%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO192+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 : 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 01:17:23 PM UTC 2026
% Result : Theorem 5.47s 1.18s
% Output : Proof 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 34 ~; 26 |; 6 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f14,conjecture,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14_neg,negated_conjecture,
~ ! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ( ~ distinct_lines(sk1,sk2)
| ~ distinct_lines(sk0,sk2) )
& apart_point_and_line(intersection_point(sk0,sk1),sk2)
& convergent_lines(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f14_nnf]) ).
cnf(c15,plain,
apart_point_and_line(intersection_point(sk0,sk1),sk2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p28,plain,
( apart_point_and_line(intersection_point(sk0,sk1),X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[c12,c15]) ).
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]) ).
cnf(c14,plain,
convergent_lines(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p18,plain,
~ apart_point_and_line(intersection_point(sk0,sk1),sk1),
inference(resolution,[status(thm)],[c9,c14]) ).
cnf(p30,plain,
distinct_lines(sk2,sk1),
inference(resolution,[status(thm)],[p28,p18]) ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p36,plain,
( distinct_lines(sk1,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p30,c4]) ).
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(p59,plain,
distinct_lines(sk1,sk2),
inference(resolution,[status(thm)],[p36,c1]) ).
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]) ).
cnf(p17,plain,
~ apart_point_and_line(intersection_point(sk0,sk1),sk0),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(p29,plain,
distinct_lines(sk2,sk0),
inference(resolution,[status(thm)],[p28,p17]) ).
cnf(p33,plain,
( distinct_lines(sk0,X0)
| distinct_lines(sk2,X0) ),
inference(resolution,[status(thm)],[p29,c4]) ).
cnf(p37,plain,
distinct_lines(sk0,sk2),
inference(resolution,[status(thm)],[p33,c1]) ).
cnf(c16,plain,
( ~ distinct_lines(sk1,sk2)
| ~ distinct_lines(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p39,plain,
~ distinct_lines(sk1,sk2),
inference(resolution,[status(thm)],[p37,c16]) ).
cnf(p61,plain,
$false,
inference(resolution,[status(thm)],[p59,p39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:20:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.47/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.47/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------