%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO184+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 : n026.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 07:17:19 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 21 ~; 22 |; 15 &)
% ( 2 <=>; 5 =>; 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 : 38 ( 0 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
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(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
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(Y,U)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_lines(U,line_connecting(X,Y)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(Y,U)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_lines(U,line_connecting(X,Y)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( distinct_lines(A,B)
| equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ~ equal_lines(U,line_connecting(X,Y))
& incident_point_and_line(Y,U)
& 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_lines(sK0,line_connecting(sK1,sK2))
& incident_point_and_line(sK2,sK0)
& incident_point_and_line(sK1,sK0)
& convergent_lines(sK0,sK3)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0,sK3]),skolemize(X,sK1),skolemize(Y,sK2),skolemize(U,sK0),skolemize(V,sK3)],[nnf_36]) ).
cnf(c_40,negated_conjecture,
~ equal_lines(sK0,line_connecting(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(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_47,negated_conjecture,
incident_point_and_line(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_51,negated_conjecture,
distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_75,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_78,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_79,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_86,negated_conjecture,
distinct_lines(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_87,negated_conjecture,
~ apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_44,c_46]) ).
cnf(c_88,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_44,c_47]) ).
cnf(c_98,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_78,c_51]) ).
cnf(c_99,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_79,c_51]) ).
cnf(c_108,negated_conjecture,
( apart_point_and_line(sK2,B)
| apart_point_and_line(sK2,A)
| apart_point_and_line(sK1,B)
| apart_point_and_line(sK1,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_75,c_51]) ).
cnf(c_109,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK1,sK2))
| apart_point_and_line(sK2,sK0)
| apart_point_and_line(sK1,line_connecting(sK1,sK2))
| apart_point_and_line(sK1,sK0) ),
inference(resolve,[status(thm)],[c_108,c_86]) ).
cnf(c_110,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK1,sK2))
| apart_point_and_line(sK2,sK0)
| apart_point_and_line(sK1,line_connecting(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_87,c_109]) ).
cnf(c_111,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK1,sK2))
| apart_point_and_line(sK2,sK0) ),
inference(resolve,[status(thm)],[c_99,c_110]) ).
cnf(c_112,negated_conjecture,
apart_point_and_line(sK2,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_88,c_111]) ).
cnf(c_107,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_98,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO184+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:05:39 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2580782 was started by sandbox on n026,
% 0.19/0.44 % Fri Sep 25 13:05:39 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 21.
% 0.19/0.48 % Level of proof is 3.
% 0.19/0.48 % Maximum clause weight is 23.000.
% 0.19/0.48 % Given clauses 35.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------