%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 07:17:36 AM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 28 ~; 15 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 8 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('theBenchmark.p',a4) ).
fof(con,conjecture,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_46,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_49,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_53,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_57,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_59,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_60,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_61,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_79,plain,
( apart_point_and_line(A,B)
| incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
fof(nnf_36,plain,
? [L,M] :
( ! [X] :
( ( ~ incident_point_and_line(X,M)
| ~ incident_point_and_line(X,L) )
& point(X) )
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ! [X] :
( ( ~ incident_point_and_line(X,sK1)
| ~ incident_point_and_line(X,sK0) )
& point(X) )
& convergent_lines(sK0,sK1)
& line(sK1)
& line(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(L,sK0),skolemize(M,sK1)],[nnf_36]) ).
cnf(c_82,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_84,negated_conjecture,
( ~ incident_point_and_line(A,sK1)
| ~ incident_point_and_line(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_88,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_59,c_60]) ).
cnf(c_107,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_53,c_82]) ).
cnf(c_108,plain,
( apart_point_and_line(A,sK1)
| ~ incident_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_84,c_79]) ).
cnf(c_132,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_49,c_46]) ).
cnf(c_116,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_132,c_88]) ).
cnf(c_125,plain,
incident_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_107,c_79]) ).
cnf(c_133,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_57,c_116]) ).
cnf(c_127,plain,
~ apart_point_and_line(A,B),
inference(resolve,[status(thm)],[c_133,c_61]) ).
cnf(c_130,plain,
~ incident_point_and_line(A,sK0),
inference(resolve,[status(thm)],[c_127,c_108]) ).
cnf(c_131,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41 % Computer : n016.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Sep 25 13:13:44 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.42 % Process 2452266 was started by sandbox2 on n016,
% 0.13/0.42 % Fri Sep 25 13:13:44 2026
% 0.13/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.43
% 0.13/0.43 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45
% 0.13/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.45 % Length of proof is 27.
% 0.13/0.45 % Level of proof is 6.
% 0.13/0.45 % Maximum clause weight is 18.000.
% 0.13/0.45 % Given clauses 44.
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------