%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO175+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 : n003.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 07:17:16 AM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 27 ~; 26 |; 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 : 40 ( 0 sgn 20 !; 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(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& distinct_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,
( ~ apart_point_and_line(sK0,sK1)
& ~ apart_point_and_line(sK0,sK2)
& distinct_points(sK0,intersection_point(sK2,sK1))
& convergent_lines(sK2,sK1)
& distinct_points(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK2,sK1]),skolemize(X,sK0),skolemize(Y,sK3),skolemize(U,sK2),skolemize(V,sK1)],[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(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
distinct_points(sK0,intersection_point(sK2,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
convergent_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_72,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
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_76,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_77,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_83,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_95,negated_conjecture,
~ apart_point_and_line(intersection_point(sK2,sK1),sK1),
inference(resolve,[status(thm)],[c_76,c_50]) ).
cnf(c_96,negated_conjecture,
~ apart_point_and_line(intersection_point(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_77,c_50]) ).
cnf(c_119,negated_conjecture,
( apart_point_and_line(intersection_point(sK2,sK1),B)
| apart_point_and_line(intersection_point(sK2,sK1),A)
| apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_75,c_49]) ).
cnf(c_120,negated_conjecture,
( apart_point_and_line(intersection_point(sK2,sK1),A)
| apart_point_and_line(intersection_point(sK2,sK1),sK1)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_119,c_47]) ).
cnf(c_121,negated_conjecture,
( apart_point_and_line(intersection_point(sK2,sK1),sK2)
| apart_point_and_line(intersection_point(sK2,sK1),sK1)
| ~ distinct_lines(sK1,sK2) ),
inference(resolve,[status(thm)],[c_120,c_48]) ).
cnf(c_122,negated_conjecture,
( apart_point_and_line(intersection_point(sK2,sK1),sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(resolve,[status(thm)],[c_121,c_95]) ).
cnf(c_113,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_122,c_96]) ).
cnf(c_123,plain,
( convergent_lines(A,sK2)
| ~ convergent_lines(A,sK1) ),
inference(resolve,[status(thm)],[c_72,c_113]) ).
cnf(c_124,plain,
~ convergent_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_123,c_83]) ).
cnf(c_118,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_50,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO175+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 13:03:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 229115 was started by sandbox on n003,
% 0.11/0.37 % Fri Sep 25 13:03:23 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 19.
% 0.11/0.40 % Level of proof is 4.
% 0.11/0.40 % Maximum clause weight is 18.000.
% 0.11/0.40 % Given clauses 42.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------