm)],[t435,t192]) ).
cnf(t368,plain,
false = true,
inference(orient,[status(thm)],[t436]) ).
fof(f0,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f0_nnf,plain,
! [X] : ~ distinct_points(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ distinct_points(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f1_nnf,plain,
! [X] : ~ distinct_lines(X,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : ~ distinct_lines(X,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f2,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f2_nnf,plain,
! [X] : ~ convergent_lines(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ convergent_lines(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f12,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/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/sandbox/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c14,c15,c22,c23,c25,c26]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t368]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 11:29:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.24/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.24/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------