%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:17:30 AM UTC 2026
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 14 ~; 7 |; 18 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('theBenchmark.p',a3) ).
fof(con,conjecture,
! [A,L,M,N] :
( ( parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> equal_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L,M,N] :
( ( parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> equal_lines(M,N) ),
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,
? [A,L,M,N] :
( ~ equal_lines(M,N)
& parallel_lines(N,L)
& parallel_lines(M,L)
& incident_point_and_line(A,N)
& incident_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equal_lines(sK0,sK1)
& parallel_lines(sK1,sK2)
& parallel_lines(sK0,sK2)
& incident_point_and_line(sK3,sK1)
& incident_point_and_line(sK3,sK0)
& apart_point_and_line(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK0,sK1]),skolemize(A,sK3),skolemize(L,sK2),skolemize(M,sK0),skolemize(N,sK1)],[nnf_36]) ).
cnf(c_40,negated_conjecture,
~ equal_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_43,plain,
( ~ convergent_lines(A,B)
| ~ parallel_lines(A,B) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_44,negated_conjecture,
parallel_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_45,negated_conjecture,
parallel_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_52,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_45,c_43]) ).
cnf(c_53,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_74,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_83,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_89,negated_conjecture,
distinct_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_110,negated_conjecture,
( convergent_lines(A,sK2)
| ~ convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_83,c_53]) ).
cnf(c_102,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_110,c_52]) ).
cnf(c_111,negated_conjecture,
convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_89,c_74]) ).
cnf(c_109,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_102,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:09:04 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3332250 was started by sandbox2 on n002,
% 0.08/0.35 % Fri Sep 25 13:09:04 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.36
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36
% 0.11/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.36 % Length of proof is 17.
% 0.11/0.36 % Level of proof is 4.
% 0.11/0.36 % Maximum clause weight is 9.000.
% 0.11/0.36 % Given clauses 36.
% 0.11/0.36
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------