%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:17:29 AM UTC 2026
% Result : Theorem 0.14s 0.59s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 30 ~; 12 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
fof(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('theBenchmark.p',cup1) ).
fof(con,conjecture,
! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_22,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_33,plain,
( convergent_lines(A,B)
| apart_point_and_line(C,B)
| apart_point_and_line(C,A)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[cup1]) ).
fof(nnf_16,plain,
? [A,L,M,N] :
( distinct_lines(M,N)
& ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_lines(sK1,sK2)
& ~ convergent_lines(sK2,sK3)
& ~ convergent_lines(sK1,sK3)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK1)
& apart_point_and_line(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK1,sK2]),skolemize(A,sK0),skolemize(L,sK3),skolemize(M,sK1),skolemize(N,sK2)],[nnf_16]) ).
cnf(c_35,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_36,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_37,negated_conjecture,
~ convergent_lines(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_38,negated_conjecture,
~ convergent_lines(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_39,negated_conjecture,
distinct_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_62,negated_conjecture,
( convergent_lines(A,sK3)
| ~ convergent_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_22,c_37]) ).
cnf(c_50,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_62,c_38]) ).
cnf(c_63,negated_conjecture,
( convergent_lines(sK1,A)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_33,c_35]) ).
cnf(c_64,negated_conjecture,
( convergent_lines(sK1,sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(resolve,[status(thm)],[c_63,c_36]) ).
cnf(c_65,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_64,c_50]) ).
cnf(c_61,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_39,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n009.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Fri Sep 25 13:06:15 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.57 % Process 1661710 was started by sandbox on n009,
% 0.10/0.57 % Fri Sep 25 13:06:15 2026
% 0.10/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.57
% 0.10/0.57 % From the command line: assign(max_seconds, 300).
% 0.14/0.59
% 0.14/0.59 % SZS status Theorem for theBenchmark
% 0.14/0.59
% 0.14/0.59 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.59 % Length of proof is 12.
% 0.14/0.59 % Level of proof is 3.
% 0.14/0.59 % Maximum clause weight is 12.000.
% 0.14/0.59 % Given clauses 26.
% 0.14/0.59
% 0.14/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------