%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO259+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 : 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 07:17:44 AM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 24 ~; 26 |; 20 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 2 sgn 20 !; 4 ?)
% 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(oag8,axiom,
! [L,M] :
( ( line(M)
& line(L) )
=> ( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',oag8) ).
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(oagco9,axiom,
! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
file('theBenchmark.p',oagco9) ).
fof(con,conjecture,
! [L,A,B,C] :
( ( distinct_points(A,B)
& distinct_points(B,C)
& distinct_points(A,C)
& line(L) )
=> ~ ( between_on_line(L,B,A,C)
& between_on_line(L,A,B,C) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,A,B,C] :
( ( distinct_points(A,B)
& distinct_points(B,C)
& distinct_points(A,C)
& line(L) )
=> ~ ( between_on_line(L,B,A,C)
& between_on_line(L,A,B,C) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_76,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_77,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_80,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B)
| ~ line(B)
| ~ line(A) ),
inference(clausify,[status(thm)],[oag8]) ).
cnf(c_81,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_83,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_89,plain,
~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(clausify,[status(thm)],[oagco9]) ).
fof(nnf_32,plain,
? [L,A,B,C] :
( between_on_line(L,B,A,C)
& between_on_line(L,A,B,C)
& distinct_points(A,B)
& distinct_points(B,C)
& distinct_points(A,C)
& line(L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( between_on_line(sK0,sK3,sK1,sK2)
& between_on_line(sK0,sK1,sK3,sK2)
& distinct_points(sK1,sK3)
& distinct_points(sK3,sK2)
& distinct_points(sK1,sK2)
& line(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(L,sK0),skolemize(A,sK1),skolemize(B,sK3),skolemize(C,sK2)],[nnf_32]) ).
cnf(c_97,negated_conjecture,
line(sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_354,plain,
( unequally_directed_lines(A,reverse_line(A))
| unequally_directed_lines(A,A)
| ~ line(A) ),
inference(factor,[status(thm)],[c_80]) ).
cnf(c_101,plain,
( unequally_directed_lines(A,reverse_line(A))
| ~ line(A) ),
inference(resolve,[status(thm)],[c_76,c_354]) ).
cnf(c_355,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_83,c_81]) ).
cnf(c_103,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_83,c_355]) ).
cnf(c_356,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_77,c_76]) ).
cnf(c_118,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,B)),line_connecting(B,A)),
inference(resolve,[status(thm)],[c_356,c_89]) ).
cnf(c_133,plain,
unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_101,c_97]) ).
cnf(c_145,plain,
( unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_133,c_77]) ).
cnf(c_227,plain,
( ~ unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK0,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_145,c_103]) ).
cnf(c_322,plain,
( unequally_directed_lines(sK0,A)
| unequally_directed_lines(sK0,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_227,c_145]) ).
cnf(c_323,plain,
( unequally_directed_lines(reverse_line(A),B)
| unequally_directed_lines(sK0,B)
| unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_322,c_77]) ).
cnf(c_324,plain,
( unequally_directed_lines(reverse_line(A),A)
| unequally_directed_lines(sK0,A) ),
inference(factor,[status(thm)],[c_323]) ).
cnf(c_325,plain,
unequally_directed_lines(sK0,line_connecting(A,A)),
inference(resolve,[status(thm)],[c_324,c_118]) ).
cnf(c_341,plain,
( unequally_directed_lines(line_connecting(B,B),A)
| unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_325,c_77]) ).
cnf(c_342,plain,
~ unequally_directed_lines(sK0,reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_103,c_325]) ).
cnf(c_357,plain,
unequally_directed_lines(sK0,reverse_line(line_connecting(A,A))),
inference(resolve,[status(thm)],[c_341,c_89]) ).
cnf(c_353,plain,
$false,
inference(resolve,[status(thm)],[c_342,c_357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO259+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n002.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 13:13:50 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3349308 was started by sandbox on n002,
% 0.18/0.44 % Fri Sep 25 13:13:50 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.49 % Length of proof is 27.
% 0.18/0.49 % Level of proof is 11.
% 0.18/0.49 % Maximum clause weight is 14.000.
% 0.18/0.49 % Given clauses 104.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------