%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO266+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 07:17:46 AM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 26 ~; 33 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 45 ( 2 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('theBenchmark.p',a1_defns) ).
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('theBenchmark.p',a4_defns) ).
fof(ax5_basics,axiom,
! [L] : equally_directed_lines(L,L),
file('theBenchmark.p',ax5_basics) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('theBenchmark.p',ax6_basics) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('theBenchmark.p',ax8_basics) ).
fof(ax9_basics,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',ax9_basics) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',ax11_basics) ).
fof(con,conjecture,
! [L,M] :
( unequally_directed_opposite_lines(L,M)
<=> unequally_directed_opposite_lines(M,L) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M] :
( unequally_directed_opposite_lines(L,M)
<=> unequally_directed_opposite_lines(M,L) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_41,plain,
equally_directed_lines(A,A),
inference(clausify,[status(thm)],[ax5_basics]) ).
cnf(c_46,plain,
( ~ unequally_directed_lines(A,B)
| ~ equally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[a4_defns]) ).
fof(nnf_37,plain,
? [L,M] :
( ( ~ unequally_directed_opposite_lines(M,L)
| ~ unequally_directed_opposite_lines(L,M) )
& ( unequally_directed_opposite_lines(M,L)
| unequally_directed_opposite_lines(L,M) ) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ unequally_directed_opposite_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK0,sK1) )
& ( unequally_directed_opposite_lines(sK1,sK0)
| unequally_directed_opposite_lines(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(L,sK0),skolemize(M,sK1)],[nnf_37]) ).
cnf(c_88,negated_conjecture,
( ~ unequally_directed_opposite_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_89,negated_conjecture,
( unequally_directed_opposite_lines(sK1,sK0)
| unequally_directed_opposite_lines(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_101,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_104,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)],[ax9_basics]) ).
cnf(c_217,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_101,c_104]) ).
cnf(c_105,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_101,c_217]) ).
cnf(c_106,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_107,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax6_basics]) ).
cnf(c_112,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_113,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_114,plain,
~ unequally_directed_lines(A,A),
inference(resolve,[status(thm)],[c_46,c_41]) ).
cnf(c_128,plain,
( unequally_directed_lines(A,B)
| unequally_directed_opposite_lines(A,B) ),
inference(resolve,[status(thm)],[c_112,c_106]) ).
cnf(c_130,plain,
( unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_lines(sK1,reverse_line(sK0)) ),
inference(resolve,[status(thm)],[c_113,c_89]) ).
cnf(c_131,plain,
( unequally_directed_opposite_lines(sK1,sK0)
| unequally_directed_lines(sK0,reverse_line(sK1)) ),
inference(resolve,[status(thm)],[c_113,c_89]) ).
cnf(c_195,plain,
( ~ unequally_directed_opposite_lines(sK0,sK1)
| unequally_directed_lines(sK1,sK0) ),
inference(resolve,[status(thm)],[c_128,c_88]) ).
cnf(c_202,plain,
( unequally_directed_lines(sK0,sK1)
| unequally_directed_lines(sK1,sK0) ),
inference(resolve,[status(thm)],[c_195,c_128]) ).
cnf(c_204,plain,
( unequally_directed_lines(sK0,A)
| unequally_directed_lines(sK1,A)
| unequally_directed_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_202,c_107]) ).
cnf(c_206,plain,
( unequally_directed_lines(sK1,A)
| unequally_directed_lines(sK0,A)
| unequally_directed_lines(sK1,sK0) ),
inference(resolve,[status(thm)],[c_202,c_107]) ).
cnf(c_218,plain,
( unequally_directed_lines(sK1,sK1)
| unequally_directed_lines(sK0,sK1) ),
inference(factor,[status(thm)],[c_204]) ).
cnf(c_207,plain,
unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_114,c_218]) ).
cnf(c_219,plain,
( unequally_directed_lines(sK0,sK0)
| unequally_directed_lines(sK1,sK0) ),
inference(factor,[status(thm)],[c_206]) ).
cnf(c_208,plain,
unequally_directed_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_114,c_219]) ).
cnf(c_211,plain,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_105,c_207]) ).
cnf(c_212,plain,
unequally_directed_opposite_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_211,c_131]) ).
cnf(c_213,negated_conjecture,
~ unequally_directed_opposite_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_212,c_88]) ).
cnf(c_214,negated_conjecture,
unequally_directed_lines(sK1,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_213,c_130]) ).
cnf(c_220,plain,
~ unequally_directed_lines(sK1,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_105,c_208]) ).
cnf(c_216,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 13:14:35 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3351822 was started by sandbox2 on n002,
% 0.16/0.43 % Fri Sep 25 13:14:35 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 34.
% 0.16/0.47 % Level of proof is 11.
% 0.16/0.47 % Maximum clause weight is 17.000.
% 0.16/0.47 % Given clauses 34.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------