%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:17:38 AM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 24 ~; 18 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 2 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oag5,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('theBenchmark.p',oag5) ).
fof(oag6,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',oag6) ).
fof(oag9,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('theBenchmark.p',oag9) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',oag11) ).
fof(con,conjecture,
! [L,M,N] :
( unequally_directed_lines(L,reverse_line(M))
=> ( unequally_directed_lines(M,reverse_line(N))
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( unequally_directed_lines(L,reverse_line(M))
=> ( unequally_directed_lines(M,reverse_line(N))
| unequally_directed_lines(L,N) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [L,M,N] :
( ~ unequally_directed_lines(M,reverse_line(N))
& ~ unequally_directed_lines(L,N)
& unequally_directed_lines(L,reverse_line(M)) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ unequally_directed_lines(sK0,reverse_line(sK1))
& ~ unequally_directed_lines(sK2,sK1)
& unequally_directed_lines(sK2,reverse_line(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(L,sK2),skolemize(M,sK0),skolemize(N,sK1)],[nnf_32]) ).
cnf(c_73,negated_conjecture,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_74,negated_conjecture,
~ unequally_directed_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_75,negated_conjecture,
unequally_directed_lines(sK2,reverse_line(sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_89,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_92,plain,
( left_convergent_lines(A,reverse_line(B))
| left_convergent_lines(A,B)
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag9]) ).
cnf(c_164,plain,
( left_convergent_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_89,c_92]) ).
cnf(c_93,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_89,c_164]) ).
cnf(c_95,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_96,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_104,plain,
~ unequally_directed_lines(sK2,sK0),
inference(resolve,[status(thm)],[c_93,c_75]) ).
cnf(c_106,plain,
( unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_95,c_75]) ).
cnf(c_165,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_95,c_96]) ).
cnf(c_117,negated_conjecture,
~ unequally_directed_lines(reverse_line(sK1),sK0),
inference(resolve,[status(thm)],[c_165,c_73]) ).
cnf(c_127,plain,
( ~ unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK2,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_106,c_93]) ).
cnf(c_141,plain,
( unequally_directed_lines(sK2,A)
| unequally_directed_lines(sK2,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_127,c_106]) ).
cnf(c_166,plain,
( unequally_directed_lines(A,sK0)
| ~ unequally_directed_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_95,c_104]) ).
cnf(c_147,plain,
~ unequally_directed_lines(sK2,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_166,c_117]) ).
cnf(c_167,plain,
unequally_directed_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_147,c_141]) ).
cnf(c_163,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_74,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:12:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1434634 was started by sandbox2 on n015,
% 0.09/0.38 % Fri Sep 25 13:12:27 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.41 % Length of proof is 20.
% 0.15/0.41 % Level of proof is 5.
% 0.15/0.41 % Maximum clause weight is 18.000.
% 0.15/0.41 % Given clauses 41.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------