%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO173+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 : n007.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 07:17:15 AM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 25 ~; 29 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',apart4) ).
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(con,conjecture,
! [X,Y,U,V] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ apart_point_and_line(sK0,sK1)
& ~ apart_point_and_line(sK2,sK1)
& distinct_lines(sK1,line_connecting(sK2,sK0))
& convergent_lines(sK1,sK3)
& distinct_points(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK3]),skolemize(X,sK2),skolemize(Y,sK0),skolemize(U,sK1),skolemize(V,sK3)],[nnf_36]) ).
cnf(c_47,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
~ apart_point_and_line(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
distinct_lines(sK1,line_connecting(sK2,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_51,negated_conjecture,
distinct_points(sK2,sK0),
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_82,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_85,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_97,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_78,c_51]) ).
cnf(c_98,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_79,c_51]) ).
cnf(c_102,plain,
( distinct_points(sK0,A)
| distinct_points(sK2,A) ),
inference(resolve,[status(thm)],[c_82,c_51]) ).
cnf(c_133,plain,
( distinct_points(A,B)
| distinct_points(sK0,B)
| distinct_points(sK2,A) ),
inference(resolve,[status(thm)],[c_102,c_82]) ).
cnf(c_158,plain,
( distinct_points(sK0,sK2)
| distinct_points(sK2,sK2) ),
inference(factor,[status(thm)],[c_133]) ).
cnf(c_138,plain,
distinct_points(sK0,sK2),
inference(resolve,[status(thm)],[c_85,c_158]) ).
cnf(c_159,negated_conjecture,
( apart_point_and_line(B,line_connecting(sK2,sK0))
| apart_point_and_line(B,sK1)
| apart_point_and_line(A,line_connecting(sK2,sK0))
| apart_point_and_line(A,sK1)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_75,c_49]) ).
cnf(c_160,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK2,sK0))
| apart_point_and_line(A,sK1)
| apart_point_and_line(sK0,line_connecting(sK2,sK0))
| ~ distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_159,c_47]) ).
cnf(c_161,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK2,sK0))
| apart_point_and_line(A,sK1)
| ~ distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_160,c_97]) ).
cnf(c_162,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK2,sK0))
| ~ distinct_points(sK0,sK2) ),
inference(resolve,[status(thm)],[c_161,c_48]) ).
cnf(c_163,negated_conjecture,
~ distinct_points(sK0,sK2),
inference(resolve,[status(thm)],[c_162,c_98]) ).
cnf(c_157,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_138,c_163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO173+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 12:59:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1053413 was started by sandbox on n007,
% 0.10/0.37 % Fri Sep 25 12:59:08 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.40 % Length of proof is 21.
% 0.15/0.40 % Level of proof is 5.
% 0.15/0.40 % Maximum clause weight is 23.000.
% 0.15/0.40 % Given clauses 54.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------