%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO170+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 : 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 07:17:14 AM UTC 2026
% Result : Theorem 0.09s 20.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 22 |; 11 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 18 !; 3 ?)
% 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,Z] :
( ( incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& distinct_points(X,Y) )
=> equal_lines(Z,line_connecting(X,Y)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& distinct_points(X,Y) )
=> equal_lines(Z,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,Z] :
( ~ equal_lines(Z,line_connecting(X,Y))
& incident_point_and_line(Y,Z)
& incident_point_and_line(X,Z)
& 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)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(X,sK1),skolemize(Y,sK2),skolemize(Z,sK0)],[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_50,negated_conjecture,
distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_74,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(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_78,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_85,negated_conjecture,
distinct_lines(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_86,negated_conjecture,
~ apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_44,c_46]) ).
cnf(c_87,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_44,c_47]) ).
cnf(c_92,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_77,c_50]) ).
cnf(c_93,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_78,c_50]) ).
cnf(c_109,negated_conjecture,
( apart_point_and_line(B,line_connecting(sK1,sK2))
| apart_point_and_line(B,sK0)
| apart_point_and_line(A,line_connecting(sK1,sK2))
| apart_point_and_line(A,sK0)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_74,c_85]) ).
cnf(c_110,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| apart_point_and_line(A,sK0)
| apart_point_and_line(sK1,line_connecting(sK1,sK2))
| ~ distinct_points(sK1,A) ),
inference(resolve,[status(thm)],[c_109,c_86]) ).
cnf(c_111,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| apart_point_and_line(A,sK0)
| ~ distinct_points(sK1,A) ),
inference(resolve,[status(thm)],[c_110,c_93]) ).
cnf(c_112,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK1,sK2))
| ~ distinct_points(sK1,sK2) ),
inference(resolve,[status(thm)],[c_111,c_87]) ).
cnf(c_113,negated_conjecture,
~ distinct_points(sK1,sK2),
inference(resolve,[status(thm)],[c_112,c_92]) ).
cnf(c_108,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_50,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO170+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/20.44 % CPULimit : 300
% 0.09/20.44 % WCLimit : 300
% 0.09/20.44 % DateTime : Fri Sep 25 13:01:09 UTC 2026
% 0.09/20.45 % CPUTime :
% 0.09/20.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/20.45 % Process 807857 was started by sandbox on n010,
% 0.09/20.45 % Fri Sep 25 13:01:09 2026
% 0.09/20.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/20.46
% 0.09/20.46 % From the command line: assign(max_seconds, 300).
% 0.09/20.47
% 0.09/20.47 % SZS status Theorem for theBenchmark
% 0.09/20.47
% 0.09/20.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/20.47 % Length of proof is 21.
% 0.09/20.47 % Level of proof is 3.
% 0.09/20.47 % Maximum clause weight is 18.000.
% 0.09/20.47 % Given clauses 40.
% 0.09/20.47
% 0.09/20.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------