%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO255+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 : n008.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 07:17:43 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 32 ~; 26 |; 15 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 2 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bf_def,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( ~ unequally_directed_lines(L,line_connecting(A,B))
& ~ ( left_apart_point(B,reverse_line(L))
| left_apart_point(B,L) )
& ~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) )
& distinct_points(A,B) ) ),
file('theBenchmark.p',bf_def) ).
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] :
( ( distinct_points(A,B)
& line(L) )
=> ~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,A,B] :
( ( distinct_points(A,B)
& line(L) )
=> ~ ( before_on_line(L,B,A)
& before_on_line(L,A,B) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_57,plain,
( ~ unequally_directed_lines(A,line_connecting(B,C))
| ~ before_on_line(A,B,C) ),
inference(clausify,[status(thm)],[bf_def]) ).
fof(nnf_32,plain,
? [L,A,B] :
( before_on_line(L,B,A)
& before_on_line(L,A,B)
& distinct_points(A,B)
& line(L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( before_on_line(sK0,sK2,sK1)
& before_on_line(sK0,sK1,sK2)
& distinct_points(sK1,sK2)
& line(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(L,sK0),skolemize(A,sK1),skolemize(B,sK2)],[nnf_32]) ).
cnf(c_63,negated_conjecture,
before_on_line(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_64,negated_conjecture,
before_on_line(sK0,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_66,negated_conjecture,
~ unequally_directed_lines(sK0,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_64,c_57]) ).
cnf(c_72,negated_conjecture,
~ unequally_directed_lines(sK0,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_63,c_57]) ).
cnf(c_83,negated_conjecture,
line(sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_90,plain,
~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
inference(clausify,[status(thm)],[oagco9]) ).
cnf(c_97,plain,
~ left_convergent_lines(A,B),
inference(clausify,[status(thm)],[oag11]) ).
cnf(c_100,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_339,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_97,c_100]) ).
cnf(c_101,plain,
( ~ unequally_directed_lines(A,reverse_line(B))
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_97,c_339]) ).
cnf(c_102,plain,
( unequally_directed_lines(A,reverse_line(B))
| unequally_directed_lines(A,B)
| ~ line(B)
| ~ line(A) ),
inference(clausify,[status(thm)],[oag8]) ).
cnf(c_103,plain,
( unequally_directed_lines(B,C)
| unequally_directed_lines(A,C)
| ~ unequally_directed_lines(A,B) ),
inference(clausify,[status(thm)],[oag6]) ).
cnf(c_104,plain,
~ unequally_directed_lines(A,A),
inference(clausify,[status(thm)],[oag5]) ).
cnf(c_340,plain,
( unequally_directed_lines(A,reverse_line(A))
| unequally_directed_lines(A,A)
| ~ line(A) ),
inference(factor,[status(thm)],[c_102]) ).
cnf(c_111,plain,
( unequally_directed_lines(A,reverse_line(A))
| ~ line(A) ),
inference(resolve,[status(thm)],[c_104,c_340]) ).
cnf(c_341,plain,
( unequally_directed_lines(B,A)
| ~ unequally_directed_lines(A,B) ),
inference(resolve,[status(thm)],[c_103,c_104]) ).
cnf(c_124,plain,
~ unequally_directed_lines(reverse_line(line_connecting(A,B)),line_connecting(B,A)),
inference(resolve,[status(thm)],[c_341,c_90]) ).
cnf(c_131,plain,
unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolve,[status(thm)],[c_111,c_83]) ).
cnf(c_141,plain,
( unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_131,c_103]) ).
cnf(c_176,plain,
( ~ unequally_directed_lines(reverse_line(sK0),A)
| unequally_directed_lines(sK0,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_141,c_101]) ).
cnf(c_204,plain,
( unequally_directed_lines(sK0,A)
| unequally_directed_lines(sK0,reverse_line(A)) ),
inference(resolve,[status(thm)],[c_176,c_141]) ).
cnf(c_342,negated_conjecture,
( unequally_directed_lines(A,line_connecting(sK1,sK2))
| ~ unequally_directed_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_103,c_72]) ).
cnf(c_328,negated_conjecture,
~ unequally_directed_lines(sK0,reverse_line(line_connecting(sK2,sK1))),
inference(resolve,[status(thm)],[c_342,c_124]) ).
cnf(c_343,plain,
unequally_directed_lines(sK0,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_328,c_204]) ).
cnf(c_338,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO255+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n008.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
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 13:11:39 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 1127602 was started by sandbox on n008,
% 0.16/0.43 % Fri Sep 25 13:11:39 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.01 (+ 0.02) seconds.
% 0.16/0.48 % Length of proof is 29.
% 0.16/0.48 % Level of proof is 7.
% 0.16/0.48 % Maximum clause weight is 11.000.
% 0.16/0.48 % Given clauses 79.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------