%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:17:20 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 13 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('theBenchmark.p',ci4) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',ceq1) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('theBenchmark.p',ax1) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('theBenchmark.p',a4) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_38,plain,
( ~ distinct_points(A,B)
| ~ equal_points(A,B) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ( ~ incident_point_and_line(X,V)
| ~ incident_point_and_line(X,U) )
& equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ incident_point_and_line(sK0,sK2)
| ~ incident_point_and_line(sK0,sK1) )
& equal_points(sK0,intersection_point(sK1,sK2))
& convergent_lines(sK1,sK2)
& distinct_points(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK3),skolemize(U,sK1),skolemize(V,sK2)],[nnf_36]) ).
cnf(c_39,negated_conjecture,
equal_points(sK0,intersection_point(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_54,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_55,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_57,plain,
( apart_point_and_line(C,B)
| distinct_points(A,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq1]) ).
cnf(c_80,plain,
( apart_point_and_line(A,B)
| incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
cnf(c_82,negated_conjecture,
convergent_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_83,negated_conjecture,
( ~ incident_point_and_line(sK0,sK2)
| ~ incident_point_and_line(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_84,negated_conjecture,
~ distinct_points(sK0,intersection_point(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_98,negated_conjecture,
~ apart_point_and_line(intersection_point(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_55,c_82]) ).
cnf(c_99,negated_conjecture,
~ apart_point_and_line(intersection_point(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_54,c_82]) ).
cnf(c_100,plain,
( apart_point_and_line(sK0,sK2)
| ~ incident_point_and_line(sK0,sK1) ),
inference(resolve,[status(thm)],[c_83,c_80]) ).
cnf(c_145,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),A)
| ~ apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_57,c_84]) ).
cnf(c_113,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(resolve,[status(thm)],[c_145,c_98]) ).
cnf(c_114,plain,
~ incident_point_and_line(sK0,sK1),
inference(resolve,[status(thm)],[c_113,c_100]) ).
cnf(c_142,plain,
apart_point_and_line(sK0,sK1),
inference(resolve,[status(thm)],[c_114,c_80]) ).
cnf(c_146,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),A)
| ~ apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_57,c_84]) ).
cnf(c_147,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(resolve,[status(thm)],[c_146,c_99]) ).
cnf(c_144,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_142,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.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
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:02:35 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2157490 was started by sandbox on n012,
% 0.08/0.35 % Fri Sep 25 13:02:35 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 22.
% 0.12/0.37 % Level of proof is 6.
% 0.12/0.37 % Maximum clause weight is 9.000.
% 0.12/0.37 % Given clauses 51.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------