%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO230+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 : n011.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 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 139 ( 46 ~; 81 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 14 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oag4,axiom,
! [L,M,N] :
( distinct_lines(L,M)
=> ( distinct_lines(M,N)
| distinct_lines(L,N) ) ),
file('theBenchmark.p',oag4) ).
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(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('theBenchmark.p',oag10) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('theBenchmark.p',oag11) ).
fof(oagco9,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('theBenchmark.p',oagco9) ).
fof(oaguc1,axiom,
! [A,B,L,M] :
( ( distinct_lines(L,M)
& distinct_points(A,B) )
=> ( left_apart_point(B,reverse_line(M))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,M)
| left_apart_point(A,M)
| left_apart_point(B,L)
| left_apart_point(A,L) ) ),
file('theBenchmark.p',oaguc1) ).
fof(con,conjecture,
! [A,B] :
( distinct_points(A,B)
=> ( ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B] :
( distinct_points(A,B)
=> ( ~ unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
& ~ distinct_lines(line_connecting(A,B),line_connecting(B,A)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_32,plain,
? [A,B] :
( ( unequally_directed_lines(line_connecting(B,A),line_connecting(A,B))
| distinct_lines(line_connecting(A,B),line_connecting(B,A)) )
& distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)) )
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_32]) ).
cnf(c_73,negated_conjecture,
( unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_74,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_79,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| left_apart_point(A,reverse_line(C))
| left_apart_point(B,D)
| left_apart_point(A,D)
| left_apart_point(B,C)
| left_apart_point(A,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[oaguc1]) ).
cnf(c_81,plain,
~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(clausify,[status(thm)],[oagco9]) ).
cnf(c_88,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_90,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[oag10]) ).
cnf(c_91,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_381,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_88,c_91]) ).
cnf(c_92,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_88,c_381]) ).
cnf(c_94,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_95,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_96,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[oag4]) ).
cnf(c_382,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| left_apart_point(A,reverse_line(C))
| left_apart_point(B,D)
| left_apart_point(A,D)
| left_apart_point(B,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_79]) ).
cnf(c_383,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| left_apart_point(A,reverse_line(C))
| left_apart_point(B,D)
| left_apart_point(A,D)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_382]) ).
cnf(c_384,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| left_apart_point(A,reverse_line(C))
| left_apart_point(B,D)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_383]) ).
cnf(c_385,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| left_apart_point(A,reverse_line(C))
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_384]) ).
cnf(c_386,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| left_apart_point(B,reverse_line(C))
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_385]) ).
cnf(c_387,plain,
( left_apart_point(B,reverse_line(D))
| left_apart_point(A,reverse_line(D))
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_386]) ).
cnf(c_388,plain,
( left_apart_point(B,reverse_line(D))
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_387]) ).
cnf(c_101,plain,
( ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_90,c_388]) ).
cnf(c_389,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_94,c_95]) ).
cnf(c_107,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,B)),line_connecting(B,A)),
inference(resolve,[status(thm)],[c_389,c_81]) ).
cnf(c_109,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK1,sK0),A)
| distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_96,c_73]) ).
cnf(c_113,negated_conjecture,
~ distinct_lines(A,B),
inference(resolve,[status(thm)],[c_101,c_74]) ).
cnf(c_390,plain,
( unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_113,c_109]) ).
cnf(c_114,plain,
unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_113,c_390]) ).
cnf(c_124,plain,
( unequally_directed_lines(line_connecting(sK0,sK1),A)
| unequally_directed_lines(line_connecting(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_114,c_94]) ).
cnf(c_204,plain,
( ~ unequally_directed_lines(line_connecting(sK1,sK0),A)
| unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(A)) ),
inference(resolve,[status(thm)],[c_124,c_92]) ).
cnf(c_312,plain,
( unequally_directed_lines(line_connecting(sK0,sK1),A)
| unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(A)) ),
inference(resolve,[status(thm)],[c_204,c_124]) ).
cnf(c_351,plain,
( unequally_directed_lines(reverse_line(A),B)
| unequally_directed_lines(line_connecting(sK0,sK1),B)
| unequally_directed_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_312,c_94]) ).
cnf(c_352,plain,
( unequally_directed_lines(reverse_line(A),A)
| unequally_directed_lines(line_connecting(sK0,sK1),A) ),
inference(factor,[status(thm)],[c_351]) ).
cnf(c_353,plain,
unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(A,A)),
inference(resolve,[status(thm)],[c_352,c_107]) ).
cnf(c_357,plain,
~ unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_92,c_353]) ).
cnf(c_391,plain,
( unequally_directed_lines(A,reverse_line(line_connecting(B,B)))
| ~ unequally_directed_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_94,c_357]) ).
cnf(c_392,plain,
~ unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(A,A)),
inference(resolve,[status(thm)],[c_391,c_81]) ).
cnf(c_380,plain,
$false,
inference(resolve,[status(thm)],[c_353,c_392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO230+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 13:08:28 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 2086853 was started by sandbox on n011,
% 0.09/0.36 % Fri Sep 25 13:08:28 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).
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.14/0.43 % Length of proof is 33.
% 0.14/0.43 % Level of proof is 12.
% 0.14/0.43 % Maximum clause weight is 34.000.
% 0.14/0.43 % Given clauses 85.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------