%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 07:17:37 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 32 ~; 15 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 34 ( 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,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(N)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unequally_directed_lines(L,N)
& ~ unequally_directed_lines(L,reverse_line(M)) )
=> ~ unequally_directed_lines(M,reverse_line(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_163,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_163]) ).
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_105,plain,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_93,c_73]) ).
cnf(c_106,plain,
( unequally_directed_lines(reverse_line(sK1),A)
| unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_95,c_73]) ).
cnf(c_164,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_95,c_96]) ).
cnf(c_116,negated_conjecture,
~ unequally_directed_lines(reverse_line(sK0),sK2),
inference(resolve,[status(thm)],[c_164,c_75]) ).
cnf(c_165,plain,
( unequally_directed_lines(A,sK1)
| ~ unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_95,c_105]) ).
cnf(c_127,negated_conjecture,
~ unequally_directed_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_165,c_74]) ).
cnf(c_139,plain,
unequally_directed_lines(reverse_line(sK1),sK0),
inference(resolve,[status(thm)],[c_106,c_96]) ).
cnf(c_149,plain,
~ unequally_directed_lines(reverse_line(sK1),reverse_line(sK0)),
inference(resolve,[status(thm)],[c_139,c_93]) ).
cnf(c_166,plain,
( unequally_directed_lines(A,sK2)
| ~ unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_95,c_127]) ).
cnf(c_150,plain,
~ unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_166,c_116]) ).
cnf(c_167,plain,
unequally_directed_lines(reverse_line(sK1),reverse_line(sK0)),
inference(resolve,[status(thm)],[c_150,c_106]) ).
cnf(c_162,plain,
$false,
inference(resolve,[status(thm)],[c_149,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:10:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 242553 was started by sandbox on n003,
% 0.09/0.36 % Fri Sep 25 13:10:37 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 21.
% 0.14/0.38 % Level of proof is 6.
% 0.14/0.38 % Maximum clause weight is 11.000.
% 0.14/0.38 % Given clauses 37.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------