%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO221+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 : n014.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 01:17:35 PM UTC 2026
% Result : Theorem 11.84s 2.19s
% Output : Proof 11.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 54 unt; 0 def)
% Number of atoms : 114 ( 23 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 69 ~; 27 |; 2 &)
% ( 0 <=>; 7 =>; 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 : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 124 ( 8 sgn 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(hi13,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(f22,conjecture,
! [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22_neg,negated_conjecture,
~ ! [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A,B,L] :
( distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B))
& ~ apart_point_and_line(B,orthogonal_through_point(L,A)) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( distinct_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1))
& ~ apart_point_and_line(sk1,orthogonal_through_point(sk2,sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f22_nnf]) ).
cnf(c26,plain,
distinct_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi14,negated_conjecture,
distinct_lines(orthogonal_through_point(sk2,sk0),orthogonal_through_point(sk2,sk1)) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t48,plain,
or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk0)),or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk1)),or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X2),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi14]) ).
cnf(t80,plain,
or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk0)),or(apart_point_and_line(X1,orthogonal_through_point(sk2,sk1)),or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X2),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X2)))) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(c25,plain,
~ apart_point_and_line(sk1,orthogonal_through_point(sk2,sk0)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t11,plain,
apart_point_and_line(sk1,orthogonal_through_point(sk2,sk0)) = false,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t132,plain,
apart_point_and_line(sk1,orthogonal_through_point(sk2,sk0)) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t142,plain,
true = or(false,or(apart_point_and_line(sk1,orthogonal_through_point(sk2,sk1)),or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X1)))),
inference(cp,[status(thm)],[t80,t132]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t52,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t707,plain,
true = or(apart_point_and_line(sk1,orthogonal_through_point(sk2,sk1)),or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X1))),
inference(step,[status(thm)],[t142,t52]) ).
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(t100,plain,
apart_point_and_line(X1,orthogonal_through_point(X2,X1)) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t708,plain,
true = or(false,or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X1))),
inference(step,[status(thm)],[t707,t100]) ).
cnf(t709,plain,
true = or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X1)),
inference(step,[status(thm)],[t708,t52]) ).
cnf(t589,plain,
or(unorthogonal_lines(orthogonal_through_point(sk2,sk0),X1),unorthogonal_lines(orthogonal_through_point(sk2,sk1),X1)) = true,
inference(orient,[status(thm)],[t709]) ).
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(t14,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t186,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),X1) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t590,plain,
true = or(false,unorthogonal_lines(orthogonal_through_point(sk2,sk1),sk2)),
inference(cp,[status(thm)],[t589,t186]) ).
cnf(t710,plain,
true = unorthogonal_lines(orthogonal_through_point(sk2,sk1),sk2),
inference(step,[status(thm)],[t590,t52]) ).
cnf(t711,plain,
true = false,
inference(step,[status(thm)],[t710,t186]) ).
cnf(t593,plain,
false = true,
inference(orient,[status(thm)],[t711]) ).
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(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]) ).
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]) ).
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]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c6,c7,c8,c9,c14,c15,c22,c23,c25]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t593]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 % Computer : n014.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 11:33:04 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.84/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.84/2.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------