%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.16s 5.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 21 |; 7 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 52 ( 2 sgn 21 !; 3 ?)
% 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(a5_defns,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('theBenchmark.p',a5_defns) ).
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,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_directed_opposite_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) )
=> equally_directed_opposite_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_38,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_39,plain,
( unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a1_defns]) ).
cnf(c_40,plain,
( ~ unequally_directed_opposite_lines(A,B)
| ~ equally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a5_defns]) ).
cnf(c_41,plain,
( unequally_directed_opposite_lines(A,B)
| equally_directed_opposite_lines(A,B) ),
inference(clausify,[status(thm)],[a5_defns]) ).
cnf(c_47,plain,
( ~ unequally_directed_lines(A,B)
| ~ equally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[a4_defns]) ).
fof(nnf_37,plain,
? [L,M,N] :
( ~ equally_directed_opposite_lines(M,N)
& equally_directed_lines(L,N)
& equally_directed_opposite_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ equally_directed_opposite_lines(sK2,sK1)
& equally_directed_lines(sK0,sK1)
& equally_directed_opposite_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(L,sK0),skolemize(M,sK2),skolemize(N,sK1)],[nnf_37]) ).
cnf(c_53,negated_conjecture,
equally_directed_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_56,plain,
( unequally_directed_lines(A,reverse_line(B))
| equally_directed_opposite_lines(A,B) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
cnf(c_57,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ equally_directed_opposite_lines(A,B) ),
inference(resolve,[status(thm)],[c_40,c_38]) ).
cnf(c_58,negated_conjecture,
~ equally_directed_opposite_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_59,negated_conjecture,
equally_directed_opposite_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_110,negated_conjecture,
~ unequally_directed_lines(sK0,reverse_line(sK2)),
inference(resolve,[status(thm)],[c_59,c_57]) ).
cnf(c_111,negated_conjecture,
unequally_directed_lines(sK2,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_116,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax6_basics]) ).
cnf(c_119,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[ax8_basics]) ).
cnf(c_120,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_122,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[ax11_basics]) ).
cnf(c_137,negated_conjecture,
~ unequally_directed_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_53,c_47]) ).
cnf(c_193,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_122,c_120]) ).
cnf(c_138,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_122,c_193]) ).
cnf(c_143,plain,
unequally_directed_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_119,c_110]) ).
cnf(c_161,plain,
~ unequally_directed_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_138,c_111]) ).
cnf(c_194,negated_conjecture,
( unequally_directed_lines(A,sK1)
| ~ unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_116,c_137]) ).
cnf(c_195,negated_conjecture,
~ unequally_directed_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_194,c_161]) ).
cnf(c_192,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_143,c_195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n004.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 13:09:11 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 3235018 was started by sandbox on n004,
% 0.16/5.44 % Fri Sep 25 13:09:11 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 0.16/5.48
% 0.16/5.48 % SZS status Theorem for theBenchmark
% 0.16/5.48
% 0.16/5.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/5.48 % Length of proof is 29.
% 0.16/5.48 % Level of proof is 5.
% 0.16/5.48 % Maximum clause weight is 24.000.
% 0.16/5.48 % Given clauses 25.
% 0.16/5.48
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------