%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO236+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 : n013.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 07:17:38 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 8 ~; 4 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 2 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a2_defns,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ),
file('theBenchmark.p',a2_defns) ).
fof(ax10_basics,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('theBenchmark.p',ax10_basics) ).
fof(con,conjecture,
! [A,L,M] :
( ( right_apart_point(A,M)
& left_apart_point(A,L) )
=> ( distinct_lines(L,M)
| unequally_directed_lines(L,M) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L,M] :
( ( right_apart_point(A,M)
& left_apart_point(A,L) )
=> ( distinct_lines(L,M)
| unequally_directed_lines(L,M) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_37,plain,
? [A,L,M] :
( ~ distinct_lines(L,M)
& ~ unequally_directed_lines(L,M)
& right_apart_point(A,M)
& left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ distinct_lines(sK2,sK1)
& ~ unequally_directed_lines(sK2,sK1)
& right_apart_point(sK0,sK1)
& left_apart_point(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(A,sK0),skolemize(L,sK2),skolemize(M,sK1)],[nnf_37]) ).
cnf(c_76,negated_conjecture,
right_apart_point(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_83,plain,
( left_apart_point(A,reverse_line(B))
| ~ right_apart_point(A,B) ),
inference(clausify,[status(thm)],[a2_defns]) ).
cnf(c_99,negated_conjecture,
left_apart_point(sK0,reverse_line(sK1)),
inference(resolve,[status(thm)],[c_83,c_76]) ).
cnf(c_114,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[ax10_basics]) ).
cnf(c_115,plain,
$false,
inference(resolve,[status(thm)],[c_114,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO236+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n013.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:08:51 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 498192 was started by sandbox2 on n013,
% 0.17/0.42 % Fri Sep 25 13:08:51 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 8.
% 0.17/0.45 % Level of proof is 3.
% 0.17/0.45 % Maximum clause weight is 4.000.
% 0.17/0.45 % Given clauses 0.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------