%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO186+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 : n019.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 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 30 ~; 26 |; 15 &)
% ( 2 <=>; 6 =>; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
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(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',cu1) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
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] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_37,plain,
( distinct_points(A,B)
| equal_points(A,B) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ~ equal_points(X,intersection_point(U,V))
& incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equal_points(sK0,intersection_point(sK1,sK2))
& incident_point_and_line(sK0,sK2)
& incident_point_and_line(sK0,sK1)
& 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_44,plain,
( ~ apart_point_and_line(A,B)
| ~ incident_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a4]) ).
cnf(c_46,negated_conjecture,
incident_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_47,negated_conjecture,
incident_point_and_line(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
distinct_points(sK0,intersection_point(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_37]) ).
cnf(c_51,negated_conjecture,
convergent_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_73,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_76,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| apart_point_and_line(A,D)
| apart_point_and_line(A,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[cu1]) ).
cnf(c_77,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_78,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_84,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_87,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(resolve,[status(thm)],[c_44,c_46]) ).
cnf(c_88,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(resolve,[status(thm)],[c_44,c_47]) ).
cnf(c_104,plain,
~ apart_point_and_line(intersection_point(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_77,c_51]) ).
cnf(c_105,plain,
~ apart_point_and_line(intersection_point(sK1,sK2),sK1),
inference(resolve,[status(thm)],[c_78,c_51]) ).
cnf(c_128,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),B)
| apart_point_and_line(intersection_point(sK1,sK2),A)
| apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_76,c_50]) ).
cnf(c_129,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),A)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_128,c_88]) ).
cnf(c_130,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| ~ distinct_lines(sK2,sK1) ),
inference(resolve,[status(thm)],[c_129,c_87]) ).
cnf(c_131,negated_conjecture,
( apart_point_and_line(intersection_point(sK1,sK2),sK1)
| ~ distinct_lines(sK2,sK1) ),
inference(resolve,[status(thm)],[c_130,c_104]) ).
cnf(c_122,negated_conjecture,
~ distinct_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_131,c_105]) ).
cnf(c_132,plain,
( convergent_lines(A,sK1)
| ~ convergent_lines(A,sK2) ),
inference(resolve,[status(thm)],[c_73,c_122]) ).
cnf(c_133,plain,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_132,c_84]) ).
cnf(c_127,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_51,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.43 % Computer : n019.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Fri Sep 25 13:03:25 UTC 2026
% 0.15/5.44 % CPUTime :
% 0.15/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.44 % Process 2810914 was started by sandbox on n019,
% 0.15/5.44 % Fri Sep 25 13:03:25 2026
% 0.15/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.46
% 0.15/5.46 % From the command line: assign(max_seconds, 300).
% 0.15/5.47
% 0.15/5.47 % SZS status Theorem for theBenchmark
% 0.15/5.47
% 0.15/5.47 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/5.47 % Length of proof is 26.
% 0.15/5.47 % Level of proof is 4.
% 0.15/5.47 % Maximum clause weight is 23.000.
% 0.15/5.47 % Given clauses 42.
% 0.15/5.47
% 0.15/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------